WO2021082130A1 - Acid fracturing simulation method considering variable-viscosity acid dynamic process - Google Patents

Abstract

Provided is an acid fracturing simulation method considering a variable-viscosity acid dynamic process: determining the relationship between the viscosity of a variable-viscosity acid and the shear rate, temperature, calcium ion concentration, pH value, and surfactant concentration, respectively, to establish a variable-viscosity constitutive equation; simulating the flow and reaction process of the variable-viscosity acid in a fracture system to obtain the pressure profile in the fracture system; taking the pressure profile in the fracture system as an internal boundary condition and the ground pressure as an external boundary condition, simulating and calculating the reaction process of variable-viscosity acid in a matrix; simulating the viscosity change of the acid in the matrix system and calculating the filtration loss rate; bringing the obtained filtration loss rate into the pressure profile in the fracture system of the step. The method solves the problem that the acid fracturing simulation technology of the prior art does not consider the dynamic filtration loss process of variable-viscosity acid, leading to the problem that the fracture length of the variable-viscosity acid fracturing simulation is not highly consistent with actual conditions, and achieves the purpose of simulating an acid-fracturing fracture morphology considering the dynamic reduction rate of variable-viscosity acid.

Description

Acid fracturing simulation method considering the dynamic process of variable viscosity Technical field

The invention relates to the field of fracturing, and in particular to an acid fracturing simulation method considering the dynamic process of variable viscosity.

Background technique

Viscosity is a kind of acid with variable viscosity first synthesized by Schlumberger in 1997. It is used in fracturing fluids for increasing oil and gas production through hydraulic fracturing and acidification. There are a large number of foreign oilfields to restore old oilfields. Successful use of production capacity and new oilfields to increase recoverable reserves. The initial viscosity of the existing variable ^{mucous acid can be about 30 mpa·s at a shear rate of 170 -1} . As the acid liquid reacts with the formation matrix, the pH value increases. When the pH value rises to about 2, the acid The viscosity of the liquid system rises sharply and can reach 1000mpa·s. Then as the acid rock reaction continues, when the pH value reaches about 4, another chemical reaction is triggered to reduce the viscosity of the residual acid to 20 mpa·s or lower. The high viscosity during the acid consumption process makes the later injected acid transfer to the formation with relatively low permeability, and prevents the development of pores and slows the loss of active acid to natural fractures, thereby achieving homogeneity and depth The purpose of acidification. The final decrease in the viscosity of the residual acid is conducive to the flowback of fracturing fluid or acid fluid.

In the field of fracturing stimulation, acid fluid loss is one of the main factors affecting the length of acid fracturing fractures. The smaller the fluid loss rate, the longer the acid fracturing fracture length. The viscosity of variable viscous acid changes continuously during the reaction process, so the fluid loss rate also changes continuously, which ultimately affects the morphology of acid fracturing cracks. The existing acid fracturing simulation technology is based on conventional acid, and does not consider the dynamic fluid loss process of the variable viscous acid, resulting in a low rate of conformity with the actual situation of the simulated seam length of the variable viscous acid fracturing.

Summary of the invention

The purpose of the present invention is to provide an acid fracturing simulation method that considers the dynamic process of changing viscous acid to solve the problem that the acid fracturing simulation technology in the prior art does not consider the dynamic fluid loss process of changing viscous acid. The problem of the low coincidence rate of the situation can achieve the goal of being able to simulate the acid fracturing fracture morphology after considering the dynamic reduction rate of the variable viscous acid.

The present invention is realized through the following technical solutions:

Consider the acid fracturing simulation method of the dynamic process of changing viscosity, including the following steps:

(a) Determine the relationship between the viscosity of variable viscosity and the shear rate, temperature, calcium ion concentration, pH value, and surfactant concentration, and establish the variable viscosity constitutive equation;

(b) Simulate the flow and reaction process of the variable viscous acid liquid in the fracture system to obtain the pressure profile in the fracture system;

(c) Using the internal pressure profile of the fracture system as the inner boundary condition, and the ground pressure as the outer boundary condition, simulate and calculate the reaction process of variable viscosity in the matrix;

(d) Simulate the viscosity change of the acid liquid in the matrix system, and calculate the fluid loss rate;

(e) Bring the obtained fluid loss rate to the pressure profile in the fracture system of step (b).

Further, the method for establishing the variable viscosity constitutive equation in the step (a) includes:

①Measure the shear stress of mucous acid under different shear rates through experiments, and obtain the rheological index of mucous acid through linear regression;

②Experimentally determine the viscosity of variable mucic acid at different pH values, and get the relationship between viscosity and pH value by fitting;

③Experimentally determine the viscosity of variable mucic acid at different calcium ion concentrations, and fit the relationship between the viscosity and the calcium ion concentration;

④Experimentally determine the viscosity of variable mucic acid at different surfactant concentrations, and fit the relationship between the viscosity and the surfactant concentration;

⑤Establish a variable viscosity constitutive equation affected by shear rate, temperature, calcium ion concentration, pH value, and surfactant concentration.

Further, the regression formula of the rheological index n in step ① is: η=Hγ ^n-1 , where η is the shear stress, Pa; H is the fluid viscosity, mPa·s; γ is the shear rate, s ^-1 .

The formula for the relationship between the viscosity μ and the pH value obtained by fitting in step ② is: μ(pH)=μ ₀ + μ _max (pH)erf(b·pH+c), where μ _max is the maximum viscosity, and μ ₀ is the initial Viscosity, mPa·s; pH is the system pH value, dimensionless; b and c are fitting coefficients, dimensionless;

The formula for the relationship between the viscosity and the calcium ion concentration obtained by fitting in step ③ is:

Among them, Ca ²⁺ is the concentration of calcium ions, and d, e, and W ₁ are all fitting coefficients;

The formula for the relationship between viscosity and surfactant concentration obtained by fitting in step ④ is:

Among them, VES means surfactant, f, g, and W ₂ are all fitting coefficients;

The constitutive equation established in step ⑤ is:

Among them, α is a constant related to the properties of variable viscosity, dimensionless; T is the formation temperature, K; T ₀ is the experimental temperature, K.

Further, the pressure profile equation in the fracture system obtained in the step (b) is:

Among them, w _a is the crack width, m; v _x and v _y are the flow velocity of the variable viscous acid in the x and y directions, m/s; μ _a is the viscosity, mPa·s; k is the matrix permeability, Md; p Is the matrix pressure, MPa; p _e is the reservoir pressure, MPa; v _lm is the dynamic fluid loss velocity of variable viscous acid at different positions on the fracture wall, m/s.

Further, in step (c), the simulation calculation of the reaction process of mucous acid in the matrix includes: calculating the shear rate and flow field, calculating the pH value and the acid concentration field, calculating the calcium ion concentration field, calculating the surfactant concentration field, Calculate the temperature field, calculate the porosity field after the acid reacts with the rock, boundary conditions and iterative calculations.

Further, the shear rate and the flow field are calculated by the flow equation, and the flow equation includes:

Where K is permeability, mD; P is pressure, MPa; φ is porosity, dimensionless; t is time, s;

Is the gradient operator;

The pH value and the acid concentration field are calculated by the acid concentration equation, and the acid concentration equation includes:

Where C _f is the molar concentration of the acid in the pores, mol/l; _De is the hydrogen ion diffusion coefficient, m ² /s; C _s is the molar concentration of the acid on the pore surface, mol/l; a _v is the pore ratio Surface, m ² /m ³ ;

The calcium ion concentration field is calculated by the calcium ion balance equation, and the calcium ion balance equation includes:

The surfactant concentration field is calculated by the surfactant balance equation, and the surfactant balance equation includes:

Among them, C _SDVA -surface active agent mass concentration, wt%; _{De, SDVA} -surface active agent effective diffusion coefficient, m ² /s;

The temperature field is calculated by the heat transfer model of the acid rock reaction exothermic heat, and the heat transfer model of the acid rock reaction exothermic heat includes:

Among them, T _f — acid temperature, K; T _s — rock temperature, K; C _Pf — acid specific heat capacity, J/kg K; C _Ps — rock specific heat capacity, J/kg K; k _ef — acid thermal conductivity, W/m K; k _es — thermal conductivity of rock, W/m K; h _c — convection heat transfer coefficient between acid and rock, W/m ² K; △H _r — reaction enthalpy, J/mol; ρ _f — acid Liquid density; ρ _s —rock density;

The porosity field after the acid reacts with the rock is calculated by the following formula:

Further, the calculation method of the filtration rate in the step (d) is:

(1) Bring the shear rate, temperature, calcium ion concentration, pH value, and surfactant concentration obtained in step (c) into the constitutive equation established in step ⑤ to obtain the viscosity u _eff distribution in the matrix system ；

(2) Bring u _eff into the flow equation to obtain the acid flow velocity at different positions, where the flow velocity on the inner boundary is the fluid loss velocity on the fracture wall.

Further, in the step (e), the fluid loss rate obtained is brought into the pressure profile in the fracture system of the step (b) until the acid injection cycle ends.

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

The present invention considers the acid fracturing simulation method of the dynamic process of changing viscous acid, overcomes the defect that the prior art does not consider the dynamic fluid loss process of changing viscous acid, which leads to the shortcomings that the length of the simulated seam length of the variable viscous acid fracturing is not high in accordance with the actual situation. Considering the dynamic process of the reaction between variable viscous acid and rock, by simulating the shear rate, temperature, calcium ion concentration, pH value, and surfactant concentration field in the formation at different times to calculate the transient acid viscosity change , And obtain the dynamic fluid loss rate of the acid liquid, and finally simulate the acid fracturing fracture morphology considering the dynamic reduction rate of the variable viscous acid, which significantly improves the accuracy of the fracture length during the simulation of the variable viscous acid fracturing.

Description of the drawings

The drawings described here are used to provide a further understanding of the embodiments of the present invention, constitute a part of the application, and do not constitute a limitation to the embodiments of the present invention. In the attached picture:

Figure 1 is a graph of the relationship between shear rate and shear stress in a specific embodiment of the present invention;

Fig. 2 is a schematic diagram of the viscosity of variable mucic acid at different pH values in a specific embodiment of the present invention;

Figure 3 is a schematic diagram of the viscosity of mucic acid under different calcium ion concentrations in specific embodiments of the present invention;

Figure 4 is a schematic diagram of the viscosity of variable mucic acid at different surfactant concentrations in specific embodiments of the present invention;

Fig. 5 is a schematic diagram of the flow velocity profile of variable viscous acid in the fracture system in a specific embodiment of the present invention;

Fig. 6 is a schematic diagram of the pressure profile of the variable viscosity in the fracture system in a specific embodiment of the present invention;

Fig. 7 is a schematic diagram of the acid concentration field in the fracture system in a specific embodiment of the present invention;

8 is a schematic diagram of the calcium ion concentration field in the fracture system in a specific embodiment of the present invention;

Fig. 9 is a schematic diagram of the surfactant concentration field in the fracture system in a specific embodiment of the present invention;

Fig. 10 is a schematic diagram of the porosity field after the reaction of the variable viscous acid with the rock in the specific embodiment of the present invention;

Figure 11 is a schematic diagram _{of the viscosity u eff} distribution in the matrix system in a specific embodiment of the present invention;

Fig. 12 is a schematic diagram of the fluid loss rate of variable viscose acid on the crack wall surface in a specific embodiment of the present invention;

Fig. 13 is a diagram of the crack morphology after the simulation of the specific embodiment of the present invention is completed.

Detailed ways

In order to make the objectives, technical solutions, and advantages of the present invention clearer and clearer, the present invention will be further described in detail below with reference to the embodiments and drawings. The exemplary embodiments and descriptions of the present invention are only used to explain the present invention, not As a limitation of the present invention.

Consider the acid fracturing simulation method of the dynamic process of variable viscosity, the specific method is as follows:

(1) Determine the relationship between viscosity and shear rate, temperature, calcium ion concentration, pH value, and surfactant concentration respectively, and establish a variable viscosity constitutive equation:

①The experimental determination of the shear stress of mucous acid at different shear rates is shown in Figure 1. The rheological index n of mucous acid is obtained by linear regression: σ=4.669·γ ^0.449 .

②Experimental measurement of the viscosity of variable mucous acid at different pH values. The experimental results are shown in Figure 2. The relationship formula between viscosity and pH value is obtained by fitting the following formula:

μ(pH)=μ ₀ +μ _max (pH)erf(b·pH+c), where b—fitting coefficient, taking 0.609; c—fitting coefficient, taking 0.136.

③The experiment measures the viscosity of mucic acid under different calcium ion concentrations. The experimental results are shown in Figure 3. The relationship between viscosity and calcium ion concentration is obtained by fitting the following formula:

Among them, d—fitting coefficient, taken as 2.302; e—fitting coefficient, taken as 15.203; W ₁ ——fitting coefficient, taken as 18.012.

④Experimentally determine the viscosity of variable mucous acid at different surfactant concentrations. The experimental results are shown in Figure 4. The relationship formula between viscosity and surfactant concentration is obtained by fitting the following formula:

Among them, f—fitting coefficient, taken as 1.000; g—fitting coefficient, taken as 6.702; W ₂ —fitting coefficient, taken as 4.334.

⑤On the basis of the above experimental results, the viscosity results of mucous acid in different environments are combined to establish a constitutive equation for variable viscosity that is affected by shear rate, temperature, calcium ion concentration, pH value, and surfactant concentration:

(2) Simulate and calculate the flow and reaction process of acid in the fracture system, as shown in Figure 5, and calculate the pressure profile in the fracture system as shown in Figure 6.

(3) Taking the internal pressure profile of the fracture system as the inner boundary condition and the ground pressure as the outer boundary condition, calculate the physical and chemical reaction process of the steering acid in the matrix system:

①Calculate the shear rate and flow field through the flow equation, where the flow equation is as follows:

②Calculate the pH value and acid concentration field through the acid concentration equation. The calculation result is shown in Figure 7. The acid concentration equation is as follows:

③Calcium ion balance equation calculates the calcium ion concentration field. The calculation result is shown in Figure 8. The calcium ion balance equation is as follows:

In the formula, C _Ca ^2+-the molar concentration of calcium ions (mol/l); _{De, Ca} ^2+-the effective diffusion coefficient of calcium ions (m2/s).

④Calculate the surfactant concentration field by the surfactant balance equation. The calculation result is shown in Figure 9. The surfactant balance equation is as follows:

C _SDVA —mass concentration of surfactant, wt%; _{De, SDVA} —effective diffusion coefficient of surfactant, m ² /s.

⑤Calculate the temperature field with the heat transfer model considering the heat released by the acid rock reaction. The heat transfer model of the acid rock reaction exothermic heat includes:

Among them, T _f — acid temperature, K; T _s — rock temperature, K; C _Pf — acid specific heat capacity, J/kg K; C _Ps — rock specific heat capacity, J/kg K; k _ef — acid thermal conductivity, W/m K; k _es — thermal conductivity of rock, W/m K; h _c — convection heat transfer coefficient between acid and rock, W/m ² K; △H _r — reaction enthalpy, J/mol; ρ _f — acid Liquid density; ρ _s —rock density;

⑥Calculate the porosity field after the acid reacts with the rock. The calculation result is shown in Figure 10.

⑦The boundary conditions (using the internal pressure profile of the fracture system as the internal solution condition, the ground pressure as the external boundary condition, etc.) and the iterative calculation steps are all existing technologies and will not be repeated here.

(4) Simulate the viscosity change of the acid liquid in the matrix system, and calculate the fluid loss rate:

Bring the shear rate, temperature, calcium ion concentration, pH value, and surfactant concentration obtained in step (3) into step ⑤ in step (1), and calculate the viscosity distribution u _eff in the matrix system.

Then _{bring u eff} into the flow equation of step (3) to obtain the acid flow velocity at different positions, where the flow velocity on the inner boundary is the fluid loss velocity on the crack wall as shown in FIG. 12.

(5) Bring the fluid loss rate into the second step, and the cycle ends until the end of acid injection. The fracture morphology obtained after the simulation is completed is shown in Figure 13.

The specific embodiments described above further describe the purpose, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only specific embodiments of the present invention, and are not intended to limit the scope of the present invention. The protection scope, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims (8)

1. The acid fracturing simulation method considering the dynamic process of changing viscosity is characterized in that it includes the following steps:

   (a) Determine the relationship between the viscosity of variable viscosity and the shear rate, temperature, calcium ion concentration, pH value, and surfactant concentration, and establish the variable viscosity constitutive equation;

   (b) Simulate the flow and reaction process of the variable viscous acid liquid in the fracture system to obtain the pressure profile in the fracture system;

   (c) Using the internal pressure profile of the fracture system as the inner boundary condition, and the ground pressure as the outer boundary condition, simulate and calculate the reaction process of variable viscosity in the matrix;

   (d) Simulate the viscosity change of the acid liquid in the matrix system, and calculate the fluid loss rate;

   (e) Bring the obtained fluid loss rate to the pressure profile in the fracture system of step (b).
2. The acid fracturing simulation method considering the dynamic process of changing viscosity according to claim 1, wherein the step (a) comprises:

   ①Measure the shear stress of mucous acid under different shear rates through experiments, and obtain the rheological index of mucous acid through linear regression;

   ②Experimentally determine the viscosity of variable mucic acid at different pH values, and get the relationship between viscosity and pH value by fitting;

   ③Experimentally determine the viscosity of variable mucic acid at different calcium ion concentrations, and fit the relationship between the viscosity and the calcium ion concentration;

   ④Experimentally determine the viscosity of variable mucic acid at different surfactant concentrations, and fit the relationship between the viscosity and the surfactant concentration;

   ⑤Establish a variable viscosity constitutive equation affected by shear rate, temperature, calcium ion concentration, pH value, and surfactant concentration.
3. The acid fracturing simulation method considering the dynamic process of changing viscosity according to claim 2, characterized in that:

   The regression formula of the rheological index n in step ① is: η=Hγ ^n-1 , where η is the shear stress, Pa; H is the fluid viscosity, mPa·s; γ is the shear rate, s ^-1 ;

   The formula for the relationship between the viscosity μ and the pH value obtained by fitting in step ② is: μ(pH)=μ ₀ + μ _max (pH)erf(b·pH+c), where μ _max is the maximum viscosity, mPa·s; μ ₀ is the initial viscosity, mPa·s; pH is the system pH value, dimensionless; b and c are fitting coefficients, dimensionless;

   The formula for the relationship between the viscosity and the calcium ion concentration obtained by fitting in step ③ is:

   

   Among them, Ca ²⁺ is the concentration of calcium ions, and d, e, and W ₁ are all fitting coefficients;

   The formula for the relationship between viscosity and surfactant concentration obtained by fitting in step ④ is:

   

   Among them, VES means surfactant, f, g, and W ₂ are all fitting coefficients;

   The constitutive equation established in step ⑤ is:

   

   Among them, α is a constant related to the properties of variable viscosity, dimensionless; T is the formation temperature, K; T ₀ is the experimental temperature, K.
4. The acid fracturing simulation method considering the dynamic process of variable viscosity according to claim 3, wherein the pressure profile equation in the fracture system obtained in the step (b) is:

   

   Among them, w _a is the crack width, m; v _x and v _y are the flow velocity of the variable viscous acid in the x and y directions, m/s; μ _a is the viscosity, mPa·s; k is the matrix permeability, Md; p Is the matrix pressure, MPa; p _e is the reservoir pressure, MPa; v _lm is the dynamic fluid loss velocity of variable viscous acid at different positions on the fracture wall, m/s.
5. The acid fracturing simulation method considering the dynamic process of mucous acid according to claim 4, characterized in that, in step (c), simulating and calculating the reaction process of mucous acid in the matrix includes: calculating shear rate and flow field, calculating pH value and acid concentration field, calculation of calcium ion concentration field, calculation of surfactant concentration field, calculation of temperature field, calculation of porosity field after acid and rock reaction, boundary conditions and iterative calculation.
6. The acid fracturing simulation method considering the dynamic process of changing viscosity according to claim 5, characterized in that:

   The shear rate and flow field are calculated by the flow equation, which includes:

   

   Where K is permeability, mD; P is pressure, MPa; φ is porosity, dimensionless; t is time, s;

   

   Is the gradient operator;

   The pH value and the acid concentration field are calculated by the acid concentration equation, and the acid concentration equation includes:

   

   Where C _f is the molar concentration of acid in the pores, mol/l;

   D _e is the hydrogen ion diffusion coefficient, m ² /s; C _s is the molar concentration of acid on the pore surface mol/l; a _v is the specific surface of the pore, m ² /m ³ ;

   The calcium ion concentration field is calculated by the calcium ion balance equation, and the calcium ion balance equation includes:

   

   The surfactant concentration field is calculated by the surfactant balance equation, and the surfactant balance equation includes:

   

   Among them, C _SDVA -surface active agent mass concentration, wt%; _{De, SDVA} -surface active agent effective diffusion coefficient, m ² /s;

   The temperature field is calculated by the heat transfer model of the acid rock reaction exothermic heat, and the heat transfer model of the acid rock reaction exothermic heat includes:

   

   

   Among them, T _f — acid temperature, K; T _s — rock temperature, K; C _Pf — acid specific heat capacity, J/kg K; C _Ps — rock specific heat capacity, J/kg K; k _ef — acid thermal conductivity, W/m K; k _es — thermal conductivity of rock, W/m K; h _c — convection heat transfer coefficient between acid and rock, W/m ² K; △H _r — reaction enthalpy, J/mol; ρ _f — acid Liquid density; ρ _s —rock density;

   The porosity field after the acid reacts with the rock is calculated by the following formula:

   
7. The acid fracturing simulation method considering the dynamic process of changing viscosity according to claim 6, wherein the calculation method of the fluid loss rate in the step (d) is:

   (1) Bring the shear rate, temperature, calcium ion concentration, pH value, and surfactant concentration obtained in step (c) into the constitutive equation established in step ⑤ to obtain the viscosity u _eff distribution in the matrix system ；

   (2) Bring u _eff into the flow equation to obtain the acid flow velocity at different positions, where the flow velocity on the inner boundary is the fluid loss velocity on the fracture wall.
8. The acid fracturing simulation method considering the dynamic process of variable viscosity according to claim 1, characterized in that, in the step (e), the obtained fluid loss velocity is brought into the pressure profile in the fracture system of the step (b) , Until the end of the acid injection cycle.

Images