CHARACTERISTICS, AND ACOUSTIC ACTIVITY BACKGROUND

In the search for hydrocarbons and development of hydrocarbon-bearing wells, hydraulic fracturing is a common technique to improve hydrocarbon recovery. Hydraulic fracturing involves injecting a high-pressure fluid into a wellbore to create or expand cracks in the subsurface formations so that natural gas and petroleum can flow more freely.

It may be difficult to determine whether a fracture downhole is operating as intended or if a flow rate through a given perforation cluster is as expected without a significant interruption of downhole operations and use of expensive and time-consuming equipment. For example, deployment of a wireline logging tool to collect flow rate data would interrupt and/or delay other downhole operations. Even if more permanent installations of flow rate sensors downhole were possible, distributing multiple sensors in a way that effectively monitors flow near different perforation clusters would be costly and tedious.

Most wells are not instrumented with anything more than a surface and/or downhole pressure meter. Downhole flow estimation is highly uncertain when using only pressure data and a model of the reservoir. There are commercial downhole flowmeters available but they suffer from technical limitations regarding placement in the wellbore, orientation, and acceptable flow rates. During hydraulic fracturing, the flow rates are so large (50,000 - 70,000 barrels per day) that mechanical flow meters often do not survive.

Fiber optic sensing systems have been developed to monitor downhole parameters such as vibration, acoustics, pressure, and temperature. Unfortunately, efforts to correlate acoustic activity with fluid flow have thus far resulted in inaccurate estimates.

BRIEF DESCRIPTION OF THE DRAWINGS

Accordingly, there are disclosed in the drawings and the following description specific methods and systems employing a flow prediction model that is a function of perforation cluster geometry, fluid characteristics, and acoustic activity. In the drawings:

FIGS. 1A-1C are schematic diagrams of illustrative well environments with distributed sensing components. FIG. 2 is a schematic diagram of an illustrative optical phase interferometric sensing arrangement.

FIG. 3 is a block diagram of an illustrative signal processing arrangement.

FIGS. 4 A and 4B are graphs showing flow parameters as a function of acoustic power.

FIG. 5 is a graph showing acoustic activity values in a "waterfall plot" as functions of time and measured depth.

FIG. 6 is a flowchart showing of an illustrative flow prediction method.

It should be understood, however, that the specific embodiments given in the drawings and detailed description thereto do not limit the disclosure. On the contrary, they provide the foundation for one of ordinary skill to discern the alternative forms, equivalents, and modifications that are encompassed together with one or more of the given embodiments in the scope of the appended claims.

DETAILED DESCRIPTION

Disclosed herein are methods and systems employing a flow prediction model that is a function of perforation cluster geometry, fluid characteristics, and acoustic activity. The flow prediction model may be used, for example, to predict fluid flow for each of one or more perforation clusters as a function of time. The predicted fluid flow for a perforation cluster may correspond to a volumetric flow rate, and may be used to make decisions related to well completion operations, treatment operations, fracturing operations, or other operations involving one or more perforation clusters. In different embodiments, the flow prediction model may be calibrated. Example calibrations involve adjusting one or more variables of a flow prediction model based on a comparison of predicted fluid flow for one perforation cluster and a surface flow rate, a comparison of a sum of predicted fluid flow for each of a plurality of perforation clusters with a surface flow rate, and/or a comparison of acoustic activity values obtained with and without a surface fluid flow.

In at least some embodiments, downhole acoustic activity is monitored before, during, and/or after downhole operations using a distributed acoustic sensing (DAS) system and/or other downhole sensors. An example DAS system involves deploying an optical fiber downhole by attaching the fiber to the outside of the casing during casing deployment and later cementing the casing (and embedding the fiber) into place. In some cases, the fiber is attached to the outside of production tubing. Acoustic activity values, derived from measurements collected by a DAS system or other downhole sensors, are provided as inputs to the flow prediction model along with perforation cluster geometry values (e.g., perforation diameter and/or number of perforations) and fluid characteristic values (e.g., effective fluid viscosity and/or estimated fluid density).

In at least some embodiments, the acoustic activity values input to the flow prediction model correspond to a broadband acoustic energy measure derived from measurements obtained by a DAS system and/or other downhole sensors. Alternatively, the acoustic activity values input to the flow prediction model correspond to an acoustic energy measure for one or more frequency ranges derived from measurements obtained by a DAS system and/or other downhole sensors. As desired, the acoustic activity values used with the flow prediction model may be averaged and/or normalized as a function of time, position, and frequency. In at least some embodiments, the perforation cluster geometry values input to the flow prediction model may be taken from, or derived by, pre-installation measurements of downhole casings and perforation tools, qualified estimates based on past performance of perforation operations in similar environments, downhole measurements of perforation flow rates, or estimates based on perforation models, among others. Meanwhile, the fluid characteristic values input to the flow prediction model may be taken from, or derived by, measurements of fluid properties taken at earth's surface (e.g., at a well of interest or in a laboratory) or in a region of interest downhole, estimates based on previous experience in related environments, or estimates based on fluid models for a given application. In some cases, fluid models may estimate the effects of temperature, pressure, and proppant additives to one or more known fluids.

In at least some embodiments, an example method includes obtaining distributed measurements of acoustic energy as a function of time and position downhole. The method also includes deriving acoustic activity values as a function of time and position from the one or more distributed measurements. The method also includes predicting fluid flow for a downhole perforation cluster as a function of time, where predicting fluid flow involves a flow prediction model that is a function of perforation cluster geometry, fluid characteristics, and at least one of the acoustic activity values. The method also includes storing or displaying the predicted fluid flow. Meanwhile, an example system includes an optical fiber and a light source to provide source light to the optical fiber, and a receiver coupled to the optical fiber. The receiver includes, for example, at least one optical fiber coupler that receives backscattered light and that produces one or more optical interferometry signals from the backscattered light. The receiver also includes photo- detectors that produce an electrical signal for each of the one or more optical interferometry signals. The system also includes at least one digitizer that digitizes each electrical signal to obtain one or more digitized electrical signals. The system also includes and at least one processing unit that processes the one or more digitized electrical signal to obtain acoustic activity values as a function of time and position, where the at least one processing unit predicts fluid flow for a downhole perforation cluster as a function of time based on a flow prediction model that is a function of perforation cluster geometry, fluid characteristics, and at least one of the acoustic activity values.

In different embodiments, the predicted fluid flow output from a flow prediction model may correspond to one perforation cluster or a plurality of perforation clusters. The predicted flow rate can be stored for later analysis and/or displayed via a monitor. As an example, the predicted fluid flow may be used for turbulent flow monitoring, plug leak detection, flow-regime determination, wellbore integrity monitoring, event detection, anomalous behavior such as increases in reservoir pressure, inter-stage fluid communication, and inter-cluster fluid communication, data visualization, and decision making. Without limitation to other embodiments, a flow prediction model may be used to plan downhole operations and/or to dynamically direct downhole operations. As an example, the flow prediction model may predict whether flow through each of a plurality of perforation clusters is occurring as well as provide information regarding the flow rate for each perforation cluster. Applying a flow prediction model during hydraulic fracturing operations enables the effects of hydraulic fracturing to be monitored. Further, the effect of adding proppants, treatments, and/or diverters can be monitored. As needed, adjustments to hydraulic fracturing operations can be made based on the predicted fluid flow obtained from a flow prediction model. Further, decisions regarding future well completion operations and/or production operations may be based on the predicted fluid flow obtained from a flow prediction model.

In some embodiments, the flow prediction model and related operations are implemented using a processing or computer system. For example, a computer system may store the flow prediction model and may store instructions to apply available perforation cluster geometry values, fluid characteristics values, and acoustic activity values to flow prediction model. Further, the computer system may visualize predicted fluid flows, flow prediction model options, and/or related data. Further, the computer system may display a plan or other response options based on one or more predicted fluid flows. For example, a plan may correspond to well treatment operations and/or proppant injection operations. Additionally or alternatively, a computer system may generate control signals to initiate or adjust a downhole operation based on one or more predicted fluid flows. Example downhole operations include, for example, well treatment operations (acidization), proppant injection operations including applying diverters (spheres) or other means of closing perforation clusters or openings from the wellbore to the reservoir, and/or fracturing operations. Various acoustic activity monitoring options, flow prediction model input options, flow prediction model analysis options, flow prediction model calibration options, and use options for predicted fluid flow results are described herein.

The disclosed methods and systems employing a flow prediction model based on acoustic activity are best understood in an application context. Turning now to the figures, FIGS. 1A-1 C show illustrative well environments 1 OA- IOC with distributed sensing components. In well environment 10A, a rig has been used to drill and complete well 12 in a typical manner, with a casing string 54 positioned in the borehole 16 that penetrate into the earth 18. The casing string 54 includes multiple tubular casing sections 61 (usually about 30 feet long) connected end-to-end by couplings 60. Typically the casing string includes many such sections 61 and couplings 60. Within the well 12, a cement slurry 68 has been injected into the annular space between the outer surface of the casing string 54 and the inner surface of the borehole 16 and allowed to set. A production tubing string 24 has been positioned in an inner bore of the casing string 54.

The well 12 is adapted to guide a desired fluid (e.g., oil or gas) from a bottom of the borehole 16 to a surface of the earth 18. Perforations 26 have been formed at a bottom of the borehole 16 to facilitate the flow of a fluid 28 from a surrounding formation into the borehole and thence to the surface. For example, the perforations 26 are shown to be near an opening 30 at the bottom of the production tubing string 24. Note that this well configuration is illustrative and not limiting on the scope of the disclosure. For example, fluid flow to or from a formation is possible at other points along the well 12 (not only at the bottom). Further, well 12 could include horizontal sections or curved sections in addition to the vertical section represented. Further, the well 12 may correspond to a production well or injection well. In alternative embodiments, optical distributed sensing components as described herein may be deployed in a monitoring well. Such a monitoring well may be cased, but does not necessarily need a production tubing string 24 or perforations 26.

The well environment 10A includes an interface 66 coupled to a fiber optic cable 44 for distributed sensing operations. The interface 66 is located on the surface of the earth 18 near the wellhead, i.e., a "surface interface". In the embodiment of FIG. 1 A, the fiber optic cable 44 extends along an outer surface of the casing string 54 and is held against the outer surface of the casing string 54 at spaced apart locations by multiple bands 58 that extend around the casing string 54. A protective covering 62 may be installed over the fiber optic cable 44 at each of the couplings 60 of the casing string 54 to prevent the fiber optic cable 44 from being pinched or sheared by the coupling' s contact with the borehole wall. The protective covering 62 may be held in place, for example, by two of the bands 58 installed on either side of coupling 60.

In at least some embodiments, the fiber optic cable 44 terminates at surface interface 66 with an optical port adapted for coupling the fiber(s) in cable 44 to a light source and a detector, which when combined into a single device is also known as an interrogator. The light source transmits light pulses along the fiber optic cable 44 which contains a fiber with scattering impurities. As each pulse of light propagates along the fiber, some of the pulse is scattered back along the fiber from every point on the fiber. Thus, the entire fiber acts as a distributed sensor. The optical port of the surface interface 66 communicates backscattered light to the detector, which responsively produces interferometry measurements from backscattered light attributes (e.g., phase or phase shift) corresponding to different points along the fiber optic cable 44. From the recovered phase information, the value of a downhole parameter sensed by the fiber at the location of the backscatter can be determined. As described herein, flow prediction can be performed at least in part on recovered phase information, which represents acoustic activity levels at different points along the fiber optic cable 44.

As shown, the well environment 10A also includes a computer 70 coupled to the surface interface 66 to control the light source and detector. The illustrated computer 70 includes a chassis 72 with at least one processing unit 73. Further the computer 70 includes an output device 74 (e.g., a monitor as shown in FIG. 1A, or a printer), an input device 76 (e.g., a keyboard), and non-transient information storage media 78 (e.g., magnetic or optical data storage disks). It should be appreciated that the computer 70 may be implemented in different forms including, for example, an embedded computer permanently installed as part of the surface interface 66, a portable computer that is plugged into or wirelessly linked to the surface interface 66 as desired to collect data, and a remote desktop computer coupled to the surface interface 66 via a wireless link and/or a wired communication network. In at least some embodiments, the computer 70 is adapted to receive digitized interferometry signals from the surface interface 66 and to responsively determine a distributed sensing signal. The distributed sensing signal may correspond to a phase or phase variance as a function of time that corresponds to a distributed sensing parameter such as temperature, acoustic energy, vibrational energy (including active or passive seismic), pressure, strain, deformation, chemical concentrations, nuclear radiation intensity, electromagnetic energy, and/or acceleration. In accordance with at least some embodiments, the computer 70 employs a flow prediction model that predicts flow as a function of time and position along the fiber optic cable 44 using acoustic activity values obtained from the distributed sensing signal.

In at least some embodiments, the non-transient information storage media 78 stores a software program for execution by computer 70. The instructions of the software program cause the computer 70 to recover phase information from digitized interferometry signals received from surface interface 66 and to perform flow prediction operations as described herein. Further, instructions of the software program may also cause the computer 70 to display information associated with distributed sensing parameter values and flow prediction results via the output device 74. Further, instructions of the software program additionally or alternatively cause the computer 70 to generate control signals to direct surface operations or downhole operations based on flow prediction results. The generation of control signals may be with or without involvement of an operator, and may be used to direct operations that adjust proppant options, fracturing options, diverter options, etc.

FIG. IB shows an alternative well environment 10B with distributed sensing components, where the fiber optic cable 44 is strapped to the outside of the production tubing 24 rather than the outside of casing 54. Rather than exiting the well 12 from the annular space outside the casing 54, the fiber optic cable 44 exits through an appropriate port in "Christmas tree" 80 (e.g., the assembly of pipes, valves, spools, and fittings connected to the top of the well 12 to direct and control the flow of fluids to and from the well 12) and couples to surface interface 66, which may include optical interrogation and receiver components to perform interferometry analysis of backscattered light along fiber optic cable 44 as described herein. Further, a computer (e.g., computer 70 in FIG. 1 A) may receive digitized interferometry signals from surface interface 66, recover phase information, and perform flow prediction as described herein. The phase information, distributed sensing parameter values, and/or flow prediction results may be stored or displayed. Further, logs and images derived from distributed sensing parameter values and/or flow prediction results may be stored or displayed. In the well environment 10B, the fiber optic cable 44 extends along the outer surface of the production tubing string 24 and is held against the outer surface of the production tubing string 24 at spaced apart locations by multiple bands 46 that extend around the production tubing string 24. In some embodiments, a portion of the fiber optic cable 44 (a "hanging tail") extends past the production tubing string 24. In the well environment 10B, two perforations 26 A and 26B have been created in borehole 16 to facilitate obtaining formation fluids from two different zones 50A and 50B defined by a packer 90 that seals an annulus around the production tubing string 24. More specifically, formation fluid enters zone 50A and production tubing string 24 via the perforation 26A, while additional formation fluid enters zone 50B and production tubing string 24 via the perforation 26B. As shown, the fiber optic cable 44 extends through the different zones 50A and 50B to enable distributed sensing operations along well 12 including zones 50A and 50B. Although only two zones 50A and 50B are shown for optical distributed sensing well environment 10B, it should be appreciated that additional zones may be defined along well 12.

FIG. 1C shows an alternative well environment IOC with distributed sensing components, where the fiber optic cable 44 is suspended inside production tubing 24. A weight 82 or other conveyance mechanism is employed to deploy and possibly anchor the fiber optic cable 44 within the production tubing 24 to minimize risks of tangling and movement of the fiber optic cable 44 from its desired location. The fiber optic cable 44 exits the well 12 via an appropriate port in Christmas tree 80 and attaches to the surface interface 66. Again, surface interface 66 and a computer (e.g., computer 70 in FIG. 1A) enables interferometry analysis of backscattered light along fiber optic cable 44, recovery of phase information, and flow prediction operations as described herein. Other alternative well environments with distributed sensing components employ composite tubing with one or more optical fibers embedded in the wall of the tubing. The composite tubing can be employed as the casing and/or the production string.

FIG. 2 depicts one illustrative arrangement 100 for optical phase interferometric sensing of backscattered light. There are various forms of backscattering. Rayleigh backscattering has the highest intensity and is centered at the wavelength of the source light. Rayleigh backscattering is due to microscopic inhomogeneities of refractive index in the waveguide material matrix. Brillouin and Raman backscattering are other types of detectable backscattering. Raman backscattering (which is due to thermal excited molecular vibration known as optical phonons) has an intensity which varies with temperature T, whereas Brillouin backscattering (which is due to thermal excited acoustic waves known as acoustic phonons) has a wavelength which varies with both temperature T and strain ε. As desired, a particular type of backscattered light may be sampled many times and averaged, which results in an effective sample rate of from tens of seconds to several minutes, depending on the desired signal-to-noise ratio, fiber length, and desired accuracy.

The arrangement 100 includes a laser 102 or other light source that generate an interrogation signal on a distributed sensing fiber 104. The laser 102 may provide a pulsed or non-pulsed interrogation signal. If a non-pulsed interrogation signal is output from the laser 102, a pulser 106 may be employed to pulse the interrogation signal. The interrogation signal may then interact with a first circulator 108 which couples the pulsed interrogation signal to the distributed sensing fiber 104. As each interrogation signal pulse travels through the distributed sensing fiber 104, a portion of the pulse energy is reflected due to reflective elements or imperfections along the distributed sensing fiber 104.

For illustrative purposes, the reflected signal is depicted in FIG. 2 as return signal

110. In some embodiments, the return signal 110 may be generated from discrete reflective elements placed along the distributed sensing fiber 104, such as fiber Bragg gratings (FBGs) arranged at positions 112 and 114. Alternatively, when performing DAS, the return signal 110 may be generated from reflections within the distributed sensing fiber 104 due to fiber imperfections (e.g., impurities). In FIG. 2, backscatter or reflection occurs at the positions 112 and 114 along the distributed sensing fiber 104. However, those of skill in the art will recognize that there may be numerous other reflection points along the distributed sensing fiber 104.

The first circulator 108 additionally couples the return signal 110 to a receiver 132. In at least some embodiments, the receiver 132 includes a second circulator 118 which conveys the return signal 110 to a 3x3 fiber optic coupler 120. The fiber optic coupler 120 distributes the return signal 110 across three paths labeled α, β, and x. The x path is terminated with an absorber and is not used further. The a and β paths are each terminated with a Faraday rotator mirror (FRM) 128 that reflects the signals back to the fiber optic coupler 120, albeit with a polarization reversal that compensates for any polarization shifts inadvertently introduced along the a and β paths. A delay coil 130 is included in the a path to introduce a delay in the reflected signal relative to the signal reflected along the β path. The fiber optic coupler 120 combines the signals from the a and β (and the unused x) paths to form three optical interferometry signals A, B, and C. The delay introduced between the a and β paths corresponds to the distance or "sensing window" LI between the reflection points 112, 1 14 on the distributed sensing fiber 104, enabling the phase change incurred over this length to be measured and monitored as an interferometric signal phase. Due to the nature of the fiber optic coupler 120, the optical interferometry signals A, B, and C have mutual phase separations of 120°. For example, as the a and β signals enter the 3x3 coupler 120, the interferometric signal A exiting the fiber optic coupler 120 may be α+βζ0 ^ο , B may be α+(βζ+120°), and C may be α+(βζ-120°).

The optical phase interferometric sensing arrangement 100 also implements single- ended detectors 134A-134C, which receive the optical interferometry signals A, B, and C and output signals X, Y, and Z. Examples of single-ended detectors 134A-134C include p- intrinsic-n field-effect-transistors (PINFETs), where optical receivers and high-gain transimpedance amplifiers are used. In at least some embodiments, the single-ended detectors 134A-134C correspond to square law detectors with a bandwidth much lower than the optical frequency (e.g., less than 1 GHz). In an exemplary operation, measurements such as dynamic strain, acoustics, and vibrations may be determined through analysis of the outputs of the single-ended detectors 134A- 134C to determine the associated optical phase shift. For more information regarding optical phase demodulation using an optical phase interferometric sensing arrangement such as arrangement 100, reference may be had to International Application Number PCT/US 14/19232, titled "Interferometric High Fidelity Optical Phase Demodulation" and filed February 28, 2014.

It should be appreciated that the flow prediction techniques disclosed herein may be used with other sensing arrangements. For example, U.S. Pat. No. 7,764,363, titled "Method And Apparatus For Acoustic Sensing Using Multiple Optical Pulses" and filed on Dec. 27, 2006 and U.S. Pat. Pub. No. 2012/00671 18, titled "Distributed Fiber Optic Sensor System With Improved Linearity" and filed Aug. 30, 2011 , describe other sensing arrangements for which the disclosed flow prediction techniques may be used. In general, the disclosed flow prediction techniques may be applied to any distributed sensing system or sensor-based system where phase modulation and phase demodulation is used to track acoustic activity along an optical fiber. Further, in some embodiments, flow prediction based on acoustic activity as described herein may be modified to account for other sensor- based or distributed sensing parameters such as strain, vibrations, etc.

FIG. 3 shows an illustrative signal processing arrangement 150 having a digitizer 152 that digitizes signals such as X, Y, and Z, and signal processor 154 that receives the digitized signals from the digitizer 152. In accordance with at least some embodiments, the signal processor 154 comprises a phase recovery module 156 (e.g., to perform quadrature demodulation of phase) and a flow prediction module 158. For example, the signal processor 154 may correspond to one or more central processing unit (CPUs) or application-specific integrated circuits (ASICs) that execute software or firmware instructions corresponding to phase recovery module 156 and flow prediction module 158. The output of the signal processor 154 corresponds to predicted fluid flow results that can be stored, visualized, correlated with other parameters, and/or used for other information extraction. Further, the predicted fluid flow results can be used to make decisions regarding downhole operations involving proppants, diverters, treatments, and/or fracturing.

In some embodiments, at least some of the components represented in arrangements 100 and 150 may be implemented with surface interface 66 (FIGS. 1 A-1 C) and/or computer 70 of FIG. 1 A. As an example, the laser 102, pulser 106, and first circulator 108 of FIG. 2 may be part of an interrogator included with surface interface 66. Further, the receiver 132, and a and β paths may correspond to receiver or interferometry components included with surface interface 66. Further, the digitizer 152 may be included with surface interface 66. Meanwhile, the signal processor 154 may be part of surface interface 66 or computer 70.

In at least some embodiments, the signal processor 154 executes instructions corresponding to phase recovery module 156 to obtain phase data correlated with acoustic activity along an optical fiber such as optical fiber 44 or 104. Acoustic activity values corresponding to the recovered phase data are provided as input to the flow prediction model 158. The flow prediction model 158 corresponds to one or more prediction models that correlate acoustic activity values with a fluid flow rate. There are various options for selecting flow prediction model 158, calibrating flow prediction model 158, and providing/adjusting inputs to flow prediction model 158. These various options can be implemented based on criteria such as the availability of data, the number of perforation clusters to be monitored, user preference, and/or other criteria. User input for the various options may be received, for example, via a graphical user interface.

With regard to selecting flow prediction model 158, a correlation between the volumetric flow rate at a perforation cluster and acoustic activity is assumed. In at least some embodiments, the correlation between the flow rate at a perforation cluster and acoustic activity is assumed to be a mathematical "Linear + Reciprocal" relationship involving fluid characteristic parameters, perforation cluster geometry parameters, and a bias value.

In different embodiments, the inputs to the flow prediction model 158 may include acoustic activity values derived from DAS system measurements and/or other downhole sensors (see e.g., the well environments 1 OA- IOC represented in FIGS. 1A-1C). An example acoustic activity value is the root mean square (RMS) of the broadband acoustic signal measured near a perforation cluster of interest. Another example acoustic activity value is the broadband acoustic power measured near a perforation cluster of interest. As desired, acoustic activity values used with the flow prediction model may be averaged and/or normalized as a function of time, position, and frequency. The fluid characteristic parameters input to the flow prediction model 158 may include, but are not limited to, effective fluid viscosity, estimated fluid density, temperature, pressure, proppant type, and fluid type. In at least some embodiments, the effective fluid viscosity corresponds to one or more values measured in a laboratory setting. For example, a Rheometer and/or other tool can be used to obtain fluid viscosity values. To the extent the laboratory setting can emulate the downhole environment, measured viscosity values can be used as the effective fluid viscosity without modification. As needed, measured viscosity values can be adjusted based on viscosity models that account for changes between the laboratory setting and a downhole environment. Accordingly, the effective fluid viscosity value used with the flow prediction model 158 may vary for different environments of interest and different fluid types. Parameters that may affect the effective fluid viscosity input to the flow prediction model 158 include, but are not limited to, base fluid properties, additives, temperature, pressure, and fluid speed. The perforation cluster geometry parameters input to the flow prediction model 158 may include, but are not limited to, perforation hole diameter (also known as "perforation diameter" or "perf diameter"), number of perforations, discharge coefficient, perforation hole area, fluid speed per perforation, volumetric flow rate per cluster, and perforation pressure loss per cluster. In some embodiments, the volumetric flow rate for a perforation cluster may be calculated by summing the volumetric flow rate of each perforation of the cluster. The volumetric flow rate for an individual perforation can be calculated, for example, as the fluid speed through the perforation multiplied by area of the perforation. As desired, the fluid speed and area related to each perforation of a cluster can be averaged or otherwise simplified to obtain a volumetric flow rate for a perforation cluster. In some embodiments, at least part of the flow prediction model 158 can be expressed as: Volumetric flow rate per perforation = bias value + linear term + reciprocal term

[Equation 1]

For Equation 1 , the bias value, the linear term, and/or the reciprocal term can be a function of any of the perforation geometry values, fluid characteristics values, and acoustic activity values described herein. One example of Equation 1 can be expressed as: Volumetric flow rate per perforation = bias value + function 1 (effective fluid viscosity, estimated fluid density, temperature, pressure, proppant type, fluid type, perforation hole diameter, discharge coefficient, perforation hole area, fluid speed, and perforation pressure loss) * RMSChannell + function2 (effective fluid viscosity, estimated fluid density, temperature, pressure, proppant type, fluid type, perforation hole diameter, discharge coefficient, perforation hole area, fluid speed, volumetric flow rate per cluster, and perforation pressure loss per cluster) / RMSChannell

[Equation 2]

For Equation 2, "functionl" multiplied by an acoustic activity value

("RMSChannell") corresponds to the linear term of Equation 1. Meanwhile, "function2" divided by the acoustic activity value corresponds to the reciprocal term of Equation 1. The "bias value" of Equation 2 corresponds to the bias value of Equation 1. In different embodiments, the bias value of Equations 1 and 2 may be a constant or a function of one or more perforation geometry values and/or fluid characteristics values. Further, function 1 and function 2 may be a constant or a function of one or more perforation geometry values and/or fluid characteristics values. In other words, there are various options available for flow prediction model 158. The particular flow prediction model 158 selected may vary depending on accuracy and complexity criteria. In at least some embodiments, at least part of the flow prediction model 158 can be expressed as:

Volumetric flow rate per perforation = a _t ^■ p + a ₂ ¹ μ + ₃ ^■ d— a ₄ ^■ d - a ₅ + a d ^■ RMS(y) + ( ₇ ^■ log _e (d - a ₈ ^■ log _e Qi - a ₉ )) - a ₁₀ /

RMS(y)

[Equation 3]

where <¾ to a ₁₀ are constants; p = estimated fluid density; μ = "marsh" viscosity (where "marsh" viscosity is defined as the viscosity of a fluid moving through a calibrated funnel; the procedure is a standardized tool used by engineers to measure the quality of drilling mud); d = perforation diameter; and y = broadband acoustic energy for a position near a perforation of interest. In at least some embodiments, a _x = 1.115, a ₂ = 0.08147, a ₄ = 140.1 , α ₅ = 42.96, α ₆ = 2.676, α ₇ = 0.05868, α ₈ = 0.1235, α ₉ = 0.3785, and α ₁₀ = 0.01842. Relating Equation 3 to Equations 1 and 2, the bias value in Equation 3 is expressed as: a ^■ p + a ₂ ^■ μ + α ₃ ^■ d— α ₄ ^■ d— α ₅ + (α ₇ ^■ log _e (d— α ₈ ^■ log _e ( i— α ₉ ))) .

Meanwhile, the linear term in Equation 3 is expressed as:

corresponds to functionl in Equation 2). Further, the reciprocal term in Equation 3 is expressed as: a ₁₀ /RMS(y) (i.e., -0.01842 corresponds to function2 in Equation 2). It should be appreciated that the value of constants (e.g., a _x to a ₁₀ ) and parameters (e.g., p, μ, d, and y) described for Equation 3 may vary for different scenarios. Further, some constants and/or parameters may be omitted in different variations of a volumetric flow rate per perforation model. Further, additional constants and/or parameters may be used in different variations of a volumetric flow rate per perforation model. Once a volumetric flow rate per perforation is determined, the volumetric flow rate for a perforation cluster can be determined by summing the volumetric flow rates for each perforation of a cluster. In some embodiments, a volumetric flow rate for a perforation cluster may be calculated based on the assumption that each perforation of a cluster has the same geometry, fluid speed, and/or other characteristics. In such case, a volumetric flow rate per perforation may simply be multiplied by the number of perforations to determine the volumetric flow rate for a perforation cluster. Alternatively, each perforation can be treated as unique. In such case, the volumetric flow rate for each perforation may be calculated separately and the results summed to obtain the volumetric flow rate for a respective perforation cluster. As desired, perforation geometry values for different perforations and/or volumetric flow rates for different perforations can be averaged or weighted to determine the volumetric flow rate for a perforation cluster.

In at least some embodiments, the flow prediction model 158 is calibrated. For example, the calibration may correspond to fitting or optimizing model parameters using a known flow rate (e.g., the surface flow input to a well) for a base fluid before additives (e.g., proppants) are added to the base fluid. More specifically, calibration of the flow prediction model may be performed by modifying the bias value, constants, or other terms of a volumetric flow rate per perforation model (e.g., modifying Equations 1, 2, or 3). Example calibrations involve adjusting one or more variables of a flow prediction model based on a comparison of predicted fluid flow for one perforation cluster and a surface flow rate, a comparison of a sum of predicted fluid flow for each of a plurality of perforation clusters with a surface flow rate, and/or a comparison of acoustic activity values obtained with and without a surface fluid flow. Further, model calibration operations may involve time- synchronizing acoustic activity values with a surface flow. Further, model calibration operations may additionally or alternatively include adjusting the flow prediction model 158 based on a comparison of acoustic activity values obtained with and without additives being added to a base fluid.

The "Linear + Reciprocal" models represented in Equations 1 -3 are examples only and are not intended to limit the invention to a particular model for calculating a volumetric flow rate per perforation and/or a volumetric flow rate per perforation cluster. As described herein, contemplated flow prediction models are a function of perforation geometry, fluid characteristics, and acoustic activity. In addition, flow prediction models may be adjusted as needed to account for different base fluids, additives, temperatures, pressures, and/or other parameters of interest.

In at least some embodiments, the inputs provided to the flow prediction model 158 changes how the predicted flow output from the flow prediction model 158 should be interpreted. For example, the acoustic activity values provided as inputs to the flow prediction model 158 may be averaged based on a predetermined spacing or timing criteria. In such case, the output of the flow prediction model 158 represents an averaged output. As an example, the acoustic activity values may correspond to acoustic activity averaged for 10 foot segments and 30 second intervals. Alternatively, the acoustic activity values may correspond to acoustic activity averaged for 30 foot segments and 10 second or 1 minute intervals. Further, the acoustic activity values input to the flow prediction model 158 may be normalized. For example, the normalization may be based on a noise-floor identified for at least one perforation cluster (e.g., when there is no fluid flow).

Further, the acoustic activity values input to the flow prediction model 158 may vary with regard to frequency band. In some embodiments, the acoustic activity values input to the flow prediction model 158 correspond to select frequency bands whose energy or intensity is being monitored. In at least some embodiments, deriving acoustic activity values to be input to the flow prediction model 158 may involve calculating phase energy for each of a limited number of frequency sub-bands of a DAS signal obtained from each digitized electrical signal (see FIGS. 2 and 3). For more information regarding energy spectrum analysis techniques that could be used to obtain acoustic activity values for select frequency bands, reference may be had to application no. PCT/US2014/047141 , entitled "Distributed Sensing Systems and Methods with Efficient Energy Spectrum Analysis", and filed July 18, 2014. In accordance with at least some embodiments, the acoustic activity values input to the flow prediction model 158 are assumed to represent acoustic activity without any artifacts from the sensor itself or from whatever modulation scheme is employed. The removal of modulation/demodulation artifacts is possible, for example, using appropriate filters.

In at least some embodiments, acoustic activity values are approximated by the root mean square (RMS) or standard deviation (STD) of a signal while the signal power is measured in time blocks chosen by the user. Thus, while acoustic activity data may be collected at 10,000 samples per second or higher, plotted acoustic activity values may be binned into large time blocks (e.g., time blocks of 10 seconds to several minutes are contemplated). Acoustic activity values plotted as a function of time and channel are sometimes referred to herein as a waterfall plot.

As an example, one channel of an acoustic activity plot may correspond to a one meter section of a borehole. For comparison, a perforation cluster is usually less than half a meter in length. As a result, DAS systems have poor spatial resolution such that acoustic activity at one point along an optical fiber is sensed at several channels. In practice, the spatial resolution will be determined by the DAS interrogation unit's compensation coil. An example compensation coil used for DAS monitoring of hydraulic fracturing provides a spatial resolution of around 10 meters. In such case, acoustic activity at one perforation cluster will be detected at 10 channels or along 10 meters of fiber. In different embodiments, the positioning of plotted acoustic activity values may be selected by a user or possibly by plotting software using predetermined criteria for interpreting acoustic activity data at multiple channels and/or the known position of perforation clusters based on well design specifications.

FIG. 4A is a graph representing the relationship between a modeled volumetric flow speed and acoustic power determined for a single wellbore stage with one perforation cluster using four different fluids: water, two types of gels, and a slurry as applied to a flow prediction model described herewith. Meanwhile, FIG. 4B is a graph representing the relationship between a modeled volumetric flow rate and acoustic power determined for a single wellbore stage with one perforation cluster using four different fluids: water, two types of gels, and a slurry. The relationships represented in FIGS. 4A and 4B can be estimated as a "Linear + Reciprocal" fit. In at least some embodiments, graphs or fitted curves such as the fitted curves shown in FIGS. 4A and 4B can be used to develop or adjust flow prediction model 158 of FIG. 3. FIG. 5 shows an example acoustic activity plot or "waterfall plot" representing acoustic activity as a function of time for several perforation clusters. Plots such as the one shown in FIG. 5 may be derived from acoustic activity data collected from a DAS system and/or other downhole sensors. In FIG. 5, the plotted data moves from left to right as a function of time. In FIG. 5, most of the acoustic activity occurs between 1500 seconds to 8500 seconds. Acoustic activity values as used in a flow prediction model (e.g., see Equations 1-3 and related discussion) may correspond to, or be derived from, acoustic activity values represented in a waterfall plot.

FIG. 6 is a block diagram of a flow prediction method 400. As shown, the method 400 includes providing source light to an optical fiber (e.g., fiber 44 or 104) at block 402. At block 404, backscattered light is received from the optical fiber. At block 406, acoustic activity values are derived as a function of time and position using the backscattered light received at block 404. For example, an optical phase interferometric sensing arrangement such as arrangement 100 (FIG. 2) and processing arrangement such as arrangement 150 may derive the acoustic activity values as described herein. In at least some embodiments, the acoustic activity values are averaged and/or normalized at block 408. At block 410, one or more flow prediction models are applied to predict flow using perforation geometry values, fluid characteristics, as well as the acoustic activity values obtained from blocks 406 or 408. At block 412, the predicted flow rate output from the flow prediction model of block 410 is stored or displayed. As an example, the predicted flow rate of block 412 may be used for turbulent flow monitoring, plug leak detection, flow-regime determination, wellbore integrity monitoring, event detection, data visualization, and decision making. In some embodiments, a computer system displays a plan based on the predicted fluid flow of block 412. The plan may correspond to well treatment operations or proppant injection operations. Additionally or alternatively, a computer system may generate control signals to initiate or adjust a downhole operation based on the predicted fluid flow of block 412. Example downhole operations include, for example, well treatment operations (acidization), proppant injection operations, and fracturing operations.

Embodiments disclosed herein include:

A: A method that comprises obtaining distributed measurements of acoustic energy as a function of time and position downhole, deriving acoustic activity values as a function of time and position from the one or more distributed measurements, predicting fluid flow for a downhole perforation cluster as a function of time, wherein said predicting involves a flow prediction model that is a function of perforation cluster geometry, fluid characteristics, and at least one of the acoustic activity values, and storing or displaying the predicted fluid flow.

B: A system that comprises an acoustic sensing arrangement that obtains distributed measurements of acoustic energy as a function of time and position downhole, and at least one processing unit that predicts fluid flow for a downhole perforation cluster as a function of time based on a flow prediction model that is a function of perforation cluster geometry, fluid characteristics, and at least one acoustic activity value derived from the distributed measurements.

Each of embodiments A and B may have one or more of the following additional elements in any combination: Element 1 : wherein the flow prediction model includes a bias value. Element 2: wherein the fluid characteristics comprise an effective fluid viscosity. Element 3: wherein the fluid characteristics comprise an estimated fluid density. Element 4: wherein the perforation cluster geometry comprises a perforation diameter. Element 5: wherein the perforation cluster geometry comprises a number of perforations. Element 6: wherein the flow prediction model comprises a first function or constant multiplied by an acoustic activity value, and a second function or constant divided by the acoustic activity value. Element 7: wherein obtaining the distributed measurements comprises providing source light to an optical fiber deployed in a downhole environment, receiving backscattered light from the optical fiber and producing one or more optical interferometry signals from the backscattered light, and converting each of the one or more optical interferometry signals to an electrical signal and digitizing each electrical signal to obtain one or more digitized electrical signals. Element 8: further comprising displaying a plan based on the predicted fluid flow, the plan related to at least one of well treatment operations and proppant injection operations. Element 9: further comprising initiating or adjusting a downhole operation based on the predicted fluid flow, the downhole operation related to at least one of well treatment operations or proppant injection operations. Element 10: wherein the flow prediction model includes a bias value. Element 11 : wherein the fluid characteristics comprise an effective fluid viscosity. Element 12: wherein the fluid characteristics comprise an estimated fluid density. Element 13: wherein the perforation cluster geometry comprises a perforation diameter. Element 14: wherein the perforation cluster geometry comprises a number of perforations. Element 15: wherein the flow prediction model comprises a first function or constant multiplied by an acoustic activity value, and a second function or constant divided by the acoustic activity value. Element 16: further comprising a monitor in communication with the at least one processing unit, wherein the at least one processing unit causes the monitor to display a plan based on the predicted fluid flow, the plan related to at least one of well treatment operations and proppant injection operations. Element 17: wherein the at least one processing unit provides a control signal to initiate or adjust a downhole operation based on the predicted fluid flow, the downhole operation related to at least one of well treatment operations and proppant injection operations. Element 18: wherein the acoustic sensing arrangement comprises an optical fiber, a light source to provide source light to the optical fiber, a receiver coupled to the optical fiber, wherein the receiver comprises at least one optical fiber coupler that receives backscattered light and that produces one or more optical interferometry signals from the backscattered light, and photo-detectors that produce an electrical signal for each of the one or more optical interferometry signals, and at least one digitizer that digitizes each electrical signal to obtain one or more digitized electrical signals.

Numerous variations and modifications will become apparent to those skilled in the art once the above disclosure is fully appreciated. For example, flow prediction models such as any of the models disclosed herein may be extended or varied for different fluid types and proppant types as well as wellbore completion types. It is intended that the following claims be interpreted to embrace all such variations and modifications.