Well analysis applications for oil and natural gas wells with intermittent flows

Abstract

Well analysis applications for oil and natural gas wells with intermittent flows are disclosed. The application allows analysis of these intermittent flow wells using equations and mathematical models to identify suitable candidates for well life-extending valves. In addition, the liquid production can be estimated after the installation of the valve and determine the optimal operating conditions, such as opening pressure, closing pressure, and choke. This may guarantee the highest amount of liquid production and extend the productive, useful life of the candidate wells.

Description

FIELD

[0001] The present invention generally relates to wells, and more specifically, to well analysis applications for oil and natural gas wells with intermittent flows.BACKGROUND

[0002] Mature oil and natural gas fields typically experience a decline in productivity due to the depletion of reservoir pressure. Such mature oil and natural gas fields may have marginal wells that have low output or are totally inactive. Valves exist that can extend the life of these mature oil and natural gas fields. See, for example, U.S. Pat. Nos. 6,827,146 and 11,473,402. However, it is not known initially whether a given well is a good candidate for these valves. Accordingly, an improved and / or alternative approach may be beneficial.SUMMARY

[0003] Certain embodiments of the present invention may provide solutions to the problems and needs in the art that have not yet been fully identified, appreciated, or solved by current well analysis technologies. For example, some embodiments of the present invention pertain to well analysis applications for oil and natural gas wells with intermittent flows. Equations and mathematical models are employed to analyze wells that operate intermittently by natural flow. Using these equations and mathematical models, such embodiments can identify candidate wells for the application of Bennu-type valves. Additionally, such embodiments can estimate liquid production after valve installation and determine the optimal operational conditions (e.g., opening pressure, closing pressure, and choke) to attempt to ensure the highest possible liquid production and extend the productive life of the candidate wells.

[0004] In an embodiment, one or more non-transitory computer-readable media store one or more computer programs. The one or more computer programs are configured to cause at least one processor to display a graphical user interface (GUI) for analyzing a candidate well with an intermittent flow and determining whether the candidate well is suitable for installation of a valve for intermittent flow wells. The one or more computer programs are also configured to cause the at least one processor to determine well coefficients and estimate well characteristics and determine whether liquid carryover exists from a bottom of the well to a surface of the well by comparing a lifting gas rate to a critical lifting rate. Responsive to a determination that the liquid carryover exists, the one or more computer programs are further configured to cause the at least one processor to estimate a liquid rate, determine a predominant flow pattern at a specified production condition, behavior of head and flowing bottom pressures, and inflow capacity of a formation of the well, based on the obtained results from the determination of the previous step, determine valve adjustment pressures at considered opening and closing conditions, and display a report to the user with solutions.

[0005] In another embodiment, a computer-implemented method includes displaying, by a computing system, a candidate selection interface for analyzing a candidate well with an intermittent flow and determining whether the candidate well is suitable for installation of a valve for intermittent flow wells. The candidate selection interface includes fields for at least one of gas liquid rate, wellhead pressure, American Petroleum Institute (API) gravity, depth, choke availability and wellhead connection points, well completion, liquid density, gas density, gas interfacial tension, liquid interfacial tension, gas wellhead pressure, tubing area, surface temperature, and compressibility factor. The computer-implemented method also includes calculating, by the computing system, a lifting gas rate and a critical lifting rate for the candidate well based on the fields of the candidate selection interface. The computer-implemented method further includes, responsive to the well being a suitable candidate due to the lifting gas rate exceeding the critical lifting rate for the candidate well, displaying, by the computing system, a valve design module including at least one of a basic well data module, a dynamic forecasting module, a valve calibration module, and a reporting module. Additionally, the computer-implemented method includes facilitating design of the valve via the valve design module, by the computing system.

[0006] In yet another embodiment, a computing system includes memory storing computer program instructions and at least one processor configured to execute the computer program instructions. The computer program instructions are configured to cause the at least one processor to display a candidate selection interface for analyzing a candidate well with an intermittent flow and determining whether the candidate well is suitable for installation of a valve for intermittent flow wells. The candidate selection interface allowing a user to effectively visualize and understand characteristics of the candidate well. The computer program instructions are also configured to cause the at least one processor to determine well coefficients and estimate well characteristics and verify whether liquid carryover exists from a bottom of the well to a surface of the well by comparing a lifting gas rate to a critical lifting rate. The computer program instructions are further configured to cause the at least one processor to, responsive to the verification that the liquid carryover exists, display a valve design module. The valve design module includes at least one of a candidate selection interface, a fluid properties interface, a well performance interface, an inflow sensitivity interface, operational conditions interface, a mechanical configuration interface, an accumulation interface, a choke diameter interface, a well production interface, a select design conditions interface, a calibration data interface, and a reporting interface for the candidate intermittent flow well.BRIEF DESCRIPTION OF THE DRAWINGS

[0007] In order that the advantages of certain embodiments of the invention will be readily understood, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments that are illustrated in the appended drawings. While it should be understood that these drawings depict only typical embodiments of the invention and are not therefore to be considered to be limiting of its scope, the invention will be described and explained with additional specificity and detail through the use of the accompanying drawings, in which:

[0008] FIG. 1 illustrates a new project creation interface, according to an embodiment of the present invention.

[0009] FIG. 2 illustrates a representation of fluid pressures and lengths in a well, according to an embodiment of the present invention.

[0010] FIG. 3 is a graph illustrating the lifting gas rate qg<sub2>lev < / sub2>as a function of time from the results shown in Table 2, according to an embodiment of the present invention.

[0011] FIG. 4 is a graph illustrating qg<sub2>lev < / sub2>as a function of the gas pressure in the wellhead Pwh<sub2>g < / sub2>from the results shown in Table 2, according to an embodiment of the present invention.

[0012] FIG. 5 is a graph illustrating the qg<sub2>lev < / sub2>that should be maintained to equal 130 MSCFD for a head gas pressure of 250 psi, according to an embodiment of the present invention.

[0013] FIG. 6 is a graph illustrating a comparison of the minimum lifting gas rate qg<sub2>lev < / sub2>and the available gas rate, according to an embodiment of the present invention.

[0014] FIG. 7 illustrates a candidate selection interface, according to an embodiment of the present invention.

[0015] FIG. 8A illustrates a fluid properties interface of a basic well data module, according to an embodiment of the present invention.

[0016] FIG. 8B illustrates a well performance interface of the basic well data module, according to an embodiment of the present invention.

[0017] FIG. 8C illustrates an inflow sensitivity interface, according to an embodiment of the present invention.

[0018] FIG. 8D illustrates an operational conditions interface of the basic well data module, according to an embodiment of the present invention.

[0019] FIG. 8E illustrates a mechanical configuration interface of the basic well data module, according to an embodiment of the present invention.

[0020] FIG. 9 illustrates an accumulation (build up) interface of the basic well data module, according to an embodiment of the present invention.

[0021] FIG. 10A illustrates a choke diameter interface of a dynamic analysis module, according to an embodiment of the present invention.

[0022] FIG. 10B illustrates a well production interface of the dynamic analysis module, according to an embodiment of the present invention.

[0023] FIG. 11A illustrates a select design conditions interface of a valve calibration module, according to an embodiment of the present invention.

[0024] FIG. 11B illustrates a calibration data interface of the valve calibration module, according to an embodiment of the present invention.

[0025] FIG. 12 illustrates a reporting interface, according to an embodiment of the present invention.

[0026] FIG. 13 illustrates a well in three pressure states, according to an embodiment of the present invention.

[0027] FIG. 14 illustrates a well completion state, according to an embodiment of the present invention.

[0028] FIG. 15 illustrates the pressure differential in a well, according to an embodiment of the present invention.

[0029] FIG. 16 illustrates time periods of each lifting cycle, according to an embodiment of the present invention.

[0030] FIGS. 17A and 17B are flowcharts illustrating a process for solving a system of equations for analyzing a well, according to an embodiment of the present invention.

[0031] FIG. 18 is an architectural diagram illustrating a computing system configured to perform well analysis, according to an embodiment of the present invention.

[0032] FIG. 19A illustrates an example of a neural network that has been trained to supplement an oil well analysis application, according to an embodiment of the present invention.

[0033] FIG. 19B illustrates an example of a neuron, according to an embodiment of the present invention.

[0034] FIG. 20 is a flowchart illustrating a process for training AI / ML model(s), according to an embodiment of the present invention.

[0035] Unless otherwise indicated, similar reference characters denote corresponding features consistently throughout the attached drawings.DETAILED DESCRIPTION OF THE EMBODIMENTS

[0036] Some embodiments pertain to well analysis applications for oil and natural gas wells with intermittent flows. The application of some embodiments allows analysis of these intermittent flow wells using equations and mathematical models to identify suitable candidates for well life-extending valves. In some embodiments, the valve may be that disclosed in U.S. Pat. No. 11,473,402. In addition, some embodiments can estimate the liquid production after the installation of the valve and determine the optimal operating conditions, such as opening pressure, closing pressure, and choke. This may guarantee the highest amount of liquid production and extend the productive, useful life of the candidate wells.

[0037] The equations and mathematical models of some embodiments simulate the inflow behavior of the formation as a function of time, the determination of the volume of gas available to displace a column of liquid from the bottom to the surface as a function of the range of pressures (opening and closing the valve), and the transfer of energy between the gas and the liquid column. In certain embodiments, a Javascript front end and Python back end are used. However, any desired programming languages may be used without deviating from the scope of the invention. In some embodiments, the application includes three main modules: project management, candidate selection, and valve design. The valve design module is further subdivided into basic well data, build up analysis, dynamic forecast, valve calibration, and reporting in some embodiments.

[0038] There are two phases in some embodiments: (1) project management and candidate selection; and (2) valve design. A user can create a well analysis project and identify, through a study based on qualitative and quantitative models, wells that are candidates for the application of the valves in the first phase. In some embodiments, the project information includes a project name, well name, field name, reservoir name, company, designer, and engineer. See new project creation interface 100 of FIG. 1, for example.Candidate Selection Module

[0039] Candidate well selection is the process of identifying and selecting wells for the application of the valves. Not all wells are suitable for these valves. Certain characteristics of the well have been classified into determinants, limiting, and complementary. From a statistical analysis perspective, each selected characteristic has a particular value in selecting the well as a candidate, ensuring success, reducing costs, and increasing production potential.

[0040] The gas-liquid ratio (GLR) and the pressure at the wellhead (Pwh) have been selected as determinants. Determinants are the most important criteria in the decision-making process in some embodiments and have the most weight in the final decision. If the well cannot meet the imposed conditions, it may automatically be deemed not to be a suitable candidate. For example, the Pwh should be greater than 300 pounds per square inch (psi) in order to be accepted. The American Petroleum Institute (API) gravity, depth, and availability of a choke are considered limiting. Limiting variables are the criteria that should be met to consider a particular option. It is necessary in some embodiments to have an API gravity greater than 20 and a depth greater than 5,000 feet. Other variables, such as well completion, connection points in the line pipe, and wellhead are considered to be complementary, meaning that they are criteria that add value to the decision, but are not essential thereto. The final selection is based on qualitative and quantitative criteria. The results are presented analytically and graphically in some embodiments.

[0041] The qualitative model in some embodiments is based on the percentage of weight given to the determining, limiting, and complementary variables, while the quantitative model uses the following studies to determine the lifting speed and the minimum speed for the discharge of liquid, which determine whether the well will be a suitable candidate.Determination of Lifting Gas Rate (qg<sub2>lift< / sub2>)

[0042] As shown in well 200 of FIG. 2, the wellhead pressure Pwh<sub2>g < / sub2>influences the bottom hole pressure Pwƒ for a given instant in time t, and thus, influences the length of the plug to be lifted Xƒ. Da is reservoir depth in feet. In this sense, its effect on each of the variables involved in the phenomenon should be considered. Under an initial condition in which there would be a balance of pressures, the Pwƒ at the at the bottom of the well is given as:Pwf=Pwh+Gg(Lt-Xf)+Gf⁢Xf(1)

[0043] Where Gg is the gas gradient in psi / feet, Gƒ is the fluid gradient in psi / feet, and Lt defines the available pipe length. Assuming the pipe tip is right at the top of the perforations but also under equilibrium, Eq. (1) can be rewritten as:Pr=Pwh+Gg(Lt-Xf)+Gf⁢Xf=Pt+Gf⁢Xf(2)

[0044] where Pr is the reservoir pressure and Pt is the pressure at the gas-liquid interface, which is a product of the gas pressure in the head and the weight of the gas column. An approximation of Pt can be estimated as:Pt=Lt-Xf+0.5 (Pwhg1⁢0⁢0)⁢ (Lt-Xf1⁢0⁢0⁢0⁢0)(3)

[0045] It should be noted that the critical variable to be defined would be given by the length of the plug to be lifted Xƒ. Consider the example well data in Table 1 below, where Pr is 1,500 psi, the API gravity is 25, Da is 6,500 feet (ft.) Lt is 6,450 ft., γg (gas specific grVITY)) is 0.7, φt (tubing diameter) is 2.441 inches (in.), Ts (surface temperature) is 85° F., and Tr (reservoir temperature) is 171° F.TABLE 1EXAMPLE PRODUCER WELL DATAXfmax (ft.)Xf (ft.)Lt − Xf (ft.)Pt (psi)Pwh (psi)383136402810757434483002150148325731932252213065338530029528743576375368268237684504422490396052551522994151600588210743436756611916453475073317244726825806153349179008781341510997595111495301105010239585492112510957665684120011675755875127512393836067135013101926258142513820645015001453

[0046] If the data in the example shown in Table 1 above is assumed, the following results can be deduced. Under equilibrium conditions and for an infinite time (t>0), the maximum liquid plug length Xƒ<sub2>max < / sub2>could be estimated from the data under consideration using the following equation:Xfmax=PrGf=3831⁢ ft.(4)

[0047] In other words, Xƒ varies from 0 to 3,831 ft. By considering different values of Xƒ, as shown in Table 1, the values of Pt and Pwh<sub2>g < / sub2>can be estimated by an iterative process of trial and error. These results can be used to estimate the number of moles n that could accumulate inside the pipe based on the following equations:η=P¯⁢At(Lt-Xf)ZR⁡(T¯+4⁢6⁢0)(5)P¯=Pwh+Pt2(6)T¯=Tf+Twh2(7)

[0048] where Tƒ and Twh represent reservoir and surface temperatures, respectively, Lt is the tubing area in in2, Z is the compressibility factor, and R is the gas universal constant, which is 0.082 L*atm / molK. From the estimated lbs-mol of gas n that are accumulated over time, the volume of gas Vg can also be calculated, as shown in Table 2 below based on Eqs. (5) and (7).TABLE 2ACCUMULATED GAS VOLUME AS A FUNCTION OF TIMEPavgTavgZVtηVgt(psi)(° F.)(dim.)(ft.)(lbs-mol)(SCF)(min.)72.5128.00.9991.331.064034.01144.80.9897.552.298718.64216.70.96103.783.70140313.91288.30.95110.005.28200220.46359.60.94116.237.04267028.76430.60.93122.458.98340840.97501.40.92128.6811.11421765.44571.80.91134.9113.445099115.47

[0049] Vt is the total volume in ft3 and SCF is standard cubic feet. FIG. 3 is a graph 300 illustrating the lifting gas rate qg<sub2>lev < / sub2>as a function of time from the results shown in Table 2, according to an embodiment of the present invention. qg<sub2>lev < / sub2>can be estimated as a volumetric ratio as follows:qglev=Δ⁢VgΔ⁢t(8)

[0050] qg<sub2>lev < / sub2>can be related to Pwh<sub2>g < / sub2>so long as Pwh<sub2>g < / sub2>is estimated at the same time t. See graph 400 of FIG. 4. The importance of FIG. 4 lies in the fact that qg<sub2>lev < / sub2>is defined for any value of the head pressure. This makes it possible, among other things, to define the optimal throttling diameter that guarantees a constant lift rate under the conditions of line pressure and keeping the valve open, as well as closing the low valve, among others. If a head gas pressure of 250 psi is considered, the lifting gas rate that should be maintained would be equal to 130 million standard cubic feet per day (MSCFD or MMSCFD), as shown in graph 500 of FIG. 5.Minimum Lifting Gas Rates (qg<sub2>min< / sub2>) for Water and Crude Oil in Gas Wells

[0051] The minimum gas speed Vg<sub2>min < / sub2>required to avoid downhole liquid loading can be estimated by using the following equation:Vgmin=2[σ⁢g⁡(ρl-ρg)ρl2]0.2⁢5(9)

[0052] where σ is the interfacial tension, ρr is the liquid phase density, and ρg is the gas phase density. Turner et al. performed an analysis of the minimum gas speed needed to produce liquid droplets or for the upward movement of a thin layer of liquid through the internal area of a pipe. See R. G. Turner, M. G. Hubbard, and A. E. Dukler, “Analysis and Prediction of Minimum Flow Rates for the Continuous Removal of Liquid from Gas Wells,” J. Pet. Tech., 21(11), p.p. 1475-82 (November 1969). Under average conditions, the physical properties for the water and condensate phases could be similar to those proposed by Turner et al. and shown below in Table 3.TABLE 3AVERAGE CONDITIONS FOR WATER AND CONDENSATE PHASESWater:Condensate:σ (dynes / cm)6020ρl (lb mass / cubic ft)6745T (° F.)120120γg0.6

[0053] At this point, Eq. (8) can be rewritten to estimate the minimum gas speed to avoid water and condensate loading as:Vgwater=5.3[ρl-0.0⁢0⁢279⁢P]0.25[0.0⁢0⁢279⁢P]0.5(10)Vgconde⁢nsate=4.0⁢3[ρl-0.0⁢0⁢279⁢P]0.2⁢5[0.0⁢0⁢279⁢P]0.5(11)

[0054] where P is the pressure in psi. The required minimum volumetric gas flow rate can be estimated using the following equation:qgmin=3.06 Vg⁢At⁢PTZ(12)

[0055] Both flow rates were estimated and plotted, as shown in graph 600 of FIG. 6. Based on the obtained results, the lifting gas rate is well below the minimum required to prevent the accumulation of water and condensate.

[0056] FIG. 7 illustrates a candidate selection interface 700, according to an embodiment of the present invention. Candidate selection interface 700 provides for entry of the following qualitative data: gas liquid rate, wellhead pressure, API gravity, depth, choke availability and wellhead connection points, and well completion. Candidate selection interface 700 also provides for entry of the following quantitative data: liquid density, gas density, gas interfacial tension, liquid interfacial tension, gas wellhead pressure, tubing area, surface temperature, and compressibility factor.

[0057] After this data is entered, the user can click the Evaluate button. This causes the application to calculate the available lift gas velocity and the minimum gas velocity for unloading in accordance with the equations above. If the available lift gas velocity is greater than the minimum gas velocity for unloading, the well is considered to be a candidate for valve installation. If not, the well is not a suitable candidate. If the well is a suitable candidate, the user can advance to the valve design module, which includes basic well data, build up analysis, dynamic forecasting, valve calibration, and reporting.

[0058] The basic well data module allows the user to record pertinent information for the well that is being analyzed. In some embodiments, this module includes four submodules. FIG. 8A illustrates a fluid properties interface 800 of a basic well data module, according to an embodiment of the present invention. The properties of the fluid involve filling in the following variables: API gravity, water and sediment percentage, gas specific gravity, reservoir temperature, and bubble point pressure (Pb). In the case of Pb being unknown, its value can be estimated using available correlations if oil-gas relation (Rp) is provided and exceeds Pb.

[0059] FIG. 8B illustrates a well performance interface 810 of the basic well data module, according to an embodiment of the present invention. A relatively simple correlation (Vogel) may be used to calculate the IPR curve of the yield-flow relationship. The static well pressure (Pws) is a known value and represents the energy of the well. On the other hand, users can select the productivity index (PI) or a flow rate (q) that corresponds to the flow pressure (Pwf) of the well from the production history. One of these two options allows estimating the IPR curve. The results are used to quantify the flow capacity of the well and compare this with the results obtained from the simulation using a valve. The backpressure factor and slug velocity should be considered. 5% and 1000 feet / min, respectively, are selected by default in this example. Users can modify these values if desired. Generally, a reserve value between 5 and 7% is considered. The mass velocity typically ranges between 900 and 1100 feet / min. It should be noted that 5 and 1,000 are default values. Clicking predict inflow performance button 812 leads to inflow sensitivity interface 820 of FIG. 8C, which allows for an estimation of different IPR curves to estimate a range of liquid production associated with the efficiency of the opening and closing operation of the valve.

[0060] FIG. 8D illustrates an operational conditions interface 830 of the basic well data module, according to an embodiment of the present invention. The operability of a well with the valve system of some embodiments depends on the flow line pressure (Pfl). This value is important in the calibration of the valve, and it corresponds to the value to be placed in the box shown in FIG. 8D. The operational conditions interface should show the pressure that conditions the closing pressure of the valve.

[0061] FIG. 8E illustrates a mechanical configuration interface 840 of the basic well data module, according to an embodiment of the present invention. In this embodiment, two pipe sections can be selected, which include length and internal diameter. However, any number of pipe segments may be accommodated without deviating from the scope of the invention. This information is important in determining the gas velocity to compare it with the critical velocities for condensate and water discharge. The depth of the medium is also required (from). These length values are in feet in this embodiment and are related to the true vertical depth (TVD).

[0062] FIG. 9 illustrates an accumulation (build up) interface 900 of the basic well data module, according to an embodiment of the present invention. The accumulation test allows for the estimation of the availability of formation gas, which will be responsible for transporting liquids from the bottom of the well to the surface. Pressure and time are represented in psi and minutes, respectively, in this embodiment. This test is used to estimate the opening and closing pressure.

[0063] FIG. 10A illustrates a choke diameter interface 1000 of a dynamic analysis module, according to an embodiment of the present invention. Interface 1000 corresponds to the choke diameter and includes the valve closing pressure, which should be at least twice the line pressure to ensure critical flow. This value will allow estimating the minimum size of the choke required for the desired operation. With these values a sensitivity analysis can be performed to estimate liquid production.

[0064] FIG. 10B illustrates a well production interface 1010 of the dynamic analysis module, according to an embodiment of the present invention. In interface 1010, users have the option to select different choke diameters. Additionally, this submodule also allows prediction of the valve opening pressure Pvo based on the optimal flow rate. In this case, the application allows selecting a pressure range within which the sensitivity analysis will be conducted, where the software determines the optimal opening pressure of the well. Finally, the production of the well under study can be estimated.

[0065] FIG. 11A illustrates a select design conditions interface 1110 of a valve calibration module, according to an embodiment of the present invention. Interface 1100 offers two ways to calibrate the valve. One is to use “default values”. Under this condition, the laboratory temperature considered is 60° F., and the operating conditions for the high temperature and low-pressure valve may be like those considered in the original design. Note that for the LPV, there are two values for the valve closing pressure Pvc: estimated and projected. Users can compare both values and decide whether to maintain or change the original design.

[0066] The other option available is to use a “custom value”. In this case, users can modify any value, such as temperature, pressures, etc., at any time. The new selected values will be used for the application to calculate the minimum conditions required to calibrate the valves.

[0067] FIG. 11B illustrates a calibration data interface 1110 of the valve calibration module, according to an embodiment of the present invention. The calibration data is represented as the opening of the pressure test frame PTRO required by the high-pressure valve, the calibrated valve closing pressure for the low-pressure valve, and the initial LPV representing the minimum pressure required to keep the valve closed. In FIGS. 11A and 11B, output data is shown after a simulation where the valve calibration values are observed.

[0068] FIG. 12 illustrates a reporting interface 1200, according to an embodiment of the present invention. Interface 1200 displays the results obtained after the simulation of a candidate well. The study variables can be observed, from the system's basic data of the reservoir / well, to the estimation of the production obtained with the optimal operational conditions of the valve tool.Production Estimation, Cycle Times, Number of Cycles, and Operational Range of the Valve

[0069] To carry out the production estimation, cycle times, number of cycles, and optimal operational range, various analyses were performed, and studies were conducted.Preliminary Analysis

[0070] The contribution of fluids from any formation is conditioned by the energy available in the reservoir. This energy, represented in terms of pressure, is responsible for the production rate, whose value will depend on the pressure that is promoted at the bottom of the well. This is usually called flowing bottom hole pressure Pwƒ. This pressure will, in turn, be able to lift a column of fluids within the production tubing, which would primarily depend on the density of the produced fluid and time since it is a low potential formation. This is shown in FIG. 13, for example.

[0071] In FIG. 13, a well 1300 is shown in three states. In state (a), Pwh=0 psi. The length of the liquid column would not be conditioned by any backpressure at the surface. However, any value of pressure generated at the surface (Pwh>0) as a result of the accumulation of a gas mass in the empty part of the tubing would condition the value of Xƒ. The greater the wellhead pressure Pwh, the greater its effect on the formation of the liquid column Xƒ (i.e., the shorter its length). See state (b), where Pwh>0 psi.

[0072] Based on the above, a mathematical model was developed that allows definition of the length of the liquid column Xƒ not only as a function of time, but also considering the effect of the weight of the gas column and the wellhead pressure Pwh. At the reservoir level, the mathematical model should take into account important variables, such as reservoir pressure Pr, the productivity index IP, the depth of the sand of the reservoir Da, the properties of the fluids, the losses due to slippage of the liquid being lifted, etc. At the tubing level, mathematical solutions should be used that allow estimation of the pressure exerted at the gas-liquid interface, which is called Pt. See FIG. 13. This value of Pt depends, among other things, on the length of the liquid column Xƒ, as well as the diameter and length of the tubing installed in the well. At this point, one should take into consideration the amount of mass that accumulates in the tubing over time, the value and behavior of which are obtained from a build-up test that, generally, should be measured in the field. This test would also allow determination of the most suitable operational conditions to keep the well producing. See state (c), where Pwh=operating pressure.Static Pressure Exerted by a Gas Column (Ptg)

[0073] The mechanical configuration of the well to be considered in the mathematical formulation may have characteristics similar to those of well 1400 of FIG. 14. Is assumed that the production pipe is at most at the top of the producing sand, and its length will be represented as Lt. The producing sand or reservoir is at a relatively greater depth and will be defined as Da. It is assumed that the formation of a liquid column Xƒ will always be above the depth or total length of the production pipe Lt.

[0074] A macroscopic balance of mechanical energy allows the following equation to be defined to estimate the pressure of a fluid Pƒ as a function of depth D:P@Df=P@supf+Gf⁢D(13)

[0075] P@Dƒ and P@supƒ represent the fluid pressure at any depth and the fluid pressure at the surface, respectively. D represents the depth at which the corresponding pressure value is to be estimated. Gƒ represents the fluid gradient, whose value can be constant or variable, depending on whether it is a liquid or gas. In the case study, the fluid to be analyzed is a gas whose density changes in the same way as pressure and temperature change. Under these conditions, Eq. (12) can be rewritten as follows:Ptg=Pwhg⁢ exp [γg53.3 ZT⁢ D](14)

[0076] Ptg would represent the pressure exerted on the gas-liquid interface due to the surface head pressure called Pwhg and the weight of the gas column at a depth D. γg represents the specific gravity of the gas and Z is its deviation factor. T is the average temperature of the system. Based on FIG. 14, the depth D could be estimated as:D=Lt-(1-(Lt⁢Cfb1⁢0⁢0⁢0⁢0⁢0⁢0))⁢ Xf(15)

[0077] Cfb represents the slip losses that occur when a liquid slug ascends through the production pipe. Many estimate a value of Cfb between 5 to 7% for every 1,000 feet of lift. By combining Eqs. (14) and (15), the pressure at the gas-oil interface within the pipe Ptg can be estimated as:Ptg=Pwhg⁢ exp [γg53.3 Z⁢T¯⁢Lt-(1-(Lt⁢Cfb1⁢0⁢0⁢0⁢0⁢0⁢0))⁢ Xf](16)

[0078] Analyzing Eq. (14), Ptg is an equation that directly depends on the value of Xƒ generated at the bottom of the well as a result of formation influx and the surface pressure that is exerted. However, it can also be said that it is time-dependent since Pwhg is a value that varies over time as observed in the build-up pressure tests measured at the field level.Determination of the Length of the Liquid Column (Xƒ)

[0079] The length of a liquid column Xƒ will depend on the formation's contribution capacity and the time during which fluid entry into the production pipe is allowed. Zimmerman proposed a methodology that allows maximizing the production of a well that produces under transient flow conditions. The methodology is based on the development of a mathematical expression that converts the productivity index J into the ascent velocity α with which the fluid from the formation ascends within the production pipe. The original methodology has been modified in this case to ensure the flow of a multiphase mixture rather than a single phase only, as presented in his original work.

[0080] Using Vogel's correlation, the production rate q for a corresponding flowing bottom-hole pressure Pwƒ can be estimated as:q=qmax [1-0.2 (PwfPr)-0.8 (PwfPr)2](17)

[0081] The reservoir pressure Pr should always be equal to or less than the bubble point pressure of the reservoir Pb. The maximum rate that the reservoir can deliver is defined as qmax and it can be determined as:qmax=Jp⁢r1.8(18)

[0082] The combination of Eqs. (17) and (18) allows the definition of the following mathematical expression valid for estimating the production rate q:q=Jp⁢r1.8[1-0.2⁢(Pw⁢fPr)-0.8⁢(Pw⁢fPr)2](19)

[0083] A particular analysis can be performed based on Eq. (19). If it is rewritten, it can be noted that the productivity index J would be given as:J=1.8Jprq[1-0.2⁢(Pw⁢fPr)-0.8⁢(Pw⁢fPr)2](20)

[0084] This means that the value of J will never be constant below the bubble point pressure Pb since it changes as the pressure Pwƒ varies at the bottom of the well. Additionally, the productivity index J defines a relationship between the rate q and its corresponding potential flow energy. In other words, J is given as BD / psi. This condition allows it to be written as an ascent velocity of the fluids within the production pipe a as follows:α=J1.4⁢4⁢Bt(21)

[0085] Bt represents the volumetric capacity of the pipe and is expressed in Bls / Mft, which allows the value of a to be expressed in ft / (psi min). Bt can be estimated using the following equation:Bt=0.9⁢7⁢1⁢4⁢3⁢ϕt⁢p2(22)

[0086] φtp represents the diameter of the production pipe and is expressed in inches.

[0087] On the other hand, the formation of a liquid column Xƒ is conditioned by the pressure at the gas-oil interface within the pipe Ptg and the pressure that can be generated at the tip of the pipe, represented as Ps, as shown in well 1500 of FIG. 15.

[0088] The pressure differential at the tip of the pipe dP within which a liquid column Xƒ would form can then be defined as:d⁢P=Ps-Ptg(23)

[0089] Note that dP will be maximum when the value of Ptg is minimum. In other words, there will practically be no gas column within the production pipe. Ps can be estimated using the following equation:Ps=Pw⁢f-Gf(Da-Lt)(24)

[0090] Also, the flow rate circulating through a pipe can be expressed as follows:q=volumetime=At⁢d⁢xd⁢t(25)

[0091] where At represents the cross-sectional area to the flow, which in this case is given by the cross-sectional area of the pipe, and dX / dt as the variation in height of a fluid column that accumulates within a pipe as a function of time. Combining Eqs. (19) and (25) gives:q=Jp⁢r1.8⁢At[1-0.2⁢(Pw⁢fPr)-0.8⁢(Pw⁢fPr)2](26)

[0092] Additionally, if Eq. (21) is considered, it can be determined that:q=1.7⁢8⁢1⁢αp⁢r1.8[1-0.2⁢(Pw⁢fPr)-0.8⁢(Pw⁢fPr)2](27)

[0093] Pwƒ will be responsible for the formation of a fluid column based on the formation's inflow capacity. In this sense, the combination of Eqs. (23) and (24) yields:Gf⁢Xf=Pw⁢f-Gf(Da-Lt)-Ptg(28)Pw⁢f=Ptg+Gf(Da-Lt)+Gf⁢Xf(29)

[0094] Note in Eq. (29) that the variable Ptg (Eq. (16)) depends not only on Xƒ, but also on time t. Thus, the solution of the mathematical model should consider this effect when being solved numerically. By combining Eqs. (27) and (29), it can be derived that:1.7⁢8⁢1⁢αp⁢r1.8⁢d⁢t=dX[1-0.2⁢(Pt⁢g+Gf(Da-Lt)+Gf⁢XfPr)-0.8(Pt⁢g+Gf(Da-Lt)+Gf⁢XfPr)2](30)

[0095] The solution of the obtained differential equation of Eq. (30) depends on the initial and boundary conditions chosen, which in this case, for T=0, would be given by:X=Xf⁢a=(Lt⁢Cf⁢b1⁢0⁢0⁢0⁢0⁢0⁢0)⁢Xf(31)

[0096] Considering the integration limits yields:1.7⁢8⁢1⁢αp⁢r1.8⁢∫0tdt=∫XfaXfdX[1-0.2⁢(Pt⁢g+Gf(Da-Lt)+Gf⁢XfPr)-0.8(Pt⁢g+Gf(Da-Lt)+Gf⁢XfPr)2](32)

[0097] Solving Eq. (32) gives:1.781αpr1.8⁢t=5⁢Pr9⁢Gf⁢ln⁢[(4⁢((Ptg+Gf⁢(Da-Lt)+Gf⁢Xf)+5⁢Pr)⁢(Ptg+Gf⁢(Da-Lt)+Gf⁢Xfa-Pr))][(4⁢((Ptg+Gf⁢(Da-Lt)+Gf⁢Xfa)+5⁢Pr)⁢(Ptg+Gf⁢(Da-Lt)+Gf⁢Xf-Pr))](33)e1.781α⁢Gf⁢t=(4⁢((Ptg+Gf⁢(Da-Lt)+Gf⁢Xf)+5⁢Pr)⁢(Ptg+Gf⁢(Da-Lt)+Gf⁢Xf⁢a-Pr))(4⁢((Ptg+Gf⁢(Da-Lt)+Gf⁢Xf⁢a)+5⁢Pr)⁢(Ptg+Gf⁢(Da-Lt)+Gf⁢Xf-Pr))(34)Xf=[4⁢((Pt⁢g+Gf⁢(Da-Lt)+5⁢Pr+4⁢Gf⁢Xf⁢a)⁢(Pt⁢g+Gf(Da-Lt)+Gf⁢Xf⁢a-Pr))]⁢e1.781α⁢Gf⁢t[4⁢((Pt⁢g+Gf⁢(Da-Lt)-Pr+5⁢Gf⁢Xf⁢a)-(4⁢(Pt⁢g+Gf⁢(Da-Lt))+5⁢Pr+4⁢Gf⁢Xf⁢a-Pr))⁢e1.781α⁢Gf⁢t]-[(Pt⁢g+Gf⁢(Da-Lt)+Gf⁢Xf⁢a-Pr)⁢4⁢(Pt⁢g+Gf⁢(Da-Lt))+5⁢Pr][4⁢((Pt⁢g+Gf⁢(Da-Lt)-Pr+5⁢Gf⁢Xf⁢a)-(4⁢(Pt⁢g+Gf⁢(Da-Lt))+5⁢Pr+4⁢Gf⁢Xf⁢a-Pr))⁢e1.781α⁢Gf⁢t](35)

[0098] The solution of Eq. (35) requires a trial-and-error process, where Eq. (16) and the polynomial derived from the build-up pressure at the wellhead Pwh<sub2>g < / sub2>t must be used simultaneously to achieve convergence of the system of equations to be solved. As can be seen, the determination of Xƒ is time dependent. Consequently, additional variables should be considered, which will be analyzed in the following section.Determination of Cycle Time (TC)

[0099] During a lifting cycle of a well that produces intermittently, the valve experiences three time periods, as shown in lifting cycle 1600 of FIG. 16. These are: (A) the pressure build up stage; (B) the gas production stage; and (C) the oil production stage. In other words, these are the three periods in the well defined as inflow, lifting, and stabilization, respectively.

[0100] During the inflow time t1, the liquid flows from the formation to the bottom of the well, storing within the production tubing. Simultaneously, the free gas from the formation accumulates within the production tubing above the column of liquids that forms at the bottom of the well. Consequently, the height of the fluid column Xƒ will be conditioned by the pressure stored in the tubing, which is reflected in the wellhead pressure Pwh<sub2>g< / sub2>. During this period, the time required to store a certain volume of gas, which is conditioned by the opening and closing pressures of the surface valve, has been defined as gas loading time tload<sub2>g < / sub2>and is considered equal to the cycle time TC, as shown in FIG. 24 (period A). In other words, t=tload<sub2>g< / sub2>=TC.

[0101] It should be noted that this period of time is also associated with a stabilization time te, which allows sufficient conditions for both liquids and gas to move from the reservoir and accumulate within the production tubing, and therefore, is within the inflow time (t=tload<sub2>g< / sub2>=ti=te).

[0102] Once the valve opens at the surface, there is a fluid production period of gas and oil (periods B and C). During the time period tdesc<sub2>g < / sub2>where only gas is discharged, the cycle time is also considered equal to the gas discharge time since no liquid discharge has yet occurred. Therefore, it is valid to consider t=tdesc<sub2>g< / sub2>=TC. However, during period C, it is clear that the discharge of any type of liquid present at the bottom of the well will take a certain amount of time that should be considered. This lifting time tlev, which is related to the average speed at which a liquid plug should ascend Vat, has been based on field experience. Most authors recommend that it be maintained in a range of 900 to 1000 ft / min. Consequently, it should be considered in mathematical solutions, and therefore t=TC=tlev.

[0103] In summary, the cycle time TC is given as:TC=ti+t lev+te(36)whereT lev=D liftV at(37)

[0104] Dlift is considered the depth from which a fluid plug will be lifted. This depth could refer to a valve, pipe tip, etc. For this analysis, the tip or end of the production pipe will be taken as Dlift.

[0105] Determining the optimal value of Tc is not an easy task, Indeed, it represents one of the most difficult variables and is generally done empirically, which requires days or even weeks of fieldwork. The reason is mainly due to the lack of knowledge of the time required for both inflow ti and stabilization te. The solution to Eq. (35) requires knowledge of a time t, which will be denoted as follows:t=TC-t lev=ti+te(38)

[0106] The number of cycles NC is given as follows.NC=1⁢4⁢4⁢0TC(39)

[0107] The effect of the lifting time they will only be considered during period C, which is when it takes effect.Determination of Flow Rate q

[0108] The flow rate can be estimated based on the value of the fluid column, the volumetric capacity of the pipe, the cycle time, and the possible slip losses that may occur when the fluids move from the bottom to the surface. The following mathematical expression allows for estimating its value:q=1.4⁢4⁢Bt(1-C fb)⁢XfΔ⁢t(40)

[0109] where q represents the flow rate and is expressed in BD. The time variable Δt to be considered in Eq. (40) will be accounted for only in this period for the determination of the flow rate q and the number of cycles NC.Determination of Lift Gas Volume Required Per Cycle Vglev<sub2>req < / sub2>

[0110] The gas rate to be produced to displace liquids from the bottom of the well should be higher than the minimum lift gas rates for both water and gas in order to avoid liquid loading at the bottom of the well. However, that alone is insufficient. It is also important to establish comparisons with the minimum rate required by the system to lift a liquid plug under the system's operating conditions.

[0111] Initially, the required gas volume should be estimated, which is based on the calculation of the gas volume needed to fill the pipe. This volume is confined between the bottom of the liquid plug when it reaches the surface and the tip or end of the production pipe, through which the gas from the reservoir circulates and is used as a transport medium.

[0112] Based on the equation of state for real gases, the gas volume required per cycle Uglev<sub2>req< / sub2>, expressed in SCF, can be estimated using the following mathematical equation:v glev req=3⁢5.3⁢6⁢P¯⁢At(Lf-Xf)Z⁡(T¯+4⁢6⁢0)(41)whereT¯=Tf+T wh2(42)

[0113] In the case of P, which represents the average pressure between the pressure just below the liquid plug when it reaches the surface and the pressure just above the liquid plug that may have formed due to slip losses, its value can be estimated as:P¯=P whg+Pt gfb2(43)

[0114] whg will be estimated at the corresponding time t. Pt<sub2>gfb < / sub2>can be estimated as:Pt gfb=P whg⁢e[γg53.3ZT⁢(Lt-(Lt⁢C fb1⁢0⁢0⁢0)⁢Xf)](44)

[0115] The required lift gas-liquid ratio RGLlev<sub2>req< / sub2>, expressed in CF / BN, can be estimated as:RGL lev req=V glev req1⁢0⁢0⁢0⁢Bt(1-Cfb)⁢Xf(45)

[0116] Therefore, the minimum gas rate per cycle required to lift a fluid column from the bottom to the surface of the well qglev<sub2>req < / sub2>can be estimated as:q glev req=qRGL lev req(46)

[0117] where q represents the optimal production rate, expressed in BD. As previously mentioned, qglev<sub2>req < / sub2>represents the gas rate that should be available at the bottom of the well to lift a liquid plug, expressed in SCFD. Consequently, it should not be confused with the minimum gas rates for water or condensate removal.

[0118] qglev<sub2>reg < / sub2>represents an excellent reference value and / or comparison with the gas production rate available in the well under the selected operational conditions. It defines whether the well is capable of autonomously lifting a column of liquids.Methodology for Solving the System of Equations

[0119] The system of equations above may be solved in accordance with process 1700 of FIGS. 17A and 17B. The process begins with determining the adjustment coefficients of the nonlinear, rational regression equation based on the pressure restoration test at 1705, which allows estimation of the wellhead pressure as a function of time. The opening and closing times are estimated at 1710 based on the opening and closing pressures of the valve required in the well. The gas volumes are estimated at 1715 based on the opening and closing pressures of the valve.

[0120] The gas rate qg<sub2>lev < / sub2>to be discharged into the well corresponding to the estimated well closing pressure is estimated at 1720. The required orifice size to discharge the gas rate determined in step 1720 is estimated at 1725 as a function of line pressure and temperature, maintaining critical flow conditions. A value of Ptg is estimated at 1730, assuming the length of the plug to be lifted Xƒ is zero. Through a trial- and error process, the value of the length of the plug to be lifted Xƒ is determined at 1735, and the value of Ptg is redetermined at 1740 as a function of the value of Xƒ determined in step 1735.

[0121] The accumulated gas volumes in the pipe is determined at 1745 as a function of Pwh<sub2>g < / sub2>corresponding to a time instant t. The rate of gas accumulation in the pipeline is estimated at 1750 and the gas volumetric factor to calculate the gas rate at operating conditions is determined at 1755. The density of the liquid mixture is determined at 1760 as a function of API, γg, T, Bo, Bg, and Rs. The critical discharge velocities of water and condensate at Pwh<sub2>g < / sub2>conditions are determined at 1765.

[0122] The time it would take for the well to discharge the accumulated gas volume during opening and closing pressures and any liquid accumulated at the bottom of the well are determined at 1770, at the gas rate estimated in step 1720. It is then verified at 1775 whether there is liquid carryover from the bottom of the well to the surface by comparing qg<sub2>lev < / sub2>and the critical lifting rate qcg.

[0123] If step 1775 is verified, the liquid rate is estimated at 1780. The predominant flow pattern at the specified production condition, as well as behavior of head and flowing bottom pressures and inflow capacity of the formation, are determined at 1785. Based on the obtained results from step 1785, the valve adjustment pressures are determined at the previously considered opening and closing conditions at 1790. A report with the obtained solutions is then issued at 1795. If step 1775 was not verified, however, a report is issued including the previously determined information and an indication that it could not be verified whether there is liquid carryover at 1795.Methodology for Selecting Candidate Wells

[0124] The minimum information required to select the candidate well is in some embodiments is GLR, Pwh<sub2>g < / sub2>Pfl, the API gravity of the produced fluid, the water cut WC, γg, Tr, Ts, φt, the average depth of the perforations Mid. Perƒs, the availability of a choke box and a connection point at the head, and the type of installation. Some of these variables are used in the respective analysis that should be done from a quantitative point of view.Well Selection Methodology

[0125] The data of a well to be evaluated should meet certain qualitative and quantitative selection criteria. For this purpose, the information has been classified herein as determinant, limiting, and complementary.Determinant

[0126] This information is required. Otherwise, the selection of the well as a candidate is rejected. Among the variables of this type are GLR, which allows, based on an estimated production rate q to determine the gas velocity under the operational conditions of the well and compare it with the critical velocities for water and condensate discharge (the computational application determines each of these velocities). If it is higher, the well is accepted as a candidate since the gas is the transport medium for these liquids from the bottom to the surface. Pwh must also be above 300 psi. Although it is not an evaluation variable, it is important to analyze the build-up time as it defines the number of cycles per day, and therefore, the production rate of the well. In this sense, it is suggested to consider this variable.Limiting

[0127] Although accepted, these variables somehow condition the installation of the valve. Within this classification are API gravity of the produced fluid, which should be greater than 25, the average depth of the perforations Mid. Perƒs., which should be greater than 500 ft., depending on the type of production method, and the availability of a choke box, which will allow, if necessary, the installation of a reducer at the valve outlet. In this case, the evaluation is simply qualitative.Complementary

[0128] These variables neither limit nor condition the selection, and in some cases, could even be overlooked. Within this classification, included are the type of installation, which is recommended to be semi-closed, ensuring efficient use of the gas. Availability of a connection point at the head, which allows for the build-up test required for the valve design is also optional. In this case, even if it is not available, there should be no problem as its installation can be suggested for the aforementioned test. Both requirements are evaluated from a qualitative point of view.

[0129] The importance of each variable was evaluated according to its classification, suggesting the following weighting criteria (in percentage form) for the selection in some embodiments: GLR (40%), Pwh (15%), Mid. Perƒs. (10%), API gravity of the produced fluid (5%), choke box availability (10%), Wellhead connection point (5%), and type of installation (15%). Well selection may depend on whether the minimum gas speed is high than the gas speed that is required to lift the fluid.

[0130] FIG. 18 is an architectural diagram illustrating a computing system 1800 configured to perform well analysis, according to an embodiment of the present invention. Computing system 1800 includes a bus 1805 or other communication mechanism for communicating information, and processor(s) 1810 coupled to bus 1805 for processing information. Processor(s) 1810 may be any type of general or specific purpose processor, including a Central Processing Unit (CPU), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), a Graphics Processing Unit (GPU), multiple instances thereof, and / or any combination thereof. Processor(s) 1810 may also have multiple processing cores, and at least some of the cores may be configured to perform specific functions. Multi-parallel processing may be used in some embodiments. In certain embodiments, at least one of processor(s) 1810 may be a neuromorphic circuit that includes processing elements that mimic biological neurons. In some embodiments, neuromorphic circuits may not require the typical components of a Von Neumann computing architecture.

[0131] Computing system 1800 further includes a memory 1815 for storing information and instructions to be executed by processor(s) 1810. Memory 1815 can be comprised of any combination of random access memory (RAM), read-only memory (ROM), flash memory, cache, static storage such as a magnetic or optical disk, or any other types of non-transitory computer-readable media or combinations thereof. Non-transitory computer-readable media may be any available media that can be accessed by processor(s) 1810 and may include volatile media, non-volatile media, or both. The media may also be removable, non-removable, or both. Computing system 1800 includes a communication device 1820, such as a transceiver, to provide access to a communications network via a wireless and / or wired connection. In some embodiments, communication device 1820 may include one or more antennas that are singular, arrayed, phased, switched, beamforming, beamsteering, a combination thereof, and or any other antenna configuration without deviating from the scope of the invention.

[0132] Processor(s) 1810 are further coupled via bus 1805 to a display 1825. Any suitable display device and haptic I / O may be used without deviating from the scope of the invention. A keyboard 1830 and a cursor control device 1835, such as a computer mouse, a touchpad, etc., are further coupled to bus 1805 to enable a user to interface with computing system 1800. However, in certain embodiments, a physical keyboard and mouse may not be present, and the user may interact with the device solely through display 1825 and / or a touchpad (not shown). Any type and combination of input devices may be used as a matter of design choice. In certain embodiments, no physical input device and / or display is present. For instance, the user may interact with computing system 1800 remotely via another computing system in communication therewith, or computing system 1800 may operate autonomously.

[0133] Memory 1815 stores software modules that provide functionality when executed by processor(s) 1810. The modules include an operating system 1840 for computing system 1800. The modules further include a well analysis module 1845 that is configured to perform all or part of the AI / ML processes described herein or derivatives thereof. Computing system 1800 may include one or more additional functional modules 1850 that include additional functionality.

[0134] One skilled in the art will appreciate that a “computing system” could be embodied as a server, an embedded computing system, a personal computer, a console, a personal digital assistant (PDA), a cell phone, a tablet computing device, a smart watch, a quantum computing system, or any other suitable computing device, or combination of devices without deviating from the scope of the invention. Presenting the above-described functions as being performed by a “system” is not intended to limit the scope of the present invention in any way, but is intended to provide one example of the many embodiments of the present invention. Indeed, methods, systems, and apparatuses disclosed herein may be implemented in localized and distributed forms consistent with computing technology, including cloud computing systems. The computing system could be part of or otherwise accessible by a LAN, a mobile communications network, a satellite communications network, the Internet, a public or private cloud, a hybrid cloud, a server farm, any combination thereof, etc. Any localized or distributed architecture may be used without deviating from the scope of the invention.

[0135] It should be noted that some of the system features described in this specification have been presented as modules, in order to more particularly emphasize their implementation independence. For example, a module may be implemented as a hardware circuit comprising custom very large scale integration (VLSI) circuits or gate arrays, off-the-shelf semiconductors such as logic chips, transistors, or other discrete components. A module may also be implemented in programmable hardware devices such as field programmable gate arrays, programmable array logic, programmable logic devices, graphics processing units, or the like.

[0136] A module may also be at least partially implemented in software for execution by various types of processors. An identified unit of executable code may, for instance, include one or more physical or logical blocks of computer instructions that may, for instance, be organized as an object, procedure, or function. Nevertheless, the executables of an identified module need not be physically located together, but may include disparate instructions stored in different locations that, when joined logically together, comprise the module and achieve the stated purpose for the module. Further, modules may be stored on a computer-readable medium, which may be, for instance, a hard disk drive, flash device, RAM, tape, and / or any other such non-transitory computer-readable medium used to store data without deviating from the scope of the invention.

[0137] Indeed, a module of executable code could be a single instruction, or many instructions, and may even be distributed over several different code segments, among different programs, and across several memory devices. Similarly, operational data may be identified and illustrated herein within modules, and may be embodied in any suitable form and organized within any suitable type of data structure. The operational data may be collected as a single data set, or may be distributed over different locations including over different storage devices, and may exist, at least partially, merely as electronic signals on a system or network.

[0138] Various types of AI / ML models may be trained and deployed without deviating from the scope of the invention. For instance, FIG. 19A illustrates an example of a neural network 1900 that has been trained to supplement an oil well analysis application, according to an embodiment of the present invention. Neural network 1900 includes a number of hidden layers. Both DLNNs and shallow learning neural networks (SLNNs) usually have multiple layers, although SLNNs may only have one or two layers in some cases, and normally fewer than DLNNs. Typically, the neural network architecture includes an input layer, multiple intermediate layers, and an output layer, as is the case in neural network 1900.

[0139] A DLNN often has many layers (e.g., 10, 50, 200, etc.) and subsequent layers typically reuse features from previous layers to compute more complex, general functions. A SLNN, on the other hand, tends to have only a few layers and train relatively quickly since expert features are created from raw data samples in advance. However, feature extraction is laborious. DLNNs, on the other hand, usually do not require expert features, but tend to take longer to train and have more layers.

[0140] For both approaches, the layers are trained simultaneously on the training set, normally checking for overfitting on an isolated cross-validation set. Both techniques can yield excellent results, and there is considerable enthusiasm for both approaches. The optimal size, shape, and quantity of individual layers varies depending on the problem that is addressed by the respective neural network.

[0141] Returning to FIG. 19A, well selection criteria information 1 to N are provided as the input layer and fed as inputs to the J neurons of hidden layer 1. This information may be any of the well information discussed herein from previous well analyses, for example. While all of these inputs are fed to each neuron in this example, various architectures are possible that may be used individually or in combination including, but not limited to, feed forward networks, radial basis networks, deep feed forward networks, deep convolutional inverse graphics networks, convolutional neural networks, recurrent neural networks, artificial neural networks, long / short term memory networks, gated recurrent unit networks, generative adversarial networks, liquid state machines, auto encoders, variational auto encoders, denoising auto encoders, sparse auto encoders, extreme learning machines, echo state networks, Markov chains, Hopfield networks, Boltzmann machines, restricted Boltzmann machines, deep residual networks, Kohonen networks, deep belief networks, deep convolutional networks, support vector machines, neural Turing machines, or any other suitable type or combination of neural networks without deviating from the scope of the invention.

[0142] Hidden layer 2 receives inputs from hidden layer 1, hidden layer 3 receives inputs from hidden layer 2, and so on for all hidden layers until the last hidden layer provides its outputs as inputs for the output layer. In this example, suggested application types, extracted information from documents, and respective confidence scores are output. While multiple suggestions are shown here as output, in some embodiments, only a single output suggestion is provided. In certain embodiments, the suggestions are ranked based on confidence scores.

[0143] It should be noted that numbers of neurons I, J, K, and L are not necessarily equal. Thus, any desired number of layers may be used for a given layer of neural network 1900 without deviating from the scope of the invention. Indeed, in certain embodiments, the types of neurons in a given layer may not all be the same. In fact, some embodiments may not use neural networks at all.

[0144] Neural network 1900 is trained to assign confidence score(s) / pseudoprobabilities to appropriate outputs. In order to reduce predictions that are inaccurate, only those results with a confidence score that meets or exceeds a confidence threshold may be provided in some embodiments. For instance, if the confidence threshold is 80%, outputs with confidence scores exceeding this amount may be used and the rest may be ignored.

[0145] Neural networks are probabilistic constructs that typically have confidence score(s). This may be a score learned by the AI / ML model based on how often a similar input was correctly identified during training. Some common types of confidence scores include a decimal number between 0 and 1 (which can be interpreted as a confidence percentage as well), a number between negative ∞ and positive ∞, a set of expressions (e.g., “low,”“medium,” and “high”), etc. Various post-processing calibration techniques may also be employed in an attempt to obtain a more accurate confidence score, such as temperature scaling, batch normalization, weight decay, negative log likelihood (NLL), etc.

[0146] “Neurons” in a neural network are implemented algorithmically as mathematical functions that are typically based on the functioning of a biological neuron. Neurons receive weighted input and have a summation and an activation function that governs whether they pass output to the next layer. This activation function may be a nonlinear thresholded activity function where nothing happens if the value is below a threshold, but then the function linearly responds above the threshold (i.e., a rectified linear unit (ReLU) nonlinearity). Summation functions and ReLU functions are used in deep learning since real neurons can have approximately similar activity functions. Via linear transforms, information can be subtracted, added, etc. In essence, neurons act as gating functions that pass output to the next layer as governed by their underlying mathematical function. In some embodiments, different functions may be used for at least some neurons.

[0147] An example of a neuron 1910 is shown in FIG. 19B. Inputs x1, x2, . . . , xn from a preceding layer are assigned respective weights w1, w2, . . . , wn. Thus, the collective input from preceding neuron 1 is w1x1. These weighted inputs are used for the neuron's summation function modified by a bias, such as:∑i=1m(wi⁢xi)+bias(44)

[0148] This summation is compared against an activation function ƒ(x) to determine whether the neuron “fires”. For instance, ƒ(x) may be given by:f⁡(x)=⁢{1if⁢ ∑ wx+bias≥00if⁢ ∑ wx+bias<0(45)

[0149] The output y of neuron 1910 may thus be given by:y=f⁡(x)⁢∑i=1m(wi⁢xi)+bias(46)

[0150] In this case, neuron 1910 is a single-layer perceptron. However, any suitable neuron type or combination of neuron types may be used without deviating from the scope of the invention. It should also be noted that the ranges of values of the weights and / or the output value(s) of the activation function may differ in some embodiments without deviating from the scope of the invention.

[0151] A goal, or “reward / objective / loss function,” is often employed. A reward function operationalizes the goal with both short-term and long-term rewards to guide the search of a state space (e.g., finding the most accurate answers to user inquiries based on associated metrics). During training, various labeled data is fed through neural network 1900. Successful identifications strengthen weights for inputs to neurons, whereas unsuccessful identifications weaken them. A cost function may be used to punish predictions that are slightly wrong much less than predictions that are very wrong. If the performance of the AI / ML model is not improving after a certain number of training iterations, a data scientist may modify the reward function, provide corrections of incorrect predictions, etc.

[0152] Backpropagation is a technique for optimizing synaptic weights in a feedforward neural network. Backpropagation may be used to “pop the hood” on the hidden layers of the neural network to see how much of the loss every node is responsible for, and subsequently updating the weights in such a way that minimizes the loss by giving the nodes with higher error rates lower weights, and vice versa. In other words, backpropagation allows data scientists to efficiently implement gradient descent, and is provably equivalent to naïve approaches.

[0153] The backpropagation algorithm is mathematically founded in optimization theory. In supervised learning, training data with a known output is passed through the neural network and error is computed with a cost function from known target output, which gives the error for backpropagation. Error is computed at the output, and this error is transformed into corrections for network weights that will minimize the error.

[0154] In the case of supervised learning, an example of backpropagation is provided below. A column vector input x is processed through a series of N nonlinear activation functions ƒi between each layer i=1, . . . , N of the network, with the output at a given layer first multiplied by a synaptic matrix Wi, and with a bias vector bi added. The network output o, given byo=fN(WN⁢fN-1(WN-1⁢fN-2(…⁢f1(W1⁢x+b1)⁢…)+bN-1)+bN)(47)

[0155] In some embodiments, o is compared with a target output t, resulting in an errorE=12⁢o-t2,which is desired to be minimized.Optimization in the form of a gradient descent procedure may be used to minimize the error by modifying the synaptic weights Wi for each layer. The gradient descent procedure requires the computation of the output o given an input x corresponding to a known target output t, and producing an error o−t. This global error is then propagated backwards giving local errors for weight updates with computations similar to, but not exactly the same as, those used for forward propagation. In particular, the backpropagation step typically requires an activation function of the form pj(nj)=ƒj′(nj), where nj is the network activity at layer j (i.e., nj=Wjoj-1+bj) where oj=ƒj(nj) and the apostrophe ′ denotes the derivative of the activity function ƒ.

[0157] The weight updates may be computed via the formulae:dj={(o-t)∘pj(nj),j=NWj+1T⁢dj+1∘pj(nj),j<N(48)∂E∂Wj+1=dj+1(oj)T(49)∂E∂bj+1=dj+1(50)Wj new=Wj old-η⁢∂E∂Wj(51)bj new=bj old-η⁢∂E∂bj(52)

[0158] where ∘ denotes a Hadamard product (i.e., the element-wise product of two vectors), T denotes the matrix transpose, and oj denotes ƒj(Wjoj-1+bj), with o0=x. Here, the learning rate η is chosen with respect to machine learning considerations. Note that the synapses W and b can be combined into one large synaptic matrix, where it is assumed that the input vector has appended ones, and extra columns representing the b synapses are subsumed to W.

[0159] The AI / ML model may be trained over multiple epochs until it reaches a good level of accuracy (e.g., 97% or better using an F2 or F4 threshold for detection and approximately 2,000 epochs). This accuracy level may be determined in some embodiments using an F1 score, an F2 score, an F4 score, or any other suitable technique without deviating from the scope of the invention. Once trained on the training data, the AI / ML model may be tested on a set of evaluation data that the AI / ML model has not encountered before. This helps to ensure that the AI / ML model is not “over fit” such that it performs well on the training data, but does not perform well on other data.

[0160] In some embodiments, it may not be known what accuracy level is possible for the AI / ML model to achieve. Accordingly, if the accuracy of the AI / ML model is starting to drop when analyzing the evaluation data (i.e., the model is performing well on the training data, but is starting to perform less well on the evaluation data), the AI / ML model may go through more epochs of training on the training data (and / or new training data). In some embodiments, the AI / ML model is only deployed if the accuracy reaches a certain level or if the accuracy of the trained AI / ML model is superior to an existing deployed AI / ML model. In certain embodiments, a collection of trained AI / ML models may be used to accomplish a task. For example, one model may be trained to recognize images, another may recognize text, yet another may recognize semantic and / or ontological associations, etc.

[0161] Some embodiments may use transformer networks such as BERT. Such transformer networks learn associations of words and phrases that have both high scores and low scores. This trains the AI / ML model to determine what is close to the input and what is not, respectively. Rather than just using pairs of words / phrases, transformer networks may use the field length and field type, as well.

[0162] NLP models such as word2vec, BERT, GPT-3, ChatGPT, other LLMs, etc. may be used in some embodiments to facilitate semantic understanding and provide more accurate and human-like answers, per the above. Other techniques, such as clustering algorithms, may be used to find similarities between groups of elements. Clustering algorithms may include, but are not limited to, density-based algorithms, distribution-based algorithms, centroid-based algorithms, hierarchy-based algorithms. K-means clustering algorithms, the DBSCAN clustering algorithm, the Gaussian mixture model (GMM) algorithms, the balance iterative reducing and clustering using hierarchies (BIRCH) algorithm, etc. Such techniques may also assist with categorization.

[0163] FIG. 20 is a flowchart illustrating a process 2000 for training AI / ML model(s), according to an embodiment of the present invention. In some embodiments, the AI / ML model(s) may be generative AI models, per the above. The neural network architecture of AI / ML models typically includes multiple layers of neurons, including input, output, and hidden layers. See FIGS. 19A and 19B, for example. The hidden layers in between process the input data and generate intermediate representations of the input that are used to generate the output. These hidden layers can include various types of neurons, such as convolutional neurons, recurrent neurons, and / or transformer neurons.

[0164] The training process begins with providing well selection criteria information, whether labeled or unlabeled, at 2010. The AI / ML model is then trained over multiple epochs at 2020 and results are reviewed at 2030. While various types of AI / ML models may be used, LLMs and other generative AI models are typically trained using a process called “supervised learning”, which is also discussed above. Supervised learning involves providing the model with a large dataset, which the model uses to learn the relationships between the inputs and outputs. During the training process, the model adjusts the weights and biases of the neurons in the neural network to minimize the difference between the predicted outputs and the actual outputs in the training dataset.

[0165] One aspect of the models in some embodiments is the use of transfer learning. For instance, transfer learning may take advantage of a pretrained model, such as ChatGPT, which is fine-tuned on a specific task or domain in step 2020. This allows the model to leverage the knowledge already learned from the pretraining phase and adapt it to a specific application via the training phase of step 2020.

[0166] The pretraining phase typically involves training the original model on an initial set of training data that may be more general. During this phase, the original model learns relationships in the data. In the fine-tuning phase (e.g., performed during step 2020 in addition to or in lieu of the initial training phase in some embodiments if a pretrained original model is used as the initial basis for the final model), the pretrained original model is adapted to a specific task or domain by training the model on a smaller dataset that is specific to the task. For instance, in some embodiments, the final model may be focused on certain types(s) of data sources. This may help the model to more accurately identify data elements therein than a generative AI model that is pretrained alone. Fine-tuning allows the final model to learn the nuances of the source, such as the specific vocabulary and syntax, certain graphical characteristics, certain data formats, etc., without requiring as much data as would be necessary to train the final model from scratch. By leveraging the knowledge learned in the pretraining phase, the fine-tuned, final model can achieve state-of-the-art performance on specific tasks with relatively little additional training data.

[0167] If the AI / ML model fails to meet a desired confidence threshold at 2040, the training data is supplemented and / or the reward function is modified to help the AI / ML model achieve its objectives better at 2050 and the process returns to step 2020. If the AI / ML model meets the confidence threshold at 2040, the AI / ML model is tested on evaluation data at 2060 to ensure that the AI / ML model generalizes well and that the AI / ML model is not over fit with respect to the training data. The evaluation data includes information that the AI / ML model has not processed before. If the confidence threshold is met at 2070 for the evaluation data, the AI / ML model is deployed at 2080. If not, the process returns to step 2050 and the AI / ML model is trained further.

[0168] It will be readily understood that the components of various embodiments of the present invention, as generally described and illustrated in the figures herein, may be arranged and designed in a wide variety of different configurations. Thus, the detailed description of the embodiments of the present invention, as represented in the attached figures, is not intended to limit the scope of the invention as claimed, but is merely representative of selected embodiments of the invention.

[0169] The features, structures, or characteristics of the invention described throughout this specification may be combined in any suitable manner in one or more embodiments. For example, reference throughout this specification to “certain embodiments,”“some embodiments,” or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases “in certain embodiments,”“in some embodiment,”“in other embodiments,” or similar language throughout this specification do not necessarily all refer to the same group of embodiments and the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0170] It should be noted that reference throughout this specification to features, advantages, or similar language does not imply that all of the features and advantages that may be realized with the present invention should be or are in any single embodiment of the invention. Rather, language referring to the features and advantages is understood to mean that a specific feature, advantage, or characteristic described in connection with an embodiment is included in at least one embodiment of the present invention. Thus, discussion of the features and advantages, and similar language, throughout this specification may, but do not necessarily, refer to the same embodiment.

[0171] Furthermore, the described features, advantages, and characteristics of the invention may be combined in any suitable manner in one or more embodiments. One skilled in the relevant art will recognize that the invention can be practiced without one or more of the specific features or advantages of a particular embodiment. In other instances, additional features and advantages may be recognized in certain embodiments that may not be present in all embodiments of the invention.

[0172] One having ordinary skill in the art will readily understand that the invention as discussed above may be practiced with steps in a different order, and / or with hardware elements in configurations which are different than those which are disclosed. Therefore, although the invention has been described based upon these preferred embodiments, it would be apparent to those of skill in the art that certain modifications, variations, and alternative constructions would be apparent, while remaining within the spirit and scope of the invention. In order to determine the metes and bounds of the invention, therefore, reference should be made to the appended claims.

Claims

1. One or more non-transitory computer-readable media storing one or more computer programs, the one or more computer programs configured to cause at least one processor to:display a graphical user interface (GUI) comprising a candidate selection interface for analyzing a candidate well with an intermittent flow and determining whether the candidate well is suitable for installation of a valve for intermittent flow wells, the GUI allowing a user to effectively visualize and understand characteristics of the candidate well;determine well coefficients and estimate well characteristics;verify whether liquid carryover exists from a bottom of the well to a surface of the well by comparing a lifting gas rate to a critical lifting rate;responsive to the verification that the liquid carryover exists:estimate a liquid rate,determine a predominant flow pattern at a specified production condition, behavior of head and flowing bottom pressures, and inflow capacity of a formation of the well,based on the obtained results from the determination of the previous step, determine valve adjustment pressures at considered opening and closing conditions, anddisplay a report to the user with solutions and a valve design module.

2. The one or more non-transitory computer-readable media of claim 1, wherein responsive to a verification that the liquid carryover does not exist, the one or more computer programs are further configured to cause the at least one processor to:provide an indication to the user via the GUI.

3. The one or more non-transitory computer-readable media of claim 1, wherein the determining of the well coefficients comprises determining adjustment coefficients of a nonlinear, rational regression equation based on a pressure restoration test that allows estimation of wellhead pressure as a function of time.

4. The one or more non-transitory computer-readable media of claim 1, wherein the estimating of the well characteristics further comprises estimating opening and closing times based on opening and closing pressures of the valve required in the well and estimating gas volumes based on the opening and closing pressures of the valve.

5. The one or more non-transitory computer-readable media of claim 4, wherein the one or more computer programs are further configured to cause the at least one processor to:estimate the lifting gas rate to be discharged into the well corresponding to the estimated well closing pressure; anddetermine a required orifice size for a pipe to discharge the lifting gas rate as a function of line pressure and temperature to maintain critical flow conditions.

6. The one or more non-transitory computer-readable media of claim 1, wherein the one or more computer programs are further configured to cause the at least one processor to:estimate a value of a pressure at a gas-oil interface within the pipe assuming that a length of a plug to be lifted is zero;estimate a value of the length of the plug to be lifted through a trial-and-error process; andredetermine the value of the pressure at the gas-oil interface based on the estimated value of the length of the plug to be lifted.

7. The one or more non-transitory computer-readable media of claim 1, wherein the one or more computer programs are further configured to cause the at least one processor to:determine accumulated gas volumes in a pipe as a function of a surface head pressure corresponding to a time instant;estimate a rate of gas accumulation in the pipe; andestimate a gas volumetric factor to calculate the lifting gas rate at operating conditions.

8. The one or more non-transitory computer-readable media of claim 1, wherein the one or more computer programs are further configured to cause the at least one processor to:determine a density of a liquid mixture;determine critical discharge velocities of water and condensate at surface head pressure conditions; anddetermine a time for the well to discharge an accumulated gas volume during opening and closing pressures and liquid accumulated at a bottom of the well.

9. The one or more non-transitory computer-readable media of claim 1, wherein the one or more computer programs are further configured to cause the at least one processor to:train an artificial intelligence (AI) / machine learning (ML) model to make probabilistic recommendations regarding whether an intermittent well is a candidate for valve installation using well selection criteria as training data;responsive to the AI / ML model reaching a target average confidence score, deploy the trained AI / ML model; anduse the trained AI / ML model to suggest the well coefficients and / or the well characteristics, to verify whether the liquid carryover exists, or both.

10. The one or more non-transitory computer-readable media of claim 1, wherein the one or more computer programs are configured to use a trained AI / ML model to suggest the well coefficients and / or the well characteristics, to verify whether the liquid carryover exists, or both.

11. The one or more non-transitory computer-readable media of claim 1, wherein the valve design module comprises at least one of a candidate selection interface, a fluid properties interface, a well performance interface, an inflow sensitivity interface, operational conditions interface, a mechanical configuration interface, an accumulation interface, a choke diameter interface, a well production interface, a select design conditions interface, a calibration data interface, and a reporting interface for the candidate intermittent flow well.

12. A computer-implemented method, comprising:displaying, by a computing system, a candidate selection interface for analyzing a candidate well with an intermittent flow and determining whether the candidate well is suitable for installation of a valve for intermittent flow wells, the candidate selection interface comprising fields for at least one of gas liquid rate, wellhead pressure, American Petroleum Institute (API) gravity, depth, choke availability and wellhead connection points, well completion, liquid density, gas density, gas interfacial tension, liquid interfacial tension, gas wellhead pressure, tubing area, surface temperature, and compressibility factor;calculating, by the computing system, a lifting gas rate and a critical lifting rate for the candidate well based on the fields of the candidate selection interface;responsive to the well being a suitable candidate due to the lifting gas rate exceeding the critical lifting rate for the candidate well, displaying, by the computing system, a valve design module comprising at least one of a basic well data module, a dynamic forecasting module, a valve calibration module, and a reporting module; andfacilitating design of the valve via the valve design module, by the computing system.

13. The computer-implemented method of claim 12, whereinthe valve design module comprises the basic well data module, andthe basic well data module comprises a well performance interface, an inflow sensitivity interface, an operational conditions interface, a mechanical configuration interface, and an accumulation interface.

14. The computer-implemented method of claim 12, whereinthe valve design module comprises the dynamic analysis module, andthe dynamic analysis module comprises a choke diameter interface and a well production interface.

15. The computer-implemented method of claim 12, whereinthe valve design module comprises the valve calibration module, andthe valve calibration module comprises a select design conditions interface and a calibration data interface.

16. A computing system, comprising:memory storing computer program instructions; andat least one processor configured to execute the computer program instructions, wherein the computer program instructions are configured to cause the at least one processor to:display a candidate selection interface for analyzing a candidate well with an intermittent flow and determining whether the candidate well is suitable for installation of a valve for intermittent flow wells, the candidate selection interface allowing a user to effectively visualize and understand characteristics of the candidate well,determine well coefficients and estimate well characteristics,verify whether liquid carryover exists from a bottom of the well to a surface of the well by comparing a lifting gas rate to a critical lifting rate, andresponsive to the verification that the liquid carryover exists, display a valve design module, whereinthe valve design module comprises at least one of a candidate selection interface, a fluid properties interface, a well performance interface, an inflow sensitivity interface, operational conditions interface, a mechanical configuration interface, an accumulation interface, a choke diameter interface, a well production interface, a select design conditions interface, a calibration data interface, and a reporting interface for the candidate intermittent flow well.

17. The computing system of claim 16, whereinthe valve design module comprises the basic well data module, andthe basic well data module comprises a well performance interface, an inflow sensitivity interface, an operational conditions interface, a mechanical configuration interface, and an accumulation interface.

18. The computing system of claim 16, whereinthe valve design module comprises the dynamic analysis module, andthe dynamic analysis module comprises a choke diameter interface and a well production interface.

19. The computing system of claim 16, whereinthe valve design module comprises the valve calibration module, andthe valve calibration module comprises a select design conditions interface and a calibration data interface.

20. The computing system of claim 16, wherein the computer program instructions are configured to use a trained AI / ML model to suggest the well coefficients and / or the well characteristics, to verify whether the liquid carryover exists, or both.

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