Method for evaluating the difference in stress sensitivity of main fractures during the fracturing fluid flowback and gas production stages

Abstract

The present invention provides a method for evaluating the difference in stress sensitivity of the main fracture during the fracturing fluid flowback and gas production stages, which relates to the field of fracturing optimization technology for gas reservoirs developed by hydraulic fracturing. This method includes: considering the stress sensitivity of the main fracture, establishing a seepage physical model and its unsteady seepage mathematical model for the long-term production stage and the fracturing fluid flowback stage of a shale gas well, linearizing and solving it; linearizing the production dynamic data, and introducing an improved pressure deconvolution algorithm to normalize the linearized production dynamic data; obtaining the double logarithmic characteristic curves of the normalized production dynamic data and the pseudo-bottom-hole flowing pressure solution during the production stage and the flowback stage, and through the mutual restriction of the two stages, obtaining the corresponding interpretation results, and then evaluating the difference in stress sensitivity of the fracture. By using the above method, the accuracy and reliability of the results can be improved, and the dynamic change of the conductivity can be obtained, providing a reference for the evaluation of the fracturing effect and the optimization of stimulation measures for multi-stage fractured horizontal wells in shale gas.

Description

Technical Field

[0001] The present invention relates to the technical field of hydraulic fracturing development of gas reservoirs, and particularly to a method for evaluating the stress sensitivity difference between the main fractures in the fracturing fluid backflow and gas production stages. Background Art

[0002] In recent years, shale gas, as an important unconventional natural gas resource, has received extensive attention in the global energy field. The development and utilization of shale gas are of great significance for alleviating energy pressure and ensuring energy security. However, due to the special geological characteristics of shale gas reservoirs, many technical challenges are faced in the development process. Among them, the hydraulic fracturing technology based on horizontal wells is one of the key technologies for the commercial development of shale gas. Hydraulic fracturing can create an artificial fracture network with high permeability, thus greatly improving the recoverability of shale gas. In the development process of shale gas wells, the fracturing fluid backflow stage and the production stage are two key stages. Due to the extremely deep burial depth, abnormal high pressure, and high closure stress of shale reservoirs, during the backflow and production stages, the formation pressure and stress state change greatly, and the stress sensitivity of the fracturing fractures shows different characteristics, which is of great significance for evaluating and predicting the production performance of shale gas wells.

[0003] The stress sensitivity of fracturing fractures refers to the property that the permeability of fracturing fractures changes with the change of the surrounding stress. Due to the change of reservoir pressure, the opening degree and conductivity of fractures will be affected, thereby affecting the gas flow and productivity. In the existing technologies, the indoor experiment simulation method of supported fractures is usually used to evaluate the conductivity and stress sensitivity of hydraulic fractures. However, the actual hydraulic fracture morphology is complex, and the underground conditions are complex. This kind of seepage experiment is usually greatly simplified and is easily affected by experimental operations and test equipment. The obtained results have great uncertainty, and the experimental method cannot obtain the dynamic change of the conductivity under the condition of considering stress sensitivity. In addition, the numerical simulation method for studying the stress sensitivity of fracturing fractures is computationally complex and time-consuming.

[0004] Therefore, the present invention studies the stress sensitivity of fracturing fractures in two different stages of backflow and production, provides an efficient and accurate method for evaluating the stress sensitivity difference of fracturing fractures in different stages of shale gas wells, and provides suggestions for the evaluation of the fracturing effect and the optimization of stimulation measures of multi-stage fractured horizontal wells in shale gas, making up for the limitations of the existing methods for the stress sensitivity difference of fracturing fractures in the fracturing fluid backflow and production stages of shale gas wells. Summary of the Invention

[0005] The object of the present invention is to provide a method for evaluating the stress sensitivity difference between the main fractures in the fracturing fluid backflow and gas production stages, so as to realize the quantitative evaluation of the stress sensitivity difference of fracturing fractures in the fracturing fluid backflow stage and the long-term production stage of shale gas wells quickly and accurately.

[0006] To achieve the above object, the method for evaluating the difference in the stress sensitivity of the main fracture between the fracturing fluid backflow and gas production stages in the present invention includes the following steps:

[0007] S1. Considering the stress sensitivity of the main fracture, for the long-term production stage and the fracturing fluid backflow stage of the shale gas reservoir with staged fracturing horizontal wells, respectively establish a trilinear seepage physical model for gas and a trilinear seepage physical model for liquid;

[0008] S2. According to the trilinear seepage physical models in step S1, considering the stress sensitivity of the main fracture, respectively establish a trilinear unsteady seepage mathematical model for gas in the long-term production stage and a trilinear unsteady seepage mathematical model for liquid in the fracturing fluid backflow stage;

[0009] S3. By defining a method for considering the pseudo-pressure of the stress sensitivity of the main fracture, respectively linearize the trilinear unsteady seepage mathematical model for gas in the long-term production stage and the trilinear unsteady seepage mathematical model for liquid in the fracturing fluid backflow stage;

[0010] S4. Solve the linearized trilinear unsteady seepage mathematical model for gas in the long-term production stage to obtain the instantaneous pseudo-bottom hole flowing pressure solution in the long-term production stage considering the stress sensitivity of the main fracture and a constant flow rate;

[0011] Solve the linearized trilinear unsteady seepage mathematical model for liquid in the fracturing fluid backflow stage to obtain the instantaneous pseudo-bottom hole flowing pressure solution in the fracturing fluid backflow stage considering the stress sensitivity of the main fracture and a constant flow rate;

[0012] S5. By defining a method for considering the pseudo-pressure of the stress sensitivity of the main fracture, linearly process the collected production dynamic data in the long-term production stage and the backflow dynamic data in the fracturing fluid backflow stage;

[0013] And use the improved pressure deconvolution algorithm to respectively normalize the production dynamic data in the long-term production stage and the backflow dynamic data in the fracturing fluid backflow stage;

[0014] S6. Fit the normalized production dynamic data in the long-term production stage and the pseudo-bottom hole flowing pressure solution of the linearized trilinear unsteady seepage mathematical model at a constant flow rate to obtain the first characteristic curve in the double logarithmic coordinates of the instantaneous pseudo-bottom hole pressure drop and the instantaneous pseudo-bottom hole pressure drop derivative with respect to time;

[0015] S7. Fit the normalized backflow dynamic data in the fracturing fluid backflow stage and the pseudo-bottom hole flowing pressure solution of the linearized trilinear unsteady seepage mathematical model at a constant flow rate to obtain the second characteristic curve in the double logarithmic coordinates of the instantaneous pseudo-bottom hole pressure drop and the instantaneous pseudo-bottom hole pressure drop derivative with respect to time;

[0016] S8. Based on the first characteristic curve and the second characteristic curve, obtain the main fracture permeability modulus and the initial main fracture permeability reflecting the permeability stress sensitivity in the long-term production stage, and the main fracture permeability modulus and the initial main fracture permeability reflecting the permeability stress sensitivity in the fracturing fluid backflow stage; thereby evaluate the difference in fracture stress sensitivity between the long-term production stage and the fracturing fluid backflow stage.

[0017] Preferably, in step S3, linearizing the three-linear unsteady-state seepage mathematical model includes:

[0018] In the main fracture flow region, the inter-fracture flow region, and the reservoir matrix flow region, linearize the three-linear unsteady-state seepage mathematical model by defining the pseudo-pressure considering the stress sensitivity of the main fracture.

[0019] Preferably, the definition of the pseudo-pressure considering the stress sensitivity of the main fracture is as follows:

[0020] In the matrix region and the inter-fracture flow region of the three-linear unsteady-state seepage:

[0021] In the long-term production stage and the fracturing fluid backflow stage, the pseudo-pressure is defined as follows:

[0022]

[0023] In the formula, m represents the gas pseudo-pressure, p represents the actual production pressure, μ represents the viscosity of shale gas, and Z represents the shale gas deviation factor.

[0024] In the main fracture flow region of the three-linear unsteady-state seepage:

[0025] For the long-term production stage, the pseudo-pressure considering the stress sensitivity of the main fracture is defined as:

[0026]

[0027] In the formula, m F represents the main fracture gas pseudo-pressure, with the unit of atm2 / cp; γ represents the main fracture permeability modulus, with the unit of atm -1 ; p F represents the pressure in the main fracture region, with the unit of atm; p ini represents the initial reservoir pressure, with the unit of atm.

[0028] For the fracturing fluid backflow stage, the pseudo-pressure considering the stress sensitivity of the main fracture is defined as:

[0029]

[0030] In the formula, m F represents the main fracture liquid pseudo-pressure, with the unit of atm.

[0031] Preferably, the linearized trilinear unsteady seepage mathematical model is as follows:

[0032] In the reservoir flow region of trilinear unsteady seepage:

[0033] During the long-term production stage and the fracturing fluid backflow stage, the linearized unsteady seepage mathematical model is as follows:

[0034]

[0035] m O | t＝0 = m i

[0036]

[0037]

[0038] During the long-term production stage, η O The calculation formula is:

[0039]

[0040] During the fracturing fluid backflow stage, η O The calculation formula is:

[0041]

[0042] In the formula, the subscript O represents the reservoir flow region; the subscript I represents the flow region between fractures; the subscript i represents the initial state; η is the diffusion coefficient, with the unit of cm2 / s; x is the distance from the horizontal wellbore, with the unit of cm; x e is the size of the reservoir in the vertical direction, with the unit of cm; x F represents the half-length of the fracture, with the unit of cm; t represents time, with the unit of s; φ represents porosity, K represents permeability, μ g represents the viscosity of shale gas, μ f represents the viscosity of the fracturing fluid, C tOg represents the comprehensive compressibility of the reservoir and shale gas in the reservoir flow region during the long-term production stage, C tOf represents the comprehensive compressibility of the reservoir and the fracturing fluid in the reservoir flow region during the fracturing fluid backflow stage.

[0043] In the flow region between fractures of trilinear unsteady seepage:

[0044] During the long-term production stage and the fracturing fluid backflow stage, the linearized unsteady seepage mathematical model is as follows:

[0045]

[0046] m I |t＝0 = m i

[0047]

[0048]

[0049] During the long - term production stage, η I The calculation formula is:

[0050]

[0051] During the fracturing fluid flow - back stage, η I The calculation formula is:

[0052]

[0053] In the formula, the subscript F represents the main fracture flow region; y represents the distance in the horizontal direction, with the unit of cm; w F is the hydraulic fracture width, with the unit of cm; d F represents the spacing between two adjacent main fractures, with the unit of cm; C tIg represents the comprehensive compressibility of the reservoir and shale gas in the flow region between fractures during the long - term production stage, C tIf represents the comprehensive compressibility of the reservoir and fracturing fluid in the flow region between fractures during the fracturing fluid flow - back stage.

[0054] In the main fracture flow region of three - linear unsteady - state seepage:

[0055] For the long - term production stage, the linearized unsteady - state seepage mathematical model is as follows:

[0056]

[0057] m F | t＝0 = m i

[0058]

[0059]

[0060]

[0061] In the formula, K Fi represents the initial permeability of the main fracture, with the unit of D; q F represents the flow rate in the main fracture, with the unit of cm3 / s; P sc represents the pressure under standard conditions, with the unit of atm; T represents the temperature; h represents the reservoir thickness, with the unit of cm; T sc represents the temperature under standard conditions, with the unit of K; CtF It represents the comprehensive compressibility of the reservoir and gas in the main fracture flow region during the long-term production stage.

[0062] For the fracturing fluid backflow stage, the linearized unsteady seepage mathematical model is as follows:

[0063]

[0064] m F | t＝0 = m i

[0065]

[0066]

[0067]

[0068] In the formula, B represents the formation fluid volume factor, p I represents the pressure in the flow region between fractures during the fracturing fluid backflow stage, C tFf represents the comprehensive compressibility of the reservoir and fracturing fluid in the main fracture flow region during the fracturing fluid backflow stage.

[0069] Preferably, in step S5, the linearization process includes:

[0070] By setting the main fracture permeability modulus value in the long-term production stage and the main fracture permeability modulus value in the fracturing fluid backflow stage, the pressure data in the production dynamic data is converted into pseudo-pressure data.

[0071] Preferably, in step S5, the normalization process is as follows:

[0072] Using Duhamel's principle and combining the nonlinear regularization method of curvature minimization, improve the pressure deconvolution algorithm based on the second-order B-spline;

[0073] Using the improved pressure deconvolution algorithm, convert the pseudo-pressure data under variable flow rates in the long-term production stage and the fracturing fluid backflow stage into pseudo-pressure data under constant flow rates, specifically as follows:

[0074]

[0075] In the formula, for the fracturing fluid backflow stage, p i represents the initial reservoir pressure; for the long-term production stage, p i represents the initial pseudo-pressure of the reservoir; q represents the flow rate of the fracturing fluid; p represents the bottom-hole flowing pressure under variable flow rates; p' u represents the pressure derivative under unit flow rate.

[0076] Preferably, in step S6, the first characteristic curve fitting includes:

[0077] By adjusting the main fracture permeability modulus, main fracture half-length, and initial main fracture permeability that reflect the stress sensitivity of permeability, the debugging of the normalized parameters calculated by pressure deconvolution and the debugging of the model parameters calculated by the seepage theory model are mutually restricted during the characteristic curve fitting process.

[0078] In particular, when adjusting the main fracture permeability modulus, repeat steps S5 to S6 to obtain the fitted first characteristic curve.

[0079] Preferably, in step S7, the second characteristic curve fitting includes:

[0080] Using the fitting parameters of the first characteristic curve, fracturing construction data, and reservoir basic data as constraint conditions, by adjusting the main fracture permeability modulus, main fracture half-length, initial main fracture permeability, and matrix permeability that reflect the stress sensitivity of permeability, the debugging of the normalized parameters calculated by pressure deconvolution and the debugging of the model parameters calculated by the seepage theory model are mutually restricted during the characteristic curve fitting process.

[0081] In particular, when adjusting the main fracture permeability modulus, repeat steps S5 to S7 to obtain the fitted second characteristic curve.

[0082] Preferably, in step S8, evaluating the stress sensitivity difference of the fracture during the long-term production stage and the fracturing fluid backflow stage includes:

[0083] Obtain the corresponding relationship chart of the conductivity and the actual bottom-hole flowing pressure on site during the long-term production stage and the fracturing fluid backflow stage, as well as the curve chart of the change in the conductivity of the fracturing fracture considering stress sensitivity.

[0084] Therefore, the method for evaluating the stress sensitivity difference of the main fracture during the fracturing fluid backflow and gas production stages of the present invention has the following technical effects:

[0085] (1) The method of the present invention uses the method of fitting the characteristic curve, which can directly interpret the main fracture permeability modulus during the fracturing fluid backflow stage and the long-term production stage, and then obtain the corresponding relationship chart of the conductivity and the actual bottom-hole flowing pressure on site in the two stages, as well as the curve chart of the change in the conductivity of the fracturing fracture considering stress sensitivity in the two stages; compared with the traditional experimental method, the method of the present invention can obtain the dynamic change characteristics of the conductivity of the fracturing fracture during the entire production process, and is not easily affected by external factors, and the interpretation result is more reliable; and compared with the numerical simulation method, the method of the present invention is simple and fast in calculation, and is more stable and efficient.

[0086] (2) Considering the stress sensitivity of the main fracture, establish the unsteady seepage mathematical model of gas during the long-term production stage and the unsteady nonlinear seepage mathematical model of liquid during the fracturing fluid flowback stage. By defining the pseudo-pressure considering the stress-sensitive influence of the main fracture, linearize the unsteady seepage model. Use the improved pressure deconvolution algorithm to normalize the production dynamic data, making the processed production dynamic data consistent with the inner boundary conditions of the linearized seepage mathematical model, so as to establish an analysis method for the characteristic curve of shale gas production dynamic data considering the stress sensitivity of the main fracture. In addition, using the pressure deconvolution algorithm to normalize the production dynamic data reduces the influence of production dynamic data errors and improves the fitting effect of the double-logarithm characteristic curve, enabling the research results on the stress sensitivity differences of the fracturing cracks during the fracturing fluid flowback and production stages of shale gas wells to be more accurate.

[0087] (3) By adjusting parameters such as the permeability modulus reflecting the stress sensitivity of the main fracture and the initial permeability of the main fracture in the mathematical model considering the stress sensitivity of the main fracture, when fitting the double-logarithm characteristic curve of the production dynamic data of a multi-stage fractured horizontal well in a shale gas reservoir and the pseudo-pressure solution of the seepage mathematical model under a constant flow rate, using the known reservoir basic data and fracturing construction data as conditional constraints, make the debugging of the normalized parameters calculated by the pressure deconvolution and the debugging of the model parameters calculated by the seepage theory model restrict each other during the characteristic curve fitting process, so as to analyze a more reliable interpretation result of the stress sensitivity parameters of the main fracture permeability; in addition, using the interpretation result of the characteristic curve fitted during the long-term production stage as the conditional constraint for the interpretation of the fracture characteristic parameters during the fracturing fluid flowback stage further reduces the multi-solution property of the interpretation result of the stress sensitivity parameters of the main fracture permeability and improves the reliability and authenticity of the interpretation result.

[0088] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0089] Figure 1 is a flow chart of a method for evaluating the stress sensitivity difference of the main fracture during the fracturing fluid flowback and gas production stages;

[0090] Figure 2 is a schematic diagram of a trilinear seepage physical model for evaluating the stress sensitivity difference of the main fracture during the fracturing fluid flowback and gas production stages;

[0091] Figure 3 is the fitting effect diagram of the double-logarithm first characteristic curve of gas during the long-term production stage of a shale gas well;

[0092] Figure 4 is a graph showing the relationship between the main fracture conductivity and the on-site bottom-hole flowing pressure during the long-term production stage of a shale gas well;

[0093] Figure 5It is the fitting effect diagram of the double logarithmic second characteristic curve of the liquid in the fracturing fluid backflow stage of a shale gas well;

[0094] Figure 6 It is the relationship chart of the main fracture conductivity and the bottom-hole flowing pressure in the field during the fracturing fluid backflow stage of a shale gas well;

[0095] Figure 7 It is the curve chart of the change of the main fracture conductivity during the long-term production stage of a shale gas well;

[0096] Figure 8 It is the curve chart of the change of the main fracture conductivity during the fracturing fluid backflow stage of a shale gas well. Specific implementation manners

[0097] As Figure 1 shown, the method for evaluating the difference in the stress sensitivity of the main fracture during the fracturing fluid backflow and gas production stages provided by the present invention includes the following steps:

[0098] S1. According to the seepage laws of gas and fracturing fluid during the fracturing development of a shale gas well, the complex flow process of gas and fracturing fluid in the reservoir is simplified into a linear flow process in three adjacent regions, namely, the main fracture flow region, the inter-fracture flow region, and the reservoir matrix flow region of trilinear unsteady seepage. Among them, the flow of fracturing fluid mainly occurs in the main fracture flow region. Therefore, considering the stress sensitivity of the main fracture, a trilinear seepage physical model of a multi-stage fractured horizontal well in a shale gas reservoir is established.

[0099] S2. According to the trilinear seepage physical model in step S1 above, considering the stress sensitivity of the main fracture, an unsteady seepage mathematical model of gas during the long-term production stage and an unsteady seepage mathematical model of liquid during the fracturing fluid backflow stage are established respectively.

[0100] S3. By defining a pseudo-pressure method considering the influence of the stress sensitivity of the main fracture, the unsteady seepage mathematical model in step S2 is linearized.

[0101] (1) For the long-term production stage

[0102] In the matrix region and the inter-fracture flow region of trilinear unsteady seepage, the pseudo-pressure is defined as:

[0103]

[0104] In the formula, m represents the gas pseudo-pressure, with the unit of atm2 / cp; p represents the actual production pressure, with the unit of atm; μ represents the viscosity of shale gas, with the unit of cp; Z represents the shale gas deviation factor.

[0105] In the main fracture region of trilinear unsteady seepage, the pseudo-pressure considering the stress sensitivity of the main fracture is defined as:

[0106]

[0107] In the formula, m F represents the pseudo-pressure of the main fracture gas, with the unit of atm2 / cp; γ represents the permeability modulus of the main fracture, with the unit of atm -1 ; p F represents the pressure in the main fracture area, with the unit of atm; p ini represents the initial reservoir pressure, with the unit of atm.

[0108] The linearized unsteady seepage mathematical model is as follows:

[0109] (a) Reservoir flow region of trilinear unsteady seepage:

[0110]

[0111] m O | t＝0 = m i

[0112]

[0113]

[0114]

[0115] In the formula, the subscript O represents the reservoir flow region; the subscript I represents the flow region between fractures; the subscript i represents the initial state; η is the diffusion coefficient, with the unit of cm2 / s; x is the distance from the horizontal wellbore, with the unit of cm; x e is the size of the reservoir in the x-axis direction, with the unit of cm; x F represents the half-length of the fracture, with the unit of cm; t represents time, with the unit of s; φ represents porosity, K represents permeability, μ g represents the viscosity of shale gas, μ f represents the viscosity of the fracturing fluid, C tOg represents the comprehensive compressibility of the reservoir and shale gas in the reservoir flow region during the long-term production stage.

[0116] (b) Flow region between fractures of trilinear unsteady seepage:

[0117]

[0118] m I | t＝0 = m i

[0119]

[0120]

[0121]

[0122] In the formula, the subscript F represents the main fracture flow region; y represents the distance in the y-axis direction, with the unit of cm; w F is the hydraulic fracture width, with the unit of cm; d F represents the spacing between two adjacent main fractures, with the unit of cm; C tIg represents the comprehensive compressibility of the reservoir and shale gas in the flow region between fractures during the long-term production stage.

[0123] (c) Main fracture flow region of trilinear unsteady-state seepage:

[0124]

[0125] m F | t＝0 = m i

[0126]

[0127]

[0128]

[0129] In the formula, q F represents the flow rate in the main fracture, with the unit of cm3 / s; h represents the reservoir thickness, with the unit of cm; T represents the temperature; T sc represents the temperature under standard conditions, with the unit of K; P sc represents the pressure under standard conditions, with the unit of atm; K Fi represents the initial permeability of the main fracture, with the unit of D; C tF represents the comprehensive compressibility of the reservoir and gas in the main fracture flow region during the long-term production stage.

[0130] (2) For the fracturing fluid flowback stage

[0131] The formula form of the seepage mathematical model of the fluid during the fracturing fluid flowback stage is similar to that of the gas during the long-term production stage. The main differences lie in considering the definition of the pseudo-pressure of the main fracture stress sensitivity and the inner boundary condition of the main fracture flow region.

[0132] In addition, there are also differences in the calculation of the diffusion coefficient, which are as follows:

[0133] (a) Reservoir flow region of trilinear unsteady-state seepage:

[0134] The unsteady-state linearized seepage mathematical model is the same as that in the long-term production stage, where η O The calculation formula is:

[0135]

[0136] In the formula, C tOf represents the combined compressibility of the reservoir and the fracturing fluid in the reservoir flow region during the fracturing fluid backflow stage.

[0137] (b) Inter - fracture flow region of three - linear unsteady - state seepage:

[0138] The unsteady - state linearized seepage mathematical model is consistent with the long - term production stage, where η I The calculation formula is:

[0139]

[0140] In the formula, C tIf represents the combined compressibility of the reservoir and the fracturing fluid in the inter - fracture flow region during the fracturing fluid backflow stage.

[0141] (c) Main - fracture flow region of three - linear unsteady - state seepage:

[0142] The pseudo - pressure considering the stress - sensitivity effect of the main fracture is defined as:

[0143]

[0144] In the formula, m F represents the pseudo - pressure of the liquid in the main fracture, with the unit of atm.

[0145] The unsteady - state linearized seepage mathematical model of the liquid is:

[0146]

[0147] m F | t＝0 = m i

[0148]

[0149]

[0150]

[0151] In the formula, B represents the formation fluid volume factor, p I represents the pressure in the inter - fracture flow region during the fracturing fluid backflow stage, and C tFf represents the combined compressibility of the reservoir and the fracturing fluid in the main - fracture flow region during the fracturing fluid backflow stage.

[0152] S4. Perform Laplace transform on the linearized unsteady seepage mathematical model considering the stress sensitivity of the main fracture, and solve it respectively to obtain the instantaneous pseudo-bottom-hole flowing pressure solution of the gas linearized unsteady seepage mathematical model in the long-term production stage considering the stress sensitivity of the main fracture and under constant flow rate, and the instantaneous pseudo-bottom-hole flowing pressure solution of the liquid linearized unsteady seepage mathematical model in the fracturing fluid backflow stage considering the stress sensitivity of the main fracture and under constant flow rate.

[0153] Among them, solve the linearized unsteady seepage mathematical model of the gas considering the stress sensitivity of the main fracture in the long-term production stage to obtain the instantaneous pseudo-bottom-hole flowing pressure solution under constant flow rate. It is:

[0154]

[0155] In the formula, the subscript w represents the bottom hole; the subscript D represents dimensionless; s is the Laplace transform parameter; C FD represents the dimensionless hydraulic fracture conductivity; α F represents the hydraulic fracture parameter in the trilinear flow model; r w represents the wellbore radius.

[0156] The above formula represents the pseudo-bottom-hole pressure solution or dimensionless bottom-hole pressure solution of the seepage mathematical model under constant flow rate in the Laplace space; through Stehfest numerical inversion, the pseudo-bottom-hole pressure solution under constant flow rate in the real space can be obtained, and further the pseudo-bottom-hole pressure derivative solution or bottom-hole pressure derivative solution under constant flow rate in the real space can be obtained.

[0157] Solve the liquid linearized unsteady seepage mathematical model in the fracturing fluid backflow stage to obtain the dimensionless instantaneous bottom-hole flowing pressure solution under constant flow rate, which is in the same form as the dimensionless instantaneous pseudo-bottom-hole flowing pressure solution in the long-term production stage.

[0158] S5. According to the method of defining the pseudo-pressure considering the stress sensitivity of the main fracture in step S3, set the main fracture permeability modulus value reflecting the stress sensitivity of permeability in the long-term production stage and the main fracture permeability modulus value reflecting the stress sensitivity of permeability in the backflow stage; convert the pressure data in the production dynamic data into pseudo-pressure data to achieve linearization processing of the data.

[0159] Normalize the production dynamic data with large errors and violent changes after linearization in the long-term production stage and the backflow stage, specifically as follows:

[0160] Based on the Duhamel principle, a non-linear regularization method introducing the idea of curvature minimization is added to the pressure deconvolution algorithm based on the second-order B-spline, namely the improved deconvolution algorithm; the improved deconvolution algorithm is used to normalize the production dynamic data, eliminate the error influence, and improve the calculation speed and stability of the algorithm, and convert the pseudo-pressure data under variable flow rates in the long-term production stage and the flow-back stage into pseudo-pressure data under constant flow rates:

[0161]

[0162] In the formula, for the flow-back stage, p i represents the initial reservoir pressure; for the long-term production stage, p i represents the initial pseudo-pressure of the reservoir; q represents the flow rate of the fracturing fluid; p represents the bottom-hole flowing pressure under variable flow rates; p′ u represents the pressure derivative under unit flow rate.

[0163] Using the above formula, when the variable flow rate q and the corresponding variable pressure p are known, the pressure under unit flow rate is calculated, and the specific process is as follows:

[0164] Through the weights of the Ilk second-order B-spline function, the pressure derivative p′ u under unit flow rate is reconstructed; then, using the mathematical properties of the convolution integral, segmented integration is performed according to the actual flow rate history to quickly analytically solve the sensitivity matrix of the pressure deconvolution calculation. Using the above method, the calculation speed and stability of the deconvolution are greatly improved, making the fitting effect between the production dynamic data and the characteristic curve of the seepage theory model better.

[0165] S6. Taking the fracturing construction data and the reservoir basic data as constraint conditions, by adjusting the main fracture permeability modulus, main fracture half-length, initial permeability of the main fracture, and matrix permeability that reflect the permeability stress sensitivity in the linearized unsteady seepage mathematical model, the debugging of the normalized parameters of the pressure deconvolution calculation and the debugging of the model parameters calculated by the linearized unsteady seepage theory model considering the main fracture stress sensitivity are mutually restricted during the characteristic curve fitting process.

[0166] Among them, every time the main fracture permeability modulus reflecting the permeability stress sensitivity is adjusted, it is necessary to return to steps S4 and S5 for repeated operations, and fit the normalized production dynamic data in the long-term production stage and the pseudo-bottom-hole flowing pressure solution of the linearized unsteady seepage mathematical model under constant flow rate to obtain a perfect first characteristic curve in the double logarithmic coordinates of the instantaneous pseudo-bottom-hole pressure drop and the instantaneous pseudo-bottom-hole pressure drop derivative with respect to time.

[0167] S7. Using the fitting parameters of the first characteristic curve, fracturing construction data, and reservoir basic data as constraint conditions, by adjusting the main fracture permeability modulus, main fracture half-length, and initial main fracture permeability that reflect the stress sensitivity of permeability, the debugging of the normalized parameters calculated by pressure deconvolution and the debugging of the model parameters calculated by the seepage theory model are mutually restricted during the characteristic curve fitting process.

[0168] Among them, each time the main fracture permeability modulus that reflects the stress sensitivity of permeability is adjusted, it is necessary to return to steps S4 and S5 for repeated operations, and fit the normalized production dynamic data during the fracturing fluid backflow stage and the pseudo-bottom-hole flowing pressure solution of the linearized unsteady seepage mathematical model under a constant flow rate to obtain a perfectly fitted second characteristic curve in the double logarithmic coordinates of the instantaneous pseudo-bottom-hole pressure drop with respect to time and the derivative of the instantaneous pseudo-bottom-hole pressure drop.

[0169] During the adjustment process of the characteristic curve fitting parameters of the fracturing fluid backflow, using the interpretation results of the fitting parameters of the double logarithmic first characteristic curve in the long-term production stage as conditional constraints can further reduce the multi-solution nature of the interpretation results and improve the accuracy of the interpretation results.

[0170] S8. According to the first characteristic curve and the second characteristic curve fitted in steps S6 and S7, interpret the main fracture permeability modulus and initial main fracture permeability that reflect the stress sensitivity of permeability during the fracturing fluid backflow stage, and the main fracture permeability modulus, initial main fracture permeability, and other reservoir parameters that reflect the stress sensitivity of permeability during the long-term production stage; and based on the dimensionless instantaneous pseudo-bottom-hole flowing pressure solution under a constant flow rate, eliminate the influence of the skin effect in the bottom-hole flowing pressure, so as to obtain the corresponding relationship charts of the conductivity and the actual bottom-hole flowing pressure during the long-term production stage and the fracturing fluid backflow stage respectively, as well as the variation curve charts of the fracturing fracture conductivity considering stress sensitivity during the long-term production stage and the fracturing fluid backflow stage. Through comparative analysis, further evaluate the stress sensitivity differences of the fracturing fractures during the fracturing fluid backflow and production stages of shale gas wells.

[0171] Verification Example

[0172] A multi-stage fractured horizontal well in a shale gas reservoir in North America has a length of 2889 m, a wellbore radius of 0.107 m, 58 fracturing stages, a main fracture spacing of 49.8 m, a reservoir temperature of 114 °C, an initial pressure of the reservoir where the well is located of 59.2 MPa, and a reservoir thickness of 36.9 m.

[0173] Establish a three-linear seepage physical model considering stress sensitivity for the gas during the long-term production stage and the liquid during the fracturing fluid backflow stage of this shale gas well as Figure 2 shown. The seepage of shale gas during the backflow stage is mainly concentrated in the main fracture area within the dashed box. According to the methods of steps S1 to S8 above, the first characteristic curve obtained is as Figure 3As shown, the main fracture permeability modulus is interpreted as 0.004 MPa according to the fitted first characteristic curve -1 , the initial conductivity of the main fracture is 7.8 mD·cm, the fracture half-length is 37 m, the matrix permeability is 0.0001 mD, the porosity of the main fracture is 0.15, and the comprehensive compressibility coefficient of the main fracture is 0.005 MPa -1 , and the conductivity of the main fracture in the long-term production stage is obtained The expression is (unit: mD·cm):

[0174]

[0175] In the formula, P 长 represents the average bottom-hole flowing pressure in the long-term production stage

[0176] For the pseudo bottom-hole flowing pressure solution at a constant flow rate considering the skin effect, subtracting the influence of the skin from the bottom-hole flowing pressure gives the main fracture pressure, and thus the corresponding relationship chart between the bottom-hole flowing pressure varying with time and the conductivity of the main fracture in the long-term production stage is obtained, as shown Figure 4 .

[0177] According to the above method, the obtained second characteristic curve is as shown Figure 5 , and the main fracture permeability modulus is interpreted as 0.012 MPa according to the fitted second characteristic curve -1 , the initial conductivity of the main fracture is 420 mD·cm, the fracture half-length is 8.5 m, the fracture porosity is 0.15, and the comprehensive compressibility coefficient of the fracture is 0.0004 MPa -1 ; therefore, the conductivity of the main fracture in the fracturing fluid flowback stage is obtained The expression is:

[0178]

[0179] In the formula, P 返 represents the average bottom-hole flowing pressure in the fracturing fluid flowback stage

[0180] Similarly, the corresponding relationship chart between the bottom-hole flowing pressure varying with time and the conductivity of the main fracture in the long-term production stage is obtained, as shown Figure 6 .

[0181] According to the results, the main fracture permeability modulus in the fracturing fluid flowback stage is about 3 times that in the long-term production stage. Thus, the curve charts of the conductivity varying with the bottom-hole flowing pressure in the long-term production stage and the fracturing fluid flowback stage are obtained respectively, as shown Figure 7 and Figure 8 . It can be seen from the trend in the figure that the stress sensitivity of the main fracture in the flowback stage is significantly stronger than that in the long-term production stage

[0182] Therefore, by adopting the above method for evaluating the stress sensitivity difference of the main fracture during the fracturing fluid flowback and gas production stages, the accuracy and reliability of the interpretation results can be improved, and the conductivity considering the stress sensitivity of the main fracture during the long-term production stage and the fracturing fluid flowback stage can be obtained, providing a reference for the evaluation of the fracturing effect and the optimization of stimulation measures in shale gas reservoirs.

[0183] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for evaluating the stress sensitivity difference of the main fracture during the fracturing fluid flowback and gas production stages, characterized in that, It includes the following steps: S1. Considering the stress sensitivity of the main fracture, establish a trilinear seepage physical model for gas and a trilinear seepage physical model for liquid respectively for the long-term production stage and the fracturing fluid backflow stage of the shale gas reservoir fractured horizontal well. S2. According to the trilinear seepage physical models in step S1, considering the stress sensitivity of the main fracture, establish a trilinear unsteady seepage mathematical model for gas in the long-term production stage and a trilinear unsteady seepage mathematical model for liquid in the fracturing fluid backflow stage respectively. S3. Define the pseudo-pressure considering the stress sensitivity of the main fracture, and linearize the trilinear unsteady seepage mathematical model for gas in the long-term production stage and the trilinear unsteady seepage mathematical model for liquid in the fracturing fluid backflow stage respectively. S4. Solve the linearized trilinear unsteady seepage mathematical model for gas in the long-term production stage to obtain the instantaneous pseudo-bottom-hole flowing pressure solution in the long-term production stage considering the stress sensitivity of the main fracture and constant flow rate. Solve the linearized trilinear unsteady seepage mathematical model for liquid in the fracturing fluid backflow stage to obtain the instantaneous pseudo-bottom-hole flowing pressure solution in the fracturing fluid backflow stage considering the stress sensitivity of the main fracture and constant flow rate. S5. Conduct linearization processing on the production dynamic data collected in the long-term production stage and the backflow dynamic data in the fracturing fluid backflow stage. Using the improved pressure deconvolution algorithm, conduct normalization processing on the production dynamic data in the long-term production stage and the backflow dynamic data in the fracturing fluid backflow stage respectively. S6. Fit the normalized production dynamic data in the long-term production stage and the pseudo-bottom-hole flowing pressure solution of the linearized trilinear unsteady seepage mathematical model under constant flow rate to obtain the first characteristic curve in the double logarithmic coordinates of the instantaneous pseudo-bottom-hole pressure drop and the instantaneous pseudo-bottom-hole pressure drop derivative with respect to time, including: By adjusting the main fracture permeability modulus, main fracture half-length, initial main fracture permeability, and matrix permeability reflecting the stress sensitivity of permeability, make the debugging of the normalized parameters calculated by the pressure deconvolution and the debugging of the model parameters calculated by the seepage theory model restrict each other during the characteristic curve fitting process. When adjusting the main fracture permeability modulus, repeat steps S5 to S6 to obtain the fitted first characteristic curve. S7. Fit the normalized backflow dynamic data in the fracturing fluid backflow stage and the pseudo-bottom-hole flowing pressure solution of the linearized trilinear unsteady seepage mathematical model under constant flow rate to obtain the second characteristic curve in the double logarithmic coordinates of the instantaneous pseudo-bottom-hole pressure drop and the instantaneous pseudo-bottom-hole pressure drop derivative with respect to time, where: When adjusting the main fracture permeability modulus, repeat steps S5 to S7 to obtain the fitted second characteristic curve. S8. According to the first characteristic curve and the second characteristic curve, obtain the main fracture permeability modulus and initial main fracture permeability reflecting the stress sensitivity of permeability in the long-term production stage, and the main fracture permeability modulus and initial main fracture permeability reflecting the stress sensitivity of permeability in the fracturing fluid backflow stage; thereby evaluate the difference in fracture stress sensitivity between the long-term production stage and the fracturing fluid backflow stage.

2. The method for evaluating the stress sensitivity difference of the main fracture during the fracturing fluid backflow and gas production stages according to claim 1, wherein Step S3 includes linearizing the trilinear unsteady-state seepage mathematical model by defining the pseudo-pressure considering the stress sensitivity of the main fracture in the main fracture flow region, the inter-fracture flow region, and the reservoir matrix flow region; Among them, in the matrix region and the inter-fracture flow region of the trilinear unsteady-state seepage: During the long-term production stage and the fracturing fluid flowback stage, the pseudo-pressure is defined as follows: In the formula, m represents the gas pseudo-pressure, p represents the actual production pressure, μ represents the viscosity of shale gas, and Z represents the shale gas deviation factor; In the main fracture flow region of the trilinear unsteady-state seepage: For the long-term production stage, the pseudo-pressure considering the stress sensitivity of the main fracture is defined as: Where m F represents the pseudo-pressure of the main fracture gas, γ represents the permeability modulus of the main fracture, and p F represents the pressure in the main fracture area, and p ini represents the initial reservoir pressure; For the fracturing fluid flowback stage, the pseudo-pressure considering the stress sensitivity of the main fracture is defined as: where m F represents the pseudo-pressure of the main fracture fluid.

3. The method for evaluating the stress sensitivity difference of the main fracture during the fracturing fluid flowback and gas production stages according to claim 2, characterized in that, The linearized trilinear unsteady-state seepage mathematical model is specifically as follows: In the reservoir flow region of the trilinear unsteady-state seepage: During the long-term production stage and the fracturing fluid flowback stage, the linearized unsteady-state seepage mathematical model is as follows: m O | t＝0 = m i During the long-term production stage, η O The calculation formula is: During the fracturing fluid flowback stage, η O The calculation formula is as follows: The subscript O represents the reservoir flow region, the subscript I represents the flow region between fractures, the subscript i represents the initial state, η represents the diffusion coefficient, x represents the distance from the horizontal wellbore, x e represents the size of the reservoir in the vertical direction, x F represents the half-length of the fracture, t represents time, φ represents porosity, K represents permeability, μ g represents the viscosity of shale gas, μ f represents the viscosity of the fracturing fluid, C tOg represents the combined compressibility of the reservoir and shale gas in the reservoir flow region during the long-term production stage, C tOf represents the combined compressibility of the reservoir and the fracturing fluid in the reservoir flow region during the fracturing fluid flowback stage; In the inter-fracture flow region of the trilinear unsteady-state seepage: During the long-term production stage and the fracturing fluid flowback stage, the linearized unsteady-state seepage mathematical model is as follows: During the long-term production stage, η I The calculation formula is: During the fracturing fluid flowback stage, η I The calculation formula is as follows: In the formula, the subscript F represents the main fracture flow region; y represents the distance in the horizontal direction, w F is the hydraulic fracture width, d F represents the spacing between two adjacent main fractures, C tIg represents the comprehensive compressibility of the reservoir and shale gas in the flow region between fractures during the long-term production stage, C tIf represents the comprehensive compressibility of the reservoir and fracturing fluid in the flow region between fractures during the fracturing fluid flowback stage; In the main fracture flow region of the trilinear unsteady-state seepage: For the long-term production stage, the linearized unsteady-state seepage mathematical model is as follows: m F | t＝0 = m i where K Fi represents the initial permeability of the main fracture, q F represents the flow rate in the main fracture, P sc represents the pressure under standard conditions, T represents the temperature, h represents the reservoir thickness, T sc represents the temperature under standard conditions, C tF represents the comprehensive compressibility of the reservoir and gas in the main fracture flow region during the long-term production stage; For the fracturing fluid flowback stage, the linearized unsteady-state seepage mathematical model is as follows: m F | t＝0 = m i where B represents the formation fluid volume coefficient, and p I represents the pressure in the flow region between fractures during the fracturing fluid backflow stage, and C tFf represents the combined compressibility of the reservoir and the fracturing fluid in the main fracture flow region during the fracturing fluid backflow stage.

4. The method for evaluating the stress sensitivity difference of the main fracture in the fracturing fluid flowback and gas production stages according to claim 1, wherein In step S5, the normalization process is specifically as follows: Using Duhamel's principle and combining the nonlinear regularization method of curvature minimization to improve the pressure deconvolution algorithm based on the second-order B-spline; Using the improved pressure deconvolution algorithm to convert the pseudo-pressure data under variable flow rates during the long-term production stage and the fracturing fluid flowback stage into pseudo-pressure data under constant flow rates.

5. The method for evaluating the stress sensitivity difference of the main fracture in the fracturing fluid flowback and gas production stages according to claim 1, wherein Step S7 includes using the fitting parameters of the first characteristic curve, the fracturing construction data, and the reservoir basic data as constraint conditions, and by adjusting the main fracture permeability modulus, the main fracture half-length, and the initial permeability of the main fracture reflecting the stress sensitivity of permeability, making the debugging of the normalized parameters calculated by the pressure deconvolution and the debugging of the model parameters calculated by the seepage theory model restrict each other during the characteristic curve fitting process.

6. The method for evaluating the stress sensitivity difference of the main fracture during the fracturing fluid backflow and gas production stages according to claim 1, wherein In step S8, evaluating the stress sensitivity difference of the fracture during the long-term production stage and the fracturing fluid flowback stage includes: Obtaining the corresponding relationship chart of the conductivity and the actual bottom-hole flowing pressure on site during the long-term production stage and the fracturing fluid flowback stage, and the curve chart of the change in the conductivity of the fracturing fracture considering stress sensitivity.

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