An analytical seepage model for multi-stage fractured horizontal wells with elastic reservoir outer boundaries

Abstract

The present invention relates to the technical field of oil and gas well production and development, and specifically discloses a multi-stage fractured horizontal well seepage analytical model with an elastic reservoir outer boundary, including establishing a multi-stage fractured horizontal well seepage physical model and a seepage mathematical model with an elastic reservoir outer boundary, which is applicable to reservoir production situations with complex outer boundaries (such as well-to-well interference), and also uses Laplace transform and Stehfest numerical inversion methods to obtain dimensionless (pseudo) pressure solutions under constant flow in real space, dimensionless flow solutions under constant bottom hole flow pressure, and dimensionless flow solutions under variable bottom hole flow pressure. Applying this analytical model to production dynamic data analysis can significantly improve the characteristic curve fitting effect and significantly enhance the accuracy of production capacity prediction. The technical solution of the present invention improves the accuracy and applicability of the description of the analytical model of multi-stage fractured horizontal well seepage in unconventional oil and gas reservoirs.

Description

Technical Field

[0001] The present invention relates to the technical field of oil and gas well production and development, and in particular to a multi-stage fractured horizontal well seepage analytical model with an elastic reservoir outer boundary. Background Art

[0002] The efficient development and utilization of unconventional oil and gas resources, such as shale oil, shale gas, and coalbed methane, has become a hot topic in the current petroleum industry. In unconventional oil and gas well testing and production performance data characteristic curve analysis techniques, the outer boundary conditions used in the seepage analysis model for multi-stage fractured horizontal wells are generally closed or constant pressure. However, in some cases, the seepage analysis model for these outer boundary types is not applicable. For example, when a new well is being fractured near a multi-stage fractured horizontal production well in a shale gas reservoir with a closed outer boundary, it interferes with the production well and replenishes its energy. In this case, the seepage analysis model for the multi-stage fractured horizontal production well with a closed outer boundary condition becomes inapplicable and difficult to apply to the characteristic curve analysis of production performance data. In such cases, the continued use of the seepage analysis model with a closed outer boundary condition results in poor performance of the production performance data characteristic curve analysis, making it difficult to fit the model solution to historical data, leading to serious problems such as strong uncertainty in interpretation parameters and poor production capacity prediction accuracy.

[0003] Therefore, an elastic outer boundary is introduced into the seepage analytical model for multi-stage fractured horizontal production wells in unconventional oil and gas reservoirs. This reservoir outer boundary type is different from a single closed outer boundary or a single constant pressure outer boundary. It can cover closed outer boundaries, constant pressure outer boundaries, and all reservoir outer boundaries between the two outer boundaries. Thus, a multi-stage fractured horizontal well seepage analytical model with an elastic reservoir outer boundary is established. This model is applied to the characteristic curve analysis of unconventional oil and gas well testing and production performance data, which can significantly improve the characteristic curve fitting effect and significantly enhance the accuracy of production prediction. Therefore, establishing a multi-stage fractured horizontal well seepage analytical model with an elastic reservoir outer boundary is of great significance to improving the development technology of unconventional oil and gas reservoirs. Summary of the Invention

[0004] In order to overcome the limitations of the existing oil and gas reservoir multi-stage fractured horizontal well seepage analysis model in characterizing the reservoir outer boundary conditions, the present invention provides a multi-stage fractured horizontal well seepage analysis model with an elastic reservoir outer boundary, thereby improving the accuracy and applicability of the description of the multi-stage fractured horizontal well seepage analysis model in unconventional oil and gas reservoirs.

[0005] The technical solutions adopted in the present invention are as follows:

[0006] A seepage analytical model for a multi-stage fractured horizontal well with an elastic reservoir outer boundary includes the following steps:

[0007] S1. Establish a physical model of seepage flow in multi-stage fractured horizontal wells with elastic reservoir outer boundary;

[0008] S2. Based on the seepage physical model of the multi-stage fractured horizontal well obtained in S1, a mathematical model of the seepage of the multi-stage fractured horizontal well with an elastic reservoir outer boundary is established. After linearizing the mathematical model of the multi-stage fractured horizontal well, a linear mathematical model of the multi-stage fractured horizontal well with an elastic reservoir outer boundary is obtained.

[0009] The Laplace transform is used to transform the linear mathematical model of a multi-stage fractured horizontal well with an elastic reservoir outer boundary into a linear mathematical model of a multi-stage fractured horizontal well with an elastic reservoir outer boundary in Laplace space. After solving the model, the dimensionless pseudo-pressure solution under constant flow rate production conditions and the dimensionless flow rate solution under constant bottom hole pressure production conditions in Laplace space are obtained.

[0010] S3, based on the dimensionless flow solution under constant bottom hole pressure in Laplace space obtained in S2, the dimensionless flow solution under variable bottom hole pressure in Laplace space is obtained by Duhamel principle;

[0011] S4, the dimensionless pseudo-pressure solution under constant flow rate production conditions in Laplace space, the dimensionless flow solution under constant bottom hole flowing pressure production conditions in Laplace space obtained by S2, and the dimensionless flow solution under variable bottom hole flowing pressure in Laplace space obtained by S3, and the corresponding dimensionless pseudo-pressure solution under constant flow rate production conditions, dimensionless flow solution under constant bottom hole flowing pressure production conditions, and dimensionless flow solution under variable bottom hole flowing pressure in real space are obtained respectively through Stehfest numerical inversion;

[0012] S5. Apply the linear mathematical model of multi-stage fractured horizontal wells with elastic reservoir outer boundaries obtained in S2, as well as the dimensionless pseudo-pressure solution under constant flow production conditions in real space, the dimensionless flow solution under constant bottom hole pressure production conditions, and the dimensionless flow solution under variable bottom hole pressure obtained in S4, to the characteristic curve analysis of unconventional oil and gas well production dynamic data, well test data interpretation, and production capacity prediction.

[0013] Preferably, in S1, according to the established multi-stage fractured horizontal well seepage physical model with elastic reservoir outer boundary, the seepage area of ​​the fluid in the reservoir is divided into three linear flow areas: the reservoir flow area with elastic outer boundary, the inter-fracture flow area and the main fracture flow area.

[0014] Preferably, in S2, the seepage equations of the three reservoir flow regions of the linear mathematical model of the multi-stage fractured horizontal well with the elastic reservoir outer boundary are established as follows:

[0015] The flow equation for the reservoir flow region with an elastic outer boundary is:

[0016]

[0017] Where, is the introduced reservoir elastic outer boundary condition, ε xD is the dimensionless elastic coefficient, when ε xD = 0, the elastic outer boundary degenerates into the reservoir closed outer boundary condition. xD >0 is the standard reservoir elastic outer boundary, and when ε xD When it is large enough, the elastic outer boundary tends to the constant pressure outer boundary condition of the reservoir; m OD is the dimensionless pseudo-pressure in the reservoir flow region, η OD is the pressure conductivity of the reservoir flow area, x eD is the dimensionless reservoir outer boundary distance in the x direction, m ID is the dimensionless pseudo-pressure in the interslit flow region, x D is the dimensionless distance;

[0018] Seepage equation in the inter-fracture flow region:

[0019]

[0020] Where m ID is the dimensionless pseudo-pressure in the interslit flow region, y D is the dimensionless distance in the y direction, y eD is half of the dimensionless distance between adjacent cracks, C RD is the dimensionless conductivity, m FD is the dimensionless pseudo-pressure in the fracture flow region, w D is the dimensionless width of the main crack;

[0021] The seepage equation in the main fracture flow region is:

[0022]

[0023] Where C D is the wellbore storage coefficient, S C is the skin coefficient, m FD is the dimensionless pseudo-pressure in the main fracture flow region, m WD is the dimensionless pseudo bottom hole pressure, C FD is the dimensionless fracture conductivity, η FD is the dimensionless crack pressure conductivity coefficient.

[0024] Preferably, in S2, the Laplace transform of the seepage equation of the main fracture flow region in the Laplace space is obtained as follows: Where, is the dimensionless pseudo bottom hole pressure at unit flow rate in Laplace space;

[0025] The seepage equation of the reservoir flow region with elastic outer boundary in Laplace space is obtained by Laplace transform:

[0026]

[0027] Preferably, in S2, the dimensionless pseudo-pressure analytical solution of the reservoir flow region in the Laplace space is obtained by solving the seepage equation of the reservoir flow region with an elastic outer boundary in the Laplace space:

[0028]

[0029] Where,

[0030] In order to couple the inter-slit flow region, when x D = 1, the dimensionless pseudo-pressure gradient is obtained from the dimensionless pseudo-pressure analytical solution of the reservoir flow area in Laplace space:

[0031]

[0032] Where,

[0033] Preferably, in S2, the Laplace transform of the seepage equation of the inter-fracture flow region in the Laplace space is obtained as follows:

[0034] The seepage equation of the interslit flow region in Laplace space is obtained by Laplace transform:

[0035]

[0036] The dimensionless pseudo-pressure gradient obtained from the coupled inter-fracture flow region is combined with the seepage equation of the inter-fracture flow region in the Laplace space to obtain the dimensionless pseudo-pressure analytical solution of the inter-fracture flow region in the Laplace space:

[0037]

[0038] To couple the main fracture flow region, the dimensionless pseudo-pressure gradient can be obtained from the dimensionless pseudo-pressure analytical solution of the inter-fracture flow region in Laplace space:

[0039]

[0040] Where,

[0041]

[0042] Preferably, in S2, the Laplace transform of the seepage equation of the main fracture flow region in the Laplace space is obtained as follows: Where, is the dimensionless pseudo bottom hole pressure at unit flow rate in Laplace space;

[0043] The seepage equation of the main fracture flow area in Laplace space is obtained by Laplace transform:

[0044]

[0045] The dimensionless pseudo-pressure gradient obtained by coupling the main fracture flow region is combined with the seepage equation of the inter-fracture flow region in the Laplace space to obtain the dimensionless pseudo-bottomhole pressure analytical solution of the main fracture flow region in the Laplace space:

[0046]

[0047] Preferably, in S2, the constant flow rate condition of the obtained seepage equation in the main fracture flow region is replaced with a constant bottom hole pressure condition, and the obtained seepage equation in the main fracture flow region under the constant bottom hole pressure is:

[0048]

[0049] where q D is the dimensionless fluid flow rate, m WDC is a dimensionless step function of constant pseudo bottom hole pressure, satisfying the following relationship:

[0050]

[0051] The Laplace transform formula for obtaining the seepage equation of the main fracture flow region in the Laplace space is used. The seepage equation of the main fracture flow region under a constant bottom hole pressure in the Laplace space is obtained as follows:

[0052]

[0053] The dimensionless pseudo-pressure gradient obtained by coupling the main fracture flow region is combined with the seepage equation of the main fracture flow region in Laplace space to obtain the dimensionless flow analytical solution of the main fracture flow region in Laplace space. for:

[0054]

[0055] Where, It is the analytical solution of dimensionless flow rate under constant bottom hole pressure in Laplace space.

[0056] Preferably, in S3, the dimensionless flow solution under the bottom hole flow pressure is determined according to the mathematical model of multi-stage fractured horizontal well seepage with elastic reservoir outer boundary in Laplace space obtained in step S2. The dimensionless flow solution of this model under varying bottom hole pressure The following relationship is satisfied:

[0057]

[0058] Where, is the dimensionless bottom hole pressure m WDV Laplace transform The dimensionless flow solution q under varying bottom flow pressure is DV The Laplace transform of is expressed as:

[0059] in, By piecewise integration method, we can obtain:

[0060]

[0061] Where, t D_l (l=0,1,2,...,n) represents the dimensionless time point corresponding to each variable bottom hole pressure data, m WDV_l (l=0, 1, 2, ..., n) represents the dimensionless bottom hole pressure data corresponding to each dimensionless time point.

[0062] Preferably, in S3, the dimensionless flow rate under the variable bottom hole pressure in the Laplace space is obtained The analytical expression is:

[0063]

[0064] The present invention has the following characteristics and advantages:

[0065] (1) Introducing elastic outer boundaries into the analytical model of seepage in unconventional oil and gas multi-stage fractured horizontal production wells can cover closed outer boundaries, constant pressure outer boundaries, and all reservoir outer boundaries between the two outer boundaries;

[0066] (2) The Laplace transform method can be used to obtain the pseudo-pressure solution under constant flow rate production conditions, the flow rate solution under constant bottom hole pressure production conditions, and the flow rate solution under variable bottom hole pressure production conditions for the analytical seepage model of multi-stage fractured horizontal wells with elastic outer boundary reservoirs. In particular, the nonlinear gas seepage model can be linearized and solved by defining pseudo-pressure for the production of unconventional gas wells.

[0067] (3) The multi-stage fractured horizontal production well seepage analysis model can overcome the limitations of the multi-stage fractured horizontal well seepage analysis model with a single closed outer boundary or a single constant pressure outer boundary currently used for the analysis of the characteristic curve of production dynamic data of unconventional oil and gas wells. By applying it to unconventional oil and gas well testing, production dynamic data characteristic curve analysis, etc., it can significantly improve the field application effect of the multi-stage fractured horizontal well seepage analysis model, which is of great significance to improving the development technology of unconventional oil and gas reservoirs.

[0068] The technical solution of the present invention is further described in detail below through the accompanying drawings and examples, but the examples should not be understood as limiting the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 This is a diagram of the trilinear seepage physical model of a multi-stage fractured horizontal well with an elastic reservoir outer boundary;

[0070] Figure 2 It is a graph of pseudo pressure and flow data;

[0071] Figure 3 This is the double logarithmic characteristic curve fitting effect diagram of pressure deconvolution data and seepage analytical model;

[0072] Figure 4 This is the Blasingame double logarithmic decreasing curve fitting effect diagram of flow deconvolution data and seepage analytical model;

[0073] Figure 5 This is a comparison chart between the output forecast of the model analytical solution and the actual production data;

[0074] Figure 6 It is the sensitivity analysis diagram of the characteristic curve under the influence of elastic coefficient;

[0075] Figure 7 This is the sensitivity analysis chart of EUR under the influence of elasticity coefficient;

[0076] Figure 8 It is an implementation flow chart. DETAILED DESCRIPTION

[0077] Unless otherwise defined, technical or scientific terms used in the present invention shall have the same meaning as commonly understood by one of ordinary skill in the art to which the present invention belongs.

[0078] A seepage analytical model for a multi-stage fractured horizontal well with an elastic reservoir outer boundary includes the following steps:

[0079] Step 1: Considering the linear flow of multi-stage fractured horizontal wells in shale gas reservoirs during production, a physical model of multi-stage fractured horizontal well seepage with elastic reservoir outer boundary is established, as shown in Figure 1 As shown in Figure 2, the elastic outer boundary can reflect the energy replenishment and closure of the reservoir outer boundary during multi-stage fractured horizontal well production. The fluid flow area in the reservoir is divided into three "linear flow" regions: the reservoir flow region with an elastic outer boundary, the interfracture flow region, and the main fracture flow region.

[0080] Step 2: Based on the physical model of seepage in the multi-stage fractured horizontal well with an elastic reservoir outer boundary in step 1, a mathematical model of seepage in the multi-stage fractured horizontal well with an elastic reservoir outer boundary is established; the mathematical model is linearized by defining a pseudo-pressure function to obtain a linear mathematical model of the multi-stage fractured horizontal well with an elastic reservoir outer boundary; the linear mathematical model is converted into a linear mathematical model of the multi-stage fractured horizontal well with an elastic reservoir outer boundary in Laplace space using Laplace transform; the converted model is solved to obtain a dimensionless pseudo-pressure solution under constant flow rate production conditions and a dimensionless flow rate solution under constant bottom hole pressure production conditions;

[0081] The pseudo-pressure is defined as:

[0082] Where m represents the gas pseudo-pressure, atm 2 / cp; p represents the actual production pressure, atm; μ is the viscosity, cp; Z is the deviation factor.

[0083] The flow equation for the reservoir flow region with an elastic outer boundary is:

[0084]

[0085] Where, is the introduced reservoir elastic outer boundary condition, ε xD is the dimensionless elastic coefficient, when ε xD = 0, the elastic outer boundary degenerates into the reservoir closed outer boundary condition. xD >0 is the standard reservoir elastic outer boundary, and when ε xD When the elastic outer boundary is large enough, it tends to the constant pressure outer boundary condition of the reservoir. Introducing the elastic outer boundary into the seepage model of multi-stage fractured horizontal wells can expand the scope of application of the model, such as when there is energy replenishment and inter-well interference around the multi-stage fractured horizontal wells; m OD is the dimensionless pseudo-pressure in the reservoir flow region, η OD is the pressure conductivity of the reservoir flow area, xeD is the dimensionless reservoir outer boundary distance in the x direction, m ID is the dimensionless pseudo-pressure in the interslit flow region, x D is the dimensionless distance;

[0086] Introduce the following Laplace transform:

[0087]

[0088] Where s is the complex variable of Laplace transform;

[0089] Using Equations (3) and (4) to perform Laplace transform, we obtain the seepage equation of the reservoir flow region with elastic outer boundary in Laplace space:

[0090]

[0091] Solving Equation (5) yields the dimensionless pseudo-pressure solution of the reservoir flow region in Laplace space:

[0092]

[0093] Where,

[0094] In order to couple the inter-slit flow region, when x D = 1, the dimensionless pseudo-pressure gradient is obtained from formula (6):

[0095]

[0096] make We can get:

[0097]

[0098] Seepage equation in the inter-fracture flow region:

[0099]

[0100] Where m ID is the dimensionless pseudo-pressure in the interslit flow region; y D is the dimensionless distance in the y direction of flow; eD is half of the dimensionless distance between adjacent cracks; C RD is the dimensionless conductivity coefficient; m FD is the dimensionless pseudo-pressure in the fracture flow region; w D is the dimensionless width of the main crack;

[0101] Introduce the following Laplace transform:

[0102]

[0103] Using Equations (3), (4) and (10) to perform Laplace transformation on the equations, we obtain the seepage equation for the interslit flow region in Laplace space:

[0104]

[0105] Solving Equation (8) and Equation (11) together, we can obtain the dimensionless pseudo-pressure analytical solution of the inter-slit flow region in Laplace space:

[0106]

[0107] To couple the main fracture flow region, the dimensionless pseudo-pressure gradient can be obtained from Equation (12):

[0108]

[0109] in,

[0110]

[0111] The seepage equation in the main fracture flow region is:

[0112]

[0113] In order to consider the influence of wellbore storage effect and skin effect, the wellbore storage coefficient C is introduced. D and skin factor S C , m FD m is the dimensionless pseudo-pressure in the main fracture flow region; WD is the dimensionless bottom hole pressure; C FD is the dimensionless fracture conductivity; η FD Dimensionless crack pressure conductivity.

[0114] Introduce the following Laplace transform:

[0115]

[0116] Where, is the dimensionless bottom hole pseudo pressure under unit flow in Laplace space;

[0117] Using Equations (4), (10), and (15) to perform Laplace transformation on the equations, we obtain the seepage equation for the main fracture flow region in Laplace space:

[0118]

[0119] Solving Equation (13) and Equation (16) together, we can obtain the dimensionless pseudo-pressure solution of the main fracture flow region in Laplace space:

[0120]

[0121] The constant flow rate condition in the model of formula (14) is replaced by the constant bottom hole pressure condition, and the seepage equation of the main fracture flow area under the constant bottom hole pressure is obtained:

[0122]

[0123] Where q D is the dimensionless fluid flow rate, m WDC is a dimensionless step function of constant pseudo bottom hole pressure, satisfying the following relationship:

[0124]

[0125] Using Equations (4), (10), and (15) to perform Laplace transformation on Equation (18), we obtain the seepage equation in the main fracture flow region under constant bottom hole pressure in Laplace space:

[0126]

[0127] Using equation (13), equation (20) is solved to obtain the dimensionless flow rate analytical solution under the condition of constant bottom hole pressure in Laplace space:

[0128]

[0129] Where, It is the dimensionless analytical solution of flow rate under constant bottom hole pressure in Laplace space;

[0130] Step 3: Use the mathematical model of multi-stage fractured horizontal well flow with elastic reservoir outer boundary in Laplace space obtained in step 2 to determine the dimensionless flow solution under the bottom hole flow pressure. The dimensionless flow solution of the model under the bottom hole pressure in the variable Laplace space By using Duhamel's principle, The following relationship is satisfied:

[0131]

[0132] Where, is the dimensionless bottom hole pressure m WDV Laplace transform, The dimensionless flow solution q under varying bottom flow pressure is DV The Laplace transform of is defined as follows:

[0133]

[0134] By piecewise integration method, we can obtain:

[0135]

[0136] Where, t D_l (l=0,1,2,...,n) represents the dimensionless time point corresponding to each variable bottom hole pressure data, m WDV_l (l=0,1,2,...,n) represents the dimensionless bottom hole pressure data corresponding to each dimensionless time point;

[0137] Therefore, the dimensionless flow rate under variable bottom hole pressure in Laplace space is obtained from equations (22), (23) and (25): The analytical expression is:

[0138]

[0139] Step 4: Based on the dimensionless pseudo-pressure solution under constant flow rate production conditions, the dimensionless flow solution under constant bottom hole flowing pressure production conditions, and the dimensionless flow solution under variable bottom hole flowing pressure obtained in the Laplace space in steps 2 and 3, Stehfest numerical inversion is applied to obtain the corresponding dimensionless pseudo-pressure solution under constant flow rate production conditions, the dimensionless flow solution under constant bottom hole flowing pressure production conditions, and the dimensionless flow solution under variable bottom hole flowing pressure in real space, respectively.

[0140] Step 5: Based on the linear mathematical model of the multi-stage fractured horizontal well with the elastic reservoir outer boundary obtained in step 2 and the dimensionless pseudo-pressure solution under constant flow production conditions in real space, the dimensionless flow solution under constant bottom hole pressure production conditions, and the dimensionless flow solution under variable bottom hole pressure obtained in step 4, the linearized production dynamic data of the multi-stage fractured horizontal well in the shale gas reservoir are normalized, and the noise influence of the production dynamic data is eliminated using the deconvolution algorithm. The data obtained by the deconvolution calculation are fitted with the solution of the seepage analytical model using the pressure deconvolution analysis method and the improved flow deconvolution algorithm based on the Duhamel principle, respectively. The parameters are inverted based on the fitting results to verify the accuracy of the model solution, and the production capacity is predicted by forward calculation based on the inversion interpretation parameters.

[0141] The cumulative production of a multi-stage fractured horizontal well in a shale gas reservoir in China is 3.56×10 8 m 3 The average daily output is 1.14×105m 3 / d, the daily production and pseudo-pressure diagram of the well are as follows Figure 2 shown.

[0142] The horizontal well reservoir temperature of this multi-stage fracturing horizontal well is 91°C, the initial pressure is 38 MPa, the reservoir thickness is 38 m, the number of main fractures is 43, and the main fracture spacing is 30.8 m. According to the on-site construction conditions, other new multi-stage fracturing horizontal wells were fracturing during the production of this well. Therefore, it can be judged that the reservoir outer boundary of this well is an elastic outer boundary type. The seepage physical model of multi-stage fracturing horizontal wells with an elastic reservoir outer boundary is applied.

[0143] First, the seepage area of ​​the fluid in the reservoir is divided into three "linear flow" regions: the reservoir flow area with an elastic outer boundary, the inter-fracture flow area, and the main fracture flow area. Then, based on the physical model, a seepage analytical model of multi-stage fractured horizontal wells in shale gas reservoirs with an elastic reservoir outer boundary is established. The nonlinear seepage analytical model is linearized by defining a pseudo-pressure function. The Laplace transform method is used to obtain the dimensionless pseudo-pressure solution of the model under constant flow rate production conditions in Laplace space and the dimensionless flow solution of the model under constant bottomhole pressure production conditions. The Duhamel principle is used to obtain the dimensionless flow solution of the model under variable bottomhole pressure in Laplace space. Finally, the Stehfest numerical inversion is used to obtain the corresponding solution in real space.

[0144] The production data is linearized according to the pseudo-pressure function, and the linearized data is normalized using the pressure deconvolution method to convert it into dimensionless pseudo-pressure data under unit flow, and the double logarithmic characteristic curves of the dimensionless pseudo-pressure and the dimensionless pseudo-pressure derivative are plotted. Then, according to the dimensionless pseudo-pressure solution under constant flow production conditions of the mathematical model of multi-stage fractured horizontal wells with elastic reservoir outer boundaries, the double logarithmic pressure characteristic curves of the dimensionless pseudo-pressure and the dimensionless pseudo-pressure derivative are plotted. The analytical solution of the theoretical model is fitted with the double logarithmic characteristic curves of the dimensionless pseudo-pressure and the dimensionless pseudo-pressure derivative plotted by the pressure deconvolution method, as shown in FIG. Figure 3 Pressure double-logarithmic characteristic curve fitting effect diagram of pressure deconvolution data and theoretical model curve.

[0145] Similarly, the flow deconvolution method is introduced to normalize the linearized production pressure data, and the flow data corresponding to the variable pseudo-pressure is converted into the flow data under the fixed pseudo-pressure. By adjusting the parameters, the production data after flow deconvolution calculation is fitted with the Blasingame production decline characteristic curve of the flow solution under the fixed bottom hole flow pressure of the seepage analytical model. Figure 4 shown.

[0146] The interpretation results of the double-logarithmic pressure characteristic curve analysis and the Blasingame production decline characteristic curve analysis can constrain each other, and ultimately the inversion interpretation of relevant parameters of the reservoir, fracture, and elastic outer boundary (effective fracture half-length, elastic coefficient, comprehensive compressibility, finite conductivity, etc.) is obtained. The interpretation results show that the dimensionless elastic coefficient is 3.0, the effective half-length of the main fracture in the multi-stage fractured horizontal well is 50.0 m, the main fracture conductivity is 9.0 mD·cm, the distance to the reservoir outer boundary is 125.0 m, the permeability of the interfracture region is 1.0 mD, and the permeability of the matrix region is 4×10 -4 mD, matrix porosity 0.06, matrix comprehensive compressibility 3.0×10 -3 MPa -1 Based on the parameters obtained by inversion interpretation, the flow rate solution under variable bottom hole pressure of the seepage analytical model is used for forward calculation to obtain the production under variable bottom hole pressure.

[0147] The variable bottom hole pressure can be set to two sections. The first section is the field measured pressure data section, and the second section is the prediction section, which is set to a constant bottom hole pressure of 0.1 MPa for a long enough time to predict EUR. Figure 5 The shale gas daily production data obtained from field monitoring is fitted with the flow solution of the seepage analytical model under variable bottom flow pressure and the production capacity prediction results. The predicted EUR is 9.16×10 8 m 3 .

[0148] Finally, a sensitivity analysis of the effect of the outer boundary elastic coefficient on the characteristic curve of shale gas well production dynamic data and daily production and cumulative production was carried out, and the dimensionless elastic coefficient values ​​were taken as 100.0, 3.0, and 0 respectively. Figure 6 Figure 3 is a sensitivity analysis diagram of the double logarithmic characteristic curve of dimensionless pressure and dimensionless pressure derivative under the influence of the elastic coefficient. It can be seen that as the elastic coefficient value of the reservoir outer boundary decreases, the pseudo-pressure and pseudo-pressure derivative of shale gas increase. When the elastic coefficient is 0, the reservoir outer boundary approaches the closed outer boundary. When the elastic coefficient is 100.0, the reservoir outer boundary is close to the constant pressure outer boundary, both of which are inconsistent with the actual working conditions. When the elastic coefficient is 3.0, the fitting effect is the best, and the characteristic curve interpretation results are more reliable.

[0149] Figure 7 The figure below shows the sensitivity analysis of daily and cumulative production under the influence of the elastic coefficient. It can be seen that as the elastic coefficient increases, the daily and cumulative production of shale gas increases accordingly. As the elastic coefficient increases, the elastic outer boundary approaches the constant pressure outer boundary condition, and the daily and cumulative production of shale gas increases accordingly. Therefore, an appropriate elastic coefficient should be selected as the basis parameter for forward calculation.

[0150] The calculation flow chart is as follows Figure 8 shown.

[0151] In summary, the present invention applies the analytical model for seepage in multi-stage fractured horizontal wells with an elastic reservoir outer boundary to the analysis of on-site production dynamic data. The analytical solution of the model can be used to perform characteristic curve fitting with production dynamic data after deconvolution normalization to eliminate the influence of data errors, thereby inverting and interpreting the reservoir model. Forward calculations using the inverted reservoir parameters can predict the production well productivity and ultimate recoverable reserves. By conducting a sensitivity analysis of the impact of reservoir parameters on the pressure characteristic curve and productivity, the important role of the elastic coefficient introduced in the elastic outer boundary condition in characteristic curve fitting and productivity prediction is demonstrated. This greatly improves the accuracy and applicability of the analytical model description for seepage in multi-stage fractured horizontal wells in unconventional oil and gas reservoirs, and has an important role in promoting production dynamic data analysis technology for the development of multi-stage fractured horizontal wells in unconventional oil and gas reservoirs.

[0152] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A method for analyzing seepage in a multi-stage fractured horizontal well with an elastic reservoir outer boundary, characterized in that: The steps include: S1. Establish a physical model of seepage flow in multi-stage fractured horizontal wells with elastic reservoir outer boundary; S2. Based on the seepage physical model of the multi-stage fractured horizontal well obtained in S1, a mathematical model of the seepage of the multi-stage fractured horizontal well with an elastic reservoir outer boundary is established. After linearizing the mathematical model of the multi-stage fractured horizontal well, a linear mathematical model of the multi-stage fractured horizontal well with an elastic reservoir outer boundary is obtained. The Laplace transform is used to transform the linear mathematical model of a multi-stage fractured horizontal well with an elastic reservoir outer boundary into a linear mathematical model of a multi-stage fractured horizontal well with an elastic reservoir outer boundary in Laplace space. After solving the model, the dimensionless pseudo-pressure solution under constant flow rate production conditions and the dimensionless flow rate solution under constant bottom hole pressure production conditions in Laplace space are obtained. S3, based on the dimensionless flow solution under constant bottom hole pressure in Laplace space obtained in S2, the dimensionless flow solution under variable bottom hole pressure in Laplace space is obtained by Duhamel principle; S4, the dimensionless pseudo-pressure solution under constant flow rate production conditions in Laplace space, the dimensionless flow solution under constant bottom hole flowing pressure production conditions in Laplace space obtained by S2, and the dimensionless flow solution under variable bottom hole flowing pressure in Laplace space obtained by S3, and the corresponding dimensionless pseudo-pressure solution under constant flow rate production conditions, dimensionless flow solution under constant bottom hole flowing pressure production conditions, and dimensionless flow solution under variable bottom hole flowing pressure in real space are obtained respectively through Stehfest numerical inversion; S5. Apply the linear mathematical model of multi-stage fractured horizontal wells with elastic reservoir outer boundaries obtained in S2, as well as the dimensionless pseudo-pressure solution under constant flow production conditions in real space, the dimensionless flow solution under constant bottom hole pressure production conditions, and the dimensionless flow solution under variable bottom hole pressure obtained in S4, to the characteristic curve analysis of unconventional oil and gas well production dynamic data, well test data interpretation, and production capacity prediction.

2. The method for analyzing seepage in a multi-stage fractured horizontal well with an elastic reservoir outer boundary according to claim 1, characterized in that: In S1, according to the established physical model of seepage in multi-stage fractured horizontal wells with elastic reservoir outer boundaries, the seepage area of ​​the fluid in the reservoir is divided into three linear flow areas: the reservoir flow area with elastic outer boundaries, the inter-fracture flow area, and the main fracture flow area.

3. The method for analyzing seepage in a multi-stage fractured horizontal well with an elastic reservoir outer boundary according to claim 1, characterized in that: In S2, the seepage equations for the three reservoir flow regions of the linear mathematical model of a multi-stage fractured horizontal well with an elastic reservoir outer boundary are established as follows: The flow equation for the reservoir flow region with an elastic outer boundary is: ； Where, is the reservoir elastic outer boundary condition introduced, is the dimensionless elastic coefficient, when When the elastic outer boundary degenerates into the reservoir closed outer boundary condition, is the standard reservoir elastic outer boundary, and when When it is large enough, the elastic outer boundary tends to the constant pressure outer boundary condition of the reservoir; is the dimensionless pseudo-pressure in the reservoir flow region, is the pressure conductivity coefficient of the reservoir flow area, for Direction dimensionless distance to the outer boundary of the reservoir, is the dimensionless pseudo-pressure in the interslit flow region, is the dimensionless distance; Seepage equation in the inter-fracture flow region: ； Where, is the dimensionless pseudo-pressure in the interslit flow region, for Dimensionless distance in direction, is half of the dimensionless distance between adjacent cracks, is the dimensionless conductivity coefficient, is the dimensionless pseudo-pressure in the fracture flow region, is the dimensionless width of the main crack; The seepage equation in the main fracture flow region is: ； Where, is the wellbore storage coefficient, is the skin coefficient, is the dimensionless pseudo-pressure in the main fracture flow region, is the dimensionless pseudo bottom hole pressure, is the dimensionless fracture conductivity, is the dimensionless crack pressure conductivity coefficient.

4. The method for analyzing seepage in a multi-stage fractured horizontal well with an elastic reservoir outer boundary according to claim 1, characterized in that: In S2, after obtaining the linear mathematical model seepage equation of the reservoir flow region with an elastic outer boundary, the Laplace transform of the seepage equation of the reservoir flow region with an elastic outer boundary in the Laplace space is obtained as follows: ; Where, is the complex variable of Laplace transform; The seepage equation of the reservoir flow region with elastic outer boundary in Laplace space is obtained by Laplace transform: 。 5. The method for analyzing seepage in a multi-stage fractured horizontal well with an elastic reservoir outer boundary according to claim 1, characterized in that: In S2, the seepage equation of the reservoir flow region with elastic outer boundary in the Laplace space is solved, and the dimensionless pseudo-pressure analytical solution of the reservoir flow region in the Laplace space is obtained as follows: ； Where, ; In order to couple the inter-slit flow region, The dimensionless pseudo-pressure gradient is obtained from the dimensionless pseudo-pressure analytical solution of the reservoir flow region in Laplace space: ； Where, .

6. The method for analyzing seepage in a multi-stage fractured horizontal well with an elastic reservoir outer boundary according to claim 1, characterized in that: In S2, the Laplace transform of the seepage equation of the inter-fracture flow region in the Laplace space is obtained as follows: ； ； ； The seepage equation of the interslit flow region in Laplace space is obtained by Laplace transform: ； The dimensionless pseudo-pressure gradient obtained from the coupled inter-fracture flow region is combined with the seepage equation of the inter-fracture flow region in the Laplace space to obtain the dimensionless pseudo-pressure analytical solution of the inter-fracture flow region in the Laplace space: ； To couple the main fracture flow region, the dimensionless pseudo-pressure gradient can be obtained from the dimensionless pseudo-pressure analytical solution of the inter-fracture flow region in Laplace space: ； Where, .

7. The method for analyzing seepage in a multi-stage fractured horizontal well with an elastic reservoir outer boundary according to claim 1, characterized in that: In S2, the Laplace transform of the seepage equation in the main fracture flow area in the Laplace space is obtained as: ； ； Where, is the dimensionless pseudo bottom hole pressure at unit flow rate in Laplace space; The seepage equation of the main fracture flow area in Laplace space is obtained by Laplace transform: ； The dimensionless pseudo-pressure gradient obtained by coupling the main fracture flow region is combined with the seepage equation of the inter-fracture flow region in the Laplace space to obtain the dimensionless pseudo-bottomhole pressure analytical solution of the main fracture flow region in the Laplace space: 。 8. The method for analyzing seepage in a multi-stage fractured horizontal well with an elastic reservoir outer boundary according to claim 1, characterized in that: In S2, the constant flow rate condition of the flow equation in the main fracture flow area is replaced by the constant bottom hole pressure condition. The flow equation in the main fracture flow area under the constant bottom hole pressure is: ； in is the dimensionless fluid flow rate, is a dimensionless step function of constant pseudo bottom hole pressure, satisfying the following relationship: ； The Laplace transform formula for obtaining the seepage equation of the main fracture flow region in the Laplace space is used. The seepage equation of the main fracture flow region under a constant bottom hole pressure in the Laplace space is obtained as follows: ； The dimensionless pseudo-pressure gradient obtained by coupling the main fracture flow region is combined with the seepage equation of the main fracture flow region in Laplace space to obtain the dimensionless flow analytical solution of the main fracture flow region in Laplace space. for: ； Where, It is the analytical solution of dimensionless flow rate under constant bottom hole pressure in Laplace space.

9. The method for analyzing seepage in a multi-stage fractured horizontal well with an elastic reservoir outer boundary according to claim 1, characterized in that: In step S3, the dimensionless flow solution under the bottom hole flow pressure is determined according to the mathematical model of multi-stage fractured horizontal well seepage with elastic reservoir outer boundary in Laplace space obtained in step S2. The dimensionless flow solution of this model under variable bottom hole pressure is , and The following relationship is satisfied: ； Where, Dimensionless bottom hole pressure Laplace transform , The dimensionless flow solution under varying bottom flow pressure is The Laplace transform of is expressed as: ; in, By piecewise integration method, we can obtain: ； Where, Indicates the dimensionless time point corresponding to each variable bottom hole pressure data, Represents the dimensionless bottomhole flowing pressure data corresponding to each dimensionless time point.

10. The method for analyzing seepage in a multi-stage fractured horizontal well with an elastic reservoir outer boundary according to claim 1, characterized in that: In S3, the dimensionless flow rate under varying bottom hole pressure in Laplace space is obtained. The analytical expression is: 。

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