Method for analyzing pressure of water injection well considering influence of fracture induced by water injection

Abstract

The application provides a water injection well pressure analysis method considering the influence of fracture induced by pressure drive water injection, which comprises the following steps: step 1, establishing a water injection well pressure analysis model considering the influence of fracture induced by pressure drive water injection; step 2, solving the water injection well pressure analysis model considering the influence of fracture induced by pressure drive water injection; step 3, obtaining a water injection well double logarithmic pressure analysis curve through analysis, and judging different flow stages of the reservoir in the fracturing process according to the curve; and step 4, analyzing the bottom hole pressure response characteristics of the pressure drive water injection well, and applying the characteristics to an actual well to verify the accuracy of the established model. The water injection well pressure analysis method considering the influence of fracture induced by pressure drive water injection establishes a water injection well pressure analysis model considering the dynamic expansion of the fracture, has certain technical difficulty, and can determine the flow stage of fluid in the reservoir at different production moments.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of pressure drive effect evaluation and reservoir parameter inversion, and particularly relates to a water injection well pressure analysis method considering the influence of pressure drive water injection induced fractures. BACKGROUND

[0002] Pressure drive water injection well bottom hole pressure analysis is of great significance to pressure drive effect evaluation and reservoir parameter inversion. Pressure drive water injection can produce dynamic fractures, and the production of dynamic fractures brings great challenges to the analysis of the bottom hole pressure of pressure drive water injection wells. Current research on dynamic fractures of water injection wells can be divided into two parts: ① research on the fracture propagation characteristics of water injection wells and influencing factors; ② research on the influence of water injection well dynamic fractures on reservoir development. These existing researches on dynamic fractures of water injection wells do not involve the influence of water injection well dynamic fractures on the bottom hole pressure of water injection wells, while the bottom hole pressure of water injection wells and its derivative change law reflect the dynamic expansion of fractures and the flow characteristics of fluid, which have wide research value.

[0003] In the Chinese patent application with the application number: CN201810765445.7, a method for simulating the dynamic extension of water injection well water pressure driven fractures is involved, which includes the following steps: obtaining the reservoir geological characteristic parameters of the existing fracture target water injection well according to the reservoir geological research; establishing a water injection well water pressure driven hydraulic fracture propagation model by comprehensively using the Darcy filtration model, the continuity equation, the material balance equation and the initial conditions; establishing a fluid and rock pore elastic deformation relationship, i.e. a fluid-solid coupling model, by using the oil-water two-phase seepage model based on the seepage mechanics theory to take the fluid amount filtered into the formation as a source term, and combining the boundary conditions established by the fluid pressure in the fracture, calculating the formation pore pressure and obtaining the strain and porosity changes caused by fluid pressure changes; then obtaining the fracture extension dynamics after fluid-solid coupling, and taking the obtained new parameters as the initial conditions for repetition, and finally obtaining the fracture extension dynamics. The invention can predict the dynamic extension of fractures in water injection wells and the dynamic changes of parameters in the reservoir according to the construction and geological parameters

[0004] In the Chinese patent application No. CN202111400752.3, a natural fracture reservoir multi-stage fracturing horizontal well interference test analysis method is disclosed. A basic physical model is established according to the injection-production well arrangement, fracturing operation parameters and reservoir basic physical property information. Based on the basic physical model, the dimensionless formation pressure drop in the Laplace domain of the hydraulic fracture, the dimensionless formation pressure drop in the Laplace domain caused by the horizontal wellbore with limited conductivity, and the dimensionless formation pressure drop in the Laplace domain caused by the injection well are calculated based on the double-porosity medium Laplace domain source function. The Laplace domain dimensionless pressure solution considering well-reservoir effect and skin factor is obtained, and the Stehfest numerical inversion is performed to obtain the real space well bottom dimensionless pressure solution. The relationship between the well bottom dimensionless pressure, pressure derivative and dimensionless time is plotted, and the analysis is completed. The invention considers that the fracture and the horizontal wellbore have limited conductivity, the method is simple, the required physical parameters are measurable, and the practicability is good.

[0005] In the Chinese patent application No. CN201710720001.7, a pressure monitoring method for determining the water direction of multi-stage fracturing horizontal well is disclosed. The method comprises the following steps: monitoring the bottom hole pressure change data of multi-stage fracturing horizontal well; considering the change of the working system of surrounding injection wells, designing the interference test between injection wells and multi-stage fracturing horizontal wells; establishing the bottom hole pressure analysis chart of multi-stage fracturing horizontal well under the interference of injection wells; fitting and analyzing the measured bottom hole pressure data to obtain the fracture and reservoir parameters under different injection rates of injection wells; determining the interwell connectivity by comparing and analyzing the parameters obtained by fitting under different injection well working systems, and determining the water direction. The method is simple, easy to understand and operate. Since the change of the injection rate of the injection well is considered, the water direction of the multi-stage fracturing horizontal well can be accurately determined. The pressure monitoring and interpretation of the multi-stage fracturing horizontal well using this method is more in line with the actual situation, and the accuracy of pressure monitoring and interpretation is improved.

[0006] The above prior art has great difference from the present application and cannot solve the technical problems we want to solve. Therefore, we have invented a new injection well pressure analysis method considering the influence of pressure drive water injection induced fracture. SUMMARY

[0007] The purpose of the present application is to provide an injection well pressure analysis method considering the influence of pressure drive water injection induced fracture, which provides strong support for the development of low permeability reservoirs developed by pressure drive water injection.

[0008] The purpose of the present application can be achieved by the following technical measures: the injection well pressure analysis method considering the influence of pressure drive water injection induced fracture, which comprises:

[0009] Step 1, a pressure analysis model of a water injection well considering the influence of fractures induced by pressure drive water injection is established;

[0010] Step 2, the pressure analysis model of the water injection well considering the influence of fractures induced by pressure drive water injection is solved;

[0011] Step 3, a double logarithmic pressure analysis curve of the water injection well is analyzed, and different flow stages of the reservoir in the fracturing process are judged according to the curve;

[0012] Step 4, the bottom hole pressure response characteristics of the pressure drive water injection well are analyzed, and are applied to an actual well to verify the accuracy of the established model.

[0013] The object of the application can also be achieved through the following technical measures:

[0014] In step 1, a pressure drive water injection oil-water seepage mathematical model and a fracture expansion model during pressure drive water injection are established, and the two models are coupled to form a pressure analysis model of a water injection well considering the influence of fractures induced by pressure drive water injection.

[0015] In step 1, before the pressure analysis model of the pressure drive water injection well is established, the following assumptions are given: (1) two-dimensional plane flow; (2) only oil and water two-phase seepage exists in the reservoir, and the oil and water are not mutually soluble and each conforms to Darcy's law; (3) the rock fluid is compressible;

[0016] (4) the heterogeneity and anisotropy of the rock are considered; (5) the effect of gravity is ignored; (6) the fracture expansion is a composite linear expansion model.

[0017] In step 1, the oil and water two-phase flow control equations are respectively:

[0018]

[0019]

[0020] In the formula, k is the absolute permeability, mD; K r is the relative permeability, decimal; μ is the viscosity, mpa.s; ρ is the density, kg / m 3 ; φ is the porosity, decimal; s is the saturation, decimal; p is the pressure of any point at any time, MPa; G is the starting pressure gradient, MPa / m; subscript: o is the oil phase, and w is the water phase.

[0021] In step 1, the auxiliary equation is:

[0022] s o +s w = 1 (3)

[0023] The initial condition is:

[0024]

[0025] where s o is oil saturation, fraction; s w is water saturation, fraction; p oi is initial formation pressure, MPa; s wi is initial water saturation, fraction.

[0026] In step 1, the inner and outer boundary conditions are:

[0027] Q pro = Q opro + Q wpro = constant (5)

[0028] Q inj = constant (6)

[0029]

[0030] where Q pro is liquid production rate, m 3 / d; Q opro is oil production rate, m 3 / d; Q wpro is water production rate, m 3 / d; Q inj is injection rate, m 3 / d.

[0031] In step 1, the well treatment conditions of injection well and production well, i.e. constant injection rate of injection well and constant production rate of production well are:

[0032]

[0033]

[0034] where p wf is bottom hole pressure of production well, MPa; p iwf is bottom hole pressure of injection well, MPa.

[0035] In step 1, equations (1)-(9) are the mathematical model of water flooding with pressure drive, based on the assumption (6) of composite linear propagation model of fracture propagation, the modified PKN model is used to consider the effect of fracture propagation of fracturing fluid loss, to achieve the description of fracture propagation of water flooding with pressure drive; according to the law of conservation, the injected fluid is equal to the sum of the fluid loss and the fluid in the fracture, so there is the total fracture volume expression:

[0036] V f = q x t (1-Ψ) (10)

[0037] where V f is total fracture volume, m3 ; q x is injection rate, m 3 / d; t is water injection time, d; Ψ is filtration ratio, decimal.

[0038] In step 1, equation (10) is used to modify the fracture length and fracture width calculation formula of PKN model to obtain the fracture length and width formula considering the influence of filtration:

[0039]

[0040]

[0041] In the formula, W(0,t) is the fracture tip width, m; v is Poisson's ratio, decimal; G T is shear modulus, MPa; H is fracture height, m;

[0042] When water injection is carried out by pressure drive, there is no proppant in the fracture, and the fracture space is the whole effective flow space, in which the flow follows the compound cubic law, and combined with Darcy formula, the fracture permeability characterization formula and the fracture conductivity characterization formula of pressure drive water injection can be obtained:

[0043]

[0044]

[0045] In the formula, K wzcf0 is the initial fracture permeability, mD; W(0,t) is the width of the fracture at any time, m; KW f is the fracture conductivity, mD·m.

[0046] In step 1, equations (11) and (12) are the fracture length and width formulas considering the influence of filtration, and equation (14) is the pressure drive fracture conductivity characterization formula; combined with the mathematical model of oil-water seepage of pressure drive water injection, the pressure analysis model of pressure drive water injection well can be formed.

[0047] In step 2, according to the given pressure analysis model of pressure drive water injection well, the pressure analysis model of pressure drive water injection well is discretized, and the finite difference method is used to solve.

[0048] In step 2, in the seepage differential equation of oil and water phases, the unknown quantities are p o , p w , s o , s w , and the independent variables are (x,y,t); the difference equations of oil and water phases can be obtained by expanding the difference of the seepage differential equation of oil and water phases:

[0049]

[0050]

[0051] wherein: β o = p o φs o (C p + C o ), β w = p w φs w (C p + C w ), V i,j = Δx i Δy j h, Q oi,j = q oi,j · Δx i Δy j h, Q wi,j = q wi,j · Δx i Δy j h, V pi,j = φ i,j · Δx i Δy j h,

[0052] wherein: V i,j is the volume of the grid (i,j), m 3 ; Q oi,j , Q wi,j is the production or injection of the grid (i,j), m 3 / d; V pi,j is the pore volume of the grid (i,j), m 3 ; T ox , T wx , T oy , T wy are the conductivities of the water and oil phases; h is the unit grid thickness, m; φ is the porosity, decimal; C p is the rock compressibility, MPa -1 ; C o is the oil compressibility, MPa -1 ; C w is the water compressibility, MPa -1 ; t is the model simulation time, d.

[0053] In step 2, the pressure is implicitly solved using the IMPES method, by s o = 1 - s w , and letting A = p o / p wThen equation (15) + equation (16) x A can eliminate the saturation term of the above equation group, and the following equation is obtained:

[0054]

[0055] Where:

[0056]

[0057] At each node, equation (17) is used to form equations, and a five-diagonal equation group is obtained. The pressure can be solved by solving the equation, and the water saturation can be explicitly solved by substituting the pressure obtained above into the water phase difference equation (16). The fracture length and width can be obtained by using equations (11) and (12), and the fracture conductivity can be obtained by combining equation (14). Finally, the fracture length, conductivity, pressure and saturation distribution are updated, and the simulation calculation at the next time is carried out, so as to realize the solution of the injection well pressure analysis model of pressure drive.

[0058] In step 3, the bottom hole pressure of the injection well obtained by solving the injection well pressure analysis model considering the influence of the fracture induced by pressure drive is dimensionless, and is fitted with the actual reservoir data to obtain the double logarithmic pressure analysis curve of the injection well. According to the curve, different flow stages of the reservoir in the fracturing process are judged.

[0059] In step 3, the obtained bottom hole pressure of the injection well and the pressure drive time are substituted into formula (19) and (20) to become dimensionless pressure and time:

[0060]

[0061]

[0062] In the formula, k is the permeability, μm 2 ; h is the thickness of the oil layer, m; q is the surface flow rate, m 3 / d; B is the volume coefficient, m 3 / m 3 ; p i is the original formation pressure, MPa; p wf is the bottom hole flowing pressure, MPa; μ is the viscosity, mpa·s; t is the time, h; φ is the porosity, decimal; r w is the wellbore radius, m.

[0063] In step 3, the dimensionless pressure, dimensionless time and actual injection well data of the reservoir are used to draw the double logarithmic pressure analysis curve of the injection well and analyze and divide different flow stages.

[0064] In step 4, the actual bottom hole pressure data of the injection well and the pressure drive time are substituted into formula (21) and (22) to become dimensionless pressure and time:

[0065]

[0066]

[0067] In the formula, k is the permeability, in μm 2 h is the oil layer thickness, in meters; q is the surface flow rate, in cubic meters per second. 3 / d; B is the volume coefficient, m 3 / m 3 ;p i The original formation pressure is given in MPa; p wf φ is the bottom hole flow pressure, MPa; μ is the viscosity, MPa·s; t is the time, h; φ is the porosity, decimal; r w Let be the radius of the wellbore, in meters (m).

[0068] In step 4, by continuously modifying the adjustable parameters in the water injection well pressure analysis model that considers the influence of water injection-induced fractures, and fitting them with the actual water injection well data, the water injection well pressure analysis model that best fits the actual water injection well data is finally obtained. The formation and fracture physical properties in this model are the formation and fracture physical properties that best fit the actual water injection well data.

[0069] This invention presents a pressure analysis method for water injection wells that considers the influence of fractures induced by pressure-driven water injection. Starting from the perspective of fracture propagation, it utilizes seepage mechanics theory and numerical simulation methods. Based on factors such as fracture propagation, fracture morphology, and fluid loss from injected fluid, it establishes an oil-water two-phase seepage model, corrects the linear fracture propagation model, and couples them to form a pressure analysis model for pressure-driven water injection wells, providing a solution method. Secondly, it analyzes the bottom-hole pressure response characteristics of pressure-driven water injection wells and applies them to actual wells to verify the accuracy of the established model. This patent provides strong support for the development of low-permeability reservoirs using pressure-driven water injection. This invention establishes a pressure analysis model for water injection wells that considers dynamic fracture propagation using seepage mechanics theory and numerical calculation methods, which has certain technical difficulties and can determine the fluid flow stages in the reservoir at different production times. Attached Figure Description

[0070] Figure 1 This is a solution block diagram for the pressure analysis model of a water injection well that considers the influence of pressure-driven water injection-induced fractures according to the present invention.

[0071] Figure 2 This is a schematic diagram of the injection-production well network in a specific embodiment of the present invention;

[0072] Figure 3 This is a double logarithmic pressure analysis curve of a pressure-driven water injection well in a specific embodiment of the present invention;

[0073] Figure 4A double logarithmic pressure analysis curve of a water injection well in a specific embodiment of the present application. DETAILED DESCRIPTION

[0074] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0075] It is also important to note that the terms used herein are not intended to limit the exemplary embodiments to the specific embodiments which are described herein. Rather, it is contemplated that the exemplary embodiments are intended to encompass all possible embodiments which are within the scope of the present application. As used herein, unless otherwise indicated, the use of the singular includes the plural and back again; and, moreover, it is also understood that when an element such as "comprising" is used, that it is intended to include many alternatives, equivalents, and / or modifications thereof.

[0076] The water injection well pressure analysis method of the present application which considers the effect of pressure drive water injection induced fractures includes the following steps:

[0077] Step one, establish a pressure drive water injection oil-water seepage mathematical model and a fracture propagation model during pressure drive water injection, and couple the two models to form a water injection well pressure analysis model which considers the effect of pressure drive water injection induced fractures;

[0078] Step two, solve the water injection well pressure analysis model which considers the effect of pressure drive water injection induced fractures;

[0079] Step three, non-dimensionalize the bottom hole pressure of the pressure drive well which is solved by the water injection well pressure analysis model which considers the effect of pressure drive water injection induced fractures, and fit it with actual reservoir data to obtain a double logarithmic pressure analysis curve of the water injection well, and determine different flow stages of the reservoir during the fracturing process according to the curve.

[0080] Step four, analyze the bottom hole pressure response characteristics of the pressure drive water injection well, and apply it to actual wells to verify the accuracy of the established model.

[0081] The following are several specific embodiments of the present application

[0082] Embodiment 1

[0083] In a specific embodiment 1 of the present application, the water injection well pressure analysis method which considers the effect of pressure drive water injection induced fractures includes the following steps:

[0084] Step one, before establishing the pressure analysis model of the water injection well, the following assumptions are given: (1) two-dimensional flow; (2) only oil and water two-phase flow exists in the reservoir, oil and water are not soluble and each conforms to Darcy's law; (3) rock fluid is compressible; (4) the heterogeneity and anisotropy of rock are considered; (5) the effect of gravity is ignored; (6) the composite linear expansion model of fracture expansion. The specific process of establishing the mathematical model of oil and water seepage and the fracture expansion model during the water injection is as follows:

[0085] The control equations of oil and water two-phase flow are respectively:

[0086]

[0087]

[0088] In the formula, k is the absolute permeability, mD; K r is the relative permeability, decimal; μ is the viscosity, mpa·s; ρ is the density, kg / m 3 ; φ is the porosity, decimal; s is the saturation, decimal; p is the pressure of any point at any time, MPa; G is the starting pressure gradient, MPa / m; subscript: o is the oil phase, w is the water phase.

[0089] The auxiliary equation is:

[0090] s o +s w =1 (3)

[0091] The initial condition is:

[0092]

[0093] In the formula, s o is the oil saturation, decimal; s w is the water saturation, decimal; p oi is the original formation pressure MPa; s wi is the initial water saturation, decimal.

[0094] The inner and outer boundary conditions are:

[0095] Q pro =Q opro +Q wpro =constant (5)

[0096] Q inj =constant (6)

[0097]

[0098] In the formula, Q pro is the liquid production, m 3 / d; Qopro is the oil production, m 3 / d; Q wpro is the water production, m 3 / d; Q inj is the water injection, m 3 / d.

[0099] The injection well and production well treatment conditions (the injection well injects at a constant flow rate and the production well produces at a constant flow rate):

[0100]

[0101]

[0102] wherein p wf is the bottom hole pressure of the production well, MPa; p iwf is the bottom hole pressure of the injection well, MPa.

[0103] The above equations (1)-(9) are mathematical models of the pressure drive water injection oil-water seepage. Based on the assumption (6) of the composite linear expansion model of the fracture expansion, a modified PKN model is used to consider the influence of the fracturing fluid loss on the fracture expansion, so as to realize the description of the fracture expansion of the pressure drive water injection. According to the conservation law, the injected fluid is equal to the sum of the fluid loss fluid and the fluid in the fracture, so there is a total fracture volume expression:

[0104] V f = q x t (1-Ψ) (10)

[0105] wherein V f is the total fracture volume, m 3 ; q x is the injection flow rate, m 3 / d; t is the water injection time, d; and Ψ is the fluid loss ratio, decimal.

[0106] The equation (10) is applied to the fracture length and fracture width calculation formula corresponding to the modified PKN model, so as to obtain the fracture length and width formula considering the influence of the fluid loss:

[0107]

[0108]

[0109] wherein W(0,t) is the fracture tip width, m; v is the Poisson's ratio, decimal; G T is the shear modulus, MPa; and H is the fracture height, m.

[0110] When the water injection is driven by pressure, there is no proppant in the fracture, and the fracture space is the whole effective flow space, in which the flow compound cubic law is applied. In combination with Darcy formula, the fracture permeability characterization formula and the fracture conductivity characterization formula of water injection driven by pressure can be obtained:

[0111]

[0112]

[0113] In the formula, K wzcf0 is the initial fracture permeability, mD; W(0, t) is the width of the fracture at any time, m; KW f is the fracture conductivity, mD·m.

[0114] Equations (11) and (12) are the fracture length and width formulas considering the influence of filtration, and equation (14) is the fracture conductivity characterization formula of water injection driven by pressure; in combination with the mathematical model of oil-water seepage of water injection driven by pressure, the pressure analysis model of the water injection well can be formed.

[0115] Step two, according to the given pressure analysis model of the water injection well, the pressure analysis model of the water injection well is discretized, and the finite difference method is used for solving. The specific steps are as follows:

[0116] In the oil-water two-phase seepage differential equation, the unknown quantities are p o , p w , s o , s w , and the independent variables are (x, y, t). The difference equations of the oil phase and the water phase can be obtained by expanding the difference of the oil phase and the water phase seepage differential equation as follows:

[0117]

[0118]

[0119] In the formula, β o = ρ o φs o (C p +C o ), β w = ρ w φs w (C p +C w ), V i,j = Δx i Δy j h, Q oi,j = q oi,j · Δx i Δy j h, Q wi,j = q wi,j• Δx i Δy j h, V pi,j = φ i,j • Δx i Δy j h,

[0120] wherein V i,j is the volume of the grid (i,j), m 3 ; Q oi,j , Q wi,j is the production or injection of the grid (i,j), m 3 / d; V pi,j is the pore volume of the grid (i,j), m 3 ; T ox , T wx , T oy , T wy are the conductivities of the water and oil phases; h is the unit grid thickness, m; φ is the porosity, decimal; Cp is the rock compressibility, MPa-1; Co is the oil phase compressibility, MPa-1; Cw is the water phase compressibility, MPa-1; t is the model simulation time, d.

[0121] The pressure is implicitly solved using the IMPES method, by s o = 1 - s w , and letting A = p o / p w , then equation (15) + equation (16) x A can eliminate the saturation term of the above equation group, and obtain:

[0122]

[0123] wherein:

[0124]

[0125] The equation is listed using equation (17) at each node, and a five-diagonal equation group is obtained, and the pressure is solved by solving the equation, and the pressure obtained above is substituted into the water phase difference equation (16), and the water saturation is explicitly solved; and equations (11) and (12) are used, and the fracture length and width are solved, and equation (14) is combined to solve the fracture conductivity; finally, the fracture length, conductivity, pressure and saturation distribution are updated, and the simulation calculation at the next time is carried out, so as to realize the solution of the pressure analysis model of the pressure drive injection well.

[0126] Step three, the dimensionless bottom hole pressure of the injection well obtained by solving the injection well pressure analysis model considering the effect of water injection induced fracture is fitted with the actual reservoir data to obtain the double logarithmic pressure analysis curve of the injection well, and the different flow stages of the reservoir in the fracturing process are determined according to the curve. The specific steps are as follows:

[0127] The dimensionless pressure and time of the bottom hole pressure of the water injection well obtained by solving the injection well pressure analysis model considering the effect of water injection induced fracture are fitted with the actual reservoir data to obtain the double logarithmic pressure analysis curve of the injection well, and the different flow stages of the reservoir in the fracturing process are determined according to the curve. The specific steps are as follows:

[0128]

[0129]

[0130] In the formula, k is the permeability, μm 2 ; h is the oil layer thickness, m; q is the ground flow, m 3 / d; B is the volume coefficient, m 3 / m 3 ; p i is the original formation pressure, MPa; p wf is the bottom hole flowing pressure, MPa; μ is the viscosity, mpa·s; t is the time, h; φ is the porosity, decimal; r w is the wellbore radius, m.

[0131] According to the dimensionless pressure, dimensionless time and actual reservoir injection well data, the double logarithmic pressure analysis curve of the injection well is drawn and the different flow stages are analyzed and divided.

[0132] Step four, analyze the response characteristics of the bottom hole pressure of the water injection well, and apply it to the actual well to verify the accuracy of the established model. The specific steps are as follows:

[0133] The dimensionless pressure and time of the actual bottom hole pressure data of the water injection well are substituted into formula (21) and (22) to become dimensionless pressure and time:

[0134]

[0135]

[0136] In the formula, k is the permeability, μm 2 ; h is the oil layer thickness, m; q is the ground flow, m 3 / d; B is the volume coefficient, m 3 / m 3 ; p i is the original formation pressure, MPa; p wf is the bottom hole flowing pressure, MPa; μ is the viscosity, mpa·s; t is the time, h; φ is the porosity, decimal; r w is the wellbore radius, m.

[0137] By continuously modifying the adjustable parameters in the pressure analysis model of the injection well that considers the influence of water injection-induced fractures, and fitting them with actual pressure-driven well data, the pressure analysis model of the injection well that best fits the actual pressure-driven well data is finally obtained. The physical properties of the formation and fractures in this model are the physical properties of the formation and fractures that are closest to those of the actual pressure-driven well.

[0138] Example 2

[0139] In a specific embodiment 2 of the present invention, a pressure analysis study of the injection well L13X63 in the L13X60 block of the Shengli Oilfield in China was conducted, taking into account the influence of fractures induced by pressure-driven water injection. For example... Figure 1 As shown in the solution block diagram of the pressure analysis model for pressure-driven water injection wells, N x N y N t NN represents the number of grid nodes in the x-direction, the number of grid nodes in the y-direction, the time node, and the total step size, respectively. In solving the pressure analysis model for pressure-driven water injection wells, the first step is to input the basic parameters required by the model: N. x N y N t ,NN,Ψ,Φ,C t ,k,h,v,G T H, s w (i), k ro (i), k rw (i), Q pro Q inj p i s oi s wc Initialize each grid and assign external boundary conditions to the model. Then, solve for k for each grid using interpolation. ro and k rw The flow coefficient of each grid is calculated using the basic parameters of the reservoir and the derived pressure analysis model of the pressure-driven water injection well. The fracture length and fracture width are calculated in discrete time. Based on the same conductivity, the actual permeability of the fracture is converted into the permeability of the reservoir grid. Then, a five-diagonal equation system is listed. The pressure value at different grid nodes is obtained by solving the equation system. The saturation is calculated explicitly and the next cycle is performed until the simulation time ends.

[0140] The average daily water injection volume of this injection well is 1954 m³. 3 The water injection duration is 10 days. The basic reservoir parameters are: effective reservoir thickness of 10m, porosity of 14.7%, average formation permeability of 27.73mD, formation crude oil viscosity of 5mPa·s, injected water viscosity of 0.89mPa·s, injection well depth of 3402m, and a five-point well pattern with a quarter-section layout is used.Figure 2 As shown in FIG. 1, the length and width of the oil reservoir are both 250 m.

[0141] Based on the physical parameters and well pattern of the injection well L13X63 in the L13X60 block of the Shengli Oilfield, an injection well pressure analysis model considering the influence of the fracture induced by pressure drive injection is established and solved, and a double logarithmic pressure analysis curve of the injection well is drawn, as shown in FIG. 2. Figure 3 The bottom hole pressure of the pressure drive well solved by the injection well pressure analysis model considering the influence of the fracture induced by pressure drive injection is dimensionless with respect to time, and is fitted with the actual oil reservoir data to obtain the double logarithmic pressure analysis curve of the injection well, and according to the curve, the oil reservoir is divided into five flow stages during the fracturing process: stage I is a linear flow stage; stage II is a fracture expansion stage, which is in the early stage of injection, and the double logarithmic pressure derivative curve is unstable, indicating that a dynamic fracture is formed by high-pressure injection; stage III is a bilinear flow stage, in which the slope of the double logarithmic pressure derivative curve is less than 0.5 due to the large liquid production of the production well in the actual oil reservoir; stage IV is a transition stage, in which the pressure waves of the injection well and the production well influence each other, and the influence of the pressure wave generated by the production well also becomes large due to the large liquid production of the production well, and the double logarithmic pressure derivative curve in this stage presents a "v" type transition flow stage; and stage V is a pseudo-closed boundary control stage.

[0142] Example 3

[0143] In the specific embodiment 3 of the application, the injection well pressure analysis research considering the influence of the fracture induced by pressure drive injection is carried out on the pressure drive well Y80X8 in the Y80 block of the Shengli Oilfield in China, as shown in FIG. 3. Figure 1 As shown in the solution block diagram of the pressure drive injection well pressure analysis model, N x , N y , N t , NN respectively represent the x-direction grid node, the y-direction grid node, the time node and the total step length. In the process of solving the pressure drive injection well pressure analysis model, the basic parameters required by the model need to be input first: N x , N y , N t , NN, Ψ, Φ, C t , k, h, v, G T , H, s w (i), k ro (i), k rw (i), Q pro , Q inj , p i , s oi , s wc , the initial value is assigned to each grid and the outer boundary condition is assigned to the model. Then the k ro and k rwThe flow coefficient of each grid is calculated by the basic parameters of the oil reservoir and the derived pressure analysis model of the pressure drive water injection well, and the fracture length and fracture width are calculated in discrete time, the actual permeability of the fracture is converted into the permeability of the oil reservoir grid according to the same flow capacity, then five-diagonal equation groups are listed, and then the pressure values at different grid nodes are obtained by solving the equation groups, the saturation is obtained by using the explicit method, and the next cycle is performed until the simulation time ends.

[0144] The average daily water injection volume of the water injection well is 1954m 3 , the water injection duration is 27d, the basic parameters of the reservoir are: the effective thickness of the reservoir is 30.1m, the porosity is 16.1%, the average formation permeability is 5.2mD, the viscosity of the crude oil is 5mPa·s, the viscosity of the injected water is 0.89mPa·s, the depth of the pressure drive well is 3460m, and a five-spot well pattern with a quarter of the well pattern is used, as shown in Figure 2 , the length and width of the oil reservoir are both 300m.

[0145] Based on the physical parameters and well pattern of the pressure drive well of the Y80-8 block in the Y80 block of Shengli Oilfield, a pressure analysis model of the water injection well considering the influence of the fracture induced by the pressure drive water injection is established and solved, and the double logarithmic pressure analysis curve of the water injection well is drawn, as shown in Figure 4 The bottom hole pressure of the pressure drive well solved by the pressure analysis model of the water injection well considering the influence of the fracture induced by the pressure drive water injection is dimensionless with respect to time, and is fitted with the actual reservoir data to obtain the double logarithmic pressure analysis curve of the water injection well, and according to the curve, it is judged that the reservoir is divided into five flow stages during the fracturing process: stage I is the linear flow stage; stage II is the fracture propagation stage, which is in the early stage of water injection, and the double logarithmic pressure derivative curve is unstable, indicating that a dynamic fracture is formed by high-pressure water injection; stage III is the bilinear flow stage, in which the slope of the double logarithmic pressure derivative curve is less than 0.5 due to the large liquid production of the production well in the actual reservoir; stage IV is the transition stage, in which the pressure waves of the water injection well and the production well influence each other, and the influence of the pressure wave generated by the production well also becomes large due to the large liquid production of the production well, and the double logarithmic pressure derivative curve in this stage presents a “v” type transition flow stage; and stage V is the pseudo-closed boundary control stage.

[0146] Finally, it should be noted that the above description is only a preferred embodiment of the present application and is not intended to limit the present application. Although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions recorded in the foregoing embodiments or make equivalent replacements to some technical features. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

[0147] In addition to the technical features described in the specification, they are known to those skilled in the art.

Claims

1. A pressure analysis method for water injection wells considering the influence of fractures induced by pressure-driven water injection, characterized in that, The pressure analysis method for injection wells that considers the influence of fractures induced by pressure-driven water injection includes: Step 1: Establish a pressure analysis model for injection wells that considers the impact of fractures induced by pressure-driven water injection; Step 2: Solve the pressure analysis model of the injection well considering the influence of fractures induced by pressure-driven water injection; Step 3: Analyze the double logarithmic pressure analysis curve of the injection well and determine the different flow stages of the reservoir during the fracturing process based on the curve. Step 4: Analyze the bottom hole pressure response characteristics of the pressure-driven water injection well and apply them to actual wells to verify the accuracy of the established model; In step 1, a mathematical model of oil-water seepage during pressure-driven water injection and a model of fracture propagation during pressure-driven water injection are established, and the two models are coupled to form a pressure analysis model for water injection wells that considers the influence of fractures induced by pressure-driven water injection. Before establishing the pressure analysis model for pressure-driven water injection wells, the following assumptions are made: (1) Two-dimensional planar flow; (2) Only oil and water two-phase flow exists in the reservoir, and oil and water are mutually insoluble and each conforms to Darcy's law; (3) Both rock and fluid are compressible; (4) The heterogeneity and anisotropy of rocks are considered; (5) The effect of gravity is ignored; (6) Fracture propagation conforms to the linear propagation model. The governing equations for oil and water two-phase flow are as follows: (1)； (2)； In the formula, k is the absolute permeability, mD; K r ρ is the relative permeability, a decimal; μ is the viscosity, mPa·s; ρ is the density, kg / m³. σ represents porosity (decimal); s represents saturation (decimal); p represents pressure at any point and time (MPa); G represents the starting pressure gradient (MPa / m); subscripts: o represents oil phase, w represents water phase, and t represents the model simulation time (d). The auxiliary equation is: (3)； The initial conditions are: (4)； In the formula, s o Oil saturation, decimal; s w p represents the degree of water saturation, a decimal. oi The original formation pressure is MPa; s wi The initial water saturation level is a decimal. The inner and outer boundary conditions are: (5)； (6)； (7)； In the formula, Q pro Q represents the liquid production rate, in m³ / d. opro Q represents oil production, in m³ / d; wpro Q represents water production, in m³ / d. inj The water injection volume is in m³ / d. Treatment conditions for injection wells and production wells, namely, constant flow injection from injection wells and constant flow production from production wells: (8)； (9)； In the formula, p wf The bottom hole pressure of the production well is measured in MPa; p iwf The bottom pressure of the injection well is in MPa. B w B is the water volume coefficient, in m³ / m³. o R is the crude oil volume coefficient, m³ / m³; h is the oil layer thickness, m; e R is the supply radius, in meters (m). w Let be the radius of the wellbore, in meters (m). Equations (1)-(9) are mathematical models of oil-water seepage in water injection for hydraulic fracturing. Based on assumption (6) that fracture propagation conforms to the linear propagation model, a modified PKN model is adopted to consider the influence of fracturing fluid loss on fracture propagation, thus realizing the description of fracture propagation in water injection for hydraulic fracturing. According to the conservation law, the injected fluid is equal to the sum of the fluid lost and the fluid in the fracture, hence the expression for the total fracture volume is: (10)； In the formula, V f q represents the total crack volume, in m³. x The injection flow rate is m³ / d; t is the injection time, d; Ψ is the filtration loss ratio, a decimal. Equation (10) is used to modify the crack length and crack width calculation formulas corresponding to the PKN model, resulting in crack length and width formulas that take into account the filtration effect: (11)； (12)； In the formula, W(0,t) is the crack root width, in meters; v is Poisson's ratio, a decimal; G T Where is the shear modulus, MPa; H is the crack height, m; During pressure-driven water injection, there is no proppant within the fracture, and the fracture space constitutes the entire effective flow space. The flow within it follows the cubic law. Combining this with Darcy's formula, we can obtain the formulas for characterizing the permeability and conductivity of fractures during pressure-driven water injection: (13)； (14)； In the formula, K wzcf0 Let be the initial permeability of the fracture, mD; W(x,t) be the width of the fracture at any given time, m; KW f The fracture conductivity is expressed as mD·m. Equations (11) and (12) are formulas for fracture length and width considering the effect of filtration loss, and equation (14) is a formula for characterizing the flow of pressure-driven fractures. Combined with the mathematical model of oil-water seepage in pressure-driven water injection, a pressure analysis model for pressure-driven water injection wells can be formed.

2. The method for pressure analysis of injection wells considering the influence of fractures induced by pressure-driven water injection according to claim 1, characterized in that, In step 2, based on the given pressure analysis model of the pressure-driven water injection well, the pressure analysis model of the pressure-driven water injection well is discretized and solved using the finite difference method.

3. The method for pressure analysis of injection wells considering the influence of fractures induced by pressure-driven water injection according to claim 2, characterized in that, In step 2, the unknown quantity in the differential equation for the seepage flow of the oil and water phases is p. o p w s o s w The independent variables are (x, y, t); by expanding the differential equations of seepage in the oil and water phases, the difference equations for the oil and water phases are as follows: (15)； (16)； in: , , , , , , , , , , , ; In the formula, V i,j Q is the volume of the grid (i,j), in m³; oi,j Q wi,j V represents the output or injection rate of grid (i,j), in m³ / d; pi,j T represents the pore volume of the grid (i,j), in m³. ox T wx T oy T wy φ represents the conductivity coefficients of the aqueous and oil phases; h represents the unit mesh thickness, in meters; φ represents the porosity, a decimal; C p The rock compressibility coefficient is given in MPa. -1 C o The oil phase compressibility coefficient is given in MPa. -1 C w The compressibility coefficient of the aqueous phase is given in MPa. -1 .

4. The method for pressure analysis of injection wells considering the influence of fractures induced by pressure-driven water injection according to claim 3, characterized in that, In step 2, the pressure is implicitly solved using the IMPES method, derived from s o =1-s w And let A = ρ o / ρ w Then equation (15) + equation (16) A. Eliminating the saturation term from the above system of equations, we get: (17)； in: (18)； At each node, equation (17) is used to set up an equation, resulting in a five-diagonal system of equations. Solve this system to obtain the pressure. Then, substitute the pressure obtained above into the water phase difference equation (16) to obtain the water saturation. Then, use equations (11) and (12) to obtain the fracture length and width. At the same time, combine equation (14) to obtain the fracture conductivity. Finally, update the fracture length, conductivity, pressure and saturation distribution, and carry out the simulation calculation for the next moment, thereby realizing the solution of the pressure analysis model of the pressure-driven water injection well.

5. The method for pressure analysis of injection wells considering the influence of fractures induced by pressure-driven water injection according to claim 4, characterized in that, In step 3, the bottom hole pressure and time of the injection well, which are obtained by the pressure analysis model of the injection well considering the influence of water injection-induced fractures, are dimensionless and fitted with the actual reservoir data to obtain the double logarithmic pressure analysis curve of the injection well. Based on the curve, the different flow stages of the reservoir during the fracturing process are determined.

6. The method for pressure analysis of injection wells considering the influence of fractures induced by pressure-driven water injection according to claim 5, characterized in that, In step 3, the obtained bottom hole pressure and pressure driving time of the pressure-driven well are substituted into formulas (19) and (20) to transform them into dimensionless pressure and time: (19)； (20)； In the formula, k is the permeability, in μm 2 h is the oil layer thickness, in meters; q is the surface flow rate, in cubic meters per day; B is the volume coefficient, in cubic meters per cubic meter; p i The original formation pressure is MPa; p wf φ is the bottom hole flow pressure, MPa; μ is the viscosity, MPa·s; t is the time, h; φ is the porosity, decimal; r w Let be the radius of the wellbore, in meters (m).

7. The method for pressure analysis of injection wells considering the influence of fractures induced by pressure-driven water injection according to claim 6, characterized in that, In step 3, based on the dimensionless pressure, dimensionless time, and actual reservoir water injection well data, a double logarithmic pressure analysis curve for the water injection well is plotted, and different flow stages are analyzed and divided.

8. The method for pressure analysis of injection wells considering the influence of fractures induced by pressure-driven water injection according to claim 7, characterized in that, In step 4, the actual bottom hole pressure data and pressure driving time of the pressure-driven well are substituted into formulas (21) and (22) to transform them into dimensionless pressure and time: (21)； (22)； In the formula, k is the permeability, in μm 2 h is the oil layer thickness, in meters; q is the surface flow rate, in cubic meters per day; B is the volume coefficient, in cubic meters per cubic meter; p i The original formation pressure is MPa; p wf φ is the bottom hole flow pressure, MPa; μ is the viscosity, MPa·s; t is the time, h; φ is the porosity, decimal; r w Let be the radius of the wellbore, in meters (m).

9. The method for pressure analysis of injection wells considering the influence of fractures induced by pressure-driven water injection according to claim 8, characterized in that, In step 4, by continuously modifying the adjustable parameters in the water injection well pressure analysis model that considers the influence of water injection-induced fractures, and fitting them with the actual water injection well data, the water injection well pressure analysis model that best fits the actual water injection well data is finally obtained. The formation and fracture physical properties in this model are the formation and fracture physical properties that best fit the actual water injection well data.

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