Rapid prediction method and system for gas-water two-phase yield of compact water-containing gas reservoir fractured well

Abstract

The invention provides a method and a system for rapidly predicting the gas-water two-phase yield of a compact water-containing gas reservoir fractured well, and the method comprehensively considers the influence of the slippage effect, the stress sensitive effect, the starting pressure gradient and the gas high-pressure physical property of gas phase seepage in a compact reservoir on a seepage mechanism. Respectively establishing gas phase correction pseudo-pressure and pseudo-time and water phase correction pseudo-pressure and pseudo-time to realize linear processing of nonlinear factors, and determining a two-phase unsteady-state seepage model; processing model parameters by adopting implicit pressure and explicit saturation, and deducing a corresponding analytical solution; determining a tight reservoir utilization range, and establishing a corresponding gas-water two-phase material balance equation for resolving average formation pressure and average water saturation to update seepage model parameters; therefore, the two-phase yield prediction of the tight reservoir in the full life cycle is realized. According to the scheme, the problems of insufficient calculation precision and low efficiency in the prior art can be solved, accurate and rapid prediction of the two-phase yield of the tight gas fractured well is achieved, and technical support is provided for efficient development of a tight water-containing gas reservoir.

Description

Technical Field

[0001] This invention relates to the field of oil and gas exploration and development data prediction technology, and in particular to a method and system for rapid prediction of gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs. Background Technology

[0002] Existing production capacity forecasting methods are mainly based on three categories: empirical formulas, analytical models, and numerical simulations. Among them, empirical formula methods are mainly calculated using the Arps formula (an empirical formula for oil recovery) and other formulas for fitting production decline curves; analytical model methods are mainly based on linear flow models and partitioned linear flow models; and numerical simulation methods are mainly based on commercial numerical simulation software such as t-Navigator, CMG, and Eclipse.

[0003] The main problems with the existing technologies mentioned above are as follows: empirical formulas are generally unable to solve the problem of predicting production output under varying flow pressures, making them difficult to apply in the field; numerical simulation methods for predicting production capacity are time-consuming and require excessive parameter inputs, typically necessitating the use of fast analytical models for prediction. However, existing analytical models still have significant shortcomings, primarily: the influencing factors involved in the model calculations are not comprehensive enough, leading to discrepancies between the calculated results and reality; furthermore, tight gas reservoirs have high water saturation, while the seepage models used are still largely limited to single-phase seepage problems; and the model calculations are based on steady-state and quasi-steady-state assumptions. Therefore, it is evident that existing analytical models suffer from low efficiency and low computational accuracy when predicting the gas-water two-phase production of tight gas wells.

[0004] The information disclosed in the background section of this invention is intended only to enhance the understanding of the general background of this invention, and should not be construed as an admission or in any way implying that such information constitutes prior art known to those skilled in the art. Summary of the Invention

[0005] To address the aforementioned problems, this invention provides a rapid prediction method for the gas-water two-phase production of fractured wells in tight water-bearing gas reservoirs. This method effectively overcomes the shortcomings of insufficient calculation accuracy and low efficiency in existing technologies, achieving accurate and rapid prediction of the two-phase production of fractured tight gas wells, and providing technical support for the efficient development of tight water-bearing gas reservoirs. It comprehensively considers the effects of slippage, stress sensitivity, initiation pressure gradient, and high-pressure gas properties on the seepage mechanism in tight reservoirs, establishing gas-phase corrected pseudo-pressure and pseudo-time, and water-phase corrected pseudo-pressure and pseudo-time to linearize nonlinear factors, thus determining the two-phase unsteady-state seepage model. Implicit pressure and explicit saturation are used to process the model parameters, deriving the corresponding analytical solution. The exploitable range of the tight reservoir is determined, and a corresponding gas-water two-phase material balance equation is established to calculate the mean formation pressure and mean water saturation to update the seepage model parameters. Finally, this method is applied to predict the two-phase production throughout the entire life cycle of the tight reservoir. Preferably, in one embodiment, the method includes:

[0006] Step S100: Based on the reservoir parameters of the tight reservoir, a two-phase unsteady flow calculation model of the tight reservoir is established by comprehensively considering the effects of slippage, stress sensitivity, initiation pressure gradient and gas high pressure properties on the seepage mechanism.

[0007] Step S200: Based on the prediction time step division approach, analyze and determine the solution function setting principle and two-phase analytical solution derivation mechanism for the two-phase unsteady seepage operation model matching;

[0008] Step S300: Based on the solution function setting principle, determine the dynamic parameter update model around the mean formation pressure and mean water saturation to update the model parameters;

[0009] Step S400: Divide the prediction time step according to the prediction period and the needs, use the original formation pressure and original water saturation of the reservoir as the initial model parameters before the update to start the calculation, substitute the reservoir number of the target reservoir, and combine the dynamic parameters to update the model and the two-phase analytical solution derivation mechanism to calculate and determine the dynamic two-phase production data of the target reservoir, so as to realize the full cycle two-phase production prediction.

[0010] Furthermore, in one embodiment, in step S100, a set modified pseudo-pressure and modified pseudo-time function are used to simultaneously characterize the effects of high-pressure gas physical parameters, reservoir stress sensitivity effect, and slippage effect related to gas phase seepage in tight reservoirs.

[0011] Preferably, in one embodiment, a modified start-up pressure gradient influence coefficient is used to characterize the effect of the start-up pressure gradient on gas phase seepage.

[0012] In one alternative embodiment, the effect of stress sensitivity on aqueous phase seepage is characterized by setting nonlinear terms around stress sensitivity and processing with aqueous phase corrected pseudo-pressure and aqueous phase corrected pseudo-time.

[0013] Furthermore, in one embodiment, a two-phase unsteady seepage calculation model is established as follows:

[0014]

[0015] In the formula, λ is the starting pressure gradient, ψ represents the gas-phase corrected pseudo-pressure, x is the x-coordinate, and G... λ To correct for the influence coefficient of the start-up pressure gradient, φ represents reservoir porosity, and k i k represents the absolute permeability of the reservoir. rg c is the relative permeability of the gas. ti μ represents the overall compressibility coefficient of the reservoir in its original state. gi The viscosity of the gas in the reservoir under its original state is represented by t. a Indicates the gas phase correction simulation time. For the aqueous phase, corrected pseudo-pressure, t w For the aqueous phase correction simulation time, μ w c is the viscosity of the aqueous phase. tw k is the overall compressibility coefficient of the reservoir water phase. rw This represents the relative permeability of the aqueous phase.

[0016] In a preferred embodiment, in step S200, the parameters in the unsteady seepage equation of the gas-water two-phase flow are processed using the implicit pressure and explicit saturation method, and the analytical solution of the model is derived using the Laplace transform method.

[0017] Furthermore, in step S300 of one embodiment, the utilization range of the tight reservoir is analyzed, and a gas-water two-phase material balance equation within the utilization range is established as a dynamic parameter update model. The average formation pressure and average water saturation of the reservoir within the utilization range are calculated as update parameters of the model.

[0018] Optionally, in one embodiment, during the analysis of the utilization range of the tight reservoir, the initiation pressure gradient characteristics of gas seepage are considered, the utilization range of the aqueous phase is taken as the reservoir utilization range, the utilization range in the X and Y directions is calculated respectively, and the utilization volume is calculated using the rectangular area.

[0019] Based on other aspects of the methods described in any one or more of the foregoing embodiments, the present invention also provides a storage medium storing program code that can implement the methods described in any one or more of the foregoing embodiments.

[0020] Based on the application of the methods described in any one or more of the above embodiments, the present invention also provides a rapid prediction system for gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs, which performs the methods described in any one or more of the above embodiments.

[0021] Compared with the closest prior art, the present invention also has the following beneficial effects:

[0022] This invention provides a method and system for rapid prediction of gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs. The method comprehensively considers the effects of slippage, stress sensitivity, initiation pressure gradient, and the influence of high-pressure gas properties on the seepage mechanism to establish a two-phase unsteady-state seepage operation model for the tight reservoir. It divides the prediction time steps to analyze and determine the principle for setting the solution function matching the seepage operation model and the derivation mechanism of the two-phase analytical solution. Based on the solution function setting principle, it determines a dynamic parameter update model around the average formation pressure and average water saturation to update the model parameters. In application, multiple prediction time steps are divided according to the prediction period and requirements. The original formation pressure and original water saturation of the reservoir are used as the initial model parameters before updating to start the operation. The target reservoir's reservoir number is substituted into the dynamic parameter update model and the two-phase analytical solution derivation mechanism to calculate and determine the dynamic two-phase production data of the target reservoir, achieving full-cycle production prediction. This scheme takes into account the influence of reservoir stress sensitivity, gas seepage slippage effect and starting pressure gradient, and breaks away from the limitations of single-phase seepage, steady-state seepage or quasi-steady-state seepage assumptions. It establishes a gas-water two-phase unsteady-state seepage calculation model, which significantly improves both calculation time and accuracy, and helps to promote the efficient and stable development of tight water-bearing gas reservoirs.

[0023] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the description, claims, and drawings. Attached Figure Description

[0024] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with the embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0025] Figure 1 This is an example diagram of the physical model of a fractured well in a tight water-bearing gas reservoir, which is part of the rapid prediction method for gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs provided in this embodiment of the invention.

[0026] Figure 2 This is a flowchart illustrating a method for rapid prediction of gas-water two-phase production in a fractured well of a tight water-bearing gas reservoir, provided in an embodiment of the present invention.

[0027] Figure 3This is an example diagram illustrating the relationship between pressure and corrected pseudo-pressure in the rapid prediction method for gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs provided in the embodiments of this invention.

[0028] Figure 4 This is an example diagram illustrating the relationship between time and corrected pseudo-time in the rapid prediction method for gas-water two-phase production of fractured wells in tight water-bearing gas reservoirs provided in the embodiments of this invention;

[0029] Figure 5 This is an example diagram of the gas phase production prediction results of the rapid prediction method for gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs provided in the embodiments of the present invention.

[0030] Figure 6 This is an example diagram showing the gas-water phase production prediction results of the rapid prediction method for gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs provided in the embodiments of this invention.

[0031] Figure 7 This is a schematic diagram of the structure of the rapid prediction system for gas-water two-phase production of fractured wells in tight water-bearing gas reservoirs provided in the embodiments of the present invention. Detailed Implementation

[0032] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings and examples. Those skilled in the art will then fully understand how the present invention uses technical means to solve technical problems and achieve technical effects, and will be able to implement the present invention specifically based on the above-described implementation process. It should be noted that, as long as there is no conflict, the various embodiments and features of the present invention can be combined with each other, and the resulting technical solutions are all within the protection scope of the present invention.

[0033] Although the flowchart describes the operations as sequential processes, many of these operations can be performed in parallel, concurrently, or simultaneously. The order of the operations can be rearranged. A process can terminate when its operation is complete, but it may also have additional steps not included in the diagram. A process can correspond to a method, function, procedure, subroutine, subroutine, etc.

[0034] Computer equipment includes user equipment and network equipment. User equipment or clients include, but are not limited to, computers, smartphones, and PDAs (Personal Digital Assistants); network equipment includes, but is not limited to, a single network server, a server group consisting of multiple network servers, or a cloud based on cloud computing consisting of a large number of computers or network servers. Computer equipment can operate independently to implement this invention, or it can connect to a network and implement this invention through interaction with other computer devices within the network. The network in which the computer equipment resides includes, but is not limited to, the Internet, wide area networks (WANs), metropolitan area networks (MANs), local area networks (LANs), and VPN networks.

[0035] The terms “first,” “second,” etc., may be used herein to describe various units, but these units should not be limited by these terms; they are used merely to distinguish one unit from another. The term “and / or” as used herein includes any and all combinations of one or more of the associated listed items. When a unit is referred to as “connected” or “coupled” to another unit, it may be directly connected or coupled to said other unit, or there may be intermediate units present.

[0036] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments. Unless the context clearly indicates otherwise, the singular forms “a” and “an” as used herein are also intended to include the plural. It should also be understood that the terms “comprising” and / or “including” as used herein specify the presence of the stated features, integers, steps, operations, units, and / or components, without excluding the presence or addition of one or more other features, integers, steps, operations, units, components, and / or combinations thereof.

[0037] Tight gas resources can be considered a clean energy source, depending on their carbon footprint, environmental impact, and the mode of extraction and utilization management. Tight gas reservoirs typically have low porosity and low permeability. Therefore, hydraulic fracturing technology is frequently used to improve the production capacity of vertical and horizontal wells. Multiple fractures are created near the wellbore after hydraulic fracturing, and this should be taken into account when predicting the production capacity of tight gas wells. Figure 1 An example diagram of a physical model for a fractured well in a tight gas reservoir is shown. Furthermore, tight gas reservoirs exhibit various nonlinear flow mechanisms, including low-velocity non-Darcy flow, stress-dependent permeability, gas slippage, and two-phase flow. Therefore, production prediction models must consider both hydraulic fractures and these various nonlinear flow mechanisms, which directly impacts the formulation of reservoir development strategies and the evaluation of hydraulic fracturing efficiency.

[0038] In recent years, several technologies for predicting tight gas well production have been proposed. Existing production prediction methods are mainly based on three categories: empirical formulas, analytical models, and numerical simulations. Empirical formula methods primarily use the Arps formula (an empirical formula for oil recovery) and other formulas fitting production decline curves. Analytical model methods are mainly based on linear flow models and partitioned linear flow models. Numerical simulation methods are mainly based on commercial numerical simulation software such as t-Navigator, CMG, and Eclipse. The main problems with these existing technologies are: empirical formula methods often cannot solve production prediction problems with varying production flow pressures, making them difficult to apply in the field; numerical simulation methods are time-consuming and require large parameter inputs, usually necessitating the use of fast analytical models for prediction. However, existing analytical models still have significant shortcomings, mainly in that: the influencing factors considered in the model calculations are not comprehensive enough, for example, the effects of reservoir stress sensitivity, gas seepage slippage effect, and starting pressure gradient are not taken into account; in addition, tight gas reservoirs have high water saturation, while the seepage models used are basically limited to single-phase seepage problems; and the model calculations are based on steady-state and quasi-steady-state assumptions. Therefore, due to the above-mentioned technical defects, existing analytical models suffer from low efficiency and low calculation accuracy when predicting the gas-water two-phase production of tight gas wells.

[0039] To address the aforementioned issues, this invention provides a rapid prediction method and system for gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs. Based on considerations of factors such as artificial fracturing, slippage effect, reservoir stress sensitivity, and gas-water two-phase flow, an accurate and efficient method for predicting gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs is established. Taking into account the slippage effect, stress sensitivity effect, starting pressure gradient, high-pressure gas properties, and gas-water two-phase flow mechanisms in tight reservoirs, linear processing methods are established for nonlinear factors in the unsteady-state flow model using modified pseudo-pressure and pseudo-time for both the gas and water phases, forming the unsteady-state gas-water two-phase flow equation for tight gas reservoirs. This provides technical support for the efficient development of tight water-bearing gas reservoirs.

[0040] The following describes the detailed flow of the method according to an embodiment of the present invention with reference to the accompanying drawings, the steps of which can be executed in a computer system containing, for example, a set of computer-executable instructions. Although the logical order of the steps is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than that shown here.

[0041] Example 1

[0042] Figure 2 This diagram illustrates a flowchart of a rapid prediction method for gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs according to Embodiment 1 of the present invention. (Refer to...) Figure 2 As can be seen, the method includes the following steps.

[0043] Step S100: Based on the reservoir parameters of the tight reservoir, a gas-water two-phase flow calculation model of the tight reservoir is established by comprehensively considering the effects of slippage, stress sensitivity, initiation pressure gradient and gas high pressure properties on the seepage mechanism.

[0044] Step S200: Based on the prediction time step division approach, analyze and determine the solution function setting principle and two-phase analytical solution derivation mechanism for the gas-water two-phase flow operation model.

[0045] Step S300: Based on the solution function setting principle, determine the dynamic parameter update model around the mean formation pressure and mean water saturation to update the model parameters;

[0046] Step S400: Divide the prediction period into multiple prediction time steps according to the required prediction period, start the calculation by using the original formation pressure and original water saturation of the reservoir as the initial model parameters before the update, substitute the reservoir number of the target reservoir into the dynamic parameter update model and the two-phase analytical solution derivation mechanism to calculate and determine the dynamic two-phase production data of the target reservoir, and realize the two-phase production prediction of the whole life cycle.

[0047] Considering that existing analytical models do not take into account reservoir stress sensitivity, gas seepage slippage effect, and the influence of the starting pressure gradient; tight gas reservoirs have high water saturation, and seepage models are limited to single-phase seepage problems; and the models are based on steady-state and quasi-steady-state assumptions, they suffer from low efficiency and low computational accuracy when applied to predict the gas-water two-phase production of tight gas wells. To overcome these technical problems, this invention provides a rapid prediction method for the gas-water two-phase production of fractured wells in tight water-bearing gas reservoirs, capable of accurately and quickly predicting the gas-water two-phase production of fractured tight gas wells.

[0048] This invention establishes an accurate and efficient method for predicting the gas-water two-phase production of fractured wells in tight water-bearing gas reservoirs, taking into account factors such as artificial fracturing, slippage effect, reservoir stress sensitivity, and gas-water two-phase flow. First, by executing step S100, based on the reservoir parameters of the tight reservoir, a gas-water two-phase flow calculation model for the tight reservoir is established, taking into account the effects of slippage effect, stress sensitivity effect, starting pressure gradient, and the influence of high-pressure gas properties on the flow mechanism.

[0049] Among them, an improved gas phase seepage treatment method is proposed around multiple nonlinear factors. In optional embodiments, the present invention comprehensively considers the slippage effect, stress sensitivity effect, starting pressure gradient, and high-pressure gas properties of gas phase seepage in tight reservoirs to determine the linear treatment method in the seepage model.

[0050] Specifically, in a preferred embodiment, the present invention employs a set modified pseudo-pressure and modified pseudo-time function to simultaneously characterize the effects of high-pressure gas physical parameters related to gas phase seepage in tight reservoirs, reservoir stress sensitivity effects, and slippage effects, wherein:

[0051] The gas-phase corrected pseudo-pressure is defined using the following formula:

[0052]

[0053] The gas-phase correction fitting time is defined using the following formula:

[0054]

[0055] In the formula, ψ represents the gas-phase corrected pseudo-pressure, in MPa. 2 / mPa.s; p represents reservoir pressure, MPa; μ g Z represents gas viscosity, mPa·s; Z represents gas compressibility factor, dimensionless; γ represents reservoir stress sensitivity index, MPa. -1 ; △p represents the pressure difference, i.e., the original reservoir pressure minus the current pressure, in MPa; b represents the slip factor, in MPa; t a The corrected time for the gas phase is represented by d; t represents time, d; μ gi The viscosity of the gas in the reservoir under its original state is expressed in mPa·s; c ti The overall compressibility coefficient of the reservoir in its original state, expressed in MPa. -1 ; c represents the mean formation pressure, in MPa. t Represents the overall compressibility coefficient of the reservoir, in MPa -1 .

[0056] In an optional embodiment, a modified starting pressure gradient influence coefficient is used to characterize the effect of the starting pressure gradient on the gas phase seepage, and the average pressure is used for approximation when solving the seepage equation.

[0057] In a preferred embodiment, the modified start-up pressure gradient influence coefficient is defined by the following formula:

[0058]

[0059] In the formula, G λ For an intermediate variable, MPa-1.

[0060] Based on the foregoing embodiments, the present invention linearizes the gas flow control equation by considering high-pressure gas properties, reservoir stress sensitivity, slippage effect, and initiation pressure gradient.

[0061] In practical applications, the gas-phase seepage equation without linearization is as follows:

[0062]

[0063] The linearized gas-phase flow equations implemented in this embodiment of the invention are as follows:

[0064]

[0065] In the formula, S g φ represents reservoir gas saturation, dimensionless; φ represents reservoir porosity, dimensionless; k i Let mD be the absolute permeability of the reservoir; k be the density of the reservoir. rg λ represents the relative permeability of the gas, dimensionless; λ is the starting pressure gradient, MPa / m; x is the x-coordinate, m.

[0066] To address the gas-water two-phase flow problem in tight gas reservoirs, this invention employs a matched analytical processing method for the two-phase flow equations, using two sets of governing equations to handle the gas and water two-phase flow problems. In order to achieve linearization of the unsteady flow model, implicit pressure and explicit saturation methods are used to process nonlinear parameters.

[0067] Regarding the processing method of the aqueous phase seepage equation, the researchers of this invention considered that the aqueous phase seepage equation needs to take into account the stress sensitivity of the reservoir, so they added nonlinear terms to the seepage control equation and used aqueous phase modified pseudo-pressure and aqueous phase modified pseudo-time processing to characterize the influence of stress sensitivity on aqueous phase seepage.

[0068] The corrected pseudo-pressure for the aqueous phase is defined by the following formula:

[0069]

[0070] The aqueous phase correction fitting time is defined using the following formula:

[0071]

[0072] In the formula, For the aqueous phase, corrected pseudo-pressure, MPa; t w The time for correcting the aqueous phase is d.

[0073] In this embodiment of the invention, the implicit pressure and apparent saturation method is used to process the gas-water two-phase flow equation. The parameters related to saturation in the control equation are explicitly processed, while the parameters related to pressure are implicitly processed using the gas-phase corrected pseudo-pressure and pseudo-time and the water-phase corrected pseudo-pressure and pseudo-time methods mentioned above.

[0074] The treated gas-water two-phase flow model is as follows:

[0075]

[0076] In the formula, μ wThe viscosity of the aqueous phase is mPa·s; c tw The comprehensive compressibility coefficient of the reservoir water phase, in MPa -1 ;k rw Let mD be the relative permeability of the aqueous phase.

[0077] Further, in step S200, the principle of setting the solution function and the derivation mechanism of the two-phase analytical solution for matching the gas-water two-phase flow operation model are determined based on the analysis of the predicted time step division approach.

[0078] The prediction time steps are divided according to demand. Based on the unit prediction time steps and the set solution function settings and transformation methods, the analytical solution of the gas-water two-phase production capacity of the seepage calculation model is derived and analyzed. In a preferred embodiment, the implicit pressure and explicit saturation methods are used to process the parameters in the gas-water two-phase unsteady seepage equation to derive the analytical solution of the gas-water two-phase unsteady seepage model.

[0079] In this embodiment of the invention, when analytically solving the steady-state seepage equation for the gas-water two-phase flow, the first step is to divide the prediction time step, and within each time step, k is... rg k rw Treating it as a function of average water saturation, λG λ The solution is processed as a function of mean formation pressure, and then the analytical solution of the model is derived using the Laplace transform method.

[0080] In a preferred embodiment, the derived analytical solution for gas-phase energy production is:

[0081]

[0082] in:

[0083]

[0084] In the formula, q gD α represents dimensionless gas production. F β F m1, m2, α I r1 and r2 are intermediate variable symbols; k Frg k represents the relative permeability of the gas phase in the fractured system. FD w is the dimensionless fracture permeability. FD x is the width of the dimensionless crack. FD x is the half-length of a dimensionless crack; eD is the dimensionless half-well spacing; s is the Laplace space constant; k I For internal zone permeability, mD; k Irg k represents the relative permeability of the gas phase in the inner zone. F Let mD be the crack permeability; y be the permeability of the crack. eD η is the dimensionless crack spacing; FDη is the dimensionless crack conductivity coefficient; ID k is the pressure conductivity coefficient of the dimensionless inner region. O For external penetration rate, mD; k Org λ represents the relative permeability of the outer gas phase. D For dimensionless starting pressure gradient; G D For intermediate variable G λ Dimensionlessness; η OD It is the dimensionless outer region pressure conductivity coefficient.

[0085] Furthermore, the analytical solution for the aqueous phase productivity is derived as follows:

[0086]

[0087] in:

[0088]

[0089] In the formula, q wD k represents the water production on the next day without dimension. Frw k represents the relative permeability of the water phase in the fracture. FD α is the dimensionless fracture permeability; Fw α Iw k is an intermediate variable. Irw η represents the relative permeability of the water phase in the inner zone. IwD k is the pressure conductivity coefficient of the dimensionless inner region. Orw k represents the relative permeability of the water phase in the outer zone. Irw η represents the relative permeability of the water phase in the inner zone. OwD η is the dimensionless outer region pressure conductivity coefficient; FwD It is the dimensionless crack conductivity coefficient.

[0090] Furthermore, this embodiment of the invention achieves prediction of gas-water two-phase production throughout the entire life cycle of tight gas fractured wells by updating model parameters. The dynamic parameter update model is determined by step 300 around the average formation pressure and average water saturation.

[0091] In a preferred embodiment, the exploitation range of the tight reservoir is analyzed, and a gas-water two-phase material balance equation within the exploitation range is established as a dynamic parameter update model. The average formation pressure and average water saturation of the reservoir within the exploitation range are calculated as update parameters of the model.

[0092] Optionally, to achieve a semi-analytical solution for the model, the model parameters need to be updated dynamically using the mean formation pressure and mean water saturation. Mass balance equations are established for both the gas and water phases, and the mean formation pressure and mean water saturation are obtained using the Newton-Raphson iteration method.

[0093] In the process of calculating the utilization range of tight gas reservoirs, the starting pressure gradient of gas seepage is taken into account. The utilization range of the aqueous phase is used as the reservoir utilization range, and the utilization ranges in the X and Y directions are calculated separately. The utilization volume is calculated using the rectangular area.

[0094] The usable range of a tight gas reservoir is calculated using the following logic:

[0095] Range of motion in the X direction:

[0096] Range of motion in the Y direction:

[0097] The activated volume of a single crack is: V inv =4y inv H(x F φ I +x inv φ O )

[0098] In the formula, φ O C represents the porosity of the outer zone, which is dimensionless. tO The outer zone comprehensive compression coefficient, MPa -1 ;φ I c represents the porosity of the inner region, which is dimensionless. tI This is the comprehensive compression coefficient for the inner region.

[0099] Based on this, a gas-water two-phase material balance equation is constructed within the operational range; reservoir material balance equations are constructed separately for the gas and water phases, thereby establishing a reservoir material balance equation between average formation pressure, average water saturation, cumulative gas production, and cumulative water production as a dynamic parameter update model, which is used to solve for average formation pressure and average water saturation.

[0100] In an optional embodiment, the reservoir mass balance equation is constructed as follows:

[0101] Gas phase mass balance equation:

[0102] Aqueous phase mass balance equation:

[0103] In the formula, q gsc Daily gas production, m 3 / d;q wsc Daily water production, m 3 / d;S gi B represents the initial gas saturation level. gi The gas volume coefficient at the original pressure; This represents the average gas saturation level. S is the gas volume coefficient under average pressure; wi B represents the initial water saturation level.wi The volume coefficient of the aqueous phase under the original pressure; This represents the average water saturation level. This is the volume coefficient of the aqueous phase under average pressure.

[0104] Based on the reservoir material balance equation that matches the operational range, the gas phase material balance equation and the water phase material balance equation are calculated using the Newton iteration method to obtain the average formation pressure and average water saturation.

[0105] In practical applications, step S400 is executed, and multiple prediction time steps are divided according to the prediction period and requirements. The original formation pressure and original water saturation of the reservoir are used as the initial model parameters before the update to start the calculation. The reservoir number of the target reservoir is substituted into the dynamic parameters and the dynamic two-phase production data of the target reservoir is calculated and determined by the dynamic parameter update model and the two-phase analytical solution derivation mechanism, so as to realize the full cycle two-phase production prediction.

[0106] In the rapid prediction process of gas-water two-phase production throughout the entire life cycle, the gas high-pressure properties, reservoir stress sensitivity effect, slippage effect, starting pressure gradient, and gas-water two-phase seepage are comprehensively considered to derive the analytical solution for predicting the gas-water two-phase production capacity of tight gas fractured wells. The model parameters are updated by the average formation pressure and average water saturation to achieve the prediction of gas-water two-phase production throughout the entire life cycle of tight gas fractured wells.

[0107] The present invention provides a rapid prediction method for gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs. This method not only fully considers the fracture network characteristics of fractured horizontal wells but also nonlinear flow mechanisms such as artificial fractures, slippage effects, reservoir stress sensitivity, and gas-water two-phase seepage. It is an accurate and efficient method for predicting gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs, providing technical support for the efficient development of these reservoirs. Its accuracy is reflected in its comprehensive consideration of reservoir characteristics, gas-water two-phase flow mechanisms, and unsteady seepage factors, resulting in higher production prediction accuracy. Its efficiency is reflected in the use of analytical models to solve for production, allowing for immediate production prediction results, and the modeling and calculation process is simple and efficient.

[0108] The present invention will be further described below with reference to specific embodiments. The scope of the present invention is not limited to the embodiments, but is defined in the claims.

[0109] Taking a tight gas-fractured horizontal well A as an example: the tight reservoir has a permeability of 1 mD, a reservoir thickness of 13 m, a porosity of 0.1, a formation pressure of 23.4 MPa, and an initial water saturation of 0.6; the horizontal section of well A is 1215 m long, with 17 fractured sections. This well exhibits significant gas-water two-phase flow. The dynamic distribution of gas-water two-phase production is shown in […]. Figure 3 , Figure 4 The rapid prediction method for gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs, as described in this patent, is used for prediction, as follows:

[0110] (1) Treatment of multiple nonlinear factors in gas phase seepage

[0111] ① In this case, the gas seepage stress sensitivity coefficient is taken as 0.01 MPa. -1 The gas slip coefficient is taken as 2 MPa, and the relationship between pressure and gas-phase corrected pseudo-pressure can then be obtained. See [reference needed]. Figure 3 , Figure 4 The information revealed in the article.

[0112] ② In this case, the starting pressure gradient is relatively small, taking 0.0001 MPa / m. Substituting into the relevant formula, the influence coefficient of the corrected starting pressure gradient can be obtained as approximately 0.219.

[0113] ③ Based on the treatment of gas seepage stress sensitivity, slippage effect, and starting pressure gradient, the equations can be linearized.

[0114] (2) Analytical processing of the two-phase flow equations respectively

[0115] ① Considering the reservoir stress sensitivity coefficient of 0.01 MPa -1 The pressure and time relationships were obtained by using aqueous phase correction pseudo-pressure and pseudo-time processing, as shown below. Figure 3 , Figure 4 As shown.

[0116] ② The equation is linearized using the implicit pressure and explicit saturation method. For example, in the first time step, with the original water saturation of 0.6, the relative permeability of the gas and water phases is assigned to 0.3124 and 0.0225 respectively, and substituted into the equation (treated as coefficients).

[0117] ③ Based on the analytical solution of the gas-water two-phase flow equation, the gas-water two-phase production can be obtained by substituting the model parameters. In this case, the minimum time is 0.01 days, the prediction is 10,000 days, and 500 time steps are taken according to the logarithmic scale. In the first step, the gas-water two-phase corrected time is updated with the original formation pressure and gas saturation, and the gas-water two-phase production is obtained as follows: 9.3 × 10⁻⁶. 5 m 3 / d、253.4m 3 / d.

[0118] (3) Solving for mean formation pressure and mean water saturation of the reservoir

[0119] ① Calculation of the exploitable range of tight gas reservoir: Substituting the parameters into the formula, the exploitable range in the X and Y directions can be calculated to be 5.44m, and the exploitable volume can be calculated to be 4073m³. 3 .

[0120] ② Substituting the parameters into the constructed gas-water two-phase mass balance equation, and using the Newton-Raphson iteration method, the average formation pressure and average water saturation within the operational range were obtained as 23.3985 MPa and 0.599998 MPa, respectively.

[0121] (4) Rapid prediction of gas-liquid two-phase production throughout the entire life cycle

[0122] Substituting the average formation pressure of 23.3985 MPa and the average water saturation of 0.599998 into the equation, the relative permeability parameter and the gas-water two-phase correction time were updated. Figure 2 The process shown above is repeated continuously to achieve rapid prediction of gas-liquid two-phase production throughout the entire life cycle.

[0123] The gas-liquid two-phase production prediction results in this case are shown below. Figure 5 , Figure 6 The results show good agreement with actual production data, demonstrating the accuracy of the gas-water two-phase production prediction method provided by this patent. Furthermore, the prediction process takes less than one second, exhibiting extremely fast prediction speed and enabling efficient analysis of specific mining examples. Therefore, this invention achieves excellent results in predicting the gas-water two-phase production of fractured wells in tight water-bearing gas reservoirs.

[0124] For the foregoing method embodiments, in order to simplify the description, they are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, because according to the present invention, some steps can be performed in other orders or simultaneously. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0125] It should be noted that, in other embodiments of the present invention, the method can also combine one or more of the above embodiments to obtain a new method for rapid prediction of gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs, so as to achieve high-quality analysis and application of dynamic production data of tight reservoir gas wells.

[0126] Example 2

[0127] It should be noted that, based on the methods in any one or more embodiments of the present invention described above, the present invention also provides a storage medium storing program code that can implement the methods described in any one or more embodiments. When the program code is executed by the operating system, it can implement the rapid prediction method for gas-water two-phase production of fractured wells in tight water-bearing gas reservoirs as described above.

[0128] Example 3

[0129] The methods described in the above-disclosed embodiments of the present invention are detailed. These methods can be implemented using various forms of devices or systems. Therefore, based on other aspects of the methods described in any one or more of the above embodiments, the present invention also provides a rapid prediction system for the gas-water two-phase production of fractured wells in tight water-bearing gas reservoirs. This system is used to execute the rapid prediction method for the gas-water two-phase production of fractured wells in tight water-bearing gas reservoirs described in any one or more of the above embodiments. Specific embodiments are given below for detailed description.

[0130] Specifically, Figure 7 The diagram shows a schematic representation of the rapid prediction system for gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs provided in an embodiment of the present invention. Figure 7 As shown, the system includes:

[0131] The two-phase flow model establishment module is configured to establish a two-phase unsteady flow calculation model of the tight reservoir based on the reservoir parameters of the set tight reservoir and comprehensively consider the effects of slippage effect, stress sensitivity effect, starting pressure gradient and gas high pressure properties on the flow mechanism.

[0132] The module for determining the derivation mechanism is configured to analyze and determine the setting principles of the solution function matching the two-phase unsteady seepage operation model and the derivation mechanism of the two-phase analytical solution based on the idea of ​​dividing the prediction time steps.

[0133] The parameter update model establishment module is configured as a dynamic parameter update model that determines the update model parameters based on the solution function setting principle and the mean formation pressure and mean water saturation.

[0134] The two-phase production prediction module is configured to divide the prediction time step according to the prediction period and the demand. It starts the calculation by using the original formation pressure and original water saturation of the reservoir as the initial model parameters before the update. It substitutes the reservoir number of the target reservoir and combines the dynamic parameters to update the model and the two-phase analytical solution derivation mechanism to calculate and determine the dynamic two-phase production data of the target reservoir, so as to realize the full cycle two-phase production prediction.

[0135] Furthermore, in one embodiment, the two-phase flow model establishment module uses a set modified pseudo-pressure and modified pseudo-time function to simultaneously characterize the effects of gas high-pressure physical parameters, reservoir stress sensitivity effect, and slippage effect related to gas phase flow in tight reservoirs.

[0136] Preferably, in one embodiment, the two-phase flow model establishment module uses a modified starting pressure gradient influence coefficient to characterize the influence of the starting pressure gradient on the gas phase flow.

[0137] In an optional embodiment, the two-phase flow model building module characterizes the effect of stress sensitivity on aqueous phase flow by setting nonlinear terms around stress sensitivity and using aqueous phase corrected pseudo-pressure and aqueous phase corrected pseudo-time processing.

[0138] Furthermore, in one embodiment, a two-phase unsteady seepage calculation model is established as follows:

[0139]

[0140] In the formula, λ is the starting pressure gradient, ψ represents the gas-phase corrected pseudo-pressure, x is the x-coordinate, and G... λ To correct for the influence coefficient of the start-up pressure gradient, φ represents reservoir porosity, and k i k represents the absolute permeability of the reservoir. rg c is the relative permeability of the gas. ti μ represents the overall compressibility coefficient of the reservoir in its original state. gi The viscosity of the gas in the reservoir under its original state is represented by t. a Indicates the gas phase correction simulation time. For the aqueous phase, correct the simulated pressure, t w For the aqueous phase correction simulation time, μ w c is the viscosity of the aqueous phase. tw k is the overall compressibility coefficient of the reservoir water phase. rw This represents the relative permeability of the aqueous phase.

[0141] In a preferred embodiment, the solution derivation mechanism determination module is configured to: process the parameters in the gas-water two-phase unsteady seepage equation using implicit pressure and explicit saturation methods, and derive the analytical solution of the model using the Laplace transform method.

[0142] Furthermore, in one embodiment, the parameter update model establishment module is configured to: analyze the utilization range of the tight reservoir, establish a gas-water two-phase material balance equation within the utilization range as a dynamic parameter update model, and calculate the average formation pressure and average water saturation of the reservoir within the utilization range as update parameters of the model.

[0143] Optionally, in one embodiment, the parameter update model establishment module analyzes the tight reservoir utilization range by the following operations: considering the initiation pressure gradient characteristics of gas seepage, taking the utilization range of the aqueous phase as the reservoir utilization range, calculating the utilization range in the X and Y directions respectively, and calculating the utilization volume using the rectangular area.

[0144] In the rapid prediction system for gas-water two-phase production of fractured wells in tight water-bearing gas reservoirs provided in this embodiment of the invention, each module or unit structure can operate independently or in combination according to the actual model parameter processing and solution requirements to achieve the corresponding technical effects.

[0145] It should be understood that the embodiments disclosed herein are not limited to the specific structures, processing steps, or materials disclosed herein, but should be extended to equivalent substitutions of these features as understood by those skilled in the art. It should also be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting.

[0146] The phrase "an embodiment" in the specification means that a specific feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Therefore, the phrase "an embodiment" appearing in various places throughout the specification does not necessarily refer to the same embodiment.

[0147] While the embodiments disclosed in this invention are as described above, the content is merely for the purpose of facilitating understanding of the invention and is not intended to limit the invention. Any person skilled in the art to which this invention pertains may make any modifications and variations in form and detail of the implementation without departing from the spirit and scope disclosed herein; however, the scope of patent protection for this invention shall still be determined by the scope defined in the appended claims.

Claims

1. A method for rapid prediction of gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs, characterized in that, The method includes: Step S100: Based on the reservoir parameters of the tight reservoir, a two-phase unsteady flow calculation model of the tight reservoir is established by comprehensively considering the effects of slippage, stress sensitivity, initiation pressure gradient and gas high pressure properties on the seepage mechanism. Step S200: Based on the prediction time step division approach, analyze and determine the solution function setting principle and two-phase analytical solution derivation mechanism for the two-phase unsteady seepage operation model matching; Step S300: Based on the solution function setting principle, determine the dynamic parameter update model around the mean formation pressure and mean water saturation to update the model parameters; Step S400: Divide the prediction time step according to the prediction period and the needs, use the original formation pressure and original water saturation of the reservoir as the initial model parameters before the update to start the calculation, substitute the reservoir number of the target reservoir, and combine the dynamic parameters to update the model and the two-phase analytical solution derivation mechanism to calculate and determine the dynamic two-phase production data of the target reservoir, so as to realize the full cycle two-phase production prediction.

2. The method according to claim 1, characterized in that, In step S100, the effects of the high-pressure physical parameters of the gas phase seepage in the tight reservoir, the reservoir stress sensitivity effect, and the slip effect are simultaneously characterized by the set modified pseudo-pressure and modified pseudo-time functions.

3. The method according to claim 1, characterized in that, The effect of the starting pressure gradient on gas phase seepage is characterized by the modified starting pressure gradient influence coefficient.

4. The method according to claim 1, characterized in that, By setting nonlinear terms around stress sensitivity, and using water phase corrected pseudo-pressure and water phase corrected pseudo-time, the influence of stress sensitivity on water phase seepage is characterized.

5. The method according to claim 1, characterized in that, The following two-phase unsteady seepage calculation model is established: In the formula, λ is the starting pressure gradient, ψ represents the gas-phase corrected pseudo-pressure, x is the x-coordinate, and G... λ To correct for the influence coefficient of the start-up pressure gradient, φ represents reservoir porosity, and k i k represents the absolute permeability of the reservoir. rg c is the relative permeability of the gas. ti μ represents the overall compressibility coefficient of the reservoir in its original state. gi The viscosity of the gas in the reservoir under its original state is represented by t. a Indicates the gas phase correction simulation time. For the aqueous phase, corrected pseudo-pressure, t w For the aqueous phase correction simulation time, μ w c is the viscosity of the aqueous phase. tw k is the overall compressibility coefficient of the reservoir water phase. rw This represents the relative permeability of the aqueous phase.

6. The method according to claim 1, characterized in that, In step S200, the parameters in the gas-water two-phase unsteady seepage equation are processed using the implicit pressure and explicit saturation methods, and the analytical solution of the two-phase unsteady seepage calculation model is derived using the Laplace transform method.

7. The method according to claim 1, characterized in that, In step S300, the utilization range of the tight reservoir is analyzed, and a gas-water two-phase material balance equation within the utilization range is established as a dynamic parameter update model. The average formation pressure and average water saturation of the reservoir within the utilization range are calculated as update parameters of the model.

8. The method according to claim 7, characterized in that, In analyzing the utilization range of tight reservoirs, the initiation pressure gradient characteristics of gas seepage are considered. The utilization range of the aqueous phase is taken as the reservoir utilization range. The utilization ranges in the X and Y directions are calculated separately, and the utilization volume is calculated using the rectangular area.

9. A storage medium, characterized in that, The storage medium stores program code that can implement the method as described in any one of claims 1 to 8.

10. A rapid prediction system for gas-water two-phase production in fractured wells of tight water-bearing gas reservoirs, characterized in that, The system performs the method as described in any one of claims 1 to 8.

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