A method, device and medium for calculating construction parameters of sand acid fracturing

Abstract

This invention discloses a method, equipment, and medium for calculating construction parameters of sand-added acid fracturing stimulation, relating to the field of carbonate reservoir stimulation. Based on the single-well production requirements of the oilfield development plan, it determines the target artificial fracture length and conductivity; determines the fracturing fluid volume required to achieve the target artificial fracture length; determines the proppant volume required for sand-added acid fracturing stimulation according to the principle that permeability is supported by the filler; establishes a flow reaction model and temperature field model within the acid fracture to determine the concentration field, velocity field, and temperature field within the fracture during acid injection; and determines the actual permeability formed by acid dissolution and the acid volume required for sand-added acid fracturing stimulation based on the acid concentration and flow rate at different times in the fracture. This invention accurately determines the construction parameters of the pre-fracturing acid, proppant, and acid for sand-added acid fracturing stimulation, providing a basis for the design and optimization of acid fracturing processes in carbonate reservoirs.

Description

Technical Field

[0001] This invention relates to the field of acid fracturing stimulation of carbonate reservoirs, specifically to a method, equipment, and medium for calculating construction parameters of sand-added acid fracturing stimulation. Background Technology

[0002] Acid fracturing with proppant is one of the most effective methods for enhancing production and efficiency in carbonate reservoirs. Its purpose is to create an artificial fracture with a combined effect of proppant-supported flow and acid dissolution flow. The pre-fracturing fluid, while fracturing the reservoir and creating an artificial fracture, carries proppant as a "bridge" to prevent compaction by the net reservoir pressure, providing a certain degree of proppant-supported flow capacity. It also reduces reservoir temperature and the reaction rate of subsequent acid, increasing the effective reach of the acid. The subsequent acid, within the created artificial fracture, undergoes non-uniform dissolution with the carbonate minerals on the fracture wall. The dissolved fracture wall forms pits and continuous grooves, further enhancing the conductivity of the artificial fracture. This combined effect of proppant-supported flow and acid dissolution flow significantly increases the long-term stable conductivity of the artificial fracture, improving the effectiveness of single-well acid fracturing. Therefore, accurately calculating and designing the pre-fracturing fluid, proppant, and acid parameters for acid fracturing is crucial for enhancing the fracturing effect.

[0003] Currently, the optimization methods for pre-fracturing fluid and proppant quantity in sand-added acid fracturing mainly draw on the principles of hydraulic fracturing, relying primarily on empirical methods, average proppant concentration, and proppant index methods for calculation. These methods fail to fully consider the production requirements of individual wells, reservoir characteristics, and proppant performance parameters within the overall development plan, leading to increased fracturing fluid and proppant quantities and reduced economic efficiency. Furthermore, acid optimization often considers the acid-rock reaction alone, neglecting the impact of heat conduction on the reaction rate. This results in inaccurate estimates of the effective acid action distance, leading to increased acid volume and failing to properly guide the design and optimization of sand-added acid fracturing processes. Summary of the Invention

[0004] The technical problem this invention aims to solve is that the calculation of parameters for sand-added acid fracturing does not fully consider the production requirements of a single well, reservoir characteristics, and proppant performance parameters in the development plan. This results in large amounts of fracturing fluid and sand used, leading to low economic efficiency. The purpose is to provide a method, equipment, and medium for calculating the construction parameters of sand-added acid fracturing. This method comprehensively optimizes the amount of fracturing fluid and proppant used by combining production requirements, reservoir characteristics, and proppant performance parameters. Based on the target artificial fracture length and target conductivity, the volume of fracturing fluid and proppant is determined. Coupled calculations of concentration field, velocity field, and temperature field are performed to construct an acid fracture model. This determines the actual permeability formed by acid dissolution and the acid volume required for sand-added acid fracturing, providing a basis for the design and optimization of acid fracturing processes in carbonate reservoirs.

[0005] This invention is achieved through the following technical solution:

[0006] The first aspect of this invention provides a method for calculating construction parameters for sand-added acid fracturing retrofitting, comprising the following specific steps:

[0007] S1. Obtain single-well reservoir parameters and determine the target artificial fracture length and target conductivity to achieve the target production of a single well when using sand-adding acid fracturing stimulation.

[0008] S2. Construct a two-dimensional propagation model of artificial fractures to determine the volume of fracturing fluid required to achieve the target artificial fracture length;

[0009] S3. Based on the average width of the artificial crack and the target flow capacity, determine the volume of proppant required for sand-filled acid fracturing based on the permeability of the sand-filled support.

[0010] S4. Based on the law of conservation of mass and the energy balance theory of external heat source, establish a flow reaction model and a temperature field model in the acid fracture, and construct an acid fracture model by combining the volume of fracturing fluid and proppant.

[0011] S5. Based on the acid fracture model, obtain the acid concentration and acid flow rate at different times of the fracture to determine the actual permeability formed by acid dissolution and the acid volume required for sand-addition acid pressure modification.

[0012] This invention comprehensively optimizes the fracturing fluid and proppant dosage by combining single-well production conditions, reservoir characteristics, and proppant performance parameters in oilfield development schemes. Based on the target artificial fracture length and target conductivity, the fracturing fluid volume and proppant volume are determined. Coupled calculations of concentration field, velocity field, and temperature field are performed to construct an acid fracture model. The actual permeability formed by acid dissolution and the acid volume required for sand-added acid fracturing are determined. The resulting acid dissolution amount and acid volume are more accurate, providing a basis for the design and optimization of acid fracturing processes in carbonate reservoirs.

[0013] Furthermore, S1 specifically includes:

[0014] S11. Obtain single-well reservoir parameters, set an interval for single-well reservoir parameters, and determine the first artificial fracture length and the first conductivity based on the single-well reservoir parameters within the interval.

[0015] S12. Determine the target production rate of a single well during acid fracturing with sand addition based on the length of the first artificial fracture and the first diversion capacity.

[0016] S13. Obtain the relationship between the length of the first artificial fracture and the production rate within the interval. Based on the relationship, determine the conductivity of the target artificial fracture with the largest increase in production rate. Based on the target production rate of a single well, determine the target conductivity required for acid fracturing stimulation of a single well based on the conductivity of the target artificial fracture.

[0017] S14. Based on the single-well production rate of the oilfield development plan, determine the target artificial fracture length during single-well sand-addition acid fracturing stimulation according to the length of the first artificial fracture.

[0018] Furthermore, the single-well reservoir parameters include: reservoir thickness, formation pressure, bottom hole flowing pressure, underground crude oil viscosity, underground crude oil volume coefficient, reservoir permeability, and single-well supply radius;

[0019] The specific range for setting single-well reservoir parameters includes: setting the calculation range for the artificial fracture length to be 0.1 times the single-well supply radius to 0.5 times the single-well supply radius; setting the increment for the artificial fracture length to be 0.05 times the single-well supply radius; and setting the calculation range for the artificial fracture conductivity to be 5 μm. 2 ·cm to 50μm 2 The increase in conductivity of artificial fractures is 5 μm in increments of cm. 2 ·cm.

[0020] Furthermore, S2 specifically includes:

[0021] S21. Obtain the sand-adding acid fracturing construction parameters and reservoir parameters. The sand-adding acid fracturing construction parameters include: fracturing fluid discharge rate, fracturing fluid viscosity, fracturing fluid comprehensive filtration loss coefficient, fracturing fluid initial filtration loss. Set the initial values ​​of the sand-adding acid fracturing construction parameters and reservoir parameters, and determine the average fracture width, compensation coefficient, and error compensation function of the artificial fractures during the sand-adding acid fracturing construction process.

[0022] S22. Based on the average width of the artificial crack, the compensation coefficient, and the error compensation function, construct a dynamic crack length expansion model for the artificial crack and calculate the dynamic crack length at time t during the sand-addition acid fracturing process.

[0023] S23. Based on the dynamic crack length at time t during the sand acid fracturing process, determine the dynamic crack width at time t and the dynamic crack width at the target crack length.

[0024] S24. Compare the dynamic width of the artificial crack opening with its initial value to obtain the difference in the initial value. If the difference is greater than the threshold, execute step S22 until the difference is less than the threshold.

[0025] S25. Compare the dynamic fracture length with the target artificial fracture length. If the dynamic fracture length is less than the target artificial fracture length, proceed to step S22 until the dynamic fracture length is not less than the target artificial fracture length, and then determine the fracturing fluid volume required for the current dynamic fracture length.

[0026] Furthermore, S3 specifically includes:

[0027] S31. Obtain the average width of the artificial crack, the permeability of the sand-filled support, the particle radius of the proppant, and the porosity of the sand-filled crack.

[0028] S32. Determine the target sand-filled crack permeability based on the average crack width of the artificial crack, the permeability of the sand-filled support, and the target conductivity.

[0029] S33. Based on the proppant particle radius and the porosity of the sand-filled cracks, determine the fractal characteristic parameters of the sand-filled cracks, and based on the fractal characteristic parameters of the sand-filled cracks, determine the actual permeability of the sand-filled cracks.

[0030] S34. Set the initial value for calculating the porosity of the sand-filled cracks. Compare the actual permeability of the sand-filled cracks with the target permeability of the sand-filled cracks. If the actual permeability of the sand-filled cracks is less than the target permeability of the sand-filled cracks, add up the porosity of the sand-filled cracks and execute step S32 until the actual permeability of the sand-filled cracks is greater than the target permeability of the sand-filled cracks. Output the current porosity of the sand-filled cracks.

[0031] S35. Based on the output porosity of the sand-filled cracks, determine the volume of proppant required for sand-addition acid fracturing modification.

[0032] Furthermore, S4 specifically includes:

[0033] S41. Based on the law of conservation of mass, the concentration field and velocity field of the unsteady flow reaction of acid in the fracture are determined by the finite difference method, the boundary conditions of the unsteady flow reaction of acid in the fracture are determined, and the unsteady flow reaction model of acid in the fracture is constructed.

[0034] S42. Based on the energy balance theory of external heat source, the finite difference method is used to determine the temperature field of acid in the fracture and the boundary conditions of the temperature field of acid in the fracture under the influence of formation heat transfer, and to construct a temperature field model of acid in the fracture.

[0035] S43. Couple the unsteady flow reaction model of acid in the fracture with the temperature field model of acid in the fracture, and introduce boundary conditions to obtain the acid fracture model.

[0036] Furthermore, S5 specifically includes:

[0037] S51. The target conductivity and average width of artificial fractures required for single-well sand-added acid fracturing stimulation are used to determine the target permeability of acid erosion.

[0038] S52. Obtain the amount of dissolution and the morphology of cracks to determine the actual permeability formed by acid dissolution;

[0039] S53. Set the initial value for acid injection calculation, compare the target permeability of acid corrosion with the actual permeability. If the actual permeability of acid corrosion is greater than the target permeability, add acid injection and execute step S52 until the actual permeability of acid corrosion is less than the target permeability, and output the current acid corrosion permeability.

[0040] S54. Calculate the volume of acid required for sand-addition acid fracturing based on the acid dissolution permeability and acid pumping time.

[0041] Furthermore, determining the actual permeability formed by acid etching specifically includes:

[0042] Set the acid co-pumping time, discretize the crack into n elements along the length direction, with each element having a length of Δx, and determine the amount of rock dissolution in element i within the time step based on the acid concentration and flow rate in each element.

[0043] The crack morphology is obtained, and the width of the dissolution crack is determined by combining it with the amount of rock dissolution over a certain period of time.

[0044] After the acid injection is completed within a certain time, the actual permeability formed by acid dissolution within a certain time is determined based on the width of the dissolution crack.

[0045] A second aspect of the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a method for calculating construction parameters for sand-addition acid fracturing modification.

[0046] A third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a method for calculating construction parameters for sand-addition acid fracturing modification.

[0047] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0048] By comprehensively optimizing the fracturing fluid and proppant dosages based on production requirements, reservoir characteristics, and proppant performance parameters, and determining the fracturing fluid and proppant volumes according to the target artificial fracture length and target conductivity, coupled calculations of concentration field, velocity field, and temperature field are performed to construct an acid fracture model. This determines the actual permeability formed by acid dissolution and the acid volume required for sand-added acid fracturing stimulation, providing a basis for the design and optimization of acid fracturing processes in carbonate reservoirs. Attached Figure Description

[0049] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0050] Figure 1 This is a flowchart of the calculation method in an embodiment of the present invention;

[0051] Figure 2This diagram shows the production output achievable by sand-addition acid fracturing modification under different artificial crack lengths and flow conduction capacities in the embodiments of the present invention.

[0052] Figure 3 This is a diagram showing the concentration distribution of acid in the crack at 60 minutes after acid injection in an embodiment of the present invention.

[0053] Figure 4 This is a flow distribution diagram of acid in the crack at 60 minutes after acid injection in an embodiment of the present invention;

[0054] Figure 5 This is a diagram showing the distribution of the corrosion crack width after acid injection in an embodiment of the present invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0056] Example 1

[0057] like Figure 1 As shown, the first aspect of this embodiment provides a method for calculating construction parameters for sand-added acid fracturing retrofitting, including the following specific steps:

[0058] S1. Obtain single-well reservoir parameters and determine the target artificial fracture length and target conductivity to achieve the target production of a single well when using sand-adding acid fracturing stimulation.

[0059] S2. Construct a two-dimensional propagation model of artificial fractures to determine the volume of fracturing fluid required to achieve the target artificial fracture length;

[0060] S3. Based on the average width of the artificial crack and the target flow capacity, determine the volume of proppant required for sand-filled acid fracturing based on the permeability of the sand-filled support.

[0061] S4. Based on the law of conservation of mass and the energy balance theory of external heat source, establish a flow reaction model and a temperature field model in the acid fracture, and construct an acid fracture model by combining the volume of fracturing fluid and proppant.

[0062] S5. Based on the acid fracture model, obtain the acid concentration and acid flow rate at different times of the fracture to determine the actual permeability formed by acid dissolution and the acid volume required for sand-addition acid pressure modification.

[0063] By comprehensively optimizing the fracturing fluid and proppant dosage based on the oilfield development plan's single-well production conditions, reservoir characteristics, and proppant performance parameters, and determining the fracturing fluid and proppant volumes according to the target artificial fracture length and target conductivity, coupled calculations of concentration field, velocity field, and temperature field are performed to construct an acid fracture model. This determines the actual permeability formed by acid dissolution and the acid volume required for sand-added acid fracturing stimulation, resulting in more accurate acid dissolution amounts and acid volumes. This provides a basis for the design and optimization of acid fracturing processes in carbonate reservoirs.

[0064] S1. Obtain single-well reservoir parameters and determine the target artificial fracture length and target conductivity to achieve the target production rate of a single well during acid fracturing stimulation:

[0065] Collect single-well reservoir parameters such as reservoir thickness, formation pressure, bottom hole flowing pressure, underground crude oil viscosity, underground crude oil volume coefficient, reservoir permeability, and single-well supply radius.

[0066] The first step is to set the length L of the artificial crack. f The calculation interval is from 0.1 times the single-well supply radius to 0.5 times the single-well supply radius, and the increment of the artificial fracture length is 0.05 times the single-well supply radius; the conductivity F of the artificial fracture is set. CD The calculation interval is 5μm 2 ·cm to 50μm 2 The increase in conductivity of artificial fractures is 5 μm in increments of cm. 2 Based on formula (1), calculate the target production Q of a single well achievable by acid fracturing with sand addition under different artificial fracture lengths and conductivity. o :

[0067]

[0068] In the formula: Q o To achieve the target production per well achievable through sand fracturing and acid spraying, m 3 / d;F CD The conductivity of the artificial fracture is μm 2 ·cm,L f is the length of the artificial fracture, in meters; h is the reservoir thickness, in meters; μ o B represents the viscosity of underground crude oil, in mPa·s. o Underground crude oil volume factor, m 3 / m 3 ;p e Formation pressure, MPa; p wf The bottom hole flowing pressure is measured in MPa and K. e Reservoir permeability, μm 2 ;r e The radius of a single well is given in meters.

[0069] The second step involves plotting a series of production curves under different artificial fracture conductivity, with the length of the artificial fracture as the x-axis and the calculated production as the y-axis. The artificial fracture length is selected as 0.3 times the single-well supply radius. The production series points under different artificial fracture conductivity are calculated, and the artificial fracture conductivity curve with the largest increase in production is identified. This artificial fracture conductivity curve is used as the standard curve, and it represents the target conductivity required for single-well sand fracturing stimulation to achieve the single-well production under the oilfield development plan.

[0070] The third step is to read the required artificial fracture length from the standard curve based on the single-well production conditions of the oilfield development plan. This fracture length is then used as the target artificial fracture length that needs to be achieved for single-well sand fracturing stimulation under the single-well production conditions of the oilfield development plan.

[0071] S2. Construct a two-dimensional artificial fracture propagation model to determine the volume of fracturing fluid required to achieve the target artificial fracture length:

[0072] The first step is to set the fracturing fluid discharge rate, fracturing fluid viscosity, fracturing fluid comprehensive filtration loss coefficient, fracturing fluid initial filtration loss and other construction parameters during the sand-addition acid fracturing operation, as well as reservoir parameters such as rock Young's modulus and rock Poisson's ratio.

[0073] The second step is to set the dynamic width W of the artificial crack opening. max The initial value for calculation is 0.02m. According to formula (2), the average width of artificial cracks during the sand-addition acid fracturing construction is calculated. Compensation coefficient α and error compensation function

[0074]

[0075] In the formula: W represents the average width of the artificial crack in meters. max The dynamic width of the artificial crack opening is in meters (m); α is the compensation coefficient, dimensionless; C t The overall filtration loss coefficient of fracturing fluid, in m / min 1 / 2 V sp The initial filtrate loss of fracturing fluid, m 3 / m 2 t represents the sand-addition acid fracturing construction time, in minutes.

[0076] The third step is to calculate the dynamic crack length L at time t during the sand-addition acid fracturing process, based on the formula (3) of the dynamic crack length expansion model for artificial cracks. f :

[0077]

[0078] In the formula: L f For dynamic seam length, m; Qf The fracturing fluid discharge rate is m. 3 / min; h is the reservoir thickness, in meters.

[0079] Fourth step: Based on the formula (4) for the dynamic crack width expansion model of artificial cracks, calculate the dynamic crack width W at time t during the sand-addition acid fracturing process. max The dynamic seam width W at seam length x dx :

[0080]

[0081] Where: ν is the Poisson's ratio of the rock, dimensionless; E is the Young's modulus of the rock, MPa; μ is the viscosity of the fracturing fluid, mPa·s; W x Let x be the dynamic slot width at slot length x, in meters; and let x be the distance between the dynamic slot length L and the wellbore, in meters.

[0082] Fifth step: Set the initial time t=5. Calculate from the second step to the fourth step. Compare the difference between the dynamic width of the artificial crack obtained in the fourth step and the initial value set in the first step. If the difference is less than or equal to 5%, proceed to the sixth step. If the difference is greater than 5%, reset the initial value of the dynamic width of the artificial crack in the second step to the value calculated in the fourth step, and repeat the second to fifth steps.

[0083] Step 6, when the dynamic seam length L f The calculation ends when the artificial fracture length is greater than or equal to the target artificial fracture length; otherwise, the next time step is set to t = t + 1, and the process returns to step two until the calculation ends. According to formula (5), the volume of fracturing fluid required to reach the target artificial fracture length is calculated as Q. frac :

[0084] Q frac =Q f ×t(5)

[0085] In the formula: Q frac The volume of fracturing fluid required to achieve the target artificial fracture length, in m 3 .

[0086] S3. Based on the average width of the artificial crack and the target conductivity, determine the volume of proppant required for sand-filled acid fracturing based on the permeability of the sand-supported structure:

[0087] The first step is to calculate the target sand-filled fracture permeability K based on the average width of the artificial fracture and the target conductivity, according to the principle that 40% permeability is supported by sand filling, and using formula (6). sand :

[0088]

[0089] Where: K sandThe permeability of the sand filling is expressed in μm. 2 ;F f-cd To achieve the target conductivity (μm) required for single-well acid fracturing stimulation under the oilfield development plan's single-well production conditions, 2 ·cm; The average width of the artificial crack is in meters (m).

[0090] The second step involves calculating the fractal characteristic parameters of the sand-filled cracks based on the proppant particle radius and the porosity of the cracks, according to formulas (7) and (8), including the maximum pore radius λ. max Minimum pore radius λ min Fractal dimension of pore structure D pf Pore ​​flow cross-sectional area A p And porosity tortuosity fractal dimension D pf :

[0091]

[0092]

[0093] In the formula: λ max R is the maximum pore radius, in meters. sand Where φ is the radius of the proppant particle, in meters; sand λ represents the porosity of the sand-filled cracks, a decimal. min D is the minimum pore radius, in meters. pf A is the fractal dimension of the pore structure, dimensionless; p The cross-sectional area of ​​the pore flow is m. 2 ;D pf Let f be the fractal dimension of the porosity tortuosity, which is dimensionless.

[0094] The third step is to calculate the actual permeability K of the sand-filled cracks according to formula (9), based on the fractal characteristic parameters of the cracks. r-sand :

[0095]

[0096] Where: K r-sand The actual permeability of the sand-filled fracture is expressed in μm. 2 .

[0097] The fourth step is to set the initial value of φ for calculating the porosity of the sand-filled cracks. sand =0.05, calculate the actual sand-filled crack permeability through steps two and three, if K r-sand <K sand Then let φ sand =φ sand +0.01, recalculate in steps two and three until K is reached. r-sand ≥K sandEnd the calculation and proceed to step five;

[0098] Fifth, based on the obtained porosity of the sand-filled cracks, calculate the volume of proppant V required for sand-addition acid fracturing modification according to formula (10). sand :

[0099]

[0100] In the formula: V sand The volume of proppant required for sand-addition acid fracturing modification, m 3 ; The average width of the artificial crack is in meters (m); L f is the dynamic fracture length, in meters; h is the reservoir thickness, in meters.

[0101] S4. Based on the law of conservation of mass and the energy balance theory of external heat sources, establish a flow reaction model and a temperature field model within the acid fracture, and construct an acid fracture model by combining the fracturing fluid volume and proppant volume:

[0102] The first step is to calculate the concentration field and velocity field of the unsteady flow reaction of the acid in the crack using the finite difference method according to the law of conservation of mass and formula (11):

[0103]

[0104] In the formula: C is the acid concentration, a decimal; t is the time of acid injection, in seconds; x is the crack length direction, in meters; z is the crack width direction, in meters; u x u z Let D be the linear velocity of the acid solution flowing in the x-direction of the seam length and the z-direction of the seam at time t, in m / s; e D e m is the effective mass transfer coefficient for hydrogen ions. 2 / s.

[0105] According to formula (12), calculate the boundary conditions for the unsteady flow reaction of acid in the crack:

[0106]

[0107] In the formula: W is the crack width, in meters; k R Let be the acid-rock reaction rate constant, (mol / L) -n / (cm 2 ·s); C represents reservoir porosity, a decimal. w C0 is the acid concentration at the fracture wall, in mol / L; C0 is the concentration of the pumped acid, in mol / L; n is the acid-rock reaction order, dimensionless; Q acid The acid discharge rate is m. 3 / min; W maxdenoted as dynamic fracture width at the artificial fracture opening, in meters; h represents reservoir thickness, in meters.

[0108] The second step is to calculate the temperature field of the acid solution inside the crack using the finite difference method according to the external heat source energy balance theory and formula (13):

[0109]

[0110] In the formula: T is the acid temperature at a certain location in the crack, in °C; K T ρ is the thermal conductivity of the acid solution within the crack, W / (m·℃); f The density of the acid solution is kg / m³. 3 C f is the specific heat capacity of the acid solution, J / (kg·℃).

[0111] According to formula (13), the temperature field boundary conditions of the acid fluid in the fracture under the influence of formation heat transfer are calculated:

[0112]

[0113] Where: T0 is the temperature of the pumped acid solution, °C; U h (t) represents the heat flow rate (W) of the acid fluid transmitted from the formation into the fracture. The heat transmitted from the formation into the fracture is calculated using heat conduction. According to formula (14), the heat U transmitted at time t is calculated. h (t):

[0114]

[0115] In the formula: ρ r Density of reservoir rock, kg / m³ 3 C r Specific heat capacity of reservoir rock, J / (kg·℃); K r t represents the thermal conductivity of the reservoir rock, W / (m·℃); t represents the time of acid injection, s; t p T is the time (s) for the acid to reach a certain location in the crack. re T represents the reservoir rock temperature, in °C. w T w v represents the temperature of the crack wall, in °C. l The rate of acid loss is expressed in m / s.

[0116] The third step is to couple the unsteady flow reaction model of the acid in the fracture with the temperature field model of the acid in the fracture, substitute the boundary conditions, and calculate the coupled concentration field and velocity field in the fracture according to formula (15):

[0117]

[0118] In the formula: C xQ represents the acid concentration at position x in the crack at time x, as a decimal. x Let m be the acid flow rate at position x in the crack at time t. 3 / s.

[0119] S5. Based on the acid fracture model, obtain the acid concentration and flow rate at different times in the fracture to determine the actual permeability formed by acid dissolution and the acid volume required for sand-based acid fracturing modification:

[0120] The first step is to calculate the target acid corrosion permeability K according to formula (19), based on the principle that 60% of the permeability is provided by acid corrosion. sand :

[0121]

[0122] In the formula: F f-cd To achieve the target conductivity (μm) required for single-well acid fracturing stimulation under the oilfield development plan's single-well production conditions, 2 ·cm; The average width of the artificial crack is in meters (m).

[0123] The second step is to set up the acid co-pump injection system. k Over time, the crack is discretized into n elements along its length, each element having a length of Δx. Based on the acid concentration and flow rate within each element calculated in step S4, the amount of rock dissolution V within element i within the time step Δt is calculated according to formula (17). i k :

[0124]

[0125] In the formula: k is the time of acid injection, in seconds; Let m be the acid flow rate of the i-th discrete unit at time k. 3 / s; Let L be the acid concentration of the i-th discrete unit at time k, a decimal, where i = 1, 2, ..., n; Δx is the length of each discrete unit, m, where L f =n·Δx,L f Δt represents the dynamic seam length in meters (m); Δt represents the calculation time unit in seconds (s).

[0126] The third step is to calculate the width V of the dissolution fracture according to formula (18) based on the amount of dissolution and the fracture morphology. aicd,i :

[0127]

[0128] Among them, V aicd,i To determine the amount of mineral dissolution in the i-th unit after acid injection at time K, m 3 Vaicd,i To determine the etch width of the i-th unit after acid injection at time K, m 3 .

[0129] After the acid injection for time K is completed, the actual permeability formed by acid erosion is calculated according to formula (19) as K. r-acid :

[0130]

[0131] Where: K r-acid To determine the actual permeability (μm) formed by acid dissolution after acid injection at time K. 2 .

[0132] The fourth step involves setting the initial calculation value for acid injection to t = 60. Using the acid concentration and flow rate at any location within the crack at that moment (from step S4), and through steps two and three in step S5, the actual permeability K formed by acid dissolution after acid injection at time t is calculated. r-acid If K dirca-dica <K, order t = t + 60s, recalculate steps S4 and S5 (steps 2 and 3) until K. r-acid ≥K acid End the calculation and proceed to step five;

[0133] Fifth, based on the acid injection time, calculate the required acid volume V for the sand-addition acid fracturing modification according to formula (20). acid :

[0134]

[0135] In the formula: V acid The volume of acid solution required for sand-addition acid fracturing modification, m 3 Q acid The acid discharge rate is m. 3 / min.

[0136] The second aspect of this embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements a method for calculating construction parameters for sand-addition acid fracturing modification.

[0137] The third aspect of this embodiment provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a method for calculating construction parameters for sand-addition acid fracturing modification.

[0138] Example 2

[0139] Step S1: Collect data from the acid fracturing well. The reservoir thickness is 10m, the formation pressure is 30MPa, the bottomhole flowing pressure is 20MPa, the underground crude oil viscosity is 5mPa·s, and the underground crude oil volume factor is 1.2m. 3 / m 3 The reservoir permeability is 0.006 μm. 2 The supply radius of a single well is 500m.

[0140] Set the length of the artificial crack L f The calculation interval is from 0.1 times the single-well supply radius to 0.5 times the single-well supply radius, and the increment of the artificial fracture length is 0.05 times the single-well supply radius; the conductivity F of the artificial fracture is set. CD The calculation interval is 50μm 2 ·cm to 50μm 2 •cm, the step size for increasing the conductivity of artificial fractures is 50μm. 2 ·cm, according to formula (1), calculate the production that can be achieved by single-well acid fracturing with sand addition under different artificial fracture lengths and conductivity parameters, such as Figure 2 As shown.

[0141] The production rate achievable by single-well sand fracturing is set at 30m³. 3 / d, yielding a target conductivity of 15μm required for single-well acid fracturing stimulation. 2 The target artificial crack length is 175m.

[0142] Step S2: Set the fracturing fluid discharge rate during the sand-addition acid fracturing operation to 5m³. 3 The fracturing fluid viscosity is 80 mPa·s, and the overall filtration loss coefficient is 0.0006 m / min. 1 / 2 The initial filtrate loss of the fracturing fluid was 0.002 m³. 3 / m 2 The rock has a Young's modulus of 27,000 MPa and a Poisson's ratio of 0.25.

[0143] Using formulas (2) to (4), at t = 13 min, the dynamic fracture length is 203 m, which is greater than the target artificial fracture length of 175 m. Using formula (5), the volume of fracturing fluid required to achieve the target artificial fracture length is calculated to be 65 m³. 3 .

[0144] Step S3: Based on the principle that 40% permeability is supported by sand filling, the target sand-filled fracture permeability is calculated to be 14.3 μm using formula (6). 2 .

[0145] 20 / 40 mesh ceramsite was selected as the proppant, with a particle radius of 0.006375 μm. The initial value for calculating the porosity of the sand-filled cracks was set as φ. sand =0.05, according to φ sand =φ sand +0.01, using formulas (7) to (9) for trial calculations, when φ sand When the value is 0.14, the actual permeability K of the sand-filled crack is calculated. r-sand =18.56μm 2 The permeability of the sand-filled fracture is greater than the target value of 14.3 μm. 2 Using formula (10), the required proppant volume for sand-addition acid fracturing modification is calculated to be 9.6 m³. 3 .

[0146] Step S4: Set the concentration of the pumped acid solution to 20% and the effective hydrogen ion mass transfer coefficient to 5 × 10⁻⁶. -8 m / s, the acid-rock reaction rate constant is 1.89 × 10 -5 (mol / L) -n / (cm 2 The reservoir porosity is 0.21, the acid-rock reaction order is 3, and the acid discharge rate is 5 m³ / s. 3 The thermal conductivity of the acid solution within the crack is 2.12 W / (m·℃), and the acid density is 1000 kg / m³. 3 The acid solution has a specific heat capacity of 1020 J / (kg·℃), the pumping temperature is 25℃, and the reservoir rock density is 2500 kg / m³. 3 The specific heat capacity of the reservoir rock is 910 J / (kg·℃), the thermal conductivity of the reservoir rock is 1.95 W / (m·℃), the temperature of the fracture wall is 120℃, and the acid loss rate is 0.002 m / s.

[0147] The concentration field and velocity field of the acid at any location in the crack at any time are calculated using formulas (11) to (15). Taking a calculation of 60 minutes as an example, the concentration distribution and flow rate distribution of the acid at this time are calculated as follows: Figure 3 and Figure 4 As shown.

[0148] Step S5: Based on the principle that 60% of the permeability is provided by acid dissolution, the target acid dissolution permeability K is calculated using formula (19). sand =21.5μm 2 .

[0149] Set the initial value for acid injection to t = 60s. Through steps S4 and S5 (second and third steps), calculate the actual permeability formed by acid dissolution after acid injection at this moment. If K... r-acid <K acidOrdered to recalculate steps S4 and S5 (steps 2 and 3) after t = t + 60; when t = 2520s, the width of the etched crack after acid injection is as follows: Figure 4 As shown, the actual permeability K formed by acid dissolution r-acid =25.8μm 2 Greater than the target acid solution erosion permeability K sand =21.5μm 2 Using formula (20), the volume of proppant required for sand-addition acid fracturing modification is calculated to be 210 m³. 3 .

[0150] Therefore, the construction parameters for the sand-addition acid fracturing modification in this embodiment are shown in Table 1:

[0151] Table 1 Construction parameters for sand-addition acid fracturing modification

[0152] Parameter name volume <![CDATA[Fracturing fluid, m 3 > 65 <![CDATA[Proppant, m 3 > 9.6 <![CDATA[Acid solution, m 3 > 210

[0153] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating construction parameters of sand-added acid fracturing retrofit, characterized in that, The specific steps include the following: S1. Obtain single-well reservoir parameters and determine the target artificial fracture length and target conductivity to achieve the target production of a single well when using sand-adding acid fracturing stimulation. S2. Construct a two-dimensional artificial fracture propagation model to determine the fracturing fluid volume required to achieve the target artificial fracture length; specifically including: S21. Obtain the sand fracturing construction parameters and reservoir parameters. The sand fracturing construction parameters include: fracturing fluid discharge rate, fracturing fluid viscosity, fracturing fluid comprehensive filtration loss coefficient, fracturing fluid initial filtration loss. Set the initial values ​​of the sand fracturing construction parameters and reservoir parameters, and determine the average fracture width, compensation coefficient, and error compensation function of the artificial fractures during the sand fracturing construction process. S22. Based on the average width of the artificial crack, the compensation coefficient, and the error compensation function, construct a dynamic crack length expansion model for the artificial crack and calculate the dynamic crack length at time t during the sand-addition acid fracturing process. S23. Based on the dynamic crack length at time t during the sand acid fracturing process, determine the dynamic crack width at time t and the dynamic crack width at the target crack length. S24. Compare the dynamic width of the artificial crack opening with its initial value to obtain the difference in the initial value. If the difference is greater than the threshold, execute step S22 until the difference is less than the threshold. S25. Compare the dynamic fracture length with the target artificial fracture length. If the dynamic fracture length is less than the target artificial fracture length, execute step S22 until the dynamic fracture length is not less than the target artificial fracture length, and determine the fracturing fluid volume required for the current dynamic fracture length. S3. Based on the average width of the artificial crack and the target flow capacity, determine the volume of proppant required for sand-filled acid fracturing based on the permeability of the sand-filled support. S4. Based on the law of conservation of mass and the energy balance theory of external heat sources, establish a flow reaction model and a temperature field model within the acid fracture, and construct an acid fracture model by combining the fracturing fluid volume and proppant volume; specifically including: S41. Based on the law of conservation of mass, the concentration field and velocity field of the unsteady flow reaction of acid in the fracture are determined by the finite difference method, the boundary conditions of the unsteady flow reaction of acid in the fracture are determined, and the unsteady flow reaction model of acid in the fracture is constructed. S42. Based on the energy balance theory of external heat source, the finite difference method is used to determine the temperature field of acid in the fracture and the boundary conditions of the temperature field of acid in the fracture under the influence of formation heat transfer, and to construct a temperature field model of acid in the fracture. S43. Couple the unsteady flow reaction model of acid in the fracture with the temperature field model of acid in the fracture, and introduce boundary conditions to obtain the acid fracture model. S5. Based on the acid fracture model, obtain the acid concentration and acid flow rate at different times of the fracture to determine the actual permeability formed by acid dissolution and the acid volume required for sand-addition acid pressure modification.

2. The method for calculating construction parameters of sand-added acid fracturing retrofitting according to claim 1, characterized in that, S1 specifically includes: S11. Obtain single-well reservoir parameters, set an interval for single-well reservoir parameters, and determine the first artificial fracture length and the first conductivity based on the single-well reservoir parameters within the interval. S12. Determine the target production rate of a single well during acid fracturing with sand addition based on the length of the first artificial fracture and the first diversion capacity. S13. Obtain the relationship between the length of the first artificial fracture and the production rate within the interval. Based on the relationship, determine the conductivity of the target artificial fracture with the largest increase in production rate. Based on the target production rate of a single well, determine the target conductivity required for acid fracturing stimulation of a single well based on the conductivity of the target artificial fracture. S14. Based on the single-well production rate of the oilfield development plan, determine the target artificial fracture length during single-well sand-addition acid fracturing stimulation according to the length of the first artificial fracture.

3. The method for calculating construction parameters of sand-added acid fracturing retrofitting according to claim 2, characterized in that, The single-well reservoir parameters include: reservoir thickness, formation pressure, bottom hole flowing pressure, underground crude oil viscosity, underground crude oil volume coefficient, reservoir permeability, and single-well supply radius. The specific range for setting single-well reservoir parameters includes: setting the calculation range for the artificial fracture length to be 0.1 times the single-well supply radius to 0.5 times the single-well supply radius; setting the increment for the artificial fracture length to be 0.05 times the single-well supply radius; and setting the calculation range for the artificial fracture conductivity to be... to The step size for increasing the conductivity of artificial fractures is .

4. The method for calculating construction parameters of sand-added acid fracturing retrofitting according to claim 1, characterized in that, S3 specifically includes: S31. Obtain the average width of the artificial crack, the permeability of the sand-filled support, the particle radius of the proppant, and the porosity of the sand-filled crack. S32. Determine the target sand-filled crack permeability based on the average crack width of the artificial crack, the permeability of the sand-filled support, and the target conductivity. S33. Based on the proppant particle radius and the porosity of the sand-filled cracks, determine the fractal characteristic parameters of the sand-filled cracks, and based on the fractal characteristic parameters of the sand-filled cracks, determine the actual permeability of the sand-filled cracks. S34. Set the initial value for calculating the porosity of the sand-filled cracks. Compare the actual permeability of the sand-filled cracks with the target permeability of the sand-filled cracks. If the actual permeability of the sand-filled cracks is less than the target permeability of the sand-filled cracks, add up the porosity of the sand-filled cracks and execute step S32 until the actual permeability of the sand-filled cracks is greater than the target permeability of the sand-filled cracks. Output the current porosity of the sand-filled cracks. S35. Based on the output porosity of the sand-filled cracks, determine the volume of proppant required for sand-addition acid fracturing modification.

5. The method for calculating construction parameters of sand-added acid fracturing retrofitting according to claim 1, characterized in that, S5 specifically includes: S51. The target conductivity and average width of artificial fractures required for single-well sand-added acid fracturing stimulation are used to determine the target permeability of acid erosion. S52. Obtain the amount of dissolution and the morphology of cracks to determine the actual permeability formed by acid dissolution; S53. Set the initial value for acid injection calculation, compare the target permeability of acid corrosion with the actual permeability. If the actual permeability of acid corrosion is greater than the target permeability, add acid injection and execute step S52 until the actual permeability of acid corrosion is less than the target permeability, and output the current acid corrosion permeability. S54. Based on the acid dissolution and permeability and the acid pumping time, calculate the volume of acid required for sand-addition acid fracturing modification. 。 6. The method for calculating construction parameters of sand-added acid fracturing retrofitting according to claim 5, characterized in that, The determination of the actual permeability formed by acid erosion specifically includes: The acid co-pumping time is set, and the crack is discretized into n elements along its length, with each element having a length of [missing information]. Based on the acid concentration and flow rate in each unit, the amount of rock dissolution in unit i within the time step is determined; The crack morphology is obtained, and the width of the dissolution crack is determined by combining it with the amount of rock dissolution over a certain period of time. After the acid injection is completed within a certain time, the actual permeability formed by acid dissolution within a certain time is determined based on the width of the dissolution crack.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements a method for calculating construction parameters for sand-addition acid fracturing as described in any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements a method for calculating construction parameters for sand-addition acid fracturing as described in any one of claims 1 to 6.

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