A method for calculating the imbibition depth of fracturing fluid during fracturing and shut-in of horizontal wells in shale reservoirs

Abstract

The present invention discloses a method for calculating the imbibition depth of fracturing fluid during the fracturing-well soaking period of a horizontal well in a shale oil reservoir. The method belongs to the field of oil and gas development and is used to solve the problem that the imbibition depth of fracturing fluid is difficult to accurately predict during the fracturing process of a shale oil reservoir. The method is based on the principle of fracturing fluid imbibition, combined with Darcy's law and the basic principles of oil and gas reservoir engineering, and comprehensively considers the combined effects of capillary force and viscous resistance on the seepage process. An expression for the imbibition volume of fracturing fluid is established by defining the seepage velocity; and the relationship between the change in water saturation in the matrix before and after imbibition and the imbibition volume is introduced. Based on the principle of equal imbibition volume, a calculation model for the imbibition depth of fracturing fluid in shale oil reservoirs is constructed, which significantly improves the accuracy of imbibition depth prediction and has good practicality and scalability. The method not only provides a scientific basis for evaluating the imbibition effect of fracturing fluid, but also provides theoretical support for the optimal design of fracturing schemes, effectively improving the efficiency of oil and gas reservoir development.

Description

Technical Field

[0001] The present invention belongs to the field of oil and natural gas development, and in particular relates to a method for calculating the imbibition depth of fracturing fluid during the fracturing-well soaking period of a horizontal well in a shale oil reservoir. Background Art

[0002] For low-porosity, low-permeability shale reservoirs, horizontal wells combined with multi-stage fracturing are an effective means of enhancing oil recovery. Post-fracturing soaking can also significantly increase production. Fracturing can create a wider fracture envelope, increasing the flow space for oil and gas, and facilitating the penetration of fracturing fluid into the matrix pores. During soaking, the penetration depth of the fracturing fluid directly reflects its penetration into the rock pores. Studying the imbibition depth of fracturing fluids is of great theoretical and practical significance for evaluating the imbibition effect of fracturing fluids, analyzing the dynamics of fracturing imbibition, and planning fracturing and recovery strategies.

[0003] At present, the research on imbibition is mainly divided into indoor experimental research and theoretical research. In terms of theoretical research, Lucas and Washburn assumed that the imbibition fluid is an incompressible Newtonian fluid, and the imbibition channel is assumed to be a uniform circular capillary tube. Based on fluid dynamics and seepage theory, they obtained the expression of the imbibition velocity, and obtained the theoretical model of the imbibition distance by integrating the velocity. (Edward W.Washburn.The Dynamics of Capillary Flow[J].Physical Review,1921,Vol.17(3):273) Based on the LW model, Benavente considered the complexity of the pore microstructure, introduced the correction of tortuosity and pore shape factor, and combined Poiseuille's law to calculate the imbibition depth. (David Benavente; Peter Lock; M García Del Cura;Salvador Predicting the Capillary Imbibition of Porous Rocks from Microstructure[J]. Transport in Porous Media, 2002, Vol. 49(1): 59-76); Wang Fei, Yang Bin et al., considering the influence of confinement effect caused by changes in osmotic pressure and viscosity, derived the imbibition momentum equation based on the momentum theorem to obtain the imbibition depth. (Wang Fei, Pan Ziqing. Numerical simulation of fracturing fluid flowback in shale reservoirs driven by chemical potential difference[J]. Petroleum Exploration and Development, 2016, 43(06): 971-977.). Yang Jian et al., considering the influence of colloidal polymer residue and capillary force in fracturing fluid, derived the invasion rate of fracturing fluid through the SUPALAK model and Darcy's law, and obtained the imbibition depth model using seepage theory and mass conservation equation. (Yang Jian, Yang Bin, Wang Liang, et al. Study on the invasion depth of fracturing fluid imbibition in the matrix pores of shale oil reservoirs in Da'anzhai section of central Sichuan [J]. Petroleum Geology and Recovery, 2023, 30(05): 84-91.); Wu Zhongxiong et al., based on the seepage theory, established the fluid motion equation considering the starting pressure gradient, thereby obtaining the reverse imbibition control equation, combined with the capillary force curve, and used the multivariate nonlinear regression method to calculate the maximum imbibition distance of reverse imbibition in shale oil reservoirs. (Wu Zhongwei, Qin Lei, Cui Chuanzhi, et al. Calculation method of the maximum imbibition distance of reverse imbibition in shale oil reservoirs [J]. Special Oil and Gas Reservoirs, 2024, 31(04): 103-108.). In terms of experiments, Ren Kai et al., considering the influence of shale bedding, used the volumetric method to calculate the imbibition amount through spontaneous imbibition experiments, processed the data, and studied the changing law of imbibition distance. (Ren Kai, Ge Hongkui, Yang Liu, et al. Shale self-imbibition experiment and its application in flowback analysis [J]. Science, Technology and Engineering, 2015, 15(30):) Yang Zhengming, Sun Daokun, et al., used a high-pressure large-scale model physical simulation system and nuclear magnetic resonance technology to establish a core imbibition physical simulation experimental method of different scales. According to the change law of the model pressure field before and after the imbibition experiment and the change law of the T2 spectrum, the imbibition distance during the imbibition process was calculated. (Yang Zhengming, Liu Xuewei, Li Haibo, et al. Analysis of factors affecting imbibition in tight reservoirs and evaluation of imbibition effects [J]. Petroleum Exploration and Development, 2019, 46(04): 739-745.).

[0004] In the above research, the theoretical model established only considers capillary self-imbibition, and the calculation process has problems such as long time consumption and inaccurate results. At the same time, the use of linear regression to solve the formula will also be interfered by factors such as excessive empiricism and difficulty in determining the number of samples. In terms of experiments, although it is possible to obtain imbibition data from fracturing fluid core samples, the experimental process is usually affected by the precision limitations of the experimental equipment and its own limitations, and the experimental conditions are difficult to accurately simulate the actual formation environment. Therefore, based on the fact that artificial fractures are related to water content, according to the imbibition principle of fracturing fluid, starting from Darcy's law, the present invention uses oil and gas reservoir methods to establish a method for calculating the imbibition depth of fracturing fluid during the fracturing-well soaking period of horizontal wells in shale reservoirs. Summary of the Invention

[0005] The present invention addresses the problem that it is difficult to accurately predict the imbibition depth of fracturing fluid during the fracturing process of shale oil reservoirs, and proposes a method for calculating the imbibition depth of fracturing fluid during the fracturing-well shut-in period of horizontal wells in shale oil reservoirs; this method starts from the imbibition principle of fracturing fluid, combines Darcy's law and the basic principles of oil and gas reservoir engineering, comprehensively considers the joint effects of capillary force and viscous resistance on the seepage process, and establishes an expression for the imbibition volume of fracturing fluid through the definition of seepage velocity; and introduces the relationship between the change in water saturation in the matrix before and after imbibition and the imbibition volume, and constructs a calculation model for the imbibition depth of fracturing fluid in shale oil reservoirs based on the principle of equal imbibition volume. The present invention can not only significantly improve the accuracy of imbibition depth prediction, but also has good practicality and scalability, providing reliable technical support and broad application prospects for shale oil reservoir fracturing projects.

[0006] In order to achieve the above technical objectives, the present invention adopts the following technical solution, including the following steps:

[0007] Step S1: Obtain reservoir physical parameters and fluid property parameters, including porosity φ, initial water saturation S mwo , bound water saturation S mwc , matrix permeability k, wetting angle θ of the wetting phase fluid, interfacial tension σ of the two phases, capillary radius r; pore tortuosity τ, fluid viscosity μ;

[0008] Step S2: In shale reservoirs, consider the original water saturation of the bedrock as S mwo , the bedrock bound water saturation is S mwc During fracturing, due to the imbibition effect, the water content within the imbibition depth range d of the bedrock surface in contact with the artificial fracture reaches the bound water saturation of the bedrock. Based on the relationship between the water content of the artificial fracture and fracturing (the S mwc >S mwo ), the imbibition volume can be expressed as:

[0009] V ms =Adφ(S mwc -Smwo ) (1)

[0010] Where: A is the imbibition area, cm 2 ;S mwc is the bound water saturation, %; S mwo is the initial water saturation, %; d is the imbibition depth, cm; φ is the porosity, %;

[0011] Step S3: Shale reservoirs are different from conventional reservoirs and have the characteristics of low porosity and low permeability. The fracturing technology is used to transform the reservoir to increase the high permeability volume space for fluid flow. The imbibition area of the fracturing fluid that invades the formation due to spontaneous imbibition is related to the injection volume of the fracturing fluid and the pore throat structure of the reservoir. Combined with the actual reservoir tortuosity and fracturing operation parameters, the imbibition volume of the fracturing fluid can be further expressed as:

[0012]

[0013] Where: k is permeability, mD; r is capillary radius, cm; τ is pore tortuosity; V ms is the imbibition volume of the fracturing fluid, cm 3 ;

[0014] Step S4: Based on the imbibition characteristics of the fracturing fluid in the porous medium, the fracturing fluid is subject to the combined effects of capillary force and viscous resistance when flowing in the pores. When the fracturing fluid flows in the pores, the capillary force acts as a driving force, pushing the fracturing fluid into the formation, while the viscous force on the pore wall acts as a resistance, inhibiting the flow of the fracturing fluid. According to Darcy's law, the seepage velocity is expressed as:

[0015]

[0016] Where: v is the seepage velocity, cm / s; μ is the fluid viscosity, mPa·s; P c is the capillary force, MPa; F v is the viscous resistance, MPa;

[0017] Step S5: After the formation is fractured, the fracturing fluid enters the matrix pores under the combined action of capillary force and viscous resistance. According to Darcy's formula, the seepage velocity is further derived as:

[0018]

[0019] Where: σ is the interfacial tension between the two phases, N / cm; θ is the wetting angle of the wetting phase fluid, ;

[0020] Step S6: Based on the definition of seepage velocity, when the fracturing fluid flows in the matrix pores, since the pores constituting the porous medium are curved and irregular, the imbibition velocity of the fracturing fluid in the pores is related to the pore shape and the imbibition surface. The seepage velocity can be expressed as:

[0021]

[0022] Where: q is the flow rate of fracturing fluid through the seepage surface, cm 3 / s;

[0023] Step S7: The imbibition volume is the volume of the fracturing fluid injected at a certain flow rate that has accumulated over a period of time. Based on the definition of imbibition volume, the imbibition volume can be expressed as:

[0024]

[0025] Where: t is time, s; V ms is the imbibition volume of the fracturing fluid, cm 3 ;

[0026] Step S8: During the fracturing period, the total volume of the imbibition surface through which the fracturing fluid passes is related to the properties of the fracturing fluid, capillary force, and viscous resistance. The integral of the imbibition volume is derived as follows:

[0027]

[0028] Step S9: During the fracturing period, the fracturing fluid enters the matrix pores due to imbibition under the action of capillary force and viscous resistance. The penetration depth of the fracturing fluid in the pores is related to the change in reservoir pore size, fluid properties, and fracturing flowback conditions. By comprehensively considering the effects of fluid properties and tortuosity on the imbibition depth, and combining actual fracturing operation, seepage theory, and Darcy's law, the expression for the imbibition depth during the fracturing period can be derived as follows:

[0029]

[0030] Furthermore, the process of step S3 is as follows:

[0031] Step S31: Since the fracturing fluid does not flow in a straight line in a porous medium but flows in a circuitous manner, in order to modify the capillary bundle model, the Gaussian-Kalman method introduces the tortuosity or tortuosity of the pores. The porosity can be expressed as:

[0032]

[0033] Step S32: Considering the effect of tortuosity on fracturing fluid imbibition, formula (9) is substituted into formula (1) to obtain formula (2) for the fracturing fluid imbibition volume related to water content:

[0034]

[0035] Furthermore, the process of step S5 is as follows:

[0036] Step S51: When the fluid flows in the pore channel, capillary force is generated due to the existence of interfacial tension. The capillary force on the fluid can be described by the classic Young-Laplace equation:

[0037]

[0038] Step S52: During fracturing, the interaction force between fluid molecules causes relative displacement of fluid molecules, generating viscous resistance. The viscous resistance is proportional to the viscosity and velocity of the fluid. Wherein, v is the fluid seepage velocity, v = dd / dt, d is the fluid invasion depth, and μ is the fluid viscosity. The imbibition process is an incompressible Newtonian fluid flowing at a low speed in a circular tube with a small radius. The flow resistance conforms to Poiseuille's law. Therefore, the viscous resistance can be expressed by the following formula:

[0039] F v =8dπμv (11)

[0040] Step S53: Substitute formula (10) and formula (11) into formula (3) to obtain:

[0041]

[0042] Therefore, the seepage velocity can be further expressed as:

[0043]

[0044] Furthermore, the process of step S6 is as follows:

[0045] Step S61: Based on the definition of seepage velocity, which is the ratio of volume flow rate to the effective imbibition surface of the fracturing fluid, the seepage velocity can be expressed as:

[0046]

[0047] Step S62: Combining formula (9) and formula (13) to obtain formula (5):

[0048]

[0049] Furthermore, the process of step S8 is as follows:

[0050] Step S81: Based on the equal fluid seepage velocity, formula (4) and formula (5) are combined to obtain:

[0051]

[0052] Step S82: By combining Darcy's law and the definition of seepage velocity, formula (4) and formula (5) are used to further calculate the flow rate. The flow rate q can be expressed as:

[0053]

[0054] Step S83: Substituting formula (15) into formula (6), the volume flow rate per unit time of the imbibition depth can be obtained. The imbibition volume is expressed as:

[0055]

[0056] Step S84: Through time integration calculation, the relationship between the seepage volume is obtained as follows:

[0057]

[0058] Furthermore, the process of step S9 is as follows:

[0059] Step S91: Combining formula (2) and formula (6), the imbibition volume can be further expressed as:

[0060]

[0061] Step S92: Based on the relationship between the imbibition volume and water saturation, capillary force, viscous resistance and property parameters of the fracturing fluid, combined with the seepage theory method, the imbibition depth of the fracturing fluid is derived:

[0062]

[0063] As a further description of the above technical solution:

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] The present invention proposes a method for calculating the imbibition depth of fracturing fluid during the fracturing and shut-in period of horizontal wells in shale oil reservoirs. The method is based on the principle of fracturing fluid imbibition, Darcy's law, and the principles of oil and gas reservoir engineering. It comprehensively considers the effects of capillary force and viscous resistance, establishes an expression for imbibition volume through the definition of seepage velocity, introduces the relationship between the change in water saturation in the matrix before and after imbibition and the imbibition volume, and establishes a calculation model for imbibition depth based on the principle of "equal imbibition volume". Compared with the existing technology, the present invention overcomes the problems of complex calculations, strong empirical linear regression, and limited sample size of existing theoretical models; and avoids the problems of limited experimental conditions, inaccurate imbibition distance measurement, and long experimental time. The present invention can more accurately predict the imbibition depth of fracturing fluid in fractures and matrices, not only providing a scientific basis for the evaluation of fracturing fluid imbibition effects, but also providing theoretical support for the optimal design of fracturing schemes, and can effectively improve the efficiency of oil and gas reservoir development. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0067] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0068] Figure 1 This is a flow chart of a method for calculating the imbibition depth of fracturing fluid during the fracturing-well soaking period of a horizontal well in a shale oil reservoir;

[0069] Figure 2 : is a fracturing invasion depth curve with different soaking times according to one embodiment of the present invention;

[0070] Figure 3 is a curve showing changes in imbibition depth over time at different permeabilities according to an embodiment of the present invention;

[0071] Figure 4 is a curve showing changes in imbibition depth over time at different pore radii according to an embodiment of the present invention;

[0072] Figure 5 is a curve showing changes in imbibition depth over time at different water saturations according to an embodiment of the present invention;

[0073] Figure 6 1 is a curve showing the change of the imbibition depth over time at different wetting angles according to an embodiment of the present invention. DETAILED DESCRIPTION

[0074] The present invention is further described below with reference to the accompanying drawings and examples to facilitate understanding by those skilled in the art. However, it should be understood that the present invention is not limited to the specific embodiments described herein. It will be apparent to those skilled in the art that any variations within the spirit and scope of the present invention as defined and established by the appended claims are intended to be protected.

[0075] Implementation Examples

[0076] A method for calculating the imbibition depth of fracturing fluid after fracturing and well soaking. The calculation process is shown in Figure 1 , including the following steps in sequence:

[0077] Step S1. Take a shale oil reservoir as an example to perform model verification analysis and obtain fluid property parameters and fracturing parameters (values are shown in Table 1):

[0078] Table 1 Fluid property parameters and reservoir parameters

[0079] parameter Value parameter Value Permeability (mD) 0.001 Immune water saturation (%) 43 Porosity (%) 4 Initial water saturation (%) 10 Tortuosity (τ) 5 Pore radius (cm) <![CDATA[8×10 -7 ]]> Viscosity (mPa·s) 1.5 Wetting contact angle (°) 78 Surface tension (N / cm) <![CDATA[8×10 -5 ]]>

[0080] S2. In shale reservoirs, the original water saturation of the bedrock is considered to be S mwo , the bedrock bound water saturation is S mwc During fracturing, due to the imbibition effect, the water content within the imbibition depth range d of the bedrock surface in contact with the artificial fracture reaches the bound water saturation of the bedrock. Based on the relationship between the water content of the artificial fracture and fracturing (the S mwc >S mwo ), the imbibition volume can be expressed as:

[0081] V ms =Adφ(S mwc -S mwo ) (1)

[0082] S3. Shale reservoirs differ from conventional reservoirs in that they have low porosity and low permeability. Squeezing technology is used to transform these reservoirs to increase the high-permeability volume for fluid flow. The contact area of the fracturing fluid invading the formation due to spontaneous imbibition is related to the injection volume of the fracturing fluid and the pore-throat structure of the reservoir. Combined with the actual reservoir tortuosity and fracturing operation parameters, the imbibition volume can be expressed as:

[0083] S31. Since fracturing fluid flows in porous media in a circuitous manner rather than in a straight line, the Gauss-Kalman method introduces the tortuosity or tortuosity of the pores to modify the capillary bundle model. Porosity can be expressed as:

[0084]

[0085] S32. Considering the effect of tortuosity on fracturing fluid imbibition, the imbibition volume of fracturing fluid can be obtained by combining the above formula:

[0086]

[0087] S4. Based on the imbibition characteristics of fracturing fluid in porous media, it is subject to the combined effects of capillary force and viscous resistance when flowing in the pores. When the fracturing fluid flows in the pores, the capillary force acts as a driving force to push the fracturing fluid into the formation, while the viscous force on the pore wall acts as resistance, inhibiting the flow of the fracturing fluid. The seepage velocity can be expressed by Darcy's law as:

[0088]

[0089] S5: After the formation is fractured, the fracturing fluid enters the matrix pores under the combined action of capillary force and viscous resistance. According to Darcy's formula, the seepage velocity is further derived as:

[0090] S51. When a fluid flows through a porous channel, capillary forces are generated due to interfacial tension. The capillary forces acting on the fluid can be described by the classical Young-Laplace equation:

[0091]

[0092] During fracturing, the fracturing fluid flows in the capillaries. The intermolecular forces between the fluid molecules cause relative displacement, generating viscous resistance. The viscous resistance is proportional to the viscosity and velocity of the fluid. The viscous resistance can be expressed as follows:

[0093] F v =8dπμv (11)

[0094] S53. Substitute formula (10) and formula (11) into formula (3) to obtain:

[0095]

[0096] Therefore, the seepage velocity can be further expressed as:

[0097]

[0098] S6. Based on the definition of seepage velocity, when fracturing fluid flows in the matrix pores, the imbibition velocity of the fracturing fluid in the pores is related to the pore shape and imbibition surface because the pores of the porous medium are curved and irregular. The seepage velocity can be expressed as:

[0099] S61. Based on the definition of seepage velocity, which is the ratio of flow rate to the effective imbibition surface of the fracturing fluid, the seepage velocity can be expressed as:

[0100]

[0101] S62. Combining formula (9) and formula (13), we can get formula (5):

[0102]

[0103] S7. The imbibition volume is the volume of fracturing fluid injected at a certain flow rate over a period of time. Based on the definition of imbibition volume, the imbibition volume can be expressed as:

[0104]

[0105] S8. During the fracturing period, the total volume of the imbibition surface through which the fracturing fluid passes is related to the properties of the fracturing fluid, capillary force, and viscous resistance. The imbibition volume is derived as:

[0106] S81. According to the equal fluid seepage velocity, formula (4) and formula (5) can be combined to obtain:

[0107]

[0108] S82. By combining Darcy's law and the definition of seepage velocity, formula (4) and formula (5) are used to further calculate the flow rate. The flow rate q can be expressed as:

[0109]

[0110] S83. Substituting formula (15) into formula (6), the volume flow rate during the imbibition depth pressure period can be obtained. The imbibition volume is expressed as:

[0111]

[0112] S84. By integrating the time, the relationship between the seepage volume and the flow volume is:

[0113]

[0114] During the fracturing period, the fracturing fluid enters the matrix pores due to imbibition, driven by capillary forces and viscous resistance. The penetration depth of the fracturing fluid in the pores is related to the changes in reservoir pore size, fluid properties, and reservoir water content. By comprehensively considering the effects of fluid properties and tortuosity on imbibition depth, and combining actual fracturing operations, seepage theory, and Darcy's law, the expression for the imbibition depth during fracturing can be derived as:

[0115] S91. Combining formula (2) and formula (7), the imbibition volume can be further expressed as:

[0116]

[0117] S92. Based on the relationship between imbibition volume and water saturation, capillary force, viscous resistance, and the properties of the fracturing fluid, combined with the seepage theory method, the imbibition depth of the fracturing fluid is derived:

[0118]

[0119] S93. In the case of a pore radius of 8×10 -7 cm, and the soaking time is 30 days. The reservoir parameters are shown in Table 1. The reservoir permeability is 0.001 mD, the irreducible water saturation is 43%, the initial water saturation is 10%, and the viscosity μ is 1.5×10 -3 N·s / cm 2 , the porosity is 4%, and the imbibition depth is:

[0120]

[0121] S94. Reservoir parameters are shown in Table 1. Under the condition that other parameters remain unchanged, the imbibition depths are calculated when the soaking time is 10 days (864000 s), 30 days (2592000 s), 50 days (4320000 s), 70 days (6048000 s) and 90 days (7776000 s). The imbibition depths under different soaking times can be seen. Figure 2 , Table 2.

[0122] Table 2 Changes of imbibition depth with different soaking times

[0123]

[0124] S95. Reservoir parameters are shown in Table 1. Other parameters remain unchanged. The imbibition depths are calculated under different permeabilities of 0.0001mD, 0.0005mD, 0.001mD and 0.0015mD with soaking times of 10d (864000s), 30d (2592000s), 50d (4320000s), 70d (6048000s) and 90d (7776000s). The changes in imbibition depth under different permeabilities can be seen. Figure 3 , Table 3.

[0125] Table 3 Changes of imbibition depth over time under different permeability conditions

[0126]

[0127] S96. Reservoir parameters are shown in Table 1. When other parameters remain unchanged, the imbibition depths at soak times of 10 days (864,000 s), 30 days (2,592,000 s), 50 days (4,320,000 s), 70 days (6,048,000 s), and 90 days (7,776,000 s) are calculated under different pore radii of 8 nm, 12 nm, 16 nm, and 20 nm, as shown in Tables 4 and 5. Figure 4 shown.

[0128] Table 4 Changes of imbibition depth over time under different pore radius conditions

[0129]

[0130] S97. Reservoir parameters are shown in Table 1. When other parameters remain unchanged, the imbibition depths at different water saturation conditions with soak times of 10 days (864,000 s), 30 days (2,592,000 s), 50 days (4,320,000 s), 70 days (6,048,000 s), and 90 days (7,776,000 s) are calculated as shown in Tables 5 and 6. Figure 5 shown.

[0131] Table 5 Changes of imbibition depth over time under different water saturation conditions

[0132]

[0133] S98. Reservoir parameters are shown in Table 1. Under the condition that other parameters remain unchanged, as shown in Table 6, Figure 6 As shown in the figure, the imbibition depths under different wetting angle conditions are calculated when the soaking time is 10d (864000s), 30d (2592000s), 50d (4320000s), 70d (6048000s) and 90d (7776000s).

[0134] Table 6 Changes of imbibition depth over time under different wetting angles

[0135]

[0136] The above description is not intended to be a formal limitation on the present invention. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any technician familiar with the present profession can use the technical content disclosed above to make some changes or modifications to equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are still within the scope of the technical solution of the present invention.

Claims

1. A method for calculating the imbibition depth of fracturing fluid during the fracturing-well soaking period of a horizontal well in a shale oil reservoir, characterized in that: The following steps are involved: Step S1: Obtain reservoir physical property parameters and fluid property parameters; Including porosity φ, initial water saturation S mwo , bound water saturation S mwc , matrix permeability k, wetting angle θ of the wetting phase fluid, interfacial tension σ of the two phases, capillary radius r, pore tortuosity τ, and fluid viscosity μ; Step S2: Consider the original water saturation of the bedrock as S mwo , the bedrock bound water saturation is S mwc During fracturing, due to the imbibition effect, the water content within the imbibition depth range d of the bedrock surface in contact with the artificial fracture reaches the bound water saturation of the bedrock. Based on the relationship between the water content of the artificial fracture and fracturing (the S mwc >S mwo ), the imbibition volume is expressed as: V ms =Adφ(S mwc -S mwo ) (1) Where: A is the imbibition area, cm 2 ; S mwc is the bound water saturation, %; S mwo is the initial water saturation, %; d is the imbibition depth, cm; φ is the porosity, %; Step S3: Using the fracturing and imbibition technology to transform the reservoir, the high permeability volume space for fluid flow is increased. The imbibition area of the fracturing fluid that invades the formation due to spontaneous imbibition is related to the injection volume of the fracturing fluid and the pore throat structure of the reservoir. Combined with the actual reservoir tortuosity and fracturing operation parameters, the imbibition volume of the fracturing fluid is further expressed as: Where: k is permeability, mD; r is capillary radius, cm; τ is pore tortuosity; V ms is the imbibition volume of the fracturing fluid, cm 3 ; Step S4: When the fracturing fluid flows in the pores, it is subjected to the combined effects of capillary force and viscous resistance. At this time, the capillary force acts as a driving force, pushing the fracturing fluid into the formation, and the viscous force on the pore wall acts as a resistance, inhibiting the flow of the fracturing fluid. According to Darcy's law, the seepage velocity is expressed as: Where: v is the seepage velocity, cm / s; μ is the fluid viscosity, mPa·s; P c is the capillary force, MPa; F v is the viscous resistance, MPa; Step S5: After the formation is fractured, the fracturing fluid enters the matrix pores under the combined action of capillary force and viscous resistance. According to Darcy's formula, the seepage velocity is further derived as: Where: σ is the interfacial tension between the two phases, N / cm; θ is the wetting angle of the wetting phase fluid, Step S6: Based on the definition of seepage velocity, when the fracturing fluid flows in the matrix pores, since the pores constituting the porous medium are curved and irregular, the imbibition velocity of the fracturing fluid in the pores is related to the pore shape and the imbibition surface. The seepage velocity is expressed as: Where: q is the flow rate of fracturing fluid through the seepage surface, cm 3 / s; Step S7: The imbibition volume is the volume of the fracturing fluid injected at a certain flow rate that has accumulated over a period of time. Based on the definition of imbibition volume, the imbibition volume is expressed as: Where: t is time, s; V ms is the imbibition volume of the fracturing fluid, cm 3 ; Step S8: During the fracturing period, the total volume of the imbibition surface through which the fracturing fluid passes is related to the properties of the fracturing fluid, capillary force, and viscous resistance. The integral of the imbibition volume is derived as follows: Step S9: By comprehensively considering the effects of fluid properties and tortuosity on imbibition depth, and combining actual fracturing operation, seepage theory, and Darcy's law, the expression for imbibition depth during fracturing is derived as follows:

2. The method for calculating the imbibition depth of the fracturing fluid during the fracturing and soaking period of a horizontal well in a shale oil reservoir according to claim 1, characterized in that: The specific process of step S3 is as follows: Step S31: Since the fracturing fluid does not flow in a straight line in a porous medium but flows in a circuitous manner, in order to modify the capillary bundle model, the Gaussian-Kalman method introduces the tortuosity or tortuosity of the pores. The porosity is expressed as: Step S32: Considering the effect of tortuosity on fracturing fluid imbibition, formula (9) is substituted into formula (1) to obtain formula (2) for the fracturing fluid imbibition volume related to water content:

3. The method for calculating the imbibition depth of the fracturing fluid during the fracturing and soaking period of a horizontal well in a shale oil reservoir according to claim 1, characterized in that: The specific process of step S5 is as follows: Step S51: When the fluid flows in the pore channel, capillary force is generated due to the existence of interfacial tension. The capillary force on the fluid is described by the classic Young-Laplace equation: Step S52: During fracturing, the interaction force between fluid molecules causes relative displacement of fluid molecules, generating viscous resistance. The viscous resistance is proportional to the viscosity and velocity of the fluid, where v is the fluid seepage velocity, v = dd / dt, d is the fluid invasion depth, and μ is the fluid viscosity. The imbibition process is an incompressible Newtonian fluid flowing at a low speed in a circular tube with a small radius. The flow resistance conforms to Poiseuille's law. Therefore, the viscous resistance is expressed by the following formula: F v =8dπμv (11) Step S53: Substitute formula (10) and formula (11) into formula (3) to obtain: Therefore, the seepage velocity can be further expressed as:

4. The method for calculating the imbibition depth of the fracturing fluid during the fracturing and soaking period of a horizontal well in a shale oil reservoir according to claim 1, characterized in that: The specific process of step S6 is as follows: Step S61: Based on the definition of seepage velocity, which is the ratio of volume flow rate to the effective imbibition surface of the fracturing fluid, the seepage velocity is expressed as: Step S62: Combining formula (9) and formula (13) to obtain formula (5):

5. The method for calculating the imbibition depth of the fracturing fluid during the fracturing and soaking period of a horizontal well in a shale oil reservoir according to claim 1, characterized in that: The specific process of step S8 is as follows: Step S81: Based on the equal fluid seepage velocity, formula (4) and formula (5) are combined to obtain: Step S82: By combining Darcy's law and the definition of seepage velocity, formula (4) and formula (5) are used to further calculate the flow rate. The flow rate q is expressed as: Step S83: Substitute formula (15) into formula (6) to obtain the volume flow rate per unit time of the imbibition depth. The imbibition volume is expressed as: Step S84: Through time integration calculation, the relationship between the seepage volume is obtained as follows:

6. The method for calculating the imbibition depth of the fracturing fluid during the fracturing and soaking period of a horizontal well in a shale oil reservoir according to claim 1, characterized in that: The specific process of step S9 is as follows: Step S91: Combining formula (2) and formula (6), the imbibition volume is further expressed as: Step S92: Based on the relationship between the imbibition volume and water saturation, capillary force, viscous resistance and property parameters of the fracturing fluid, combined with the seepage theory method, the imbibition depth of the fracturing fluid is derived:

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