Multistage fracturing horizontal well seepage analysis model with elastic reservoir outer boundary

Abstract

The invention relates to the technical field of oil and gas well production and development, and particularly discloses a multi-stage fracturing horizontal well seepage analysis model with an elastic reservoir outer boundary, which comprises the following steps of: establishing a multi-stage fracturing horizontal well seepage physical model and a seepage mathematical model with the elastic reservoir outer boundary; the method is suitable for reservoir production conditions (such as inter-well interference) under complex outer boundaries, and Laplace transformation and Stehfest numerical inversion methods are used for obtaining a dimensionless (quasi) pressure solution under fixed flow, a dimensionless flow solution under fixed bottomhole flow pressure and a dimensionless flow solution under variable bottomhole flow pressure in a real space. When the analytical model is applied to production dynamic data analysis, the characteristic curve fitting effect can be remarkably improved, and the accuracy of productivity prediction is remarkably enhanced. According to the technical scheme, the accuracy and applicability of description of the seepage analysis model of the multi-stage fractured horizontal well of the unconventional oil and gas reservoir are improved.

Description

Technical Field

[0001] The 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 have become a hot area in today's petroleum industry. In the unconventional oil and gas well testing and production dynamic data characteristic curve analysis technology, the outer boundary conditions of the multi-stage fractured horizontal well seepage analysis model used are generally closed outer boundaries or constant pressure outer boundaries. However, in some cases, the seepage analysis model under these outer boundary types is not applicable. For example, when a new well is fractured near a multi-stage fractured horizontal production well in a shale gas reservoir with a closed outer boundary, it will interfere with the production well and have the effect of replenishing energy for the well. At this time, the seepage analysis model of the multi-stage fractured horizontal production well with a closed outer boundary condition will no longer be applicable. The seepage analysis model of the multi-stage fractured horizontal well with a closed outer boundary condition will be difficult to apply to the characteristic curve analysis of production dynamic data. At this time, if the seepage analysis model with a closed outer boundary condition is still used, the characteristic curve analysis effect of production dynamic data will be poor, and the model solution will be difficult to fit historical data, resulting in serious problems such as strong uncertainty in interpretation parameters and poor accuracy in production capacity prediction.

[0003] Therefore, an elastic outer boundary is introduced into the seepage analytical model of unconventional oil and gas multi-stage fracturing horizontal production wells. This reservoir outer boundary type is different from the reservoir outer boundary form of 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 fracturing horizontal well seepage analytical model with an elastic reservoir outer boundary is established. It is applied to the characteristic curve analysis of unconventional oil and gas well testing and production dynamic data, which can significantly improve the characteristic curve fitting effect and significantly improve the accuracy of production prediction. Therefore, the establishment of a multi-stage fracturing 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 make up for the limitations of the existing oil and gas reservoir multi-stage fractured horizontal well seepage analytical model in characterizing the reservoir outer boundary conditions, the present invention provides a multi-stage fractured horizontal well seepage analytical model with an elastic reservoir outer boundary, thereby improving the accuracy and applicability of the description of the multi-stage fractured horizontal well seepage analytical model for unconventional oil and gas reservoirs.

[0005] The technical solution adopted by the present invention is as follows:

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

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

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

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

[0010] S3, based on the dimensionless flow solution under constant bottom hole pressure production conditions 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, through the dimensionless pseudo-pressure solution under constant flow production conditions in Laplace space obtained in S2, the dimensionless flow solution under constant bottom hole flowing pressure production conditions in Laplace space obtained in S3, and the dimensionless flow solution under variable bottom hole flowing pressure in Laplace space obtained in S3, the corresponding dimensionless pseudo-pressure solution under constant flow production conditions in real space, the dimensionless flow solution under constant bottom hole flowing pressure production conditions, and the dimensionless flow solution under variable bottom hole flowing pressure are obtained through Stehfest numerical inversion;

[0012] S5. 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, are applied to the characteristic curve analysis of unconventional oil and gas well production dynamic data, well test data interpretation, and 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: a reservoir flow area with elastic outer boundary, an inter-fracture flow area and a 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] In the formula, 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 inter-slit flow region, x D is the dimensionless distance;

[0018] The seepage equation in the inter-fracture flow region is:

[0019]

[0020] In the formula, m ID is the dimensionless pseudo-pressure in the inter-slit 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] In the formula, C D is the wellbore storage coefficient, S C is the skin factor, 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 fracture conductivity coefficient.

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

[0025] After Laplace transformation, the seepage equation of the reservoir flow region with elastic outer boundary in Laplace space is obtained as follows:

[0026]

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

[0028]

[0029] In the formula,

[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] In the formula,

[0033] Preferably, in S2, the Laplace transformation of the seepage equation of the inter-slit 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 transformation:

[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 Laplace space, and the dimensionless pseudo-pressure analytical solution of the inter-fracture flow region in Laplace space is obtained:

[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] In the formula,

[0041]

[0042] Preferably, in S2, the Laplace transformation of the seepage equation of the main fracture flow region in the Laplace space is obtained as follows: In the formula, 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 transformation:

[0044]

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

[0046]

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

[0048]

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

[0050]

[0051] The Laplace transformation formula for obtaining the seepage equation of the main fracture flow region in Laplace space is used to obtain the seepage equation of the main fracture flow region under a constant bottom hole pressure in Laplace space:

[0052]

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

[0054]

[0055] In the formula, 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 seepage flow of multi-stage fractured horizontal wells 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 Satisfies the following relationship:

[0057]

[0058] In the formula, is the dimensionless bottom hole pressure m WDV Laplace transform The dimensionless flow solution q is given by varying bottom flow pressure. DV The Laplace transform of is expressed as:

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

[0060]

[0061] In the formula, 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 Laplace space is obtained: The analytical expression of 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 production conditions, the flow solution under constant bottom hole pressure production conditions, and the flow solution under variable bottom hole pressure production conditions for the analytical model of seepage flow in 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 embodiments, but the embodiments should not be construed as limiting the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It 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 It is the fitting effect diagram of the double logarithmic characteristic curve of the pressure deconvolution data and the seepage analytical model;

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

[0073] Figure 5 It 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 It 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 common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0078] A seepage analytical model for a multi-stage fractured horizontal well with an elastic reservoir outer boundary comprises 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, such as Figure 1 As shown in the figure, the elastic outer boundary can reflect the energy replenishment and closure of the reservoir outer boundary during the production of multi-stage fracturing horizontal wells; the seepage area of ​​the fluid in the reservoir is divided into three "linear flow" areas: the reservoir flow area with an elastic outer boundary, the inter-fracture flow area, and the main fracture flow area.

[0080] Step 2: According to the physical model of seepage of the multi-stage fractured horizontal well with the elastic reservoir outer boundary in step 1, a mathematical model of seepage of the multi-stage fractured horizontal well with the 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 the elastic reservoir outer boundary, and the linear mathematical model is converted into a linear mathematical model of the multi-stage fractured horizontal well with the elastic reservoir outer boundary in Laplace space by Laplace transformation, and the converted model is solved to obtain a dimensionless pseudo-pressure solution under constant flow production conditions and a dimensionless flow solution under constant bottom flow 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] In the formula, 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. 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 the existence of energy replenishment and well-to-well interference around 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, x eD is the dimensionless reservoir outer boundary distance in the x direction, m ID is the dimensionless pseudo-pressure in the inter-slit 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 transformation, 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] In the formula,

[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] The seepage equation in the inter-fracture flow region is:

[0099]

[0100] In the formula, m ID is the dimensionless pseudo-pressure in the inter-slit 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; 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 equation group, we obtain the seepage equation of the inter-fracture 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 fracture conductivity.

[0114] Introduce the following Laplace transform:

[0115]

[0116] In the formula, is the dimensionless bottom hole pseudo pressure at unit flow rate in Laplace space;

[0117] Using equations (4), (10) and (15) to perform Laplace transformation on the equation group, we obtain the seepage equation of the main fracture flow area 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 equation (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] In the formula, q D is the dimensionless fluid flow rate, m WDC is a step function of dimensionless constant pseudo bottom hole pressure, satisfying the following relationship:

[0124]

[0125] Using equations (4), (10) and (15) to perform Laplace transformation on equation group (18), we obtain the seepage equation of the main fracture flow area 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 fixed bottom hole pressure in Laplace space:

[0128]

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

[0130] Step 3: Use the mathematical model of multi-stage fractured horizontal well seepage 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, Satisfies the following relationship:

[0131]

[0132] In the formula, is the dimensionless bottom hole pressure m WDV The Laplace transform of The dimensionless flow solution q is given by the variable bottom flow pressure. DV The Laplace transform of is defined as follows:

[0133]

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

[0135]

[0136] In the formula, 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 by equations (22), (23) and (25): The analytical expression of is:

[0138]

[0139] Step 4, according to the dimensionless pseudo-pressure solution under constant flow 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 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;

[0140] Step 5, according to 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, the noise influence of the production dynamic data is eliminated by using the deconvolution algorithm, the data obtained by the deconvolution calculation are fitted with the solution of the seepage analytical model by using the pressure deconvolution analysis method and the improved flow deconvolution algorithm based on the Duhamel principle, the parameter inversion is performed based on the fitting effect, the accuracy of the model solution is verified, and the forward calculation is performed to predict the production capacity according to the inversion interpretation parameters.

[0141] The cumulative production of a multi-stage fractured horizontal well in an actual block of 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 is 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 38MPa, the reservoir thickness is 38m, the number of main fractures is 43, and the main fracture spacing is 30.8m. According to the on-site construction situation, other new multi-stage fracturing horizontal wells are undergoing fracturing construction during the exploitation of this well. It can be judged that the reservoir outer boundary of this well is an elastic outer boundary type, and the seepage physical model of a multi-stage fracturing horizontal well with an elastic reservoir outer boundary is applied.

[0143] Firstly, the seepage area of ​​the fluid in the reservoir is divided into three "linear flow" areas: the reservoir flow area with an elastic outer boundary, the inter-fracture flow area and the main fracture flow area. Then, according to 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 production conditions in Laplace space and the dimensionless flow solution of the model under constant bottom hole pressure production conditions. The Duhamel principle is used to obtain the dimensionless flow solution of the model under variable bottom hole 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 by the pressure deconvolution method to be converted into dimensionless pseudo-pressure data under unit flow, and the double logarithmic characteristic curves of dimensionless pseudo-pressure and dimensionless pseudo-pressure derivative are plotted; then, 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 is obtained, and the double logarithmic pressure characteristic curves of dimensionless pseudo-pressure and dimensionless pseudo-pressure derivative are plotted; the analytical solution of the theoretical model is fitted with the double logarithmic characteristic curves of dimensionless pseudo-pressure and dimensionless pseudo-pressure derivative plotted by the pressure deconvolution method, as shown in FIG. Figure 3 The pressure double logarithmic characteristic curve fitting effect diagram of the pressure deconvolution data and the 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 flow pressure of the seepage analytical model. Figure 4 shown.

[0146] The interpretation results of the above-mentioned double logarithmic pressure characteristic curve analysis and Blasingame production decline characteristic curve analysis can constrain each other, and finally the inversion interpretation of the relevant parameters of the reservoir, fracture and elastic outer boundary (effective fracture half-length, elastic coefficient, comprehensive compression coefficient, limited conductivity, etc.) is obtained; the interpretation results show that the dimensionless elastic coefficient is 3.0, the effective half-length of the main fracture of the multi-stage fracturing horizontal well is 50.0m, the main fracture conductivity is 9.0mD·cm, the distance to the reservoir outer boundary is 125.0m, the permeability of the inter-fracture area is 1.0mD, and the permeability of the matrix area is 4×10 -4 mD, matrix area porosity 0.06, matrix area comprehensive compression coefficient 3.0×10 -3 MPa-1 According to the parameters obtained by inversion interpretation, the flow solution under variable bottom hole pressure of the seepage analytical model is used for forward calculation, and the production under variable bottom hole pressure can be obtained.

[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 by field monitoring and the fitting effect of the flow solution under variable bottom flow pressure of the seepage analytical model and the production capacity prediction results are shown. 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 the daily and cumulative production was carried out, and the dimensionless elastic coefficient values ​​were taken as 100.0, 3.0, and 0, respectively. Figure 6 This is a sensitivity analysis effect diagram of the double logarithmic characteristic curve of dimensionless pressure and dimensionless pressure derivative under the influence of 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, which is inconsistent with the actual working conditions. When the elastic coefficient is 3.0, the fitting effect is best, and the characteristic curve interpretation results are more reliable.

[0149] Figure 7 This is the sensitivity analysis effect diagram of daily production and cumulative production under the influence of elastic coefficient. It can be seen that with the increase of elastic coefficient, the daily production and cumulative production of shale gas increase accordingly. When the elastic coefficient is larger, the elastic outer boundary approaches the constant pressure outer boundary condition, and the daily production and cumulative production of shale gas increase accordingly. The appropriate elastic coefficient should be selected as the forward calculation basis parameter.

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

[0151] In summary, the present invention applies the analytical model of seepage of multi-stage fractured horizontal wells with elastic reservoir outer boundary to the analysis of on-site production dynamic data. The analytical solution of the model can be used to fit the characteristic curve with the production dynamic data after the deconvolution normalization process to eliminate the influence of data errors, and the reservoir model can be inverted and interpreted; forward calculation using the inverted reservoir parameters can predict the production capacity and final recoverable reserves of the production well. By conducting a sensitivity analysis of the influence of reservoir parameters on the pressure characteristic curve and production capacity, the important role of the elastic coefficient in the introduced elastic outer boundary conditions in characteristic curve fitting and production capacity prediction is demonstrated, which greatly improves the accuracy and applicability of the description of the analytical model of seepage of multi-stage fractured horizontal wells in unconventional oil and gas reservoirs, and has an important role in promoting the 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 only descriptions of the preferred modes of the present invention, and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

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

2. The analytical model of seepage flow 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 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.

3. The analytical model of seepage flow of multi-stage fractured horizontal wells with elastic reservoir outer boundary according to claim 1, characterized in that: In S2, the seepage equations of the three reservoir flow regions of the linear mathematical model of multi-stage fractured horizontal wells with elastic reservoir outer boundaries are established as follows: The flow equation for the reservoir flow region with an elastic outer boundary is: In the formula, 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 inter-slit flow region, x D is the dimensionless distance; The seepage equation in the inter-fracture flow region is: In the formula, m ID is the dimensionless pseudo-pressure in the inter-slit 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; The seepage equation in the main fracture flow region is: In the formula, C D is the wellbore storage coefficient, S C is the skin factor, 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 fracture conductivity coefficient.

4. The analytical model of seepage flow in multi-stage fractured horizontal wells with 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 s is the complex variable of Laplace transform; After Laplace transformation, the seepage equation of the reservoir flow region with elastic outer boundary in Laplace space is obtained as follows:

5. The analytical model of seepage flow of multi-stage fractured horizontal wells with 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: In the formula, 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: In the formula, 6. The analytical model of seepage flow in multi-stage fractured horizontal wells with elastic reservoir outer boundary according to claim 1, characterized in that: In S2, the Laplace transformation of the seepage equation of the inter-fracture flow region in the Laplace space is obtained as: After Laplace transformation, the seepage equation of the interslit flow region in Laplace space is obtained: 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 Laplace space, and the dimensionless pseudo-pressure analytical solution of the inter-fracture flow region in Laplace space is obtained: 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: In the formula, 7. The analytical model of seepage flow in multi-stage fractured horizontal wells with elastic reservoir outer boundary according to claim 1, characterized in that: In S2, the Laplace transformation of the seepage equation in the main fracture flow area in Laplace space is obtained as: In the formula, 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 transformation: The dimensionless pseudo-pressure gradient obtained by coupling the main fracture flow area is combined with the seepage equation of the inter-fracture flow area in Laplace space to obtain the dimensionless pseudo-bottomhole pressure analytical solution of the main fracture flow area in Laplace space:

8. The analytical seepage model of a multi-stage fractured horizontal well with an elastic reservoir outer boundary according to claim 1, characterized in that: In S2, the constant flow condition of the seepage equation in the main fracture flow area is replaced by the constant bottom hole flow pressure condition, and the seepage equation in the main fracture flow area under the constant bottom hole flow pressure is obtained as follows: where q D is the dimensionless fluid flow rate, m WDC is a step function of dimensionless constant pseudo bottom hole pressure, satisfying the following relationship: The Laplace transformation formula for obtaining the seepage equation of the main fracture flow region in Laplace space is used to obtain the seepage equation of the main fracture flow region under a constant bottom hole pressure in Laplace space: The dimensionless pseudo-pressure gradient obtained by coupling the main fracture flow area is combined with the seepage equation of the main fracture flow area in Laplace space to obtain the dimensionless flow analytical solution of the main fracture flow area in Laplace space. for: In the formula, It is the analytical solution of dimensionless flow rate under constant bottom hole pressure in Laplace space.

9. The analytical seepage model of 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 flow pressure is determined according to the mathematical model of seepage flow in multi-stage fractured horizontal wells 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 Satisfies the following relationship: In the formula, is the dimensionless bottom hole pressure m WDV Laplace transform The dimensionless flow solution q is given by varying bottom flow pressure. DV The Laplace transform of is expressed as: in, By piecewise integration method, we can obtain: 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.

10. The analytical model of seepage flow in multi-stage fractured horizontal wells with elastic reservoir outer boundary according to claim 1, characterized in that: In S3, the dimensionless flow rate under variable bottom hole pressure in Laplace space is obtained The analytical expression of is:

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