BACKGROUND OF THE DISCLOSURE

Field of the Disclosure

[0001] The present disclosure generally relates to a method of optimizing a drilling operation using empirical data.

Description of the Related Art

[0002] US 8,082,104 discloses a method of identifying one or more rock properties and/or one or more abnormalities occurring within a subterranean formation. The method includes obtaining a plurality of drilling parameters, which include at least the rate of penetration, the weight on bit, and the bit revolutions per minute, and then normalizing these plurality of drilling parameters by calculating a depth of cut and an intrinsic drilling impedance. Typically, the intrinsic drilling impedance is specific to the type of bit used to drill the wellbore and includes using a plurality of drill bit constants. From this intrinsic drilling impedance, the porosity and/or the rock strength may be determined which is then compared to the actual values to identify the specific type of the one or more abnormalities occurring. Additionally, the intrinsic drilling impedance may be compared to other logging parameters to also identify the specific type of the one or more abnormalities occurring.

[0003] US 9,085,958 discloses a method of determining an optimal value for a control of a drilling operation. Drilling data from a drilling operation is received. The drilling data includes a plurality of values measured for each of a plurality of drilling control variables during the drilling operation. An objective function model is determined using the received drilling data. The objective function model maximizes a rate of penetration for the drilling operation. Measured drilling data is received that includes current drilling data values for a different drilling operation. An optimal value for a control of the different drilling operation is determined by executing the determined objective function model with the measured drilling data that includes the current drilling data values for the different drilling operation as an input. The determined optimal value for the control of the different drilling operation is output. [0004] US 2016/0076357 discloses a method for selecting a drill bit, the method includes obtaining a plurality of data of a first well within an earth formation, correlating the plurality of data of the first well to identify a set of reduced variables of the plurality of data, segmenting the reduced set of the plurality of data into a plurality of facies based on one of drillability and steerability, performing analysis of drilling performance of each of the plurality of facies, and selecting a drill bit based on the drilling performance.

[0005] US 2016/0313217 discloses a method for detecting a malfunction during a drilling operation carried out by making use of a drill bit, the method including the following: a) the comparison of a first magnitude (E) representative of the mechanical specific energy (MSE), with a first threshold value (Emax); b) when the first magnitude is greater than the first threshold value, the comparison of the ratio (E/S) between the first magnitude and a second magnitude (S) representative of the drilling force with a second threshold value ((E/S) max); c) the detection of a malfunction in the drilling operation when the ratio (E/S) between the first magnitude (E) and the second magnitude (S) is greater than the second threshold value ((E/S) max). The method provides the ability to ensure more precise detection of a malfunction during drilling operations.

[0006] WO 2016/154723 discloses a method for drilling a new oil or gas well in a selected geographical location including extracting drilling modes from historic drilling data obtained from a group of drilled wells in the selected geographical location using a pattern recognition model. Each drilling mode represents a distinct pattern that quantifies at least two drilling variables at a specified drilling depth. The method also comprises selecting a sequence of drilling modes at positions along a reference well as reference drilling modes that represent more efficient values for a selection of one or more of the at least two drilling variables compared to other extracted drilling modes; associating drilling parameter settings with the reference drilling modes; and drilling the new oil or gas well applying at least some of the drilling parameter settings. [0007] Hamzaban, M., & Memarian, H. (2008, January 1 ). Determination of Relationship between Drilling Parameters by Clustering Techniques. International Society for Rock Mechanics. This paper discloses that, during of drilling practice, force is transmitted to bit by mechanical devices. Bit is the major element for applying stress on rock. Under this stress, not only the rock is crushed, but also the bit is worn. In accord with high price of drilling bits, especially in deep drillings of oil and gas wells, wearing phenomenon of bits imposes high costs on drilling operations. Therefore, optimization of bit wear will have significant effect in reduction of drilling costs. In this study, relationship between drilling parameters is investigated. By means of these relations, conditions of high penetration rates can be determined and according to these conditions, drilling parameters are optimized. Results of this investigation denote the pairs of parameters which have direct or inverse relations.

SUMMARY OF THE DISCLOSURE

[0008] The present disclosure generally relates to a method of optimizing a drilling operation using empirical data. In one embodiment, a method for drilling a wellbore includes: generating an optimal cluster using historical drilling data; drilling an interval of the wellbore; and while drilling the wellbore interval: generating a working cluster using data collected while drilling the wellbore interval; identifying a plurality of data points proximate to a centroid of the working cluster; selecting one of the data points that converges toward a centroid of the optimal cluster; and adjusting one or more drilling control parameters using the convergent data point.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] So that the manner in which the above recited features of the present disclosure can be understood in detail, a more particular description of the disclosure, briefly summarized above, may be had by reference to embodiments, some of which are illustrated in the appended drawings. It is to be noted, however, that the appended drawings illustrate only typical embodiments of this disclosure and are therefore not to be considered limiting of its scope, for the disclosure may admit to other equally effective embodiments. [0010] Figures 1 and 2 illustrates drilling of a first wellbore while measuring data, according to one embodiment of the present disclosure.

[0011] Figure 3 illustrates processing of data collected during drilling of the first wellbore to generate an optimal cluster (OPC).

[0012] Figures 4A-4D illustrate formulas used to generate the OPC.

[0013] Figure 5 illustrates drilling of a second wellbore using the OPC to control drilling parameters.

[0014] Figure 6A illustrates an algorithm used to control the drilling parameters. Figure 6B illustrates non-linear convergence theory behind the algorithm.

[0015] Figures 7A-7F illustrate formulas used in the algorithm.

[0016] Figures 8A and 8B illustrate alternative formulas usable with the algorithm, according to other embodiments of the present disclosure.

[0017] Figure 9 illustrates a measurement while drilling (MWD) tool which may also be used to measure data, according to another embodiment of the present disclosure.

DETAILED DESCRIPTION

[0018] Figure 1 illustrates drilling of a first wellbore 1 a while measuring data, according to one embodiment of the present disclosure. The first wellbore 1 a may be drilled using a drilling system 2. The drilling system 2 may include a drilling rig 2r, a fluid handling system 2f, a blowout preventer (BOP) 2b, a drill string 3, and a controller, such as programmable logic controller (PLC) 2p. The drilling rig 2r may include a derrick 4d, top drive 5, draw works 6, and a floor 4f at its lower end having an opening through which the drill string 3 extends downwardly into the first wellbore 1 a via a wellhead 19h. The BOP 2b may be connected to the wellhead 19h.

[0019] The drill string 3 may include a bottomhole assembly (BHA) 3b and a pipe string 3p. The pipe string 3p may include joints of drill pipe connected together, such as by threaded couplings. The BHA 3b may be connected to the pipe string 3p, such as by threaded couplings, and include a drill bit 7 and one or more drill collars 8. The BHA members 7, 8 may be interconnected, such as by threaded couplings. The drill bit 7 may be rotated 9r by the top drive 5 via the pipe string 3p.

[0020] Alternatively, the BHA 3b may include a drilling motor for rotation of the drill bit 7 instead of or in addition to the top drive 5. Alternatively, the drill string may include coiled tubing instead of the pipe string 3p.

[0021] An upper end of the pipe string 3p may be connected to a quill of the top drive 5. The top drive 5 may include a motor for rotating 9r the drill string 3. The top drive motor may be electric or hydraulic. A frame of the top drive 5 may be coupled to a rail (not shown) of the derrick 4d for preventing rotation of the top drive frame during rotation 9r of the drill string 3 and allowing for vertical movement of the top drive with a traveling block 6t of the draw works 6. The frame of the top drive 5 may be suspended from the derrick 4d by the traveling block 6t. The traveling block 6t may be supported by wire rope 6r connected at its upper end to a crown block 6c. The wire rope 6r may be woven through sheaves of the blocks 6c,t and extend to a winch 6w for reeling thereof, thereby raising or lowering the traveling block 6t relative to the rig floor 4f.

[0022] The wellhead 19h may be mounted on a casing string 10 which has been deployed into the first wellbore 1 a and cemented 1 1 therein. A lower section of the first wellbore 1 a may be vertical (shown) or deviated (not shown), such as slanted or horizontal.

[0023] Alternatively, if the lower section of the first wellbore 1 a is deviated, the BHA may further include a steering tool, such as a bent sub or rotary steering tool, and a telemetry uplink for communication with the PLC 2p.

[0024] The fluid system 2f may include a mud pump 12, a drilling fluid reservoir, such as a pit 13 or tank, a solids separator, such as a shale shaker 14, a pressure sensor 15, one or more flow lines, such as a return line 16r, a supply line 16s, and a feed line 16f, a mud logging tool 17, and a stroke counter 18. A first end of the return line 16r may be connected to a flow cross 19x mounted on the wellhead 19h and a second end of the return line may be connected to an inlet of the shaker 14. A lower end of the supply line 16s may be connected to an outlet of the mud pump 12 and an upper end of the supply line may be connected to an inlet of the top drive 5. The pressure sensor 15 may be assembled as part of the supply line 16s. A first end of the feed line 16f may be connected to an outlet of the pit 13 and a second end of the feed line may be connected to an inlet of the mud pump 12.

[0025] The pressure sensor 15 may be in data communication with the PLC 2p and may be operable to monitor standpipe pressure (SPP). The stroke counter 18 may also be in data communication with the PLC 2p and may be operable to monitor a flow rate of the mud pump 12. The PLC 2p may also be in communication with a hook load cell (HKL) clamped to the wire rope 6r, and a position sensor of the winch 6w for monitoring depth of the BHA 3b. The PLC 2p may use a plurality of depth measurements and the time interval therebetween to calculate rate of penetration (ROP). The PLC 2p may further be in communication with a torque sensor and tachometer of the top drive 5. The torque sensor may measure torque exerted on the quill of the top drive 5 (TOQ) by the top drive 5. The tachometer may measure the angular speed (RPM) of the top drive quill. The PLC 2p may know parameters of the drill string 3 for calculating weight on bit (WOB) using the HKL and torque on bit (TOB) using the TOQ. The drill string parameters may further include drill bit type and drill bit size. The PLC 2p may record the various measurements and calculations in a memory unit (MEM) 20a for later use. The drill string parameters may also be recorded in the MEM 20a for later use.

[0026] The mud pump 12 may pump drilling fluid 21 from the pit 13, through the supply line 16s, and to the top drive 5. The drilling fluid 21 may include a base liquid. The base liquid may be refined or synthetic oil, water, brine, or a water/oil emulsion. The drilling fluid 21 may further include solids dissolved or suspended in the base liquid, such as organophilic clay, lignite, and/or asphalt, thereby forming a mud.

[0027] The drilling fluid 21 may flow from the supply line 16s and into a bore of the pipe string 3p via the top drive 5. The drilling fluid 21 may flow down the pipe string 3p, through a bore of the BHA 3b, and exit the drill bit 7, where the fluid may circulate cuttings away from the bit and return the cuttings up an annulus 22 formed between an inner surface of the casing 10 or the first wellbore 1 a and an outer surface of the drill string 3. The returns 23 (drilling fluid 20 plus cuttings) may flow up the annulus 22, to the wellhead 19h, and exit the wellhead through the flow cross 19x. The returns 23 may continue through the return line 16r. The returns 23 may then flow into the shale shaker 14 and be processed thereby to remove the cuttings, thereby completing a cycle. As the drilling fluid 21 and returns 23 circulate, the drill string 3 may be rotated 9r by the top drive 5 and lowered 9a by the traveling block 6t, thereby extending the first wellbore 1 a to a hydrocarbon-bearing formation or to a depth sufficient for geothermal power generation.

[0028] Alternatively, the first wellbore 1 a may be used for mining operations, such as a blasthole. Alternatively, the drill bit 7 may be percussively driven instead of or in addition to rotary driven.

[0029] As the drilling fluid 21 is being pumped into the first wellbore 1 a by the mud pump 12 and the returns 23 are being received from the return line 16r, the mud logging tool 17 may analyze the cuttings. The mud logging tool 17 may include an extractor for separating gas entrained in the cuttings, a gas analyzer, and a carrier system for delivering the gas sample to the analyzer. The gas analyzer may be a chromatograph or optical analyzer. The mud logging tool 17 may further include a source rock analyzer (SRA) for elemental analysis and/or mineral composition of the cuttings. The SRA may include a pyrolyzer, such as an oven or laser, an infrared cell, and a flame ionization detector. The measurements by the mud logging tool 17 may be recorded in a MEM 20b for later use. Parameters of the drilling fluid 21 , such as density (aka mud weight) and resistivity may be measured by the mud logging tool and/or input by the mud engineer and stored in the MEM 20b for later use.

[0030] Figure 3 illustrates processing of data collected during drilling of the first wellbore 1 a to generate an optimal cluster (OPC) 24. Figures 4A-4D illustrate formulas used to generate the OPC 24. Once drilling of the first wellbore 1 a has concluded, the measured data from the two memory units 20a,b may be supplied to the computer 25. Depth intervals may also be supplied to the computer 25 according to criteria, such as geologic formations. The computer 25 may process the retrieved data, calculate a depth of cut (DOC) according to the formula of Figure 4B. The computer 25 may also calculate a drilling impedance (DRIMP) according to the formula of Figure 4C, and add the calculated DOC and DRIMP to the measured data. In the DRIMP formula of Figure 4C, the exponential constant x for Bit Size may range between one-quarter and one and the exponential constant y for DOC may range between one and two, such as the sum of the exponential constants x and y being equal to two. The computer 25 may also calculate a mechanical specific energy (MSE) and add the calculated MSE to the measured data. The computer 25 may then parse the data into clusters for each depth interval according to a Maximum Likelihood Estimation (MLE) method.

[0031] Alternatively, the computer 25 may utilize other methods for parsing the data into clusters, such as support vector machine, artificial neural network, k-nearest neighbors, and classification and regression trees.

[0032] For each depth interval, the computer 25 may also select the optimal cluster according to one or more criteria, such as DOC, DRIMP, loading, vibration, SPP, flow rate, and MSE. The vibration and loading criteria may each include a plurality of sub criteria, such as longitudinal and torsional. The clusters may be ranked according to greater DOCs, lesser DRIMPs, lesser loadings, lesser vibrations, between specified ranges of SPP and flow rate, and lesser MSEs. The computer 25 or a technician may then select the optimal cluster 24 for each depth interval based on rankings of the criteria.

[0033] The computer 25 may then streamline the OPC 24 for each depth interval for real time processing according to the formula of Figure 4A. The data collected from the memory unit 20b may not be available in real time. Each data point of the streamlined OPC 24 may include one or more control components OPC ^c and one or more feature components OPC ^F . As shown, each data point of the OPC 24 includes a pair of control components, such as WOB and RPM, and a pair of feature components, such as DOC and DRIMP. Once streamlining of the OPC 24 has been completed, the computer 25 may calculate a centroid (CNT) of the OPC 24 for each depth interval using the formula of Figure 4D, where d is the total number of components of each data point, such as four, and nope is the total number of data points in the OPC.

[0034] Alternatively, the control component of the optimal cluster OPC 24 may include flow rate of the mud pump 12 and/or SPP instead or in addition to WOB and/or RPM. Alternatively, the feature components of the OPC 24 may include TOB and/or MSE instead of or in addition to DOC and DRIMP. Alternatively, the OPC 24 for one depth interval may include different control components and/or feature components than the OPC for a different interval. Alternatively, data collected during drilling of the upper portion of each depth interval of the second wellbore 1 b may be used to generate the OPC 24 instead of or in addition to data collected during drilling of the first wellbore 1 a. Alternatively, although the OPC 24 is illustrated in Figure 3 by plotting WOB and RPM, this is for illustration simplicity and the OPC 24 may be plotted using the feature components instead or may not need to be plotted at all.

[0035] Figure 5 illustrates drilling of a second wellbore 1 b using the OPC 24 to control drilling parameters. Figure 6A illustrates an algorithm 26a-g used to control the drilling parameters. Figure 6B illustrates non-linear convergence theory behind the algorithm 26a-g. Figures 7A-7F illustrate formulas used in the algorithm 26a-g.

[0036] Drilling of the second wellbore 1 b may be similar to drilling of the first wellbore 1 a except that the PLC 2p may be supplied with the OPC 24 of each depth interval and configured to perform the algorithm of Figure 6A in real time during the drilling operation such that the PLC 2p may adjust the drilling control parameters, such as RPM (depicted by arrow to top drive 5) and WOB (depicted by arrow to the winch 6w).

[0037] The algorithm 26a-g may begin at step 26a once the PLC 2p collects sufficient data while drilling the second wellbore 1 b to generate a working cluster (WKC) at step 26a. The WKC may also be generated using the maximum likelihood criterion. The WKC may include the same components as that of the streamlined OPC 24 shown in Figure 4A. The PLC 2p may know the control components, such as WOB and RPM, from the set points of the draw works 6 and the top drive 5. The PLC 2p may calculate the ROP using the position sensor of the winch 6w and time. The PLC 2p may calculate DOC and DRIMP using the formulas of Figures 4B and 4C. The PLC 2p may calculate the centroid of the WKC (CNTWKC) using the formula of Figure 4D.

[0038] At step 26b, the PLC 2p may identify a plurality of data points proximate to the centroid of the WKC by generating a hypersphere (HYSP) about the centroid of the WKC. The HYSP may be generated using the formula of Figure 7A which defines a maximum radius (radmax) thereof according to a maximum distance (DST) of the data points of the WKC from the centroid thereof. In the formula of Figure 7A, nwKc is the total number of data points in the WKC. The PLC 2p may calculate the distance of each data point of the WKC to the centroid thereof using the formula of Figure 7B. In the formula of Figure 7B, d is the total number of components of each data point of the WKC, such as four.

[0039] The PLC 2p may start by using a fraction, such as one-tenth of the maximum radius, and determine how many data points are included in the HYSP. If a sufficient number of points are included, such as greater than or equal to two (shown), the PLC 2p may proceed to the next step 26c. If the number of points is insufficient, the PLC 2p may enlarge the fraction, such as to one-fifth, of the maximum radius and thereof and repeat the analysis.

[0040] At step 26c, the PLC 2p may select one of the data points in the HYSP that converges toward the centroid of the OPC 24 using the formula of Figure 7C. In the formula of Figure 7C, the subscript k is the current iteration of the algorithm and ΠΗΥΞΡ is the total number of data points in the HYSP. The formula of Figure 7C identifies the convergent data point (CVG) by that which has the least distance to the centroid of the OPC 24.

[0041] At step 26d, an adjustment (ADJ) to the drilling control parameters, such as WOB and RPM, may be calculated by the PLC 2p using the formula of Figure 7E. The formula of Figure 7E is based on the non-linear convergence theory illustrated in Figure 6B and utilizes the CVG of the current iteration, the CVG of the previous iteration (k-1 ), the centroid of the WKC, the data point of the WKC of the current iteration, and the data point of the WKC of the previous iteration. During the first iteration of the algorithm 26a- g, the portion of the formula of Figure 7E utilizing data points of the previous iteration may be set to zero. In the formula of Figure 7E, the constant epsilon may be greater than zero and less than one. The adjustment may be calculated for each control component of the WKC.

[0042] At step 26e, the control parameters are adjusted according to the formula of Figure 7D. In the formula of Figure 7D, nc is the total number of control components of each WKC data point, such as two. Once adjusted, the PLC 2p may output the respective adjusted RPM control parameter to the top drive 5 and the adjusted WOB control parameter to the winch 6w.

[0043] At step 26f, the PLC 2p may generate a new data point for the WKC using the adjusted control parameters as the control components. The PLC 2p may generate the feature components for the new data point by obtaining a position measurement from the winch, calculating ROP, and then calculating the DOC and the DRIMP using the formulas of Figures 4B and 4C. The PLC 2p may then recalculate the centroid of the WKC using the new data point and the formula of Figure 4D.

[0044] At step 26g, the PLC 2p may calculate the distance between the centroid of the WKC and the centroid of the OPC using the formula of Figure 7B. The PLC 2p may then compare the centroid distance to a convergence threshold using the formula of Figure 7F. The convergence threshold may be the distance of the most distant data point of the WKC from the centroid of the OPC 24 multiplied by a constant alpha. The constant alpha may be greater than zero and less than one. If the centroid distance is greater than the convergence threshold, then the PLC 2p may return to step 26b for another iteration of the algorithm 26a-g to further converge the WKC to the OPC. If the centroid distance is less than or equal to the convergence threshold, then the PLC 2p may return to step 26f for monitoring convergence. The algorithm 26a-g may be repeated while drilling each depth interval of the second wellbore 1 b.

[0045] Referring to Figure 6B, the shortest path between the two centroids of the working cluster and the optimal cluster is along the linear path DST(CNTOPCCNTWKC). However, that linear path cannot be used for drilling optimization in order to find a set of control parameters that reduces the centroid-centroid distance between the working cluster and the optimal cluster. This is due to non-linearity of the drilling system. To reach the centroid of the OPC 24, the non-linear path may be divided into a sequence of small steps using the convergent data points as guide posts. Optimization is reached when the centroid of the WKC has been sufficiently pulled to be in proximity of the centroid of the OPC 24.

[0046] Figures 8A and 8B illustrate alternative formulas usable with the algorithm 26a-g, according to other embodiments of the present disclosure. The formula of Figure 8A may be used during step 26c to identify the CVG in addition to the formula of Figure 7C. This additional formula of Figure 8A may be used if the formula of Figure 7C fails to select only one data point. The formula of Figure 8A would then be used to select which of the HYSP data points selected by the formula of Figure 7C has control components that are closest to the centroid of the WKC and that data point would be selected as the CVG.

[0047] The formula of Figure 8B may be used to check the adjusted control parameters during step 26e after the adjusted parameters are calculated but before they are implemented. If the adjusted control parameters do not fit within a window bounded by minimum and maximum parameters, then it is likely that one of the clusters is corrupt. If the data check using the formula of Figure 8B fails, then the PLC 2p may abort the algorithm 26a-g and alert a technician. The clusters may then be sent to a technical center for repair of the data and/or diagnosis of a faulty sensor of the drilling system 2. The minimum and maximum boundary parameters may be preset and may be derived from operational limits of the top drive 5 and/or BHA 3b. [0048] Figure 9 illustrates a measurement while drilling (MWD) tool 27 which may also be used to measure data, according to another embodiment of the present disclosure. The MWD tool 27 may be assembled as part of the BHA 3b. The MWD tool 27 may include a cover, a body, a control circuit, an electric battery, a suite of sensors, and a data connector. The suite of sensors may include one or more pressure sensors, one or more accelerometers, one or more load cells, one or more temperature sensors, and/or one or more magnetometers.

[0049] The MWD tool 27 may record the measurements during drilling of the first wellbore 1 a and the data may be recovered from a memory unit of the control circuit after drilling of the first wellbore and used to construct the optimal cluster 24. Use of the MWD tool 27 may allow the criteria for selecting the optimal cluster 24 to include vibration data, such as longitudinal vibration, torsional vibration, and/or transverse vibration.

[0050] Alternatively, the BHA 3b may further include a telemetry uplink for transmitting the measurements to the PLC 2p during drilling of the first and second wellbores 1 a,b. Alternatively, other sources of downhole data may be used to construct the optimal cluster 24, such as data measured by a wireline deployed logging tool or a logging while drilling tool.

[0051] While the foregoing is directed to embodiments of the present disclosure, other and further embodiments of the disclosure may be devised without departing from the basic scope thereof, and the scope of the invention is determined by the claims that follow.