The present disclosu re relates to systems, methods and com puter program products for determining operating conditions in a schedu led or in a cu rrent production run of a chemical production plant including at least one catalytic reactor.

Background

Catalytic reactors are widely used in the chemical industry to convert raw materials to valu able chemicals. The performance of the catalyst - like conversion, selectivity and yield - is connected to the operation parameters of the reactor and the age of the catalyst. To achieve certain performance targets, the plant operators have to adjust the reactor parame ters according to experience and engineering knowledge. Often, reactor models based on kinetics, heat and mass transfer phenomena are used to describe the performance of the catalyst and enable a more directed control of the reactor operation. However, such models are com plex, and the experimental determination of kinetic and transport parameters is quite tedious and expensive.

More recently, models of hybrid type were published, which rely partially on process knowledge, but also use machine learning methods. For instance, Clough and Ramirez (AIChEJ 22, 1976, p. 1097) and Gujarati and Babu (Chem.Eng.Sci. 65, 2010, p. 2009) pub lished knowledge-based models for styrene reactors and used it to optimize the reactor op eration for maximizing the styrene yield or the process economics. I n both cases, the kinetic rate equations and coefficients were taken from previous literature. The models are of lim ited practical util ity, considering that the kinetic coefficients shou ld be individual ly calculat ed for each actual catalyst (different catalysts have different reaction rates for al l chemical transformations occu rring in the system). Moreover, no catalyst aging rate was taken into consideration.

Tamsiian et al. (Com p. Chem. 40, 2012, p. 1) developed a model based on kinetic equations disclosed in the literatu re and fitted the rate coefficients by using styrene plant data from 5 days of operation.

H. Lim et al. (I nd. Eng. Chem. Res. 43, 2004, p. 6441) developed a hybrid model consisting of a first-principle (knowledge based) part to describe the dependence of the catalyst perfor mance (conversion and selectivities) on the reactor operation parameters pressu re, tem per atu re, STO ratio and ethyl benzene flow rate as in put variables; and a neu ral network model to predict a deactivation factor to be used in the first-principle model. The neu ral network predicts an u pdated deactivation factor based on the deactivation factor, i n let temperature, total pressu re and partial pressu res of ethyl benzene and steam of the latest time step.

Shah hossei ni et al . (I nt. J . Chem. React. Eng. 9, 2011) developed a hybrid model to optimize the performance of an adiabatic industrial reactor system. First, they fitted a kinetic model using 7 data points measu red in an experimental isothermic reactor. With the kinetic coeffi cients thus estimated, they used a Tabu search algorithm or a genetic algorithm to effi- ciently optimize the operating conditions for maximizing two objective functions, the ethyl benzene conversion and the styrene selectivity. Catalytic activity was modeled as an exponential function of time, decaying from 100% to 40% over 48 months, based on litera tu re values. The modeli ng of deactivation in this fashion can not reflect the effects of differ ent operating scenarios, which is mandatory for a ru n- and plant-specific prediction of de activation.

Wu et al. (Lectu re Notes in Computer Science, 10357, pp. 301-312, 2017) and WO 2018/035718 A1 disclose a data-d riven model for real-time prediction of styrene pro duction volu me based on real operating data. 33 sensor-based predictors were identified from a com bination of Principal Com ponent Analysis (PCA) and Random Forest variable im portance analysis. Th ree models, a Generalized Regression Neu ral Network (GRN N) , a GRN N after Kal man-filtering and a Random Forest Regression Model, were com pared for predicting the yield of styrene monomers. Wu et al focus on predicting the current styrene production based on available sensor data, with the stated motivation that this information is usual ly on ly available after analytical testing, which can take several hours. The present ed methods however do not relate to making performance prediction based on user-defined operating scenarios or forecasting of the performance, including the styrene monomer yield, at futu re points in time. No deactivation of the catalyst is considered.

Thus, a num ber of knowledge-based or kinetic models have been developed for modeling styrene production in catalytic reactors and more recently, elements of machine learning (M L) have been integrated (hybrid models) , though in several cases for optimization of the kinetic model rather than the performance modeling itself. I n al l hybrid modeling and ma chi ne learning approaches, the M L methods are trained on smal l datasets, typical ly consist ing of a single run of a single experimental or production plant.

Knowledge-based or ki netic, hybrid reactor models are com plex and often necessitate sim plifying assu m ptions in order to reduce the com puting effort. I n most cases, not al l of the physico-chemical processes which contribute to the performance and aging of a catalyst are u nderstood. For instance, in the case of the styrene catalyst, the potassiu m loss is con trol led by the temperatu re gradients occu rring along the catalyst bed depth and within the catalyst particles, as wel l as the STO ratio, the carbon dioxide content in the gaseous mix tu re (resu lting from coke gasification), as wel l as the pressu re gradient along the bed, mak ing an exact estimation of the potassiu m evaporation rate im possible. One can not calcu late a priori the potassium loss rate at every point of the reactor bed in order to estimate the aging rate of the catalyst within the catalyst bed and over the lifetime of the catalyst.

An object of the present disclosu re is to provide a method for determi ning operating condi tions in a chemical production plant includi ng at least one catalytic reactor, which al lows for robust, stable and reliable reactor operation and enhances process control in catalyst- based production plants.

Su mmary According to a first aspect of the invention, a system for determining an operating condition of a chemical production plant including at least one catalytic reactor is provided. The sys tem comprises: a com mu nication interface and a processing device in commu nication with the com mu nica tion interface, the system configured to:

- receive, via the com mu nication interface, operating data indicative of a pre-defined oper ating condition for the schedu led production run, or measu red operating data indicative of a current operating condition for the current production ru n, wherein at least one operating data point includes a desired operating value indicative of the change in the cu rrent operat ing condition,

- receive, via the com mu nication interface, a catalyst age indicator associated with a period of time the catalyst has been used in the current or schedu led production run,

- determine, via the processing device, at least one target operating parameter for the oper ating condition of the schedu led production ru n or the change in the cu rrent production run based on the operating data and the catalyst age indicator using a data-d riven model, pref erably a data-d riven machine learning model, wherein the data-driven model is parameter ized according to a training dataset, wherein the training dataset is based on sets of histori cal data com prising operating data, catalyst age indicator, and the at least one target oper ating parameter,

- provide, via the com mu nication interface, the at least one target operating parameter for the operating condition of the scheduled or the change in the current production run.

According to another example of the first aspect of the invention, a system for determining an operating condition of a chemical production plant including at least one catalytic reactor is provided. The system comprises a communication interface and a processing device in com mu nication with the com mu nication interface.

(a) for a scheduled production ru n, the system is configured to:

- receive, via the com mu nication interface, operating data indicative of a pre-defined oper ating condition for the schedu led production run,

- receive, via the com mu nication interface, a catalyst age indicator associated with a period of time the catalyst has been used in the schedu led production run,

- determine, via the processing device, at least one target operating parameter for the oper ating condition of the schedu led production ru n based on the operating data and the cata lyst age indicator using a data-d riven model, wherein the data-d riven model is parameter ized according to a training dataset, wherein the training dataset is based on sets of histori- cal data comprising operating data, catalyst age indicator, and the at least one target oper ating parameter,

- provide, via the com mu nication interface, the at least one target operating parameter for the operating condition of the schedu led production ru n, or

(b) for a change in a cu rrent production ru n, the system is configured to:

- receive, via the com mu nication interface, measu red operating data indicative of a current operating condition for the cu rrent production run, wherein at least one operating data point includes a desired operating value indicative of the change in the current operating condi tion,

- receive, via the com mu nication interface, a catalyst age indicator associated with a period of time the catalyst has been used in the cu rrent production run,

- determine, via the processing device, at least one target operating parameter for the oper ating condition of the change in the current production ru n based on the operating data and the catalyst age indicator using a data-d riven model, wherein the data-d riven model is pa rameterized according to a training dataset, wherein the training dataset is based on sets of historical data com prising operating data, catalyst age indicator, and the at least one target operating parameter,

- provide, via the com mu nication interface, the at least one target operating parameter for the operating condition of the change in the cu rrent production run.

According to a second aspect of the invention, a system for optimizing an operating condi tion of a scheduled production run or of a change in a cu rrent production run of a chemical production plant is provided. The system com prises the system outlined above and an opti mization processing device, the optimization processing device configu red to:

- receive, via the com mu nication interface, for more than one operating condition of the scheduled production ru n or of the change in the cu rrent production run, the determined target operating parameter(s) ,

- determine, via the optimization processing device, based on the received target operating parameter(s) for each operating condition a minimu m or maximu m value of the target oper ating parameter(s) or a minimu m or maximu m value of at least one optimization parameter derived from the target operating parameter(s) ,

- provide, via the com mu nication interface, the minimu m or maximu m value indicative of an optimal operating condition of the scheduled production ru n or the cu rrent production run e.g. the minimu m or maximu m value of the target operating parameter(s) or the minimu m or maximu m value of the optimization parameter derived from the target operating parame- ter(s) . According to another exam ple of the second aspect of the invention, a system for optimizing an operating condition of a chemical production plant is provided. The system comprises the system outlined above and an optimization processing device, the optimization pro cessing device configu red to:

- receive, via the com mu nication interface, for more than one operating condition as deter mined either (a) for schedu led production ru ns or (b) for changes in a cu rrent production run, the determined target operating parameter(s) ,

- determine, via the optimization processing device, based on the received target operating parameter(s) for each operating condition a minimu m or maximum value of the target oper ating parameter(s) or a minimu m or maximu m value of an optimization parameter derived from the target operating parameter(s) ,

- provide, via the communication interface, the minimu m or maximu m value indicative of an optimal operating condition in either (a) the scheduled production run or (b) the current production ru n, e.g. the minimu m or maximum value of the target operating parameter(s) or a minimu m or maximu m value of the optimization parameter derived from the target operat ing parameter(s) .

According to a third aspect of the invention, a production monitoring and/or control system is provided that includes a commu nication interface com mu nicatively coupled, e.g. via wired or wireless con nection, to the system for determining the operating condition as lined out above or to the system for optimizing the operating condition as lined out above. The pro duction monitoring and/or control system may include a display device, which is configured to receive, and display determined operating condition(s) . The production monitoring and/or control system may include a control unit, which is configured to receive determined operat ing condition (s) to control a current or schedu led production run in the chemical production plant based on the determined operating condition (s) . The determined operating condi- tion(s) preferably include(s) determined target operating parameter(s) and optional ly oper ating data fu rther optional ly including desired operating value(s) .

According to a fou rth aspect of the invention, a com puter-im plemented method for deter mining an operating condition for a schedu led production ru n or for a change in a current production ru n of a chemical production plant including at least one catalytic reactor is pro vided. The method comprises the steps:

- receiving, via the communication interface, operating data indicative of a pre-defined op erating condition of the scheduled production ru n, or measu red operating data indicative of the cu rrent operating condition, wherein at least one operating data point includes a desired operating value indicative of the change in the current operating condition,

- receiving, via the communication interface, a catalyst age indicator associated with a peri od of time the catalyst has been used in the cu rrent or schedu led production run, - determining, via the processing device, at least one target operating parameter for the operating condition of the scheduled or the change in the cu rrent production run based on the operating data and the catalyst age indicator using a data-d riven machine learning model, wherein the data-d riven model is parameterized according to a training dataset, wherein the training dataset is based on sets of historical data com prising operating data, catalyst age indicator, and the at least one target operating parameter,

- providing, via the com mu nication interface, the at least one target operating parameter for the operating condition of the scheduled or the change in the cu rrent production ru n.

According to another exam ple of the fou rth aspect of the invention, a com puter- im plemented method for determining an operating condition of a chemical production plant including at least one catalytic reactor is provided. The method com prising the steps:

(a) for a schedu led production ru n, the method comprising the steps:

- receive, via the com mu nication interface, operating data indicative of a pre-defined oper ating condition for the schedu led production run,

- receive, via the commu nication interface, a catalyst age indicator associated with a period of time the catalyst has been used in the scheduled production run,

- determine, via the processing device, at least one target operating parameter for the oper ating condition of the schedu led production run based on the operating data and the cata lyst age indicator using a data-d riven model, wherein the data-d riven model is parameter ized according to a training dataset, wherein the training dataset is based on sets of histori cal data com prising operating data, catalyst age indicator, and the at least one target oper ating parameter,

- provide, via the com mu nication interface, the at least one target operating parameter for the operating condition of the schedu led production run, or

(b) for a change in a cu rrent production run, the method comprising the steps:

- receive, via the com mu nication interface, measured operating data indicative of a current operating condition for the cu rrent production run, wherein at least one operating data point includes a desired operating value indicative of the change in the current operating condi tion,

- receive, via the com mu nication interface, a catalyst age indicator associated with a period of time the catalyst has been used in the cu rrent production run,

- determine, via the processing device, at least one target operating parameter for the oper ating condition of the change in the current production ru n based on the operating data and the catalyst age indicator using a data-d riven model, wherein the data-d riven model is pa- rameterized according to a training dataset, wherein the training dataset is based on sets of historical data com prising operating data, catalyst age indicator, and the at least one target operating parameter,

- provide, via the com mu nication interface, the at least one target operating parameter for the operating condition of the change in the cu rrent production run.

According to a fifth aspect of the invention, a method for optimizing an operating condition of a schedu led production run or of a change in a current production run of a chemical pro duction plant is provided. The method com prises the steps of:

- receive, via the com mu nication interface, for more than one operating condition of the scheduled production ru n or of the change in the cu rrent production run, the determined target operating parameter(s) ,

- determine, via the optimization processing u nit, based on the received target operating parameter(s) for each operating condition a minimu m or maximum value of the target oper ating parameter(s) or a minimu m or maximu m value of an optimization parameter derived from the target operating parameter(s) ,

- provide, via the com mu nication interface, the minimu m or maximu m value indicative of an optimal operating condition of the scheduled production ru n or the cu rrent production run e.g. the minimu m or maximum value of the target operati ng parameter(s) or the minimu m or maximu m value of the optimization parameter derived from the target operating parame- ter(s) .

According to another exam ple of the fifth aspect of the invention, a method for optimizing an operating condition of a scheduled production ru n or of a change in a cu rrent production run of a chemical production plant, the method com prising the steps of:

- receive, via the com mu nication interface, for more than one operating condition as deter mined either (a) for schedu led production ru ns or (b) for changes in a cu rrent production run, the determined target operating parameter(s) ,

- determine, via the optimization processing device, based on the received target operating parameter(s) for each operating condition a minimum or maximum value of the target oper ating parameter(s) or a minimu m or maximu m value of an optimization parameter derived from the target operating parameter(s) ,

- provide, via the com mu nication interface, the minimu m or maximum value indicative of an optimal operating condition in either (a) the scheduled production run or (b) the current production ru n, e.g. the minimu m or maximum value of the target operating parameter(s) or a minimu m or maximu m value of the optimization parameter derived from the target operat ing parameter(s) . d

According to a sixth aspect of the invention, a method for monitoring and/or control ling a chemical production plant is provided, which includes the steps of performing the method for determining or optimizing an operating condition as lined out above. The method may further include displaying determined operating condition(s) on a display device and/or con trol ling a cu rrent or schedu led production ru n in the chemical production plant based on the determined operating condition (s) . The determined operating condition (s) preferably in clude determined target operating parameter(s) and/or operating data optional ly including desired operating value(s) .

According to a seventh aspect of the invention, a method for training a data-d riven model for determining an operating condition for a schedu led production run or for a change in a current production run of a chemical production plant including at least one catalytic reactor is provided. The method com prises the steps:

- receiving, via a com mu nication interface, a training dataset based on sets of historical data com prisi ng operating data, catalyst age indicator, the at least one target operating pa rameter, optional ly plant metadata,

- trai ning, via a processing device, the data-d riven model by adjusting the parameterization according to the training dataset,

- providing, via a com munication interface, a trained data-d riven model.

According to an eights aspect of the invention, a com puter program or a computer program product or com puter readable non-volatile storage mediu m com prising computer readable instructions, which when loaded and executed by a processing device perform the methods disclosed herein.

According to a ninth aspect of the invention, a catalyst including a catalyst type identifier associated with a data-d riven model trained according to the methods lined out herein is provided, wherein the model is trained for the catalyst type indicated by the catalyst type identifier. I n other words, a catalyst system including a catalyst and a catalyst type identifier associated with a data-d riven model trained according to the methods lined out herein is provided, wherein the model is trained for the catalyst type indicated by the catalyst type identifier.

According to a tenth aspect of the invention, a catalyst including a catalyst type identifier associated with the com puter programs l ined out herein is provided. I n other words, a cata lyst system including catalyst and a catalyst type identifier associated with the com puter programs lined out herein is provided.

According to a eleventh aspect of i nvention, a chemical process using a catalyst associates with a data-d riven model trained according to the methods lined out herein is provided, wherein the data-d riven model is used to design the plant com ponents and to optimize the operation of the chemical process for achieving target performances, i n particu lar to an op erating condition of a chemical production plant including at least one catalytic reactor.

The fol lowing disclosu re applies to the systems, methods, com puter programs, com puter readable non-volatile storage media, catalysts, chemical processes and computer program products disclosed herein alike. Therefore, no differentiation is made between systems, methods, computer programs, computer readable non-volatile storage media or computer program products. All featu res are disclosed in con nection with the systems, methods, computer programs, computer readable non-volatile storage media, catalysts, chemical pro cesses and com puter program products disclosed herein.

The present invention provides systems or methods for determining operating conditions or operating parameters based on a merely data-d riven model, which al lows for more robust, stable and reliable reactor operation and en hances process control in catalyst-based pro duction plants. I n particu lar, the determination is more accu rate than known approaches based on kinetic models or hybrid models, since no a priori information on the reaction ki netics and hence no estimations or simplifying assu m ptions regarding the u nderlying pro cesses are required.

Specifical ly, the determination takes accou nt of the catalyst deactivation by providing the catalyst age indicator associated with a period of time the catalyst has been used in the current production ru n. I ncluding the catalyst age indicator as model in put parameter al lows for more accu rate determination of operating conditions, since the model inherently takes account of catalyst deactivation or ageing. With the catalyst deactivation considered the determination of operating parameters is applicable to a wide range of chemical production plants and operating parameters. I n contrast data-d riven models not taking catalyst aging into accou nt are on ly narrowly applicable. I n particu lar such models are restricted to the chemical production plant the model was trained for, sometimes even only a single run in the production plant and a narrow range of operating conditions.

The systems and methods of the present disclosu re perform short-term discrete prediction as wel l as time-series forecasting. I n the latter case they are able to cover the ful l deactiva tion process of the catalyst du ring a whole production ru n. The methods and systems ena ble the plant operator to i mprove and opti mize operation policies on a day-to-day basis ac cording to the energy costs, market su pply of the raw material or need for the plant product, and other limitations which may occu r in the plant, like outages of different plant parts or utilities.

Moreover, the systems and methods al low for predicting short-term and/or forecasting long-term behavior of a catalyst-based production plant using operating data of the plant and the catalyst age indicator. This allows for enhanced process control in catalyst-based production plants, since e.g. plant operators can easily assess schedu led or current runs based on the operati ng conditions present in the production plant. As such the system pro vides a powerful tool for plan ning, monitoring and controlling the production process. I n one em bodiment of the present invention the chemical production plant com prises one or more catalytic reactor(s) . I n the context of the present invention the term“catalytic reactor” shal l mean a chemical reactor in which a catalyzed chemical reaction takes place and which general ly contains a catalyst. The catalytic reactor may be a fixed bed catalytic reactor. The chemical production plant may be a styrene production plant.

I n this context, a data-d riven model, preferably data-d riven machine learning model or a merely data-d riven model, refers to a trained mathematical model that is parametrized ac cording to a training data set to reflect reaction kinetics or physico-chemical processes of the chemical production plant or the catalytic reactor. An u ntrained mathematical model refers to a model that does not reflect reaction kinetics or physico-chemical processes, e.g. the u ntrained mathematical model is not derived from physical law providing a scientific generalization based upon empirical observation. Hence, the kinetic or physico-chemical properties may not be inherent to the u ntrained mathematical model. The u ntrained model does not reflect such properties. Featu re engineering and training with respective training data sets enable parametrization of the u ntrained mathematical model. The resu lt of such training is a merely data-driven model, preferably data-d riven machine learning model, which as a result of the training process, preferably solely as a resu lt of the training pro cess, reflects reaction kinetics or physico-chemical properties.

Historical data in this context refers to data sets including at least operating data, catalyst age indicator, and the at least one target operating parameter, wherein each data set is as sociated with a single production ru n. Hence each data set includes data associated with the production run from production start to production end for one catalyst. Such data may be measu red and recorded du ring the production run over the catalyst’s lifetime, e.g. from production start after catalyst exchange to the production end, when the catalyst requires exchange again.

The chemical reaction catalyzed is not restricting the scope of this invention. As an exam ple, the catalyst may be a dehydrogenation catalyst. Particu larly, the catalyst of the catalytic reactor may be an i ron oxide-based catalyst for the dehyd rogenation of al iphatic or al kylar- omatic hyd rocarbons to form the corresponding u nsatu rated hyd rocarbons. Exam ples of such dehyd rogenation processes are the dehyd rogenation of ethyl benzene to styrene, of isopropyl benzene to al pha-methylstyrene, of butene to butadiene or of isoamylene to iso- prene. The methods and systems are particularly usefu l in styrene production plants. Pref erably the chemical production plant is a styrene production plant converting ethyl benzene to styrene using a styrene catalyst. The preparation of styrene typical ly includes heteroge neously catalyzed dehyd rogenation of ethyl benzene in the presence of steam. The catalytic dehyd rogenation of aliphatic or al kylaromatic hyd rocarbons is usual ly carried out industrial ly in the presence of steam at tem peratures in the range from 500 to 700 °C. I n these process es, the hyd rocarbon and the steam are typical ly mixed and passed over the iron oxide dehy d rogenation catalyst at elevated tem peratures and low pressures. The term operating data refers to a quantity indicative of the operation status of the chemi cal production plant. I n particular such quantities relate to measu rement data col lected dur ing the production ru n of the chemical production plant and may be directly or indirectly derived from such measu rement data. I n a preferred embodiment the operating data in cludes sensor data measu red through sensors instal led in the chemical production plant, quantities directly or indirectly derived from such sensor data, analytical data measu red in samples taken from the chemical production plant, quantities directly or indirectly derived from such analytical data or combinations thereof.

Sensor data may include measu red quantities available in chemical production plants by means of instal led sensors, e.g. temperatu re sensors, pressu re sensors, flow rate sensors, etc. Analytical data may include quantities provided from analytics measurements of sam ples extracted at any point in the process or in time from the chemical production plant. I n particular, such analytical data may include a composition of a reactant, starting material, a product and/or a side product as determined e.g. via gas chromatography from sam ples extracted du ring the production process at different stages of the production process, e.g. before or after catalytical reactor(s) . Analytical data preferably forms the basis for deter mining catalyst performance characteristics.

The set of operating data may include raw data, which refers to basic, non-processed ana lytical and/or sensor data, or processed or derived parameters, which are directly or indi rectly derived from raw data. I n case of a chemical production plant derived parameters may include averaged in let tem peratu re over mu ltiple catalytic reactors derived from the respec tive temperatu re sensors; steam-to-oil ratio derived from the raw data of a steam flow rate and a reactant flow rate; conversion and selectivity derived from the analytical data before and after the reactor(s) ; any type of normalized data, e.g. production values normalized by catalyst volu me or catalyst mass; any data derived from the time-series data, e.g. cumula tive production amount, maximu m load to date, or any com bination thereof.

Particu larly for chemical production plants conversion, selectivity and yield may be derived from analytical data. Here conversion refers to the fraction, preferably the percentage of reactant converted total ly in the reactor. I n case of e.g. styrene production this corresponds to the conversion of the starting material ethyl benzene into any product. Selectivity of the desired product refers to the amou nt of converted reactant which is transformed into a de sired product. I n case of e.g. styrene production this corresponds to the selectivity of the reaction ethyl benzene-to-styrene. Yield of a desired product refers to the mathematical product of conversion and the product specific selectivity. Yield may be represented by the percentage of reactant entered into the reactor, which is converted to desired product.

I n a further embodiment plant metadata indicative of a physical plant layout is received via the commu nication interface. Plant metadata may include plant-specific quantities that de scribe e.g. the properties of the reactor(s), which are pre-defined by the physical plant lay out and may be relevant to the plant or reactor performance. Plant metadata for instance includes a num ber of reactors the reactant mixtu re su bsequently passes through, e.g. 2 or 3 reactors, a total catalyst volu me, a catalyst volume by reactor, dimensions (length, diameter, height... ) of each reactor, catalyst type used in the plant or com binations thereof. I n a fur ther embodiment the determination, via the processing unit, of the at least one target oper ating parameter is additional ly based on the plant metadata using the data-driven model, wherein the training dataset is based on sets of historical data additional ly comprising plant meta data. I ncluding plant metadata into the determination of operating conditions al lows to build a data-d riven model applicable to different plants, which in tu rn increases the nu mber of data points available to train the data-driven model. As a resu lt, the data-d riven model broadly captu res operating conditions of different plants ru n ning u nder different operating conditions with different physical plant layouts al lowing for more accurate determination.

I n a further embodiment the sets of historical data include data from multiple production runs, multiple plants and/or mu ltiple catalyst batches of the same type of catalyst. I ncluding multiple production ru ns into the training al lows to cover different operating conditions of the same or different plant(s) . I ncluding data from mu ltiple catalyst batches al lows to take account of differences between catalyst batches. Data from mu ltiple catalyst batches may include data from mu ltiple production ru ns, wherein for at least one of the productions runs a different production batch of the same type of catalyst was used. By including mu ltiple plants data from one or more production ru ns from different plants may be included. Thus, operating conditions in different plants may be covered providing a broader applicability of the model. I n this context the same type of catalyst refers to the same type of catalyst for mulation. Mu ltiple catalyst batches include catalysts of the same type provided from differ ent manufactu ring batches or different delivery date.

I n a further embodiment the catalyst age indicator is based on a time point, a time period, a quantity derived from time dependent operating data and/or a quantity cu mulatively derived from time dependent operating data. The catalyst age indicator may be specified by the time spent by the catalyst in the reactor at reaction conditions since its first contact with the reactant mixture. Additional ly or alternatively, the cumu lative load or the cu mu lative production volume of the catalyst may be used as catalyst age indicator, which is preferably defined by the total amou nt of reactant feed or converted reactant since the start of the ru n u p to a prediction start point in time. Apart from the indicators mentioned here any other quantity that can serve as an indicator for the catalyst age may be utilized. The catalyst age indicator may be provided via a client device, where the plant operator enters the time of production ru n start or the period since production ru n start u p to the prediction start point in time. Alternatively or additional ly, the catalyst age indicator may be determined based on a time series of operating data preferably since production run start, wherein the production run start may be determined based on an operation profile in the operating data. Such op eration profile may include certain tem peratu re, pressure, flow rate profile(s) or combina tions of such profile(s) .

The operating condition for the scheduled or the change in the cu rrent production refer to an operating condition under which the chemical production plant may ru n in the future or after the prediction start point in time. Such an operating condition may include one or more operating condition (s) for a discrete point in time, for mu ltiple discrete points in time, a pe- riod of time or several time intervals. I n the latter case an operating condition may include different time intervals, for which at least one pre-defined or desired operating value takes different values in different intervals. Multiple discrete points in time, the period of time or the time intervals may extend from the prediction start point in time over the remaining pro duction ru n u p to production run end, at which point the catalyst needs exchanged.

The operating condition for the scheduled production ru n may refer to operating data of a pre-defined operating condition of the chemical production plant prior to production run start. The pre-defined operating condition may include a set of pre-defined operating data specifying the operating condition. Determining the operating condition for schedu led pro duction ru ns is particu larly usefu l for production design and plan ning prior to production ru n start. The operating condition for a cu rrent production ru n may refer to a change in operat ing conditions as currently set in the chemical production plant. The operating condition may include a set of operating data specifying the cu rrent operating conditions, wherein the operating data are in at least one operating data point different to the operating parameters as currently set in the chemical production plant. Determining the operating condition for current production ru ns is particularly useful for monitoring and control ling production dur ing the cu rrent production run.

Determining the operating condition includes predicting or forecasting the catalyst or reac tor performance/behavior and is used in a general manner to describe the application of the data-d riven model for a set of appropriate in put parameters. I n the example of a styrene production plant, the determination for instance refers to the determination of the reactor in let tem peratu re and associated selectivity of the ethyl benzene-to-styrene reaction, given a specific operating condition via the operating data. Such a selection of output parameters of the model may be driven by the fact that most plants are ru nning in a way that the opera tors adjust inlet temperatu res to achieve a certain desired conversion. However, given the same dataset, a model may be developed in analogous fashion as fu rther detailed below, having different assignments of in puts and outputs, e.g. using the reactor temperatu re as in put to predict the conversion that is to be expected under the operating condition.

I n one embodiment the determination of at least one target operating parameter for the operati ng condition is based on a short-term model determining target operating parame ters for discrete points in time or a long-term model determining target operating parame ters for a period of time particularly in the futu re. I n case of a short-term model the at least one target operating parameter for the operating condition is determined based on a short time frame. Here a short time frame may refer to a discrete or single point in time. The short-term model may be based on different machine learning tech niques including e.g. regression models, such as linear regression models, non-linear regression models, Bayesi an linear regression, random forest models, neu ral networks or a com bination thereof. Other approaches may also be applied. Preferably the short-term model does not have an intrinsic time dependency. Fu rther preferred the short-term model predicts the performance or op erating condition at time t based on the model in put at that same time t. I n case of the scheduled production run, the operating data may specify the pre-defined operating condition. The catalyst age indicator may be estimated for the schedu led produc tion ru n e.g. u nder the assu mption of a pre-defined operating condition constant over time or pre-defined changes over time or based on a preceding production run. The determina tion via the short-term model may for instance be applied to more than one discrete point in time for a pre-defined operating condition remaining constant over the total production ru n and the catalyst age indicator may be estimated for each of the discrete points in time.

Such an im plementation is particu larly advantageous for designing and planning futu re pro duction ru ns.

I n case of the cu rrent production run, the operating data may specify the operating condi tion as cu rrently set in the chemical production with at least one desired operating value indicative of a change in or deviation from current operating condition. The determination via the short-term model may for instance be applied to one or more than one discrete point(s) in time for determining the effect of the at least one desired operating value indica tive of a deviation from operating conditions as cu rrently set in the chemical production. Such an implementation is particu larly advantageous for monitoring and control ling current production ru ns.

I n case of a long-term model the at least one target operating parameter for the operating condition is determined based on a long time frame. Here a long time frame may refer to multiple points in time in the future. The nu mber of points and hence the forecasting hori zon depends on the time scale of the time dynamics in the production plant. For catalyst- based production processes such dynamics may be determined by the catalyst aging dy namics and their time horizon. For a heterogenous catalyst reaction like the styrene produc tion such a time scale may lie in the range of weeks, months or years. The long-term model may be based on a time series forecasting method. Such methods for instance include known regression methods, such as autoregression models, in particu lar Autoregression (AR) , Moving Average (MA), Autoregressive Moving Average (ARMA) , Autoregressive I nte grated Moving Average (ARI MA) , Vector Autoregression (VAR), Vector Autoregression Mov ing-Average (VARMA), Vector Autoregression Moving-Average with Exogenous Regressors (VARMAX), random forest models, neu ral networks, convolutional neu ral networks, recur rent neu ral networks or a combination thereof. Other approaches may also be applied.

I n one embodiment a time series of the at least one target operating parameter as meas u red, predicted or derived during the current or a previous production ru n up to a prediction start point in time is received via the com mu nication interface. E.g. in case of a schedu led run target operating parameter as measu red, predicted or derived du ring a previous produc tion may be used. Preferably at least one target operating parameter is determined for one or more points in time fol lowing the prediction start point in time based on the operating data optional ly including the desired operating value, the time series of the at least one tar get operating parameter, the catalyst age indicator and optional ly the plant meta data using the data-driven model. Fu rther preferred the data-d riven model includes an intrinsic time- dependence. I n this em bodiment the at least one target operating parameter may include u ncontrol led or endogenous parameters, which are not control lable in the chemical produc tion plant via machine settings. I n contrast the operating data including at least one desired operating value may include control led or exogeneous parameters, which are control lable in the chemical production plant via machine settings. The determination of target operating parameters at a prediction start time t may include the determination e.g. for times t, ... , t+N , with N > 0, based on u ncontrol led parameters or a su bset of uncontrol led parameters u p to time point t-1 or less and optional ly based on control led parameters or a su bset of control led parameters e.g. at time points t, ... , t+N , optional ly fu rther including e.g. t-1, t-2, ... or at other time points suited to make forecast with the specific structu re of the chosen model.

Preferably the long-term model is a time series-based model including an intrinsic time de pendency and forecasting the target operating parameters at times t, ... , t+N based on the model in put at time points u p to time point t-1. Here t refers to the starting point of predic tion in time. As such the long-term models al lows for determining reactor or catalyst per formance and changes of reactor or catalyst performance for preferably extended periods of time without available information of u ncontrol led parameters beyond the starting point of the forecast. These models have at least some intrinsic time dependency and forecast the performance at times t, ... , t+N based on u ncontrol led parameters u p to time point t-1 and optional ly based on control led parameters e.g. at time points t, ... , t+N or at other time points suited to make forecast with the specific structu re of the chosen model.

I n one embodiment the processing device is further configu red to pre-process operating data prior to the determination via the data-d riven model. Preferably the pre-processing includes a transformation to quantities independent of a physical plant layout. Pre processing al lows for taking systematic and non-systematic differences between different plants into account. Hence it enables broad applicability of the determination of target op erating parameters even if data from a specific plant in question was not used for training the data-d riven model. I n particu lar the transformation includes systematic factors as in put parameters for the data-d riven model and/or normalization of operating data.

I n a further embodiment the data-d riven model is validated before determining the at least one target operating parameter. Such validation en hances interpretability and confidence on the determined target operating parameters. For validation operating data and the at least one target operating parameter as measu red or derived du ring the cu rrent production run for one or more point(s) in time may be received via the com mu nication interface. The op erating data may be used to determine the at least one target operating parameter corre sponding to a point in time, where a measu red target operating parameter is available. The result of the determined target operating parameter for a point in time and the measured operating parameter corresponding to the same point in time may be com pared. If the com parison leads to a valid model operation, e.g. if the difference is less than a th reshold or no systematic errors are identified, the determination of at least one target operating parame ter for the operating condition based on the set of operating data including at least one de sired operating value may fol low. If the comparison leads to an invalid model operation, an alert may be triggered, e.g. via a display device or audio device, signifying that the model operation is not suitable for monitoring and/or control ling the su bject chemical plant u nder current operating conditions.

I n a further embodiment the data-d riven model is selected based on catalyst type before determining the at least one target operating parameter. The catalyst type may be received via the metadata signifying the type of catalyst used, e.g. via a catalyst type identifier. The catalyst type may specify the catalyst formu lation. Such option al lows for a high ly flexible use of the systems, computer programs, computer program products and methods, not on ly covering different chemical production plants but also different catalyst types. A further degree of flexibility may be added by selecting the data-d riven model based on in put and output parameter identifier before determining the at least one target operating parameter. The in put and output parameter identifier may specify, which parameters are used as oper ating data and which parameters are used as target operating parameter in the system or method. I n such im plementations different data-d riven models may be stored in a memory of the system including catalyst type and/or parameter identifier for each model, based on which the selection step may be performed.

I n one embodiment the training of the data-d riven model is performed based on training data, which includes the catalyst type identifier. The trained model may be stored together with the catalyst type identifier and may be provided together with catalysts of that type, preferably i ncluding a catalyst type identifier. Such identification may be im plemented elec tronical ly via a catalyst I D stored i n a data base or in a mobile storage mediu m attached to the catalyst delivery container e.g. in connection with the respective chemical production plant. I n such case the model is preferably trained based on training dataset measu red in production ru ns, which used catalysts of the same catalyst type as i ndicated by the catalyst type identifier. Hence the catalyst may be bundled with the data-d riven model and can aid more robust control for the production plant run ning with the catalyst of specific catalyst type.

A method of predicting short-term and forecasting long-term behavior of a catalyst e.g. i n a fixed bed catalytic reactor as a function of reactor operation parameters or operating data and catalyst age or a catalyst age indicator is provided. The method uses a data d riven model, preferably a data d riven machine learning model, which does not involve a priori in formation on reaction kinetics. The model is able to predict both the short-term and long term behavior of the catalyst as a fu nction of in put parameters, including typical reactor operating parameters or operating data and parameters derived from sensor and analytical raw data available in the production plant. A software product for performing the method is also provided. As an application exam ple, the method is used to predict and forecast the behavior of a catalyst and a tech nical reactor for converting ethyl benzene to styrene.

The present disclosu re provides a com puter-implemented method of predicting short-term and forecasting long-term performance of a catalyst in a chemical production plant includ ing a catalytic reactor, including catalyst aging effects. The method involves using a math- ematical model of the chemical production plant and particularly the catalytic reactor which is based on machi ne learning, involves no a priori information on reaction kinetics and uses in put parameters selected from sensor raw data, derived parameters, reactor operating pa rameters or operating data, plant metadata and parameters indicative of the catalyst age or a catalyst age indicator.

I n one embodiment, the operating data are selected from sensor data available from the chemical production plant, particularly the catalytic reactor, analytical data from e.g. gas chromatography (GC) analytics, and derived parameters as laid out above.

I n one em bodiment, the operating data i nclude in let tem peratu re and outlet tem peratu re of one or more catalytic reactor(s) , preferably of each of the one or more catalytic reactors, in let pressu re and outlet pressu re of one or more catalytic reactor(s) , preferably of each of the one or more catalytic reactors, and com position of the reaction mixtu re at the in let a nd outlet of one or more catalytic reactor(s), preferably of each of the one or more catalytic reactors.

I n one em bodiment, particu larly applicable to a styrene production plant, the operating data include steam-to-oil (STO) ratio, liquid hourly space velocity (LHSV) , total production of styrene normal ized by catalyst volu me, target ethyl benzene conversion, styrene selectivity, average inlet temperature, normalized pressu re after the last catalytic reactor, normalized pressu re d rop over the one or more catalytic reactors, temperatu re loss over the one or more catalytic reactors, normalized deviation of temperatu re loss com pared to an expected (calcu lated on the basis of conversion) value. An advantage of such a parameter set is that it is stil l interpretable, as many of the parameters correspond to actual operating parame ters or can easily be interpreted i n that context. Other approaches to reduce the nu m ber of dimensions of the problem (e.g., PCA or RFA) can lead to parameters which are usefu l for the modeling process and predictive accu racy, but often lack interpretability.

The data-d riven model preferably performs time-series forecasting and is able to cover the ful l deactivation process of the catalyst du ring a whole production ru n in the reactor system. The model enables the plant operator to im prove and optimize operation policies on a day- to-day basis according to the energy costs, market su pply of the raw material or need for the plant product, and other li mitations which may occu r in the plant, li ke outages of differ ent plant parts or utilities.

I n one embodiment, the forecast period spans the remaining lifetime of the catalyst as de termined from limitations of the operating condition, preferably a maximum reactor temper atu re that may be operated. The model allows for determining the remaining lifetime of a catalyst in use based on the forecasted operating conditions and the limitations of these operating conditions, e.g. a maximu m reactor temperatu re or pressu re that may be operat ed. This enables the operator to reliably plan the time left u ntil the next catalyst exchange and also to simu late different operation policies in order to extend the catalyst lifetime, if needed, or to get the maximu m production rate from the remaining time u ntil the next plan ned plant shutdown.

I n one embodi ment, the data-d riven model is used to predict operating condition of a cata lyst i n a production plant which has not provided historical data for training the data-d riven model.

I n one embodiment the output of the data-d riven model is used for optimizing an operating condition of a schedu led production ru n or a cu rrent production ru n of a chemical produc tion plant. I n such an embodiment target operating parameter(s) as determined via the da ta-d riven model for more than one operating condition are received and fed into an optimi zation processing device. The optimization may include one or more optimization target(s) . The optimization target may be specified by e.g. the optimization parameter(s) or the target parameter(s) to be optimized. I n this context optimization target may fu rther include finding a minimu m or a maximum of the specified optimization parameter(s) or the target parame- ter(s) . I n addition to the target parameter(s) for more than one operating condition the op timization target(s) may be received and fed to the optimization processing device. E.g. an operator may be provided with a selection of possible optimization targets and the chosen optimization target may be received based on the users selection.

I n case of one or more optimization target(s) one optimal solution may exist and may be provided as a resu lt of the optimization. Such optimal solution may be provided to a system for monitoring and/or control ling. The optimal solution may be displayed on a display device or used to control the chemical production process. I n case of more than one optimization target or a mu lti-objective optimization one or more optimal solutions may exist and may be provided as a resu lt of the optimization. The mu ltiple optimal solutions may be provided to a system for monitoring and/or control ling and displayed on a display device. I n such a case the operator of the plant is enabled to chose between the multiple optimal solutions, which sim plifies the decision process in com plex situation of operating the chemical production plant.

I n a fu rther em bodiment the optimization processing device determines based on target operating parameter(s) as output by the data-d riven model, a minimum or maximum value of the target operating parameter(s) or a minimum or maximum value of at least one optimi zation parameter derived from the target operating parameter(s) . I n one exem plary scenario a remaining life time of the catalyst may be the optimization parameter derived from the target operating parameter(s) and finding the maximum is the target of the optimization process. Furthermore, constraints may be included into the optimization problem. Con straints on the target operating parameter(s) side may include the maximu m reactor tem perature, minimu m selectivity or minimal production volu me per day. I n another exem plary scenario a production volu me over the catalyst’s remaining lifetime or u ntil a schedu led point in time for catalyst exchange may be the optimization parameter derived from the tar get operating parameter(s) and finding the maximu m is the target of the optimization pro cess. Constraints on the target operating parameter(s) side may include the maximu m reac- tor temperatu re, minimum selectivity or minimal and optional ly maximal production volu me per day.

I n another exemplary scenario mu ltiple objectives may be com bined. E.g. a remaining life time of the catalyst at production volu me over the catalyst lifetime may be the optimization parameters derived from the target operating parameter(s) and finding the maximum re maining lifetime combined with the maximu m production volu me is the target of the optimi zation process. Constraints on the target operating parameter(s) side may include the max imum reactor temperature, minimu m selectivity or minimal production volu me per day. I n a further example the mu ltiple objectives further include the optimal timing for catalyst ex change fu rther considering cost aspects such as remaining production volume, energy de mand, expense of catalyst exchange or com binations thereof. For mu lti objective optimiza tion known pareto optimization tech niques may be used.

I n one embodiment, the data-d riven model is used to simulate expected catalyst perfor mance, production rates (e.g. total amou nt of styrene produced over a period of time) , ener gy demands (associated with e.g. reactor or steam-reactant heating) and costs or profits (e.g. related to reactant costs, market prices of product, energy costs, ... ) for chosen sets of operati ng data or operation parameters in a catalytic reactor. Here production yield, energy consum ption, C0 ₂ -emission, costs, side products, catalyst exchange intervals, remaining lifetime or com binations thereof may be target operating parameter(s) or optimization pa- rameter(s) derived from the target operating parameter(s) . I n the optimization different constrai nts may be defi ned e.g. constrai nts for the operating data the determination of tar get parameters is based on.

I n one embodiment, the data-d riven model is used to simulate expected catalyst perfor mance, production rates and energy demands for chosen sets of operating data which are not actually achievable in a given plant setup (for instance, a lower pressu re level (deeper vacuu m) , a lower STO ratio, or an additional reactor) . This can hel p the plant manager to better evaluate the economics of potential upgrades to the plant.

I n one embodiment, the data-d riven model is used to simulate and/or evaluate expected performance and operating conditions for new plants where the catalyst has not been used previously.

The present disclosu re also provides a com puter program product configured to perform the methods of the present disclosu re. I n one embodiment, the com puter program product is a computer program implemented in a chemical production plant or a styrene production plant, particularly in a computing u nit (a com puter) integrated therein and/or con nected thereto. I n one embodiment, the computer program product is integrated into the dash board of the chemical production plant or styrene production plant.

I n one embodiment, the com puter program product com prises an interface for entering op erating conditions for the chemical production plant. Operati ng conditions can be historical data from previous production ru ns or actual operating conditions of the chemical produc tion plant in the current run.

I n one embodiment of the computer program product, in put parameters or operating data for a forecast are u ploaded manual ly into the computer program product and/or read out from a process control system by the com puter program product. I n one embodiment, the in put parameters or operating data are provided in a formatted data table. I n one embodi ment, a graphical user interface is provided for the manual u ploadi ng of data i nto the com puter program product. I n another embodiment, an application program ming interface is provided for u ploading data into the computer program product.

I n one embodiment, the user of the com puter program product provides al l information specified above (e.g., raw data, corresponding u nits, plant metadata) to the com puter pro gram product. This information can be entered manual ly, u ploaded via a structu red data file, or su pplied via an application programming interface (manual ly or automatical ly) . For long term forecasting, the in put time series of the target operati ng parameters preferably covers at least the range required by the time lag structu re used in the model. Potential ly also con trol parameters may be included, if their time lags are used in the model as wel l.

I n one em bodiment, exogenous operati ng parameters are entered by the user, e.g., for mu l tiple operating scenarios for which performance is to be predicted. Al l additional data pro cessing, including formatting, aggregation and prediction, are performed by the software product.

I n one embodiment, the forecast produced by the com puter program product is presented to the user via a graphical user interface, as a structured data file, or via an application pro gram ming interface.

According to a further embodiment, the com puter program product is a computer program product that when loaded into a memory of a computing device and executed by at least one processor of the com puting device executes the steps of the above described computer im plemented method.

The computer program product may be used with or incorporated in a computer system that may be a standalone unit or include one or more remote terminals or devices in communica tion with a central com puter via a network such as, for exam ple, the I nternet or an i ntranet. As such, the com puter or processor and related components described herein may be a por tion of a local com puter system or a remote com puter or an on-line system or com binations thereof. Any database and the com puter program product descri bed herein may be stored in com puter internal memory or in a non-transitory com puter readable medium.

Another aspect of the present disclosu re is a com puter system for forecasting performance of a catalyst in a chemical production plant or for determining operating conditions of a chemical production plant. The com puter system com prises at least an interface com ponent configu red to access and read operation parameters or operating data and catalyst-specific parameters, particularly catalyst age indicator, and a processor u nit implementing a data- d riven model and configured to predict performance of the catalyst by feeding the data- d riven model with the reactor operation parameters or operating data and the catalyst- specific parameters provided via the interface com ponent. I n one em bodiment, the comput er system is configu red to be cou pled to chemical production plant incl uding a catalytic re actor via a wired and/or wireless com munication con nection, and to access and read out the reactor operation parameters or operating data and/or the catalyst-specific parameters at least partly automatical ly from a process control system of the chemical production plant including a catalytic reactor via the interface com ponent.

A fu rther aspect of the present disclosu re is a com puter-im plemented method for training a data-d riven model of a chemical production plant including one or more catalytic reactors based on machine learning for predicting or forecasting performance of a catalyst in the catalytic reactor(s) . The method com prises providing a mathematical model as initial basis, providing historical data e.g. from a pl urality of production ru ns of the same type of catalyst and/or from a plu rality of production ru ns in a plu ral ity of chemical production plants or cat alytic reactors comprising the same type of catalyst, and, optional ly, previously determined target operating parameters or operation and performance parameters of the chemical pro duction plant and in particular the catalytic reactor(s) , accessing and im porting the provided historical data into the mathematical model, adapting parametrisation of the data-d riven mathematical model to the provided historical data, providi ng an u pdate of the data-d riven mathematical model on the basis of the adapted parametrisation, and iteratively repeating the method steps by setting the u pdated data-d riven mathematical model as initial basis.

Another aspect of the present disclosu re is a computer implemented method for determin ing operation and/or performance parameters or target operati ng parameters of a chemical production plant including one or more catalytic reactors. The method com prises accessing sensor data indicative of operating condition present in the reactor system and catalyst specific sensor data indicative of the catalyst presently used in the reactor system, deter mining operation and/or performance parameters or target operating parameters of the chemical production plant using a data-d riven model, wherein the data-d riven model is pa rameterized according to a training data set, wherein the training data set includes histori cal data e.g. from a plurality of production ru ns of the same type of catalyst and/or from a plu rality of production runs in a plu ral ity of catalytic reactors comprising the same type of catalyst and previously determined operation and performance parameters or target operat ing parameters, and providing the determined operation and/or performance parameters or target operati ng parameters of the chemical production plant includi ng one or more catalyt ic reactors.

A fu rther aspect of the present disclosu re is a com puter-im plemented method for determin ing operation and/or performance parameters of a chemical production plant including one or more catalytic reactors. The method com prises accessing sensor data indicative of oper ating conditions present in the reactor system and catalyst specific sensor data indicative of the catalyst presently used in the reactor system, determining operation and/or perfor- mance parameters or target operating parameters of the chemical production plant using a data-d riven model, wherein the data-d riven model is parameterized according to a training data set, wherein the training data set includes historical data e.g. from a plurality of pro duction runs of the same type of catalyst and/or from a plu rality of production ru ns in a plu rality of reactor systems com prising the same type of catalyst and previously determined operation and performance parameters or target operating parameters of the chemical pro duction plant, and providing the determined operation and/or performance parameters or target operating parameters of the chemical production plant.

Another aspect of the present disclosu re is a control system for control li ng a chemical pro duction plant including one or more catalytic reactors. The control system com prises a computer system as described above, and a control u nit which is configured to control an actual and/or schedu led production ru n in the chemical production plant on the basis of the provided operation and/or performance parameters or target operating parameters of the chemical production plant.

A com puter program may be stored and/or distributed on a suitable mediu m, such as an optical storage medium or a solid-state mediu m su pplied together with or as part of other hardware, but may also be distributed in other forms, such as via the internet or other wired or wireless telecommunication systems.

However, the computer program may also be presented over a network like the World Wide Web and can be downloaded into the working memory of a data processor from such a net work.

According to a fu rther exem plary embodiment of the present invention, a data carrier or a data storage medium for making a computer program available for down loading is provided, which computer program is arranged to perform a method according to one of the previous ly described embodiments of the present invention.

It is to be u nderstood that the em bodiments described herein are not mutual ly exclusive of each other, and that one or more of the described embodiments may be combined in vari ous ways, as wou ld be appreciated by one of ordinary skil l in the art.

A com puter program performing any of the methods of the present invention may be stored on a com puter-readable storage mediu m (e.g., a non-transitory computer-readable storage medium). A computer-readable storage medium may be a floppy disk, a hard disk, a CD (Compact Disk) , a DVD (Digital Versatile Disk) , a USB (U niversal Serial Bus) d rive, a RAM (Random Access Memory) , a ROM (Read On ly Memory) and an EPROM (Erasable Pro gram mable Read On ly Memory). A com puter-readable mediu m may also be a data com mu nication network, for example the I nternet, which al lows down loading a program code. The methods, systems and devices described herein may be im plemented as software in a Digi tal Signal Processor, DSP, in a micro-control ler or in any other side-processor or as hard ware circuit within an application specific integrated circuit, ASIC, CPLD, FPGA or other suitable device. The present invention can be im plemented in digital electronic circuitry, or in com puter hardware, firmware, software, or in combinations thereof, e.g. in available hardware of conventional mobile devices or in new hardware dedicated for processing the methods described herein, as wil l be described in greater detail below.

Brief description of the drawings

Exem plary em bodiments of the present invention are il lustrated in the appended drawings.

It is to be noted, however, that the appended drawings il lustrate on ly particu lar embodi ments of the present invention and are therefore not to be considered limiting of its scope. The present invention may encom pass other equal ly effective embodiments.

Fig. 1 il lustrates an exemplary em bodiment of a method for determining an operating condi tion for a schedu led production ru n or for a change in a cu rrent production ru n of a chemical production plant including at least one catalytic reactor.

Fig. 2 shows a high-level workflow of pre-processing raw data from an individual plant into dataset ready for model training or predictions;

Fig. 3 shows an exam ple workflow for the identification of a raw data set selection as basis for the model;

Fig. 4 shows an exemplary implementation of a system for determining operating conditions for the schedu led production ru n or for the change in the cu rrent production run of the chemical production plant;

Detailed description

The present disclosu re provides a com puter-implemented method of predicting short-term and/or forecasting long-term performance of a catalyst in a chemical production plant in cluding at least one catalytic reactor, including catalyst aging effects. The method involves using a mathematical model particu larly of the catalytic reactor which is based on machine learning, involves no a priori information on reaction kinetics and uses in put parameters selected from sensor raw data, derived parameters, reactor operating parameters, plant metadata and parameters indicative of the catalyst age. The methods, systems, com puter programs and com puter program products disclosed herein are further described for a sty rene production plant, which serves as an example. The methods, systems, com puter pro grams and com puter program products disclosed herein are applicable to other production plants with at least one catalytic reactor, particularly with fixed bed reactors.

I n case of a styrene production plant a feed stream com prising ethyl benzene is mixed with steam in a mixer. The mixed stream is fed into a catalytic reactor including a potassiu m- promoted iron oxide-based catalyst for dehyd rogenation to styrene monomer. The styrene production plant fu rther includes tem peratu re sensors, pressu re sensors, flow sensors or the like at various locations to monitor plant operation.

I n the process for the production of styrene monomer, ethyl benzene may be dehyd rogenat ed in adiabatic radial flow reactors. The ethyl benzene is mixed with steam in a specific pro portion known as the steam-to-oil (STO) ratio to supply the heat for the endothermic dehy d rogenation process and prevent reduction and coking of the potassiu m-promoted iron ox ide-based catalyst used in the process. The reaction is ru n at high temperatu res and su b- atmospheric pressu re, in a setu p that usual ly com prises at least two consecutive reactors. I ntermediate re-heating may compensate the energy consu med by the reaction. The low pressure, the dilution with steam, and the high temperatu re favor the dehydrogenation of ethyl benzene, leading to a higher equilibriu m conversion.

Over the lifetime of the catalyst, potassiu m, which is a coke gasification promotor, evapo rates from the catalyst and is carried downstream the catalyst bed to the cooler exit thereof, causing activity loss by catalyst coking. To com pensate for the aging of the catalyst, the plant operators increase the inlet temperatu res over the catalyst lifetime, in order to keep the ethyl benzene conversion rate constant. The higher temperatures negatively affect the selectivity towards styrene by enhancing cracking and formation of by-products like ben zene and toluene. Moreover, the potassium deposits within the catalyst bed and the fines produced from the catalyst cause an increase of the reactor inlet pressu re, which is ther modynamical ly u nfavorable. When the in let temperatu res or pressures have increased above the operational limits of the plant, the ru n has to be stopped and the catalyst needs to be exchanged.

The catalyst performance and its aging rate depend on the operation parameters of the re actors, e.g., the inlet temperatu res, the STO ratio, the inlet pressu res and outlet pressu res, the ethyl benzene flow rate, the nu mber of reactors used etc. The process economics can be greatly im proved by optimization of the reactor operation. This has been attempted in the past by usi ng different kinds of reactor models, which have been fitted to catalyst ru n data originating from experimental or industrial reactors. The models were based on knowledge or assu m ptions regardi ng the reaction kinetics for the main and secondary reactions, mass, heat and im pu lse transport phenomena, adsorption/desorption of different chemical spe cies present in the system, coke gasification and potassium loss kinetics, etc. The methods, systems, computer programs and com puter program products described herein, al low for more robust and reliable process control.

Figu re 1 il lustrates an exemplary em bodiment of a method for determining an operating condition for a schedu led production run or for a change in a cu rrent production run of a chemical production plant including at least one catalytic reactor.

If the determination concerns a schedu led production ru n, operating data indicative of a pre-defined operating condition for the schedu led production ru n is received in a first step 10 via the commu nication interface. The pre-defined operating data may result from a pre- vious production ru n. If the determination concerns the change in the cu rrent production run, measu red operating data indicative of a cu rrent operating condition for the current pro duction ru n is received in a first step 10 via the commu nication interface. Furthermore, at least one operating data point may be adjusted such that is includes a desired operating value indicative of the change in the current operating condition. The operating data may include sensor data measu red through sensors installed in the chemical production plant, quantities directly or indirectly derived from such sensor data, analytical data measu red in samples taken from the chemical production plant, and/or quantities directly or indirectly derived from such analytical data.

Fu rthermore, a catalyst age indicator associated with a period of time the catalyst has been used in the current or schedu led production ru n is received via the communication inter face. The catalyst age indicator may be based on a point in time, a time period, a quantity derived from time dependent operating data and/or a quantity cumu latively derived from time dependent operating data. Additional ly, plant metadata indicative of a physical plant layout may be received, via the com mu nication interface.

I n a second step 12 the operating data and the plant metadata may be pre-processed, via the processing device, prior to determination of the at least one target operating parameter. Preferably the pre-processing includes a transformation to quantities independent of the physical plant layout.

I n a third step 14 at least one target operating parameter for the operating condition of the scheduled production run or the change in the current production ru n based on the operat ing data and the catalyst age indicator using a data-d riven model is determined, via the pro cessing device. The determination of the at least one target operating parameter may addi tional ly be based on the plant metadata. The data driven model is parameterized according to a training dataset. The training dataset may be based on sets of historical data compris ing operating data, catalyst age indicator, the at least one target operating parameter and optional ly the plant meta data. The sets of historical data may include data from mu ltiple runs, multiple plants and/or mu ltiple catalyst batches. The determination of the at least one target operating parameter may be based on a short-term model determining target operat ing parameters for discrete points in time or a long-term model determining target operating parameters for a period of time.

I n case of a long term model, a time series of the at least one target operating parameter as measu red, predicted or derived during the cu rrent or a previous production ru n up to a pre diction start point in time may be received via the communication interface in step 10. The determination (14) , via the processing u nit, of the at least one target operating parameter for one or more points in time following the prediction start point in time may be based on the operating data including the desired operating value, the time series of the at least one target operating parameter, the catalyst age indicator and optional ly the plant meta data using the data-d riven model. Preferably the data-d riven model includes an intrinsic time- dependence. I n a fou rth step 16 the at least one target operating parameter for the operating condition of the schedu led or the change in the current production ru n may be provided via the com mu nication interface.

I n a fifth step 18 the determined target operating condition may be provided to an optimiza tion processing device for optimizing an operating condition of a scheduled production ru n or of a change in a cu rrent production ru n of a chemical production plant. Here for more than one operating condition of the scheduled production run or of the change in the cur rent production ru n, the determined target operating parameter(s) may be received, via the com mu nication interface between the optimization processing device and the processing device. Based on the received target operating parameter(s) a minimu m or maximum value of a target operating parameter or a minimu m or maximum value of an optimization parame ter derived from the target operating parameter(s) may be determined, via the optimization processing device, and the minimu m or maximu m value indicative of an optimal operating condition of the scheduled production run or for the change in the cu rrent production ru n may be provided via the com mu nication interface.

Pre-Processing of operating data

Figu re 2 shows an exem plary workflow of pre-processing data into a format appropriate for model training, predictions via the short-term model or forecasting via the long-term model.

I n a first step measured operating data is received optional ly followed by a pre-processing method. If the data is prepared for training, such operating data may include sets of histori cal data from multiple ru ns, mu ltiple plants and/or mu ltiple catalyst batches. If the data is prepared for prediction or forecasting, such operating data may include measured operating data indicative of the cu rrent operating condition for the cu rrent production ru n. The operat ing data preferably includes sensor data measu red through sensors instal led in the styrene production plant, and/or analytical data measu red in sam ples taken from the styrene pro duction plant.

For each production plant, there are many sensors available, typical ly hu ndreds or even thousands, that provide raw data at their individual sam pling rate. I n addition, analytical data, e.g. results from gas chromatography are available for specific times at which sam ples have been taken from the plant. How often this data is available varies between plants, but typical frequencies are once per day u p to once per week.

I n a first pre-processing step, the operating parameters may be selected from the operating data, which form the input parameters for the data-d riven model. These input parameters may be derived from raw parameters such as sensor data or analytical data. An exem plary process on how to select these raw parameters from al l available parameters when setting u p the data driven model is outlined in more detail below.

I n a second pre-processing step data from analytics and selected sensors may be com bined based on their timestam p and particu larly pre-processed onto a com mon time scale. For many plants only daily aggregates of the raw sensor data may be available, rather than high frequency raw data, and this is also a typical frequency at which analytical data is available, daily averaging may be used to bring al l data on the same time basis. Other merging tech niques can be applied as wel l and are wel l-known, e.g. interpolation of the daily data (both analytical and sensors) and sampling at higher or lower frequencies of interest, e.g. to cre ate hou rly data.

Additional ly, plant metadata may be received. The plant metadata, e.g. the catalyst active volu me and the num ber of reactors, may be added as nu merical or categorical variables to the dataset to complete the set of in put parameters of the model including derived parame ters.

I n a third pre-processing step, the received and selected operating data may be filtered and smoothed. Here e.g. a point in time and du ration of maintenance intervals, startup phases, irregu larities and outliers may be identified and optional ly filtered. To achieve this, many options are known to someone skil led in the art, and any com bination of such methods may be used. For instance the procedure includes, applying viable absolute th resholds based on catalyst domain knowledge, like a minimu m reactor tem peratu re, a maximum steam/oil- ratio and a maximum pressu re after the reactors; identifying outliers by com paring each value or set of values to the distribution of al l other values of the same parameter or set of parameters available from the respective production plant, e.g. using absolute thresholds based on distribution metrics like 6 times the interquartile range (a conservative threshold used in the example application) or alternatively based on the estimated likelihood of the data point originating from the overal l distribution and/or identifying irregu larities based on big ju mps of parameters com pared to the month ly coefficient of variation for this parameter.

I n a fou rth pre-processing step, missing data points on the com mon time scale may be de tected and su bstituted with statistical ly determined values. Such potential ly missing param eters may be im puted. Specifical ly, analytical data may be im puted, if these data have been sampled less frequently than the chosen time basis. I mputations may be determined from different methods, e.g. sim ple mean im putation, forward or backward fil ling, weighted means or estimates from Kal man filters or comparable estimation methods. The same methods may be applied to replace outliers. The start of ru n may be identified based on criteria defined by experts, e.g. as the first data point with an hou rly space velocity >0.2/h in the styrene catalyst exam ple. Al l derived parameters may then be calcu lated, including e.g. the cumu lative plant production.

Depending on the natu re of the derived parameters, especial ly the cu mu lative parameters, the identified startu p phases, downtimes etc. may be removed from the dataset before or after calculating the respective derived parameters. I n an exem plary em bodiment, the cu mulative production since the start of the run, which the implemented age indicator is based upon, is calcu lated before the startu p phases were removed from the data set as they contribute to ageing of the catalyst, even though these phases are not part of the op erating conditions covered by to model. One fu rther pre-processing step not depicted in Figu re 2 may be the transformation of data from different plants to com mon units. It is preferable and straightforward to do this before the workflow in Figure 2 is started, even though this may also be performed before or after any step in the process.

At this point, the data is ready to be used for training, forecasting with a long-term model or predicting with a short-term model. However, since the filtering procedu res may result in some gaps in the data, and the time scales for forecasting are typical ly much longer, e.g. months, com pared to the available time basis, e.g. days, an additional aggregation step, e.g. weekly mean or median aggregation, may be performed on the data before it is used in the long-term model.

Parameter selection process

The operating data or raw parameters of interest may be determined via the workflow sketched in Figu re 3. The parameters available to the catalyst experts, serve as the basis, consisting of a combination of raw sensor data, analytical data and some typical operating parameters derived from the them, e.g. conversion, space velocity, steam/oil-ratio, selectivi ty. I n a first step, if data from mu ltiple plants is used, only parameters available from al l plants of interest may be selected (if only one plant is to be model led, this criterium is ob solete) , and redu ndant parameters (e.g. rescaled parameters) and zero-variance- parameters may be dropped.

Next, a correlation matrix of the remaining parameters may be calcu lated and clustering, e.g. hierarchical clustering, of the parameters may be carried out to identify pairs or clusters of parameters carrying similar information. I nstead of a clustering algorith m, a simple filter for high (anti-)correlation values, e.g. (>0.90 or < -0.90) or (>0.95 or < -0.95) can be ap plied. However, clustering of the correlation values with al l other parameters fu rther al lows to identify parameters which might have lower direct correlation but have very similar corre lation values with all other parameters. From each cluster of two or more parameters, on ly a single parameter may be retained based on a certain selection criteria like: the parameter needs to be available for al l plants; the typical parameters routinely used by the operator need to be kept (which is the exception that may lead to keeping more than a single param eter) and the parameter should represent an interpretable quantity, which is also the rea soning not to reduce the dimensionality via a principal component transformation or similar methods that produce featu res not directly interpretable by the operator.

Based on these criteria, the parameter set can be iteratively reduced, by adapting the clus ter threshold if necessary. The num ber of parameters may be reduced iteratively until a set of parameters (1, ... , M) remains, where only low correlation between parameters persists. Some remaining relatively high correlation values stem from parameters which may be im portant to the operator and may therefore not be removed. Once the parameter set has been reduced, the raw sensor and analytical data are identified which are required to obtain al l these remaining parameters.

Normalization of parameters and plant metadata

Different plants vary in their production levels, their typical operating conditions and often exhibit systematic differences. To accou nt for such differences between different plants one of two strategies or a com bination of two strategies may be applied as lined out below.

I n a fu rther pre-processing step normalization may be performed. I n one embodiment plant metadata indicative of the physical plant layout may be received. Such plant metadata may include the reactor layout such as the num ber of reactors, the active catalyst volume, reac tor types, dimensions or combinations thereof.

Normalization of the operating data may be performed to make the model input parameters (except for the plant metadata) as independent as possible from the specific plant layout. For many parameters, e.g. steam/oil-ratio, conversion, selectivity, there is no need for nor malization. Additional ly, parameters like liquid hou rly space velocity (LHSV) is intrinsical ly normalized by the catalyst volume. Additional ly or alternatively, the amount of total product over the catalyst production run per catalyst or the cu mulative total production may be nor malized by the active catalyst volu me, because this is a more com parable measu re for the “age” of each u nit volu me of catalyst than the time on stream (where variations in produc tion levels are not captu red) or the u n normalized cu mu lative production (which wil l have a different meaning for differently sized reactors) .

Additional ly or alternatively, pressu res may be normalized to their initial values during the start of the run, e.g. the median value of the first 90 days on stream, in order to focus on the aging effect rather than the - in some cases more pronou nced - interplant differences. Ad ditional ly or alternatively, the pressure d rop over each u nit like a reactor or a heat exchang er may be normalized by the space velocity or the total flow rate, since it is known that it varies with the superficial linear velocity of the gas mixtu re. Additional ly or alternatively, an average in let temperatu re of more than one, e.g. 2 or 3, reactors may be determined.

U ltimately, there are other plausible ways of making the operating data, analytical data and any quantity derived therefrom comparable between plants beyond the examples mentioned in this section; and there may be other useful reactor/plant metadata, specifical ly regarding reactor geometries, that may be used in a similar fashion.

The reason for finding such normalized parameters is that the usage of data from mu ltiple different plants offers a num ber of significant advantages: 1) the parameter space covered by an aggregated data set is much larger than that of any individual plant, which typical ly operates arou nd a relatively narrow set of operating parameters the operator is familiar with, since wrongly deviating from this may cause severe monetary losses. Therefore, the model (s) trained on such an aggregated dataset may provide predictions outside the oper ating range of a specific plant as it includes information not available from their own historic data. 2) Owing to the long lifetime of the exemplary styrene catalyst (2-3 years) , only 1-4 runs of a certain type of catalyst are available per plant, severely limiting the nu m ber of de activation processes that can be observed per plant (each run only provides a single inde pendent observation of catalyst deactivation) . The aggregated dataset al lows to include a larger nu m ber of deactivations into the training data. 3) Combined with the selection pro cess of parameters, which em phasizes interpretability and availability of the commonly used operating parameters, this al lows the trained model (s) to be applied to plants where no pri or actual data is available - a situation often encountered when tech nical proposals need to be provided for new plants , which wou ld not be possible if the model was strictly linked to a specific sensor set available at a specific plant.

Short-term model (s)

For the short-term prediction of the catalyst behavior, any regression model may be used and those skil led in the art know a variety of the typical model candidates. Depending on the nature of the data in chemical production plants, typical ly a low nu mber of independent ru ns and - even after normalization of a nu m ber of parameters - some potential plant- specific biases, models of relatively simple natu re and not too flexible may be chosen. I n such a scenario with low num ber of independent ru ns a highly flexible model, e.g. a random forest regression wil l fit the training dataset better but may poorly extrapolate to new data. Hence depending on the nu mber of runs available a suited type or com bination of regres sion-based model may be chosen.

One possible model may be an ensem ble of linear models trained on subsets of the training data in order to e.g. predict the average reactor inlet temperatu re and the selectivity of the reaction. Using such an ensemble has two advantages: first, using model ensembles for prediction, e.g. by retrieving the median prediction of al l models, can lead to more accurate predictions [e.g. Ensem ble Methods - Foundations and Algorithms, Zhi-Hua Zhou; CRC Press 2012] ; and second, training an ensemble this way provides an estimate of the model u ncertainty by using the range of predictions (or the 10% and 90% percentile, or any other range of prediction quantiles, ....).

When using training data from multiple catalyst batches, multiple runs and/or mu ltiple plants, the training and test data set may be split by individual ru ns. Additional ly, or alterna tively, the training and validation data set may be split by individual plants or catalyst batches. For exam ple, a random set of about 75% in the training set may be selected and the parameters may optional ly be normalized (to zero mean and u nit variance) during pre processing. The remaining data may be used as validation data set to test the trained mod el.

Long-term model (s)

For time-series forecasting, a large num ber of mathematical models may be used, ranging from autoregressive models to recurrent neu ral networks. The requirements for models to apply to the exem plary problem at hand include: 1) applicability to mu ltivariate time-series, i.e. prediction of mu ltiple endogenous (uncontrol led) parameters which undergo long-term trends that are to be forecasted, e.g., pressu res, in let tem peratu re or selectivity; 2) integra tion of exogenous (control led) parameters, i.e., highly influential parameters which are known or wil l be control led external ly and therefore do not require forecasting by the model, like the steam/oil-ratio, LHSV, target conversion.

A preferred em bodiment of the method involves a mathematical model which al lows for regu larization to avoid overfitting, which can easily occu r when mu ltiple time lags are in cluded in the mathematical model. I n one embodiment of generating the mathematical model used in the method of the present disclosu re, an ensem ble of mathematical models is im plemented which is main ly based on combinations of penalized linear models and pe nalized vector autoregressive models with exogenous variables (VARX) . For an overview of penalized VAR(X) models, including different structured regularization methods, see e.g. [arXiv:1508.07497vl (Nicholson et al 2018, VARX-L: Structu red Regu larization for Large Vector Autoregressions with Exogenous Variables)] and references therein.

The train/test split is carried out as for the short-term model between ru ns. Al l candidate models may be trained to predict endogenous variables at time t based on exogenous varia bles at time t and the history of endogenous variable u p to a maximum time lag m (t-m, ... t- 1). Iteratively applying such a model step by step, and at each new step using the forecast of the endogenous variables as in put for the next step, al lows to make forecasts going an arbitrary nu mber of steps ahead.

The training procedure may be performed using leave-one-out cross-validation on the level of plants. Here for N plants in the dataset, N sets of training data may be generated (con sisting of data from al l other plants) , their parameters may optional ly be standardized to have mean 0 and a com parable range of values, and the trained models may be evaluated on the plant that was left out (validation set). U ltimately, the model hyperparameters (e.g. regu larization parameters) may be selected, which give the most robust performance on the N validation sets, e.g. measured by the average root mean squared error of the one-step- ahead forecast, and the model may be trained on the ful l training set.

As the mathematical model used in the method of the present disclosure is based on ma chine learning, it has to be trained with historical data from at least one production run in a chemical production plant including at least one catalytic reactor prior to being used for predicti ng short-term or forecasting long-term performance including aging of a catalyst used in such a reactor system. I n one embodiment of the method of the present disclosu re, the model has been trained using historical data from a plu rality of production ru ns of the same type of catalyst. I n a fu rther em bodiment of the method, the model has been trained using historical data from production ru ns in a plurality of reactor systems com prising the same type of catalyst. I n both of these em bodiments, the historical data may be provided from different manufactu ring batches of the same type of catalyst. I n one em bodiment of the method, the operating data and potential ly the catalyst age indicator of the plurality of production ru ns have been normalized prior to being used for training the model e.g. as de scribed in the section above. It has been fou nd that using operating data from more than one production run, be it from one and the same plant or from different plants, en hances the prediction quality and broad ens the operating parameter range covered by the prediction or forecasting model. I ncluding data originating from mu ltiple runs and plants fu rther im proves the generalizability of the prediction or forecasting for application to a production plant from which no data was avail able du ring training of the model. It is however preferred that al l data used to train the model are provided from plants using the same catalyst formu lation, since different cata lysts differ significantly in their catalytic properties (reaction rates) and morphological prop erties (transport properties). This includes the use of catalyst of the same type provided from different manufacturing batches or different delivery date.

I n one embodiment, the in put parameters for the model are selected from sensor data available from the reactor system, analytical data e.g. from gas ch romatography (GC) ana lytics, and derived parameters as laid out in the respective section above.

I n one embodiment, the operating data or reactor operation parameters include in let tem perature and outlet tem perature of each reactor, inlet pressure and outlet pressu re of each reactor, and com position of the reaction mixture at the inlet and outlet of each reactor.

I n one embodiment, the operating data or in put parameters of the model include steam-to- oil (STO) ratio, liquid hou rly space velocity (LHSV), total production of styrene normalized by catalyst volume, target ethyl benzene conversion, styrene selectivity, average in let tem perature, normalized pressure after the last reactor, normalized pressu re d rop over the re actors, tem peratu re loss over reactors, normalized deviation of tem perature loss com pared to the expected (calcu lated on the basis of conversion) value.

An advantage of the parameter set used in the methods or systems of the present disclo su re is that it is stil l interpretable, as many of the parameters correspond to actual operat ing parameters or can easily be interpreted in that context. Other approaches to reduce the num ber of dimensions of the problem (e.g., PCA or RFA) can lead to parameters which are useful for the modeling process and predictive accuracy, but often lack interpretability.

The mathematical model used in the method of the present disclosu re performs time-series forecasting and is able to cover the fu l l deactivation process of the catalyst during a whole production ru n in the reactor system. The model enables the plant operator to improve and optimize operation policies on a day-to-day basis according to the energy costs, market su pply of the raw material or need for the plant product, and other limitations which may occu r in the plant, like outages of different plant parts or utilities.

The su bject matter of the present disclosu re is fu rther described and explained in the fol lowing working examples. Examples

Generation of dataset for training the mathematical models To develop the mathematical models, data was used from several production ru ns of the same catalyst type (BASF S6-42) . The dataset covers 11 industrial plants with 2 or 3 reac tors and information about 1-4 production runs in each of the plants. For each individual plant, a ful l set of parameters (includi ng analytical data and sensor data) was col lected. The sensor data were typical ly available at a daily resolution, while the analytical data was available at a daily to weekly resolution.

The process of parameter selection for the model has been described above (Figure 3)

Table 1 lists the operating data from raw sensor and analytical parameters which were se- lected at each point in time in order to derive al l relevant parameters for the model. These u nits and formatting choices are only one exam ple which can be used; the temperatu re cou ld e.g. also be specified in degree Fah ren heit, the pressu re cou ld be specified in mm Hg, another date and time format may be used, etc.

Table 1

The num ber of reactors and the total catalyst volume were additional ly used as metadata. The fol lowing Table 2 lists the set of parameters (derived parameters and plant metadata) used for training of the different models.

Table 2 Exemplary application: short-term model

Model Development

As described above, ensem bles of 50 linear regression models have been trained on a su b set of the training dataset, with each su bset split between runs. Each of the 50 reduced training sets contained randomly chosen -74% of the available ru ns, to both improve the prediction and provide estimates about the local u ncertainty of model predictions (given that each model is trained on different subsets of e.g. operating conditions) . I m portantly, the su bsets of data need to be split between ru ns (or alternatively between plants) , i nstead of a random sam pling of training data points. Otherwise, there wil l hardly be any variation between the models, as al l models are trained on a nearly identical distribution of operating conditions.

I n the presented example, specifical ly the parameters“tem perature” (average reactor inlet temperatu re) and “selectivity” (of the reaction to the desired product styrene) have been predicted using al l other parameters from Table 2.

I n this specific im plementation, the reaction tem peratu re itself is one of the major influenc ing factors for the observed selectivity. Therefore, the prediction of both parameters is car ried out in two steps. First, a 50-model ensemble is trained to predict the temperatu re based on al l parameters from Table 2 (excluding selectivity and temperature). A second ensem ble of 50 models was trained to predict selectivity using al l parameters from Table 2 as i nput (excl uding on ly selectivity) . This second ensem ble is then used to predict selectivi ty using the predicted temperatu re from the first model ensem ble as one of the in put pa rameters.

I n the practical use of this developed model, the workflow of su bsequently predicting both parameters have been im plemented in a single prediction fu nction, which receives the in put parameters and predicts both temperatu re and selectivity. Therefore, the combination of both model ensem bles may be regarded as a single entity of a“short-term” model from the outside for al l uses of the model.

Beyond the direct use of the parameters in Table 2, also i nteraction terms were considered, and final ly e.g. the“steam/oil-ratio - conversion” interaction was integrated into the short term model predicting the tem peratu re. Such interactions or higher order polynomial terms, e.g. quad ratic terms for the temperatu re for the selectivity prediction, can easily be im ple ment into predictive models using statistical program ming languages without the need to extend the basic set of parameters su pplied to the model.

Which type of model to choose, whether or not to use ensem bling techiques, and which higher-order terms, transformations or interactions of the in put parameters to use, depends on the specific question and dataset; and is a typical model development procedu re for data scientists.

Short-term model use case 1

I n one exem plary use case, a plant operator may want to use a short-term model to esti mate the required reactor tem peratu re to achieve a desired target conversion rate at speci fied operati ng conditions that might not have previously been used i n his plant. I n case of a styrene production plant such operating conditions may be an increased steam/oil-ratio or a lower LHSV or a change in the feed com position. Ideal ly, the starting point for this predic- tion should be the current plant status, including the normalized age parameter“total Pro- duction”.

Model im plementation

Figu re 4 il lustrates a client server set-u p of a production monitoring and/or control system including a client side with a processing device including a user application, a server side with a processing device for a service provider. The client side and the server side may be com mu nicatively cou pled, e.g. wired or wireless, via the com mu nication interface. The client side may include a display device. Preferably the client-side user application is configu red to receive and display operating data, desired values, catalyst age indicator, plant metadata, target operating parameters or the determined operating condition. Fu rther preferred the client-side user application is configu red to receive target operating parameters or the de termined operating condition to control the cu rrent or schedu led production run in the chemical production plant based on the target operating parameters or the determined op erating condition. The client-side user application may be an embedded part of the chemi cal plant’s process monitoring and/or control ling system.

Raw sensor and analytical data are recorded at a production plant together with the neces sary plant metadata since the start of the production run. These data are pre-processed accordi ng to the data pre-processing workflow as e.g. sketched i n Figu re 2, specifical ly us ing the identical workflow (filter steps, im putations, th resholds, aggregations, ... ) as was used for preparing the training dataset for the respective model. Preferably, this pre processing is im plemented by the same party that has developed the model and can be pro vided to a user appl ication e.g. via direct integration of a pre-processing function, or via an application program ming interface (API) .

After the data has been pre-processed, the user may adjust operating parameters of inter est to provide a desired operating value indicative of the change in the cu rrent operating condition. The set of adjusted in put parameters (also referred to as operating scenario, or prediction scenario) is su bsequently transferred to a prediction function. This prediction fu nction might e.g. be i mplemented local ly in the user application or add ressable via an API and carries out al l operations as described above. The resu lts are reported back to the user application e.g. i n order to com pare and choose between different scenarios. The user may fu rther associate the in put parameters and/or the predicted parameters with e.g. costs or other quantities that can influence the decision process regarding which operating parame ters to use in the plant.

Figure 4 visualizes an exemplary implementation concept. The raw data is automatical ly or manual ly col lected at the production plant and transferred to the service provider via an API, which processes the raw data into the correct format according to the workflow e.g. as laid out above. The transformed dataset can be provided to the user, e.g. the plant operator and based on the cu rrent values, different scenarios may be defined. These scenarios can be transferred to the same or a second API ru n ning the model (s) , which provides the corre sponding prediction or forecast back to the user.

Short-term model Use case 2

I n a second use case, an expert may want to provide estimates for the development of the reactor tem peratu re and the corresponding selectivity before the catalyst is instal led at the plant. This scenario e.g. occu rs frequently du ring the preparation of tech nical proposals, which provide one or more hypothetical operating scenarios and thei r im pl ications to a cus tomer, before a decision to purchase the catalyst is made. Therefore, accurate predictions for plants which have never provided data for model training are desired.

Making a few simplifying assum ptions, e.g. estimating the“age” parameter total Production based on a hypothetical run data, usual ly involving constant operating parameters for the fu l l run, su bstituting the temperatu re loss over the reactors with an estimated value based on the operating conditions, etc., the short-term model presented above can be used for this pu rpose given the typical set of operating parameters provided by the customer. That this can be served by the model is a direct resu lt of the selection criteria used in the param eter selection workflow (Figu re 3) , specifical ly to keep al l parameters as inputs to the model that are typical ly used by operaters to monitor and control their plant.

Model presentation to user

The interface of the user application may contain a block of in put parameters to the model, which may be fil led automatical ly or manual ly, and which can be used to interactively speci fy operating scenarios; a block for model output (e.g. average reactor in let tem peratu re and selectivity with the prediction range) for the specified scenario; and optional ly as further output a local response of the model predictions to a parameter of interest (e.g. predicted reactor in let tem peratu re for a range of target conversions) .

The input parameter block may be fil led automatical ly if current plant operating data are available (e.g. use case 1) or may be defined com pletely manual ly if no actual plant data is available (e.g. use case 2) . Based on the user-adjusted in put parameters, the parameters predicted by the model, in this exam ple reactor inlet temperatu re and styrene selecitivity may be displayed to the user as e.g. text (for predicting a single poi nt) , or e.g. in graphical form (local model response to variation of si ngle parameter). These serve only as examples, as there are more ways in which such a model may be used; in terms of use cases, im ple mentation, and presentation to a model user.

Exemplary application: long-term model

Model Development

Starting from the processed dataset that was used to develop the short-term model (Table 2) , a few additional steps are taken to prepare the dataset for trai ning the long-term model. First, a smal ler nu mber of parameters are selected from the l ist, and second, each parame ter is aggregated on a weekly basis.

The input parameters of the model may be constant (reactors, CatVolu me), may be con trol led (conversion, SOR, LHSV), can be calculated based on these constant or control led values (total Production), or are not control led in the operating scenarios of interest (tem perature, selectivity, pressureOut, deltaP, deltaT, dTdev_norm).

The latter set of parameters are label led endogenous or uncontrol led parameters, while the former (which are known th roughout the forecasting range, given that the operating scenar ios are carried out as plan ned) are label led exogenous or control led parameters. Table 3 provides an overview of parameters used for developing the exemplary forecast model and their assign ment to both types of parameters.

Table 4

I n developing the exemplary model, a number of different VARX-type candidate models as described above were trained, where the candidates differed e.g. in their regu larization method (elasticnet, ridge) , or their nu mber of maximum time lags (4-10 weeks) .

For al l of these different com binations of model , the traini ng procedu re was carried out the same way, using leave-one-out cross-validation on the plant level. Al l trained models are candidate models for an ensemble that final ly com prises the long-term model.

While al l training was performed for one-step ahead forecasts (which can, iteratively ap plied, forecast an arbitrary number of steps), the final selection of models should also per form wel l for longer forecasts. I n order to evaluate this, forecasts were performed starting at mu lti ple points of each available ru n in the training and test dataset, using the actual exog enous variables of those ru ns as operating scenarios and determine for each step ahead the error distribution for the forecasts. Models were selected that provided no clear long-term biases and a narrow error distribu tion th roughout the whole range (even though a moderate widening of the error distribution for longer forecasts has to be expected) for the reactor in let tem peratu re and the selectivity on both the training and test datasets. Model selection was based on error distributions of forecasts performed on test and training sets from 30 model candidates.

I n this exem plary development of a long-term model for a styrene catalyst, the final ly se lected models were 3 two-stage models with a maximum time lag of 10 weeks trained on local slopes employing different types of regu larization. For the ensem ble forecast, al l mod els are iteratively run independent from each other and on ly the com plete individual fore casts are averaged to provide an ensem ble prediction. I n the presented exam ple, this was a more efficient implementation com pared to aggregating the forecasts after each individual step, which wou ld be one possible alternative im plementation for an ensemble prediction.

Just as with the single models, the final ensem ble is evaluated on the test data to get the error distributions for N days ahead, which is in the exemplary implementation provided as error estimates of the forecasts.

As with the short-term exam ple above, the ensemble forecast together with the expected error distribution can be viewed as a single entity of a“long-term” model for application of the model by a user, regard less of the details of the u nderlying procedu re (ensemble aver aging, mu lti-step models, ... ) .

Long-term model use case

I n an exem plary use case, a plant operator might want to estimate the remaining catalyst lifetime dependi ng on different scenarios of operati ng the plant and plant-specific limits on the operating parameters. Such scenarios may include changes to the LHSV, steam/oil- ratio or target conversion levels; there are many motivations to contemplate different sce narios, but an exemplary question would be whether the gain in catalyst lifetime run ning the plant at lower production levels during a phase with low prices of styrene is u ltimately worth it.

The end of the catalyst lifetime may depend on many conditions defined local ly at each production plant, but one limitation of catalyst lifetime is in al l cases the reactor tempera tu re or pressu re which may not exceed a plant specific threshold. With predictions from the long-term model , the end of the catalyst l ifetime may be esti mated based on this th reshold and com pared for different user-defined scenarios.

Model im plementation

The model may be conceptual ly implemented analogous to what is described in Figu re 4, with some minor changes. The processing function, implemented e.g. local ly or via an API, needs to be adapted to provide the data format used for long-term model training, in this specific exam ple a weekly aggregation step after the procedu re performed for data for the short-term model . The forecasting fu nction, i m plemented e.g. local ly or via an API , now not on ly receives a set of operating conditions to predict a single point, but instead the lagged endogenous data required by the model, as wel l as operating scenario values for the exoge nous parameters. Simi larly, the model output is the fu l l forecast of al l or on ly some endoge nous variables of the model.

Model presentation for user

I n the im plementation of a long-term model endogenous parameters used in the models need to be available for at least the last L weeks, where L is the maximu m time lag used in any of the model elements com prised i n the“long-term” model. This data may be automati cal ly obtained from plant raw data as described in the data pre-processing and preparation sections, or data of appropriate format may be manual ly entered or uploaded.

A control parameter in put block may be used by the operator to create operating scenarios over an extended period of time, e.g.in the exam ple application the steam/oil-ratio, target conversion and LHSV can be plan ned ahead in u p to th ree independent segments, to si mu late also futu re changes. These scenarios may also be much more com plex than described here. The plan ned operating scenarios may be visual ly displayed, preferably together with the history of these parameters to easier retain continuity in some of the controls. The con trol parameters selected for user manipu lation may consist of an arbitrary su bset of al l ex ogenous parameters used in the model . I n this specific implementation, the other 3 exoge nous parameters are either constant, or can directly be derived from the other inputs and/or time.

The forecasts provided by the long-term model may be displayed in table format, ready for export of the data and e.g. further analysis based on the forecasted trends, or the resu lts may be graphical ly displayed to the user for a visual inspection of one or more different plan ned scenarios.

The interface may contain a section, where selected control (exogenous) parameters can be defi ned for user-defined operating scenarios (e.g. target conversion, LHSV and steam/oil- ratio; plots representing the actual data u p to the start of prediction and for the operating scenarios going forward) . I n another section of the i nterface, selected endogenous parame ters may be presented to the user (e.g. reactor inlet tem perature and styrene selectivity; the start of the prediction may be marked by a horizontal dashed l ine, beyond that point every thing is forecasted by the model and includes estimates of the forecast error). I n addition, the predictions of al l or some endogenous parameters may be presented as a data frame which can be exported by the user.