Methods and equipment for determining the final recoverable reserves of fractured horizontal wells in tight reservoirs

Abstract

This application provides a method and equipment for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir. The method includes: establishing a well test model of the tight reservoir considering heterogeneity, stress sensitivity, and weak recharge effects; based on this well test model, using an analysis method derived from historical production data and the relationship between production-standardized pseudo-pressure and time, inverting and determining the fracture parameters of the horizontal well; calculating linear flow parameters based on the fracture parameters; and finally, simulating and calculating the final recoverable reserves of the fractured horizontal well in the tight reservoir based on the linear flow parameters. This application increases the accuracy of the predicted final recoverable reserves and reduces the prediction error by inverting and determining the fracture parameters of the horizontal well and calculating the linear flow parameters and final recoverable reserves based on the inverted parameters.

Description

Technical Field

[0001] This application relates to the field of tight oil and gas reservoir development technology, and in particular to a method and equipment for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir. Background Technology

[0002] With the decline in the scale and number of conventional oil and gas discoveries and the continuous breakthroughs in unconventional resource exploration and development technologies, unconventional oil and gas resources have gradually become an important part of my country's oil and gas production, among which tight gas reservoirs are rich in reserves.

[0003] The final recoverable reserves predicted by a single well can be used to predict the final recoverable reserves of fractured horizontal wells in tight gas reservoirs. Existing methods for predicting the final recoverable reserves by a single well mainly include empirical methods, probabilistic methods, modern production decline analysis methods, analytical prediction methods, and numerical simulation methods. However, the accuracy of the analysis results is low, and the error in predicting tight gas production capacity is large. Summary of the Invention

[0004] This application provides a method and equipment for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir, which solves the problems of low accuracy of the final recoverable reserves predicted by a single well and large error in the prediction of tight gas production capacity.

[0005] Firstly, this application provides a method for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir, including:

[0006] Obtain fracture parameters of a horizontally fractured well in a target tight reservoir, including fracture half-length and permeability.

[0007] Based on the fracture parameters of the horizontal well in the target tight reservoir, calculate the linear flow parameters of the horizontal well in the target tight reservoir.

[0008] Based on the linear flow parameters of the fractured horizontal well in the target tight reservoir, the final recoverable reserves of the fractured horizontal well in the tight reservoir are calculated.

[0009] Optionally, obtain the fracture parameters of the horizontal well in the target tight reservoir fracturing process, specifically including:

[0010] Obtain historical production data and production conditions of the target tight reservoir, and construct a well test model of the target tight reservoir;

[0011] Based on the production conditions of the target tight reservoir and the well test model of the target tight reservoir, calculated production data are obtained.

[0012] Based on historical production data and calculated production data, determine the model parameters of the well test model for the target tight reservoir;

[0013] Crack parameters are extracted from the model parameters.

[0014] Optionally, based on the fracture parameters of the fractured horizontal well in the target tight reservoir, the linear flow parameters of the fractured horizontal well in the target tight reservoir are calculated, specifically including:

[0015] The linear flow parameters of the fractured horizontal well in the target tight reservoir are calculated according to the first formula, where the first formula is:

[0016]

[0017] Wherein, LFP is the linear flow parameter, x0 is the length of the horizontal well fractured in the target tight reservoir, y0 is twice the fracture half-length, L is the fracture spacing, h is the thickness of the target tight reservoir, and k is the average permeability.

[0018] Optionally, based on the production conditions of the target tight reservoir and the well test model of the target tight reservoir, computational production data is calculated, specifically including:

[0019] Substitute the production conditions of the target tight reservoir into the well test model of the target tight reservoir to calculate the bottom hole pressure of the fractured horizontal well in the target tight reservoir;

[0020] Calculated production data is obtained by calculating the bottom hole pressure of a horizontal well fracturing the target tight reservoir.

[0021] Secondly, this application provides an apparatus for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir, comprising:

[0022] The acquisition module is used to acquire fracture parameters of the target tight reservoir fractured horizontal well, including fracture half-length and permeability.

[0023] The processing module is used to calculate the linear flow parameters of the fractured horizontal well in the target tight reservoir based on the fracture parameters; and

[0024] Based on the linear flow parameters of the fractured horizontal well in the target tight reservoir, the final recoverable reserves of the fractured horizontal well in the tight reservoir are calculated.

[0025] Optionally, the acquisition module is specifically used for:

[0026] Obtain historical production data and production conditions of the target tight reservoir, and construct a well test model of the target tight reservoir;

[0027] Based on the production conditions of the target tight reservoir and the well test model of the target tight reservoir, calculated production data are obtained.

[0028] Based on historical production data and calculated production data, determine the model parameters of the well test model for the target tight reservoir;

[0029] Crack parameters are extracted from the model parameters.

[0030] Optionally, the processing module is specifically used for:

[0031] The linear flow parameters of the fractured horizontal well in the target tight reservoir are calculated according to the first formula, where the first formula is:

[0032]

[0033] Wherein, LFP is the linear flow parameter, x0 is the length of the horizontal well fractured in the target tight reservoir, y0 is twice the fracture half-length, L is the fracture spacing, h is the thickness of the target tight reservoir, and k is the average permeability.

[0034] Optionally, the processing module is specifically used for:

[0035] Substitute the production conditions of the target tight reservoir into the well test model of the target tight reservoir to calculate the bottom hole pressure of the fractured horizontal well in the target tight reservoir;

[0036] Calculated production data is obtained by calculating the bottom hole pressure of a horizontal well fracturing the target tight reservoir.

[0037] Thirdly, this application provides an electronic device, including: a processor, and a memory communicatively connected to the processor;

[0038] The memory stores the instructions that the computer executes;

[0039] The processor executes computer execution instructions stored in memory to implement the determination method of the first aspect above.

[0040] Fourthly, this application provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the determination method described in the first aspect above.

[0041] This application provides a method and equipment for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir. The method calculates the bottom hole pressure of the horizontal well and generates calculated production data based on an analytical method derived from the relationship between pressure and time in a production-standardized simulation. Based on historical production data and the calculated production data, the fracture parameters of the horizontal well are inverted and determined. Linear flow parameters are calculated based on the fracture parameters, and then the linear flow parameters of the target fractured horizontal well in the tight reservoir are calculated based on the determined fracture parameters and relevant reservoir parameters. Finally, the final recoverable reserves of the fractured horizontal well in the tight reservoir are calculated based on the linear flow parameters. Using the calculated parameters to determine the linear flow parameters and the final recoverable reserves of the fractured horizontal well in the tight reservoir improves the accuracy of the calculation results and reduces prediction errors. Attached Figure Description

[0042] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0043] Figure 1 A flowchart illustrating a method for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir, provided as an embodiment of this application;

[0044] Figure 2 A flowchart illustrating a method for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir, provided as an embodiment of this application;

[0045] Figure 3 A schematic diagram of a well test model provided in an embodiment of this application;

[0046] Figure 4 A schematic diagram of linear flow in a horizontal well fractured in a tight reservoir, provided as an embodiment of this application;

[0047] Figure 5 A flowchart illustrating a method for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir, provided as an embodiment of this application;

[0048] Figure 6 A schematic diagram illustrating gas production and time as provided in an embodiment of this application;

[0049] Figure 7 A schematic diagram illustrating a production-standardized pseudo-pressure and mass balance time provided for an embodiment of this application;

[0050] Figure 8 A schematic diagram of a horizontal well plan for fracturing a tight reservoir, provided for an embodiment of this application;

[0051] Figure 9 Fitting simulation results of the final recoverable reserves of a fractured horizontal well in a tight reservoir provided for embodiments of this application;

[0052] Figure 10 A schematic diagram of a device for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir, provided for an embodiment of this application;

[0053] Figure 11 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application.

[0054] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0055] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0056] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties. Furthermore, the collection, use and processing of the relevant data must comply with the relevant laws, regulations and standards of the relevant countries and regions, and corresponding operation portals are provided for users to choose to authorize or refuse.

[0057] The predicted final recoverable reserves (EUR) of a single well refers to the final recoverable reserves predicted for a well that has been producing for many years, based on its declining production pattern and using trend prediction methods. Methods for predicting the final recoverable reserves of gas wells mainly include empirical methods, probabilistic methods, modern production decline analysis methods, analytical prediction methods, and numerical simulation methods. Their classification and application conditions are shown in Table 1. Empirical methods, as a gas reservoir engineering method based on statistical regression theory, are represented by Arps decline, expansion exponential decline, Duong method decline, and power exponential decline analysis. Although convenient to use, the results are greatly affected by data fluctuations, resulting in low calculation accuracy. Probabilistic methods consider some physical parameters affecting gas well production, but they have uncertainties. Modern production decline analysis methods, analytical prediction methods, and numerical simulation methods can predict various production conditions, but the model input parameters are complex, and the calculation accuracy is limited by the reliability of the input parameters.

[0058] Table 1 Commonly Used Evaluation Methods and Applicable Conditions for EUR in Tight Gas Wells

[0059]

[0060]

[0061] Due to the complexity of the post-pressure seepage environment and the reservoir properties of tight sandstone reservoirs, existing EUR evaluation methods have significant errors and limitations in application. For example, the advantages and disadvantages of the three empirical methods are analyzed in Table 2.

[0062] Table 2 Analysis of the advantages and disadvantages of the three empirical methods

[0063]

[0064]

[0065] This application establishes an improved well test model considering the complex seepage environment of a fractured horizontal well in tight gas reservoirs. Based on the well test model, calculated production data is obtained by fitting the production dynamic history and standardizing the production to simulate the relationship between pressure and time. Based on the production history data and the calculated production data, fracture parameters are obtained. Then, the linear flow parameters of the fractured horizontal well in tight reservoirs are calculated using the square root of time method and fracture parameters. Based on the linear flow parameters, the final recoverable reserves of the fractured horizontal well in tight reservoirs are calculated.

[0066] Figure 1 A flowchart illustrating a method for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir, as provided in this application embodiment, is shown below. Figure 1 As shown, the method includes the following steps:

[0067] S101. Obtain the fracture parameters of the horizontal well in the target tight reservoir.

[0068] More specifically, the fracture parameters of the horizontally fractured well in the target tight reservoir are obtained, including fracture half-length and permeability. The fracture half-length and permeability are obtained from simulation calculations using specialized software.

[0069] S102. Based on the fracture parameters of the horizontal well in the target tight reservoir, calculate the linear flow parameters of the horizontal well in the target tight reservoir.

[0070] More specifically, the linear flow parameters of the fractured horizontal well in the target tight reservoir are calculated based on the fracture half-length and permeability. The linear flow parameters are calculated using the first formula, where:

[0071]

[0072] Where LFP is the linear flow parameter, x0 is the length of the horizontal well fractured in the target tight reservoir, y0 is twice the fracture half-length, L is the fracture spacing, h is the thickness of the target tight reservoir, and k is the average permeability.

[0073] S103. Calculate the final recoverable reserves of the fractured horizontal well in the target tight reservoir based on the linear flow parameters of the fractured horizontal well in the tight reservoir.

[0074] More specifically, based on the linear flow parameters of the fractured horizontal well in the target tight reservoir and its abandonment pressure, software simulation is used to predict the production capacity of the fractured horizontal well under the abandonment pressure. The final recoverable reserves of the fractured horizontal well are obtained when its production is zero. Calculating the final recoverable reserves of the fractured horizontal well also includes comparing the calculated results with the actual final recoverable reserves of the well, conducting error analysis, and verifying the accuracy and practicality of the method.

[0075] In the method for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir provided in this application embodiment, the fracture half-length and permeability are obtained, and the linear flow parameters of the target tight reservoir fractured horizontal well are calculated based on the fracture half-length and permeability. Then, the cumulative production when the production of the target tight reservoir fractured horizontal well is zero is calculated based on the linear flow parameters, which is the final recoverable reserves of the tight reservoir fractured horizontal well. Using fracture parameters to calculate the linear flow parameters and the final recoverable reserves of the tight reservoir fractured horizontal well improves the accuracy of the calculation results and reduces prediction errors.

[0076] Figure 2 A flowchart illustrating a method for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir, as provided in this application embodiment, is shown below. Figure 2 As shown, obtaining fracture parameters for a horizontally fractured well in a target tight reservoir includes the following steps:

[0077] S201. Obtain historical production data and production conditions of the target tight reservoir, and construct a well test model of the target tight reservoir.

[0078] More specifically, the production history data of the well test model of the target tight reservoir is the actual production history data of the target tight reservoir, the production conditions of the well test model of the target tight reservoir are the basic production conditions required to establish the well test model, and the well test model of the target tight reservoir includes a physical model and a mathematical model.

[0079] For example, the well test model for the target tight reservoir is shown below:

[0080] Figure 3 This is a schematic diagram of a well test model provided in an embodiment of this application, as shown below. Figure 3As shown, based on the actual production and development of horizontal wells in the Sulige tight gas reservoir, a radial composite reservoir is established, considering formation heterogeneity and the characteristics of high-permeability zones formed by fracturing, i.e., the original reservoir fluid replenishes the fracturing-affected zone. After multi-stage hydraulic fracturing, a main fracture is formed in the reservoir of the horizontal well in the tight gas reservoir; this area is called the fracturing-affected zone (inner zone). The reservoir stimulation effect gradually weakens as the main fracture extends outward. The area at the very end of the fracturing-affected zone has a certain improvement in flow capacity compared to the original reservoir and is considered the fracturing-affected zone (outer zone). The reservoir outside the fracturing-affected zone is called the original reservoir (original zone).

[0081] The physical model assumes the following conditions: the outer zone, inner zone, and artificial fracture zone are all single-medium; the top and bottom layers of the reservoir are sealed, and the reservoir is horizontally uniform in thickness; the fluid is a single-phase, slightly compressible liquid, and its seepage in the reservoir conforms to Darcy's linear flow law; the hydraulic main fracture is a finite-conducting fracture that completely penetrates the entire reservoir vertically; the fluid in the outer zone flows linearly into the inner zone, and the fluid in the inner zone flows unidirectionally towards the main fracture, finally flowing through the hydraulic main fracture to the wellbore; pressure drop loss and gravity effects inside the horizontal wellbore are not considered; the well produces at a constant rate, and the effects of wellbore reservoir effect and skin effect are considered; geological heterogeneity, stress sensitivity, and weak recharge effect at the boundary are considered.

[0082] Figure 4 A schematic diagram of linear flow in a fractured horizontal well in a tight reservoir, as provided in this application embodiment, is shown below. Figure 4 As shown, fluid flow in the reservoir can be divided into three stages: linear flow from the fracturing zone (inner zone) to the main fracture; linear flow from the fracturing-affected zone (outer zone) to the fracturing-modified zone (inner zone); and linear flow from the main fracture to the horizontal well. Since the original permeability of the tight gas reservoir is extremely low, the flow from the original reservoir to the fracturing-affected zone (outer zone) is considered a weak recharge effect and can be treated as a mixing boundary. Based on the heterogeneity, stress sensitivity, and weak recharge effect of the tight reservoir, a mathematical model of the target tight reservoir is established using the fracture network discretization approach. The mathematical model includes equations for the weak recharge effect, stress sensitivity effect, fluid flow in the fracturing-modified zone (inner zone), fluid flow in the main fracture, and production conditions. Assuming the total number of main fractures is n, one-quarter of main fracture j is taken as the research object.

[0083] The equation for the weak supply effect is shown below:

[0084] Considering the weak recharge effect from the original reservoir to the fracturing zone, the pseudo-pressure change at the interface between the original reservoir and the fracturing zone can be expressed as:

[0085]

[0086] In the formula S fs To replenish epidermal factors, y represents the vertical distance. eWhere m1 represents the vertical boundary size, m2 represents the pseudo-pressure in the fracturing effective zone (outer zone), and m3 represents the pseudo-pressure of the original reservoir gas (original zone). The expressions for both are... Where m is the pseudo-pressure of the gas, p is the actual pressure of the gas, μ is the gas viscosity, and Z is the gas compressibility factor.

[0087] Based on the heterogeneous variation in permeability, the flow rate change at the interface between the original reservoir and the fracturing-affected zone (outer zone) can be:

[0088]

[0089] In the formula, K2 is the permeability of the outer zone, in μm. 2 The permeability of the K3 original reservoir area, in μm. 2 .

[0090] Substituting formula (2) into formula (1) yields

[0091]

[0092] In the formula, m3 is the original reservoir gas pseudo-pressure, which can be expressed as m i Therefore, formula (3) can be further expressed as:

[0093]

[0094] Where β is the supply resistance coefficient, expressed by the following formula:

[0095]

[0096] The stress-sensitive effect equation is shown below:

[0097] During the seepage process, the fluid in the outer zone satisfies the continuity equation:

[0098]

[0099] Where Φ is porosity, in %; t is the production time of the fractured horizontal well; and the equation of motion v2 and the gas state equation ρ are respectively:

[0100]

[0101] Where K2 is the external permeability, p is the actual gas pressure in MPa, M is the molecular weight of the gas in kg / kmol, and R is the universal gas constant with a value of 0.008314 MPa. -1 ·m 3 / (kmol·K), where T is the absolute temperature of the gas, in K.

[0102] Characterizing reservoir stress sensitivity using a permeability index model:

[0103]

[0104] Where γ is the stress sensitivity coefficient, with units of MPa. -1 By integration, we can obtain:

[0105]

[0106] Among them, P i Assuming the original reservoir pressure, substituting equations (7) and (9) into equation (6), and combining this with the rock state equation, we can obtain:

[0107]

[0108] The rock state equation is C f =(dV p / V f )×(1 / dp), C f Rock compressibility coefficient, in MPa -1 C t The overall compressibility factor is expressed in MPa. -1 α is the modified stress sensitivity coefficient.

[0109] The inner boundary conditions are:

[0110]

[0111] Where m1 is the pseudo-pressure of gas in the fracturing zone (inner zone), y Fj The length of the j-th main crack is half.

[0112] The fluid flow equations in the inner zone are shown below:

[0113] During the seepage process, considering the mass exchange in the inner zone and the fluid inflow in the outer zone, the fluid flow in the inner zone satisfies the following equation:

[0114]

[0115] Where v1 is the fluid seepage velocity in cm / s, q1 is the flow rate in the inner zone, and ()1 represents the inner zone.

[0116] Similarly, using a derivation method similar to formulas (7)-(9), the fluid satisfies the following equation:

[0117]

[0118] Where x is the horizontal distance, m1 is the pseudo-pressure of the inner matrix, and K1 is the inner permeability, in μm. 2 The expression for q1 is as follows:

[0119]

[0120] Among them, P i p1 represents the original reservoir pressure, and p2 represents the internal zone pressure, both in MPa.

[0121] The control conditions for the inner and outer boundaries are:

[0122]

[0123] Where, x e ω represents the size of the horizontal boundary. Fj Let be the width of the j-th main crack.

[0124] The initial conditions are:

[0125] m1| t＝0 =m i (16)

[0126] The fluid flow equation in the main fracture is as follows:

[0127] During the seepage process, the fluid in the main fracture satisfies the continuity equation:

[0128]

[0129] Where v F The seepage velocity of the main fracture, ρ_gas density, ρ_v F The component of mass seepage velocity in the main fracture, where ()2 represents the outer zone and q2 is the flow rate of fluid from the inner zone into the main fracture, is expressed as follows:

[0130]

[0131] Similarly, using a derivation method similar to formulas (7)-(9), the fluid in the main fracture can be obtained to satisfy the following equation:

[0132]

[0133] Where, m F The pseudo-gas pressure in the main fracture is given by m1, and the pseudo-gas pressure in the inner zone is given by m2, in MPa. 2 / cp, K Fj Let the permeability of the j-th main fracture be (). F Represents a crack system.

[0134] The control conditions for the inner and outer boundaries are:

[0135]

[0136] Among them, T sc is the gas temperature under standard conditions, and h is the thickness.

[0137] The initial conditions are:

[0138] m| t＝0 =m i (twenty one)

[0139] The production condition equations are as follows:

[0140] Considering that horizontal wells produce at a constant rate, the production condition equation is obtained:

[0141]

[0142] Where, q wj q is the flow rate under the j-th main fracture. sc This is the production rate of a fractured horizontal well under standard conditions, in cubic meters (m³). 3 / d.

[0143] S202. Based on the production conditions of the target tight reservoir and the well test model of the target tight reservoir, calculate and obtain the calculated production data.

[0144] More specifically, the production conditions of the target tight reservoir are substituted into the well test model of the target tight reservoir to calculate the bottom hole pressure of the fractured horizontal well in the target tight reservoir. Then, the calculated production data is obtained based on the bottom hole pressure of the fractured horizontal well in the target tight reservoir. The production conditions include the initial composition of the target tight reservoir, and the calculated production data includes the fitted gas production, the fitted cumulative gas production, the fitted pressure, and the fitted pressure derivative.

[0145] For example, when calculating the bottom hole pressure of a horizontal well in a target tight reservoir fractured, to facilitate the solution of the equation, dimensionless quantities are first defined. The model is then simplified using dimensionless variables to obtain a dimensionless mathematical model, which is then used to solve the problem.

[0146] Dimensionless quantities are defined as follows:

[0147] The dimensionless distance is:

[0148]

[0149] Where, r m R is the original reservoir radius; m It is the wellbore radius; r mD x is the dimensionless radial distance; w It is the horizontal distance from the wellhead; x wD ω is the dimensionless distance of the wellhead in the horizontal direction; F The main crack width, in meters (m); ω FD y is the width of the dimensionless principal crack; F The main crack is half its length; x D yD These are dimensionless wellhead coordinates.

[0150] Dimensionless time and flow are respectively:

[0151]

[0152]

[0153] Where q is the underground production, q sc This is the surface yield of tight gas under standard conditions, in cubic meters (m³). 3 / d, q D It is dimensionless output, where t is time, in hours (h). D It is dimensionless time, μ is crude oil viscosity in mPa·s, and φ is porosity in %.

[0154] Dimensionless pressure:

[0155]

[0156]

[0157] Where, p sc This represents the actual pressure of the gas under standard conditions.

[0158] The conductivity of the dimensionless fracture and the conductivity of the inner zone are as follows:

[0159]

[0160] Among them, C FD R is a dimensionless quantity representing the conductivity of the main fracture. CD K is a dimensionless quantity representing the conductivity of the fracturing zone. F ω F For traffic diversion capability, y F Main crack half length, x e This represents the size of the horizontal boundary.

[0161] The dimensionless crack diffusion ratio and the outer zone diffusion ratio are as follows:

[0162]

[0163] Among them, κ FD κ is a dimensionless quantity representing the diffusion ratio of the main crack. 2D is a dimensionless quantity representing the diffusion ratio in the outer region.

[0164] The dimensionless stress sensitivity coefficient and the supply resistance coefficient are as follows:

[0165]

[0166] Where, αD γ is the dimensionless quantity of the corrected stress sensitivity coefficient, and β is the stress sensitivity coefficient. D To replenish the dimensionless quantity of the drag coefficient, y eD is a dimensionless quantity of the vertical boundary, and ()3 is the original region.

[0167] The dimensionless mathematical model is as follows:

[0168] The dimensionless mathematical model of the outer region is obtained by transforming according to formula (10) as follows:

[0169]

[0170] Among them, y FDj Let be the dimensionless quantity of the half-length of the j-th main crack.

[0171] The dimensionless mathematical model of the inner region is obtained by transforming according to formula (13) as follows:

[0172]

[0173] Where, m 1D For the dimensionless pressure in the inner region, m 2D The pressure is dimensionally unpredictable in the outer regions.

[0174] The dimensionless mathematical model of the main fracture zone is transformed according to formula (19) as follows:

[0175]

[0176] Where, m FD The dimensionless quantity of the main fracture pressure, q wDj Let k be the dimensionless flow rate at the j-th crack node. FDj Let be a dimensionless quantity representing the diffusion ratio of the j-th main crack.

[0177] Considering the nonlinearity of the equations caused by stress sensitivity, the dimensionless well test mathematical model is linearized using the Pedrosa perturbation transform method. The Pedrosa perturbation transform method is a linearization approach, and the introduced perturbation transform equation is as follows:

[0178]

[0179] Where, m D ξ is a dimensionless intermediate variable. D This is the perturbation transformation function.

[0180] Substituting formula (33) into the dimensionless well test mathematical model, the linearized well test mathematical model can be obtained by solving the zero-order equation. Then, the linearized well test mathematical model is solved using the Laplace transform method, and the bottom hole pressure can be obtained by solving the model simultaneously:

[0181]

[0182] Where, m wD The simulated pressure of the gas at the bottom of the well is the bottom pressure. Let be the dimensionless flow rate of the j-th crack in Laplace space, and s be a Laplace space variable.

[0183] in,

[0184]

[0185] Using the superposition principle formula proposed by Van Everdingen et al., and considering the skin effect and wellbore storage effect, the wellbore pressure expression can be further obtained, and the bottom hole pressure in the real space can be obtained.

[0186] Subsequently, based on known parameters of the target tight reservoir and actual historical production information, historical data of production dynamics is used for historical fitting. By introducing a production-standardized pseudo-pressure-time relationship, the bottom hole pressure is converted into a production-time relationship. Based on this relationship, calculated production data is generated, transforming variable-production conditions into constant-production conditions. Specifically, the fitted gas production and fitted cumulative gas production are obtained from the calculated production data through historical fitting, and the fitted pressure and its derivative are obtained by introducing a production-standardized pseudo-pressure-time relationship. The calculation process for the calculated production data is as follows:

[0187]

[0188]

[0189]

[0190] Where RNP represents pressure, RNP′ represents the pressure derivative, and m w For the simulated pressure of the gas at the bottom of the well, t e For the time to reach material equilibrium, q w This refers to the production output of gas wells.

[0191] Then, by dimensionless transformation, we get:

[0192]

[0193]

[0194]

[0195] Among them, RNP D RNP' represents dimensionless pressure. D q represents the dimensionless pressure derivative.wD For dimensionless production in real space, m wD For the dimensionless bottom-hole gas pseudo-pressure in real space, t eD The time for dimensionless mass equilibrium.

[0196] S203. Based on historical production data and calculated production data, determine the model parameters of the well test model for the target tight reservoir.

[0197] More specifically, based on the curves generated from historical production data and calculated production data, the model parameters are continuously adjusted to make the calculated production data curves closer to the historical production data curves. The closer they are, the higher the similarity between the model and the actual tight reservoir. Among them, historical production data includes gas production, cumulative gas production, pressure, and pressure derivative, which are obtained through formulas (36)-(41) similar to those used to obtain calculated production data. Calculated production data includes fitted gas production, fitted cumulative gas production, fitted pressure, and fitted pressure derivative.

[0198] S204. Extract crack parameters from model parameters.

[0199] More specifically, fracture parameters are extracted from the model parameters. These fracture parameters include fracture half-length and permeability.

[0200] In the method for determining the final recoverable reserves of fractured horizontal wells in tight reservoirs provided in this application embodiment, a target tight reservoir model considering heterogeneity and stress sensitivity is established. Based on the target tight reservoir model, historical production data and calculated production data are obtained through historical fitting and the introduction of a production-standardized pseudo-pressure-time relationship. Dynamic parameter adjustments are then performed based on the historical and calculated production data to obtain model parameters that more closely approximate the actual tight reservoir. By constructing a well test model that more closely resembles the actual tight reservoir and determining the fracture parameters of the target tight reservoir through dynamic parameter adjustments, the accuracy of the well test model and model parameters is improved, thereby reducing the final prediction error.

[0201] Figure 5 A flowchart illustrating a method for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir, as provided in this application embodiment, is shown below. Figure 5 As shown, an application analysis was conducted on five typical tight sandstone gas wells in the Sulige gas field, including the following steps:

[0202] S501, Collect data.

[0203] More specifically, based on actual data and geological conditions of the Sulige Gas Field, and referencing data from adjacent wells, data from wells such as Su36-8-15H2 are compiled. The Sulige Gas Field is the location of typical tight sandstone gas wells studied, with an exploration area of ​​approximately 36,000 square kilometers and natural gas reserves of approximately 1.1 × 10⁻⁶. 12 m3 The Sulige Gas Field is not only the largest natural gas field in my country at present, but also my country's first large gas field with world-class reserves. The Upper Paleozoic strata of the Sulige Gas Field, from bottom to top, include the Carboniferous Benxi Formation, the Permian Shanxi Formation, the Lower Shihezi Formation, the Upper Shihezi Formation, and the Shiqianfeng Formation. The reservoir lithology is mainly grayish-white medium to coarse-grained, argillaceous coarse to medium-grained lithic quartz sandstone, and grayish-white coarse-grained, coarse to medium-grained lithic sandstone. The Sulige tight gas reservoir is a nearly north-south trending banded sandstone body, forming a large lithological trap or stratigraphic-lithological trap. The gas reservoir is a large-area, complex, and continuous area, with sand bodies distributed in bands. The physical properties of Sulige vary considerably, deteriorating sharply at the periphery. It is basically a large gas reservoir with low porosity, low permeability, and low abundance.

[0204] S502. Establish a well test model.

[0205] More specifically, a well test model is established based on the collected geological data and taking into account the formation heterogeneity, stress sensitivity, and weak boundary recharge effect.

[0206] S503. Based on the well test model and production conditions, calculate the production data.

[0207] More specifically, based on the established well test model and collected production condition data, historical data on production dynamics are used for historical fitting to obtain the relationship between gas production and cumulative gas production and time, such as... Figure 6 As shown, the curves depicting the relationship between gas production and cumulative gas production and time are included, as well as the curves showing the relationship between fitted gas production and fitted cumulative gas production and time. By introducing the relationship between production-standardized pseudo-pressure and time, the relationship between production-standardized pseudo-pressure and mass balance time is obtained, as shown below. Figure 7 As shown, the curves include the relationship between actual pressure and the derivative of actual pressure and the mass equilibrium time, as well as the curves between fitted pressure and the derivative of fitted pressure and the mass equilibrium time.

[0208] S504. Based on historical production data and calculated production data, determine the model parameters of the well test model.

[0209] More specifically, historical production data and the correlation curves of calculated production data, such as... Figure 6 and Figure 7 As shown, by continuously adjusting the model parameters in the well test model, the correlation curves in the historical production data and the calculated production data gradually approach each other, thereby determining the model parameters of the well test model.

[0210] S505. Extract crack parameters from model parameters.

[0211] More specifically, fracture parameters are extracted from the model parameters. The tight reservoir parameters and fracture parameters are shown in the table below:

[0212] Table 3. Parameter fitting results for well Su36-8-15H2

[0213] well name Su36-8-15H2 well <![CDATA[Effective horizontal section length x0 (m)]]> 316 Effective reservoir thickness h (m) 6.5 <![CDATA[Increased production reservoir width y0 (m)]]> 140 Permeability k(md) 0.06 Crack spacing L (m) 45.14

[0214] Figure 8 A schematic diagram of a horizontal well planar fractured in a tight reservoir provided in this application embodiment, as shown below. Figure 8 As shown, the width y0 of the production-enhancing reservoir is twice the half-length of the fracture.

[0215] S506. Calculate the linear flow parameters.

[0216] More specifically, the linear flow parameters are calculated based on the extracted crack parameters and the first formula, and the results are as follows:

[0217] S507. Calculate the final recoverable reserves.

[0218] More specifically, based on the calculated linear flow parameters and the abandonment pressure of the tight reservoir, software simulation is used to predict the production capacity of fractured horizontal wells in the tight reservoir under the abandonment pressure, thereby obtaining the predicted final recoverable reserves. The results are as follows: Figure 9 As shown, the result is 4.11672 × 10 7 m 3 .

[0219] S508, Method Validation.

[0220] More specifically, to verify the accuracy and reliability of this method, several typical gas wells with long-term production or no production capacity in the Sulige gas field study area were selected for verification. This application selected four actual wells for example verification, and the process of predicting the final recoverable reserves using this method is the same as described above. The final recoverable reserves predicted from the actual wells in the fractured horizontal wells of the tight reservoir were compared with the actual final recoverable reserves of the fractured horizontal wells in the tight reservoir, and error analysis was conducted. The summary of well test parameter interpretation results and error comparison analysis are shown in Table 4.

[0221] Table 4 Summary of Errors in Final Recoverable Reserves

[0222]

[0223] The results show that the average error is less than 5%, which is within the allowable range. The method for predicting the final recoverable reserves of fractured horizontal wells in tight reservoirs proposed in this application can predict the final recoverable reserves of a single tight gas well relatively well.

[0224] In the method for determining the final recoverable reserves of fractured horizontal wells in tight reservoirs provided in this application embodiment, a well test model that more closely resembles the actual tight reservoir is constructed by considering the complex seepage environment of the tight reservoir. Model parameters are determined based on this model, and fracture parameters that more closely resemble the actual tight reservoir are extracted. Finally, the final recoverable reserves are calculated based on the fracture parameters and relevant reservoir parameters. The improved well test model is applicable to tight sandstone oil and gas reservoirs, and the accuracy of the model is improved through parameter inversion, thereby further reducing prediction errors. Verification analysis also proves the reliability of the method.

[0225] This application provides a device for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir. A schematic diagram of the device is shown below. Figure 10 As shown, the well test simulation device 1000 includes:

[0226] The acquisition module 1001 is used to acquire fracture parameters of the target tight reservoir fractured horizontal well, wherein the fracture parameters include fracture half length and permeability;

[0227] Processing module 1002 is used to calculate the linear flow parameters of the fractured horizontal well in the target tight reservoir based on the fracture parameters of the fractured horizontal well in the target tight reservoir; and

[0228] Based on the linear flow parameters of the fractured horizontal well in the target tight reservoir, the final recoverable reserves of the fractured horizontal well in the tight reservoir are calculated.

[0229] Module 1001 is used specifically for:

[0230] Obtain historical production data and production conditions of the target tight reservoir, and construct a well test model of the target tight reservoir;

[0231] Based on the production conditions of the target tight reservoir and the well test model of the target tight reservoir, calculated production data are obtained.

[0232] Based on historical production data and calculated production data, determine the model parameters of the well test model for the target tight reservoir;

[0233] Crack parameters are extracted from the model parameters.

[0234] Processing module 1002 is specifically used for:

[0235] The linear flow parameters of the fractured horizontal well in the target tight reservoir are calculated according to the first formula, where the first formula is:

[0236]

[0237] Where LFP is the linear flow parameter, x0 is the length of the horizontal well fractured in the target tight reservoir, y0 is twice the fracture half-length, L is the fracture spacing, h is the thickness of the target tight reservoir, and k is the average permeability.

[0238] Processing module 1002 is specifically used for:

[0239] Substitute the production conditions of the target tight reservoir into the well test model of the target tight reservoir to calculate the bottom hole pressure of the fractured horizontal well in the target tight reservoir;

[0240] Calculated production data is obtained by calculating the bottom hole pressure of a horizontal well fracturing the target tight reservoir.

[0241] like Figure 11 As shown, one embodiment of this application provides an electronic device 1100, which includes a memory 1101 and a processor 1102.

[0242] The memory 1101 is used to store computer instructions that can be executed by the processor;

[0243] When executing computer instructions, processor 1102 implements each step of the method for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir as described in the above embodiments. For details, please refer to the relevant descriptions in the embodiments of the method for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir.

[0244] Optionally, the memory 1101 can be either independent or integrated with the processor 1102. When the memory 1101 is configured independently, the electronic device also includes a bus for connecting the memory 1101 and the processor 1102.

[0245] This application also provides a computer-readable storage medium storing computer instructions. When a processor executes the computer instructions, it implements each step in the method for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir as described above.

[0246] This application also provides a computer program product, including computer instructions, which, when executed by a processor, implement each step in the method for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir as described above.

[0247] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this application are indicated by the following claims.

[0248] It should be understood that this application is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. A method for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir, characterized in that, include: Obtain fracture parameters of a horizontally fractured well in a target tight reservoir, wherein the fracture parameters include fracture half-length and permeability; Based on the fracture parameters of the fractured horizontal well in the target tight reservoir, calculate the linear flow parameters of the fractured horizontal well in the target tight reservoir. Based on the linear flow parameters of the fractured horizontal well in the target tight reservoir, calculate the final recoverable reserves of the fractured horizontal well in the tight reservoir. Specifically, obtaining fracture parameters for horizontal wells fractured in the target tight reservoir includes: Obtain the production history data and production conditions of the target tight reservoir, and construct a well test model of the target tight reservoir; Based on the production conditions of the target tight reservoir and the well test model of the target tight reservoir, calculated production data are obtained; Based on the production history data and the calculated production data, determine the model parameters of the well test model for the target tight reservoir; Extract the crack parameters from the model parameters; Based on the fracture parameters of the fractured horizontal well in the target tight reservoir, the linear flow parameters of the fractured horizontal well in the target tight reservoir are calculated, specifically including: The linear flow parameters of the fractured horizontal well in the target tight reservoir are calculated according to the first formula, wherein the first formula is: Wherein, LFP is the linear flow parameter, x0 is the length of the horizontal well fractured in the target tight reservoir, y0 is twice the fracture half-length, L is the fracture spacing, h is the thickness of the target tight reservoir, and k is the average permeability.

2. The determination method according to claim 1, characterized in that, Based on the production conditions of the target tight reservoir and the well test model of the target tight reservoir, calculated production data is obtained, specifically including: Substitute the production conditions of the target tight reservoir into the well test model of the target tight reservoir to calculate the bottom hole pressure of the fractured horizontal well of the target tight reservoir; The calculated production data is obtained based on the bottom hole pressure of the horizontal well fractured in the target tight reservoir.

3. A device for determining the final recoverable reserves of a fractured horizontal well in a tight reservoir, characterized in that, include: The acquisition module is used to acquire fracture parameters of a horizontal well in a target tight reservoir fractured, wherein the fracture parameters include fracture half-length and permeability; The processing module is used to calculate the linear flow parameters of the fractured horizontal well in the target tight reservoir based on the fracture parameters of the fractured horizontal well in the target tight reservoir; and Based on the linear flow parameters of the fractured horizontal well in the target tight reservoir, calculate the final recoverable reserves of the fractured horizontal well in the tight reservoir. The acquisition module is specifically used for: Obtain the production history data and production conditions of the target tight reservoir, and construct a well test model of the target tight reservoir; Based on the production conditions of the target tight reservoir and the well test model of the target tight reservoir, calculated production data are obtained; Based on the production history data and the calculated production data, determine the model parameters of the well test model for the target tight reservoir; Extract the crack parameters from the model parameters; The processing module is specifically used for: The linear flow parameters of the fractured horizontal well in the target tight reservoir are calculated according to the first formula, wherein the first formula is: Wherein, LFP is the linear flow parameter, x0 is the length of the horizontal well fractured in the target tight reservoir, y0 is twice the fracture half-length, L is the fracture spacing, h is the thickness of the target tight reservoir, and k is the average permeability.

4. The determining device according to claim 3, characterized in that, The processing module is specifically used for: Substitute the production conditions of the target tight reservoir into the well test model of the target tight reservoir to calculate the bottom hole pressure of the fractured horizontal well of the target tight reservoir; The calculated production data is obtained based on the bottom hole pressure of the horizontal well fractured in the target tight reservoir.

5. An electronic device, characterized in that, include: A processor, and a memory communicatively connected to the processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory to implement the determination method as described in any one of claims 1 to 2.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the determination method as claimed in any one of claims 1 to 2.

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