A calculation method for hydraulic fracture propagation in high-temperature deep shale formations considering thermal effects

Abstract

The present invention discloses a method for calculating the expansion of hydraulic fractures in high-temperature deep shale formations taking into account thermal effects, including: collecting formation parameters, fluid physical parameters, and engineering parameters of high-temperature deep shale horizontal wells; establishing fluid flow, rock deformation, and near-fracture formation energy control equations; discretizing fluid flow, rock deformation, and near-fracture formation energy control equations; combining initial and boundary conditions, assembling discrete equations, and solving the length and width of hydraulic fractures, the pressure inside the fractures, the temperature inside the fractures and the fracture wall, and the amount of liquid inflow in each cluster; determining whether the fractures are expanded and their extension directions based on the maximum tensile stress criterion; continuing to calculate the expansion of the fractures in the next time step until the fracturing time ends, and determining the morphology of each cluster of fractures at the end of fracturing. The present invention solves the problem that the existing calculation method cannot take into account the objective factor of the influence of the additional thermal stress on the expansion of the fractures, and improves the hydraulic fracturing optimization theory and method of high-temperature shale formations.

Description

Technical Field

[0001] The invention relates to a method for calculating the expansion of hydraulic fractures in high-temperature deep shale formations taking thermal effects into consideration, and belongs to the technical field of unconventional oil and gas production enhancement and transformation. Background Art

[0002] With the continuous consumption of conventional oil and gas resources, unconventional resources such as shale gas have become a hot spot for exploration and development. At present, the development technology of shale gas shallower than 3500m has become mature, and the development of deep shale gas has become an important direction for technological breakthroughs. Deep shale reservoirs have the characteristics of large ground stress and high temperature, which brings great challenges to hydraulic fracturing operations.

[0003] When hydraulic fracturing is carried out in high-temperature deep formations, low-temperature fracturing fluid is quickly injected into the high-temperature formation, and the liquid in the fracture rapidly exchanges heat with the formation. The formation rock shrinks due to the cooling effect, thereby generating low-temperature induced thermal stress. This additional stress is tensile stress on the fracture wall, which can effectively offset some of the resistance of the rock during cracking. However, most of the current hydraulic fracturing design fracture extension models only consider the fluid-solid coupling effect during the flow of liquid and the deformation of the formation rock, and have not yet considered the impact of this additional thermal stress on fracture extension, which has certain limitations.

[0004] In view of this, the present invention proposes a calculation method for hydraulic fracture expansion in high-temperature deep shale formations taking into account thermal effects, aiming to improve the theory and method of hydraulic fracturing in high-temperature formations and guide the optimal design of hydraulic fracturing in deep shale reservoirs. Summary of the invention

[0005] In order to overcome the problems in the prior art, the present invention provides a method for calculating the expansion of hydraulic fractures in high-temperature deep shale formations taking into account thermal effects. The method solves the problem that the existing calculation methods cannot take into account the objective factor of the impact of the additional thermal stress on the expansion of the fractures, and is used to simulate the morphology of hydraulic fractures formed by high-temperature formation fracturing construction, providing a favorable theory and method for the optimization design of hydraulic fracturing in high-temperature shale formations.

[0006] The present invention provides a technical solution to solve the above technical problems: a method for calculating the expansion of hydraulic fractures in high-temperature deep shale formations taking into account thermal effects, comprising the following steps:

[0007] Establish the governing equations for fluid flow in fractures, fluid flow in wellbore, energy governing equations for formations in and near fractures, and rock deformation governing equations and their discrete formats;

[0008] According to the formation parameters, fluid physical parameters and perforation parameters of the target deep shale horizontal well, the discrete format of each control equation is assembled and combined with the initial boundary conditions to determine the length, height, width, internal pressure, internal and wall temperature of each cluster of fractures and the amount of fluid inflow of each cluster during the fracturing process;

[0009] According to the formation parameters, perforation parameters and displacement discontinuity of each cluster of fracture tips of the target deep shale horizontal well, and based on the maximum tensile stress criterion, the turning angle of each cluster of fracture tips during the fracturing process is determined;

[0010] According to the turning angle of each cluster of crack tips and the flow rate of fracturing fluid allocated to each cluster of cracks during the fracturing process, the crack extension calculation for the next time step is continued until the fracturing time is over, and the length, height and width of each cluster of cracks at the end of fracturing are determined;

[0011] The fracture morphology is drawn based on the fracture length, fracture height, and fracture width data of each cluster at the end of fracturing.

[0012] A further technical solution is that the flow control equation of the fluid in the slit is:

[0013]

[0014] Where: w is the slit width, m; t is the time, s; Q i is the injection flow rate of fracture i, m 3 / s;x in,i is the coordinate of the injection point in the i crack; p is the pressure inside the crack, Pa; C L is the filtration coefficient, m·s 1 / 2 ; δ is the Kronecker symbol; μ is the liquid viscosity, Pa·s;

[0015] The wellbore fluid flow control equation is:

[0016]

[0017] in:

[0018]

[0019]

[0020] Where: p heel is the injection pressure at the heel of the horizontal well, Pa; p f,i is the pressure at the opening of the i-th cluster of cracks, Pa; Δp pf,i is the friction pressure drop at the i-th cluster perforation hole, Pa; Δp w,j is the fluid flow pressure drop in the jth horizontal well section, Pa; n pf is the number of perforation holes, d pf is the perforation hole diameter, m; α is the hole flow coefficient, dimensionless; ρ l is the density of fracturing fluid, kg / m 3 ; L w,j is the length of the jth horizontal well, m; qw,j is the flow rate of the jth horizontal well, m 3 / s; Q is the total flow rate of fracturing fluid, m 3 / s;d w is the horizontal wellbore diameter, m; i is the number of each cluster of fractures; j is the number of each horizontal well section;

[0021] The energy control equations of the formations within and near the fractures include:

[0022] Energy conservation equation of fluid in crack:

[0023]

[0024] in:

[0025]

[0026] Where: T f is the temperature of the liquid in the crack, °C; V l is the liquid velocity at the average slit width, m / s; ρ l is the liquid density, kg / m 3 ;c l is the specific heat capacity of the liquid, J / (kg·℃); T fw Crack wall temperature, °C; α T is the heat transfer coefficient, W / (m 2 ℃); k l is the thermal conductivity of the liquid, W / (m·℃); N u is the Nusselt number;

[0027] Energy conservation equation of formation rock:

[0028]

[0029] in:

[0030]

[0031] k eff =φk l +(1-φ)k r

[0032] (ρc) eff =φρ l c l +(1-φ)ρ r c r

[0033] Where: T r is the formation rock temperature, °C; y is the vertical distance from any point to the fracture wall, m; k effis the effective thermal conductivity of porous media, W / (m·℃); (ρc) eff is the product of the effective specific heat capacity and density of the liquid and rock; is the rock porosity, dimensionless; k r is the thermal conductivity of the formation rock, W / (m·℃); ρ r is the density of the formation rock, kg / m 3 ;c r is the specific heat capacity of formation rock, J / (kg·℃);

[0034] Energy conservation equation of the crack wall:

[0035]

[0036] Where: L is the thickness of the filtration zone, m;

[0037] The rock deformation control equation is:

[0038]

[0039] Where: e ij is the strain tensor, dimensionless; u i,j is the derivative of displacement, dimensionless; σ ij is the stress tensor, Pa, σ ij，j is the stress tensor derivative in the j direction, Pa / m; G is the rock shear modulus, Pa; δ ij is the Kronecker function.

[0040] A further technical solution is that the discrete format includes:

[0041] The fluid flow control equations are expressed in the following discretized format:

[0042]

[0043] in:

[0044]

[0045] Where: h is the crack height, m; △s is the spatial step of the discrete unit, m; n is the time step; i is the spatial step;

[0046] The temperature gradient at the wall of the formation rock fracture is:

[0047]

[0048] Where: T res is the reservoir temperature, °C; T fini is the initial temperature of the fracture fracturing fluid, °C;

[0049] The discrete format of the energy control equation of the crack wall is:

[0050]

[0051] in:

[0052]

[0053]

[0054] The discretized format of the energy equation of the fluid in the crack is:

[0055]

[0056] The discrete format of the rock deformation control equation is:

[0057] σ xx =2GD x (2f ,xy +yf ,xyy )+2GD y (f ,yy +yf ,yyy )

[0058] σ yy =2GD x (-yf ,xyy )+2GD y (f ,yy -yf ,yyy )

[0059] σ xy =2GD x (f ,yy +yf ,xyy )+2GD y (-yf ,xyy )

[0060] in:

[0061]

[0062] Where: xx , σ yy , σ xy is the normal stress and shear stress in the global coordinate system (x-0-y), MPa; D x , D y is the vertical displacement and shear displacement in the global coordinate system, m; f ,xy 、f ,xyy 、f ,yy 、f ,yy are the partial derivatives of the function f(x,y); a is the half length of the fracture unit, m;

[0063] Coordinate transformation formula:

[0064]

[0065]

[0066] Where: is the horizontal and vertical coordinates in the local coordinate system; c x 、c y is the origin of the local coordinate system, β is the angle between the crack unit and the x-axis of the global coordinate system, °;

[0067] Stress-strain equilibrium relationship:

[0068]

[0069] in:

[0070]

[0071] Where: is the tangential stress and normal stress of crack element i in the local coordinate system, Pa; is the fluid pressure in the fracture unit i, Pa; is the thermal stress of crack unit i, Pa; is the normal displacement and tangential displacement of crack element j in the local coordinate system, m; is the stress influence coefficient of the displacement discontinuity of crack unit j on crack unit i, Pa / m; β j is the angle between the j unit and the x-axis of the global coordinate system, °; is the partial derivative equation of each order of Papkovitch function;

[0072] The thermal stress calculation formula is:

[0073]

[0074] Where: α s is the thermal expansion coefficient of rock, ℃ -1 ; E is the Young's modulus of rock, Pa; ν is the Poisson's ratio of rock, dimensionless; T rwi is the wall temperature of crack unit i, °C;

[0075] The relationship between crack width and discontinuous displacement is:

[0076]

[0077] Where: is the normal displacement of crack j element corresponding to the crack length s, m.

[0078] A further technical solution is that the formation parameters include: maximum horizontal principal stress, minimum horizontal principal stress, rock Young's modulus, rock Poisson's ratio, reservoir thickness, rock fracture toughness, formation porosity, rock density, original formation temperature, rock thermal expansion coefficient, rock thermal conductivity, and rock specific heat capacity;

[0079] The fluid physical property parameters include: fracturing fluid viscosity, fracturing fluid loss coefficient, fracturing fluid density, fracturing fluid thermal conductivity, fracturing fluid specific heat capacity, and fracturing fluid temperature;

[0080] The engineering parameters include: inner diameter of the fracturing string, fracturing displacement, cluster spacing, number of clusters, number of perforation holes, diameter of perforation holes, and flow coefficient of the holes.

[0081] A further technical solution is that the initial boundary conditions include:

[0082] Boundary conditions and initial condition equations for fluid flow in cracks:

[0083]

[0084] Where: Q is the hydraulic fracturing pump injection rate, m 3 / min; L f is the crack half length, m;

[0085] The boundary condition equation for rock solid deformation is:

[0086]

[0087] Where: H , σ h are the maximum and minimum horizontal principal stresses of the formation, Pa, respectively;

[0088] The boundary condition and initial condition equation of the fluid temperature in the crack:

[0089]

[0090] Where: T fini is the liquid temperature at the seam, °C, t pump is the fracturing fluid pumping time, s.

[0091] A further technical solution is to assemble the discrete format of each control equation according to the formation parameters, fluid physical parameters, and perforation parameters of the target deep shale horizontal well and combine the initial and boundary conditions to determine the length, height, width, and internal pressure, internal and wall temperatures of each cluster of fractures and the amount of fluid inflow of each cluster during the fracturing process, including:

[0092] The wellbore fluid flow control equation and the discrete format are combined, and the initial and boundary conditions are combined to assemble the stiffness matrix and load matrix under the fluid-solid coupling effect. The length, width, internal pressure of each cluster of cracks and the amount of liquid inflow of each cluster are calculated at each time step during the fracturing process using the Newton-Raphason method.

[0093] After obtaining the width of the crack and the amount of fluid inflow in each cluster, the energy control equation of the crack wall is discretized and combined with the initial and boundary conditions to obtain the fluid temperature and crack wall temperature in each crack unit through successive iterations; the crack wall temperature is substituted into the calculation formula of the thermal stress to obtain the thermal stress of the crack unit at this time step; the thermal stress is substituted into the stress-strain equilibrium relationship to obtain the stress boundary of each crack unit at this time step, and then the Newton-Raphason method is repeatedly used to solve the matrix until the length, width, pressure in the crack, temperature of each cluster of cracks and the amount of fluid inflow in each cluster reach the convergence conditions.

[0094] A further technical solution is to determine the turning angle of each cluster of fracture tips during fracturing based on the formation parameters, perforation parameters and displacement discontinuity of each cluster of fracture tips of the target deep shale horizontal well and the maximum tensile stress criterion, including:

[0095] Based on the maximum tensile stress criterion, the rock failure and crack steering equations are established to determine whether the crack unit meets the extension condition. If the crack unit does not meet the extension condition, the time step is adjusted until the tip crack unit is destroyed.

[0096] According to the formation parameters and perforation parameters of the target deep shale horizontal well, the turning angle of each cluster of fracture tips in this time step is calculated to determine the fracture extension direction.

[0097] A further technical solution is that the rock failure and crack diversion equation is:

[0098]

[0099] in:

[0100]

[0101] Where: θ tip is the turning angle of the tip crack unit, °; K Ⅰ , K Ⅱ They are type I and type II stress intensity factors, MPa·m 0.5 ;(D n ) tip ,(D s ) tip are the vertical and tangential displacement discontinuities of the tip crack unit, m.

[0102] The present invention has the following beneficial effects: compared with the prior art, the method specifically targets the thermal effect caused by the injection of low-temperature fracturing fluid into high-temperature formations during the fracturing of high-temperature deep shale horizontal wells, establishes the temperature field of the hydraulic fractures and the formation near the fractures during the fracturing of high-temperature deep shale horizontal wells, couples the interaction between fluid and solid, and proposes a calculation method for the expansion of hydraulic fractures in high-temperature deep shale formations that takes thermal effect into consideration; since the method fully considers the influence of the thermal effect caused by the injection of low-temperature fracturing fluid into high-temperature formations, the expansion path of each cluster of fractures can be accurately predicted; the problem that the influence of temperature on the morphology of hydraulic fractures in high-temperature deep shale formations cannot be quickly and accurately obtained on site is solved, and the gap in the theory and method of hydraulic fracturing in high-temperature deep shale formations is filled. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 It is a calculation flow chart of the method of the present invention;

[0104] Figure 2 is the morphology of each cluster of fractures after fracturing of the target well of the embodiment;

[0105] Figure 3 It is a comparison diagram of the crack morphology of each cluster with and without considering the thermal effect. DETAILED DESCRIPTION

[0106] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0107] A method for calculating the expansion of hydraulic fractures in high-temperature deep shale formations taking into account thermal effects of the present invention comprises the following steps:

[0108] Step 1: Collect formation parameters, fluid physical parameters, and engineering parameters of high-temperature deep shale horizontal wells;

[0109] The formation parameters include: maximum horizontal principal stress, minimum horizontal principal stress, rock Young's modulus, rock Poisson's ratio, reservoir thickness, rock fracture toughness, formation porosity, rock density, formation original temperature, rock thermal expansion coefficient, rock thermal conductivity, rock specific heat capacity;

[0110] Fluid physical parameters include: fracturing fluid viscosity, fracturing fluid loss coefficient, fracturing fluid density, fracturing fluid thermal conductivity, fracturing fluid specific heat capacity, and fracturing fluid temperature;

[0111] Engineering parameters include: inner diameter of fracturing string, fracturing displacement, cluster spacing, number of clusters, number of perforations, perforation diameter, and perforation flow coefficient;

[0112] Step 2: Based on the laminar flow theory and the principle of mass conservation, establish the control equation of the fluid in the fracture to obtain the pressure distribution of the fluid in the fracture;

[0113] Mass conservation equation of fluid in the crack:

[0114]

[0115] Where: w is the crack width, m; t is the time, s; q is the flow rate in the crack, m 3 / s;q L is the fracturing fluid loss velocity, m / s; Q i is the injection flow rate of fracture i, m 3 / s;x in,i is the coordinate of the injection point of crack i; δ is the Kronecker symbol;

[0116] The pressure drop equation of fluid in the crack:

[0117]

[0118] Where: q is the volume flow rate in the slit, m 2 / s; p is the pressure inside the crack, Pa; μ is the liquid viscosity, Pa·s;

[0119] Fracturing fluid loss equation:

[0120]

[0121] Where: C L is the filtration coefficient, m·s 1 / 2 ; τ x is the time when the crack unit at x is exposed to the liquid, s; ​​t-τ x is the time when the crack unit at position x is first exposed to the liquid, s;

[0122] Substituting equations (2) and (3) into equation (1), we obtain the governing equation for fluid flow in the slit:

[0123]

[0124] Step 3: Based on fluid mechanics theory, establish the wellbore fluid flow control equation of deep shale horizontal wells;

[0125] Fluid pressure drop equation along the way:

[0126]

[0127] in:

[0128]

[0129]

[0130] Where: p heel is the injection pressure at the heel of the horizontal well, Pa; p f,i is the pressure at the opening of the i-th cluster of cracks, Pa; Δp pf,i is the friction pressure drop at the i-th cluster perforation hole, Pa; Δp w,j is the fluid flow pressure drop in the jth horizontal well section, Pa; n pf is the number of perforation holes, d pf is the diameter of the perforation hole, m; α is the hole flow coefficient, generally 0.8 to 0.85, dimensionless; ρ l is the density of fracturing fluid, kg / m 3 ; L w,j is the length of the jth horizontal well, m; q w,j is the flow rate of the jth horizontal well, m 3 / s; Q is the total flow rate of fracturing fluid, m 3 / s;d w is the horizontal wellbore diameter, m; i represents the number of each cluster of fractures; j represents the number of each horizontal well section;

[0131] Step 4: Based on the principles of mass conservation and energy conservation, establish energy control equations in and near fracture formations to obtain the temperature distribution of the fluid in the fracture;

[0132] Energy conservation equation of the fluid in the crack:

[0133]

[0134] in:

[0135]

[0136] Where: T f is the temperature of the liquid in the crack, °C; V l is the liquid velocity at the average slit width, m / s; ρ l is the liquid density, kg / m 3 ;c l is the specific heat capacity of the liquid, J / (kg·℃); T fw Crack wall temperature, °C; α T is the heat transfer coefficient, W / (m 2 ℃); k l is the thermal conductivity of the liquid, W / (m·℃); N u is the Nusselt number. For Newtonian fluid, N is the number of laminar flows. u Generally, it is 4 to 4.5;

[0137] Energy conservation equation of formation rock:

[0138]

[0139] in:

[0140]

[0141] Where: T r is the formation rock temperature, °C; y is the vertical distance from any point to the fracture wall, m; k eff is the effective thermal conductivity of porous media, W / (m·℃); (ρc) eff is the product of the effective specific heat capacity and density of the liquid and rock; is the rock porosity, dimensionless; k r is the thermal conductivity of the formation rock, W / (m·℃); ρ r is the density of the formation rock, kg / m 3 ;c r is the specific heat capacity of formation rock, J / (kg·℃);

[0142] Energy conservation equation of the crack wall:

[0143]

[0144] Where: L is the thickness of the filtration zone, m

[0145] Step 5: Based on the theory of elastic mechanics, establish the control equation of formation rock deformation to obtain rock deformation displacement and its corresponding stress field;

[0146]

[0147] Where: e ij is the strain tensor, dimensionless; u i,j is the derivative of displacement, dimensionless; σ ij is the stress tensor, Pa, σ ij，j is the stress tensor derivative in the j direction, Pa / m; G is the rock shear modulus, Pa; δ ij is the Kronecker function. When i=j, δ ij =1, otherwise δ ij =0;

[0148] Step 6: Based on the finite difference method, the discrete formats of the fluid flow control equation and the energy control equation are established; based on the displacement discontinuity method, the discrete format of the rock deformation control equation is established;

[0149] According to the finite difference method, the discretization format of the fluid flow control equation (4) is obtained as follows:

[0150]

[0151] in:

[0152]

[0153] Where: h is the crack height, m; △s is the spatial step of the discrete unit, m; n represents the time step, i represents the spatial step;

[0154] By performing Laplace transformation and its inverse transformation on equation (10), the temperature gradient at the wall of the rock fracture in the formation is obtained as follows:

[0155]

[0156] Where: T res is the reservoir temperature, °C; T fini is the initial temperature of the fracture fracturing fluid, °C;

[0157] Substituting equation (16) into equation (12) and performing finite difference, we can obtain the discrete format of the energy control equation of the crack wall:

[0158]

[0159] in:

[0160]

[0161] The discretization format of the energy equation (8) of the fluid in the crack is:

[0162]

[0163] Based on the displacement discontinuity method, the discrete format of the rock deformation control equation (13) can be obtained as:

[0164]

[0165] in:

[0166]

[0167] Where: xx , σ yy , σ xy is the normal stress and shear stress in the global coordinate system (x-0-y), MPa; D x , D y is the vertical displacement and shear displacement in the global coordinate system, m; f ,xy 、f ,xyy 、f ,yy 、f ,yy are the partial derivatives of each order of function f(x,y); a is the half length of the crack unit, m.

[0168] The crack is equally divided into N discontinuous displacement units. The stress and displacement at any i crack unit under the full coordinates can be obtained by adding the stress and displacement of N discontinuous displacement units at that location according to the superposition principle. Considering that the normal stress and shear stress of the i crack unit are represented by local coordinates, coordinate transformation is required, and the formula is:

[0169]

[0170] Where: is the horizontal and vertical coordinates in the local coordinate system; c x 、c y is the origin of the local coordinate system, β is the angle between the crack unit and the x-axis of the global coordinate system, °.

[0171] From equation (20) to equation (22), we can get the stress-strain equilibrium relationship of the i-th crack unit:

[0172]

[0173] in:

[0174]

[0175] Where: s i, σ n i is the tangential stress and normal stress of crack unit i in the local coordinate system, Pa; is the fluid pressure in the fracture unit i, Pa; is the thermal stress of crack unit i, Pa; is the normal displacement and tangential displacement of crack element j in the local coordinate system, m; is the stress influence coefficient of the displacement discontinuity of crack unit j on crack unit i, Pa / m; β j is the angle between the j unit and the x-axis of the global coordinate system, °; are partial derivative equations of various orders of Papkovitch function.

[0176] According to the principle of thermoelasticity, the calculation equation of the thermal stress on crack unit i is:

[0177]

[0178] Where: α s is the thermal expansion coefficient of rock, ℃ -1 ; E is the Young's modulus of rock, Pa; ν is the Poisson's ratio of rock, dimensionless; T rwi is the wall temperature of crack unit i, °C.

[0179] The relationship between crack width and discontinuous displacement is:

[0180]

[0181] Where: is the normal displacement of crack j element corresponding to the crack length s, m;

[0182] Step 7, combining the initial and boundary conditions, and assembling the discrete deformation control equation, flow control equation, and energy control equation, to solve the length and width of the hydraulic fracture, as well as the pressure inside the fracture, the temperature inside the fracture and the fracture wall, and the amount of liquid inflow in each cluster;

[0183] The initial and boundary conditions include:

[0184] Boundary conditions and initial condition equations for fluid flow in cracks:

[0185]

[0186] Where: Q is the hydraulic fracturing pump injection rate, m 3 / min; L f is the crack half length, m;

[0187] The boundary condition equation for rock solid deformation is:

[0188]

[0189] Where: H , σ h are the maximum and minimum horizontal principal stresses of the formation, Pa respectively.

[0190] The boundary condition and initial condition equation of the fluid temperature in the crack:

[0191]

[0192] Where: T fini is the liquid temperature at the seam, °C, t pump is the fracturing fluid pumping time, s;

[0193] The specific process of this step is:

[0194] By combining equations (5) to (7), (14) to (15) and (20) to (25), and combining the initial boundary conditions (27) and (28), the stiffness matrix and load matrix under fluid-solid coupling are assembled, and the length, width, internal pressure and liquid inflow of each cluster of cracks at each time step in the fracturing process are calculated using the Newton-Raphason method.

[0195] After obtaining the width of the crack and the amount of fluid inflow in each cluster, equations (16) to (19) and (26) are combined, and combined with the initial boundary condition equation (29), the fluid temperature in each crack unit and the crack wall temperature are obtained through successive iterations; the crack wall temperature is substituted into equation (25) to obtain the thermal stress of the crack unit at this time step. Substitute the thermal stress into equation (23) to obtain the stress boundary of each crack unit at this time step, and then repeatedly use the Newton-Raphason method to solve the matrix until the length, width, pressure in the crack, temperature of each cluster of cracks and the amount of fluid inflow in each cluster reach the convergence condition;

[0196] It should be pointed out that the solution of thermal stress in the first time step does not require solving the temperature according to the energy equation, but only needs to be solved according to the initial value conditions;

[0197] Step 8: Based on the maximum tensile stress criterion, establish the rock failure and crack steering equation to determine whether the crack extends and its extension direction;

[0198] The rock failure and crack diversion equations are:

[0199]

[0200] in:

[0201]

[0202] Where: θ tip is the turning angle of the tip crack unit, °; K Ⅰ , K Ⅱ They are type I and type II stress intensity factors, MPa·m 0.5 ;(D n ) tip ,(D s ) tip are the vertical and tangential displacement discontinuities of the tip crack unit, m;

[0203] The specific process of this step is:

[0204] Based on the maximum tensile stress criterion, the rock failure and crack steering equations are established to determine whether the crack unit meets the extension condition. If the crack unit does not meet the extension condition, the time step is adjusted until the tip crack unit is destroyed.

[0205] Then, according to the formation parameters, perforation parameters and hydraulic fracture parameters of the deep shale horizontal well, equations (30) and (31) are combined to calculate the turning angle of each cluster of fracture tips at this time step and determine the fracture extension direction.

[0206] Step 9, according to the turning angle of each cluster of crack tips and the flow rate of fracturing fluid allocated to each cluster of cracks during the fracturing process, continue to calculate the crack extension of the next time step until the fracturing time is over, and determine the length, height and width of each cluster of cracks at the end of fracturing;

[0207] Step 10: Output the length, width and height data of each cluster of cracks at the end of fracturing, and draw the morphology of each cluster of cracks after fracturing.

[0208] Example 1

[0209] Taking a well in a domestic deep shale gas block as an example, the fracture morphology after fracturing is simulated using the main parameters of the fractured horizontal well and the reservoir shown in Table 1, and the simulation time is 20 minutes.

[0210] Carry out example calculations according to the steps described above, and output the length, width, and height data of each cluster of cracks at the end of fracturing based on the calculation results, and draw the fracture morphology of each cluster of cracks during fracturing (such as Figure 2 At the same time, the differences in fracture morphology under and without considering thermal effects are compared (as shown in Figure 3 shown).

[0211] Table 1. Data table of target horizontal wells in a deep shale gas reservoir area

[0212]

[0213]

[0214] This method specifically targets the thermal effect caused by the injection of low-temperature fracturing fluid into high-temperature formations during the fracturing of high-temperature deep shale horizontal wells. It establishes the temperature field inside and near the hydraulic fractures of high-temperature deep shale horizontal wells, couples the interaction between fluid and solid, and proposes a calculation method for the expansion of hydraulic fractures in high-temperature deep shale formations taking into account the thermal effect.

[0215] Since this method fully considers the thermal effect caused by the injection of low-temperature fracturing fluid into high-temperature formations, it can accurately predict the expansion path of each cluster of fractures; it solves the problem of being unable to quickly and accurately obtain the impact of temperature on the morphology of hydraulic fractures in high-temperature deep shale formations on site, and fills the gap in the theory and method of hydraulic fracturing in high-temperature deep shale formations.

[0216] The above description is not intended to impose any form of 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 profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical contents disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent change and modification 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 still falls within the scope of the technical solution of the present invention.

Claims

1. A method for calculating the expansion of hydraulic fractures in high-temperature deep shale formations taking into account thermal effects, characterized in that: The following steps are involved: Collect formation parameters, fluid physical parameters, and engineering parameters of high-temperature deep shale horizontal wells; Establish the governing equations for fluid flow in fractures, fluid flow in wellbore, energy governing equations for formations in and near fractures, and rock deformation governing equations and their discrete formats; According to the formation parameters, fluid physical parameters and perforation parameters of the target deep shale horizontal well, the discrete format of each control equation is assembled and combined with the initial boundary conditions to determine the length, height, width, internal pressure, internal and wall temperature of each cluster of fractures and the amount of fluid inflow of each cluster during the fracturing process; According to the formation parameters, perforation parameters and displacement discontinuity of each cluster of fracture tips of the target deep shale horizontal well, and based on the maximum tensile stress criterion, the turning angle of each cluster of fracture tips during the fracturing process is determined; According to the turning angle of each cluster of crack tips and the flow rate of fracturing fluid allocated to each cluster of cracks during the fracturing process, the crack extension calculation for the next time step is continued until the fracturing time is over, and the length, height and width of each cluster of cracks at the end of fracturing are determined; The fracture morphology is drawn based on the fracture length, fracture height, and fracture width data of each cluster at the end of fracturing.

2. The method for calculating the expansion of hydraulic fractures in high-temperature deep shale formations considering thermal effects according to claim 1, characterized in that: The flow control equation of the fluid in the slit is: Where: w is the seam width, m; t is time, s; Q i is the injection flow rate of fracture i, m 3 / s;x in,i is the coordinate of the injection point in the i crack; p is the pressure inside the crack, Pa; C L is the filtration coefficient, m·s 1 / 2 ;δ is the Kronecker symbol;μ is the liquid viscosity, Pa·s; The wellbore fluid flow control equation is: in: Where: p heel is the injection pressure at the heel of the horizontal well, Pa; p f,i is the pressure at the opening of the i-th cluster of cracks, Pa; Δp pf,i is the friction pressure drop at the i-th cluster perforation hole, Pa; Δp w,j is the fluid flow pressure drop in the jth horizontal well section, Pa; n pf is the number of perforation holes, d pf is the perforation hole diameter, m; α is the hole flow coefficient, dimensionless; ρ l is the density of fracturing fluid, kg / m 3 ; L w,j is the length of the jth horizontal well, m; q w,j is the flow rate of the jth horizontal well, m 3 / s; Q is the total flow rate of fracturing fluid, m 3 / s;d w is the horizontal wellbore diameter, m; i is the number of each cluster of fractures; j is the number of each horizontal well section; The energy control equations of the formations within and near the fractures include: Energy conservation equation of fluid in crack: in: Where: T f is the temperature of the liquid in the crack, °C; V l is the liquid velocity at the average slit width, m / s; ρ l is the liquid density, kg / m 3 ;c l is the specific heat capacity of the liquid, J / (kg·℃); T fw Crack wall temperature, °C; α T is the heat transfer coefficient, W / (m 2 ℃); k l is the thermal conductivity of the liquid, W / (m·℃); N u is the Nusselt number; Energy conservation equation of formation rock: in: k eff =φk l +(1-φ)k r (p.c.) eff =fr l c l +(1-φ)ρ r c r Where: T r is the formation rock temperature, °C; y is the vertical distance from any point to the fracture wall, m; k eff is the effective thermal conductivity of porous media, W / (m·℃); (ρc) eff is the product of the effective specific heat capacity and density of the liquid and rock; is the rock porosity, dimensionless; k r is the thermal conductivity of the formation rock, W / (m·℃); ρ r is the density of the formation rock, kg / m 3 ;c r is the specific heat capacity of formation rock, J / (kg·℃); Energy conservation equation of the crack wall: Where: L is the thickness of the filtration zone, m; The rock deformation control equation is: Where: e ij is the strain tensor, dimensionless; u i,j is the derivative of displacement, dimensionless; σ ij is the stress tensor, Pa, σ ij，j is the stress tensor derivative in the j direction, Pa / m; G is the rock shear modulus, Pa; δ ij is the Kronecker function.

3. The method for calculating the expansion of hydraulic fractures in high-temperature deep shale formations taking into account thermal effects according to claim 2, characterized in that: The discrete formats include: The fluid flow control equations are expressed in the following discretized format: in: Where: h is the crack height, m; △s is the spatial step of the discrete unit, m; n is the time step; i is the spatial step; The temperature gradient at the wall of the formation rock fracture is: Where: T res is the reservoir temperature, °C; T fini is the initial temperature of the fracture fracturing fluid, °C; The discrete format of the energy control equation of the crack wall is: in: The discretized format of the energy equation of the fluid in the crack is: The discrete format of the rock deformation control equation is: s xx =2GD x (2f ,xy +yf ,xyy )+2GD y (f ,yy +yf ,yyy ) σ yy =2GD x (-yf ,xyy )+2GD y (f ,yy -yf ,yyy ) σ xy =2GD x (f ,yy +yf ,xyy )+2GD y (-yf ,xyy ) in: Where: xx , σ yy , σ xy is the normal stress and shear stress in the global coordinate system (x-0-y), MPa; D x , D y is the vertical displacement and shear displacement in the global coordinate system, m; f ,xy 、f ,xyy 、f ,yy 、f ,yy are the partial derivatives of each order of function f(x,y); a is the half length of the crack unit, m; Coordinate transformation formula: Where: is the horizontal and vertical coordinates in the local coordinate system; c x 、c y is the origin of the local coordinate system, β is the angle between the crack unit and the x-axis of the global coordinate system, °; Stress-strain equilibrium relationship: in: Where: is the tangential stress and normal stress of crack element i in the local coordinate system, Pa; is the fluid pressure in the fracture unit i, Pa; is the thermal stress of crack unit i, Pa; is the normal displacement and tangential displacement of crack element j in the local coordinate system, m; is the stress influence coefficient of the displacement discontinuity of crack unit j on crack unit i, Pa / m; β j is the angle between the j unit and the x-axis of the global coordinate system, °; is the partial derivative equation of each order of Papkovitch function; The thermal stress calculation formula is: Where: α s is the thermal expansion coefficient of rock, ℃ -1 ; E is the Young's modulus of rock, Pa; ν is the Poisson's ratio of rock, dimensionless; T rwi is the wall temperature of crack unit i, °C; The relationship between crack width and discontinuous displacement is: Where: is the normal displacement of crack j element corresponding to the crack length s, m.

4. The method for calculating the expansion of hydraulic fractures in high-temperature deep shale formations taking into account thermal effects according to claim 2, characterized in that: The formation parameters include: maximum horizontal principal stress, minimum horizontal principal stress, rock Young's modulus, rock Poisson's ratio, reservoir thickness, rock fracture toughness, formation porosity, rock density, original formation temperature, rock thermal expansion coefficient, rock thermal conductivity, and rock specific heat capacity; The fluid physical property parameters include: fracturing fluid viscosity, fracturing fluid loss coefficient, fracturing fluid density, fracturing fluid thermal conductivity, fracturing fluid specific heat capacity, and fracturing fluid temperature; The engineering parameters include: inner diameter of the fracturing string, fracturing displacement, cluster spacing, number of clusters, number of perforation holes, diameter of perforation holes, and flow coefficient of the holes.

5. The method for calculating the expansion of hydraulic fractures in high-temperature deep shale formations taking into account thermal effects according to claim 3, characterized in that: The initial boundary conditions include: Boundary conditions and initial condition equations for fluid flow in cracks: Where: Q is the hydraulic fracturing pump injection rate, m 3 / min; L f is the crack half length, m; The boundary condition equation for rock solid deformation is: Where: H , σ h are the maximum and minimum horizontal principal stresses of the formation, Pa, respectively; The boundary condition and initial condition equation of the fluid temperature in the crack: Where: T fini is the liquid temperature at the seam, °C, t pump is the fracturing fluid pumping time, s.

6. A method for calculating the expansion of hydraulic fractures in high-temperature deep shale formations taking into account thermal effects according to claim 5, characterized in that: According to the formation parameters, fluid physical parameters, and perforation parameters of the target deep shale horizontal well, the discrete format of each control equation is assembled and combined with the initial and boundary conditions to determine the length, height, width, internal pressure, internal and wall temperatures of each cluster of fractures during the fracturing process, and the amount of fluid inflow of each cluster, including: The wellbore fluid flow control equation and the discrete format are combined, and the initial and boundary conditions are combined to assemble the stiffness matrix and load matrix under the fluid-solid coupling effect. The length, width, internal pressure of each cluster of cracks and the amount of liquid inflow of each cluster are calculated at each time step during the fracturing process using the Newton-Raphason method. After obtaining the width of the crack and the amount of fluid inflow in each cluster, the energy control equation of the crack wall is discretized and combined with the initial and boundary conditions to obtain the fluid temperature and crack wall temperature in each crack unit through successive iterations; the crack wall temperature is substituted into the calculation formula of the thermal stress to obtain the thermal stress of the crack unit at this time step; the thermal stress is substituted into the stress-strain equilibrium relationship to obtain the stress boundary of each crack unit at this time step, and then the Newton-Raphason method is repeatedly used to solve the matrix until the length, width, pressure in the crack, temperature of each cluster of cracks and the amount of fluid inflow in each cluster reach the convergence conditions.

7. A method for calculating the expansion of hydraulic fractures in high-temperature deep shale formations taking into account thermal effects according to claim 6, characterized in that: According to the formation parameters, perforation parameters and displacement discontinuity of each cluster of fracture tip units of the target deep shale horizontal well, and based on the maximum tensile stress criterion, the turning angle of each cluster of fracture tip during the fracturing process is determined as follows: Based on the maximum tensile stress criterion, the rock failure and crack steering equations are established to determine whether the crack unit meets the extension condition. If the crack unit does not meet the extension condition, the time step is adjusted until the tip crack unit is destroyed. According to the formation parameters and perforation parameters of the target deep shale horizontal well, the turning angle of each cluster of fracture tips in this time step is calculated to determine the fracture extension direction.

8. The method for calculating the expansion of hydraulic fractures in high-temperature deep shale formations taking into account thermal effects according to claim 7, characterized in that: The rock failure and crack diversion equations are: in: Where: θ tip is the turning angle of the tip crack unit, °; K Ⅰ , K Ⅱ They are type I and type II stress intensity factors, MPa·m 0.5 ;(D n ) tip ,(D s ) tip are the vertical and tangential displacement discontinuities of the tip crack unit, m.

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