Non-isothermal three-dimensional fractured core acidification numerical simulation method

Abstract

The invention discloses a non-isothermal three-dimensional fractured core acidification numerical simulation method which comprises the following steps: S1, constructing a fractured core acidification numerical simulation physical model, dividing grids and endowing physical parameters; s2, calculating a fluid channeling coefficient; s3, solving a matrix and fracture pressure control equation, calculating seepage velocity and molar reaction heat, and recording current injection pressure; s4, solving a temperature control equation of the matrix, the fracture acid liquor and the rock, and calculating an effective diffusion coefficient, an acid liquor reaction rate constant and a mass transfer coefficient of the acid liquor; s5, solving a matrix and fracture acid liquor concentration control equation, and calculating the porosity, the pore throat radius, the permeability and the pore specific surface area of the current time step; and S6, judging whether the wormhole breaks through the rock core or not according to the injection pressure of the current time step, and obtaining a three-dimensional fractured rock core acidification numerical simulation result. According to the method, the three-dimensional fracture network and the non-isothermal field are deeply coupled, so that the precision of three-dimensional fractured core acidification numerical simulation is effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of oil and gas field development, and particularly relates to a non-isothermal three-dimensional fractured core acidizing numerical simulation method in the acidizing process. Background Technique

[0002] The acidizing numerical simulation technology is one of the core means to optimize the reservoir stimulation plan in the oil and gas development field. Existing research mostly focuses on the simulation of the acidizing process under two-dimensional or simplified models. Through methods such as dual-scale continuous models and discrete fracture networks, the influence law of fractures on the propagation of acid-etched wormholes has been initially revealed. However, in actual acidizing operations, the temperature difference between the acid fluid and the reservoir and the reaction heat release effect will significantly change the acid-rock reaction kinetic characteristics, thereby affecting the wormhole morphology and conductivity. Traditional models often simplify the temperature field as a steady state or ignore the heat effect, resulting in insufficient simulation accuracy of the dynamic heat transfer process when low-temperature acid fluid is injected into a high-temperature formation.

[0003] The current technology has significant limitations: on the one hand, most three-dimensional acidizing models are limited to isothermal conditions or a single temperature boundary assumption, and cannot simulate the transient heat transfer between the acid fluid and the rock and the dynamic evolution of the temperature field during the acid injection process; on the other hand, the temperature distribution of the fractured core is affected by the coupling of the fracture geometry, acid injection rate, and initial geothermal gradient, and the existing methods fail to deeply couple the three-dimensional fracture network with the non-isothermal field, resulting in the difficulty of quantifying the dynamic influence of the sudden change in the rheological properties of the acid fluid (such as the viscosity decrease and shunt ability weakening at high temperatures) on the wormhole branching pattern. Therefore, it is urgent to construct a three-dimensional non-isothermal fractured core acidizing numerical simulation method to accurately depict the multi-field coupling effect of heat-flow-fluidization and provide a more scientific theoretical basis for the acidizing process design of complex reservoirs. Summary of the Invention

[0004] The purpose of the present invention is to provide a non-isothermal three-dimensional fractured core acidizing numerical simulation method. The principle of this method is reliable and the operation is simple. By deeply coupling the three-dimensional fracture network with the non-isothermal field, the accuracy of the three-dimensional fractured core acidizing numerical simulation is effectively improved, which is of great significance for realizing the efficient development of oil and gas fields and improving the oil and gas recovery rate.

[0005] To achieve the above technical objectives, the present invention adopts the following technical solutions.

[0006] A non-isothermal three-dimensional fractured core acidizing numerical simulation method successively includes the following steps: S1: Construct a physical model for the fractured core acidizing numerical simulation, divide the grid and assign physical parameters; S2: Calculate the crossflow coefficient NNC according to the current pore permeability state; S3: Solve the matrix and fracture pressure control equations, calculate the seepage velocity and the molar reaction heat, and record the current injection pressure; S4: Solve the temperature control equations of the matrix, fracture acid fluid, and rock, and calculate the effective diffusion coefficient of the acid fluid, the acid fluid reaction rate constant, and the mass transfer coefficient; S5: Solve the acid fluid concentration control equations of the matrix and fracture, and calculate the porosity, pore throat radius, permeability, and pore specific surface area at the current time step; S6: Determine whether the injection pressure at the current time step is greater than 1% of the initial injection pressure: if it is greater, the wormhole has not broken through the core, repeat steps S2 - S5, otherwise it means the wormhole has broken through the core, and obtain the numerical simulation results of three - dimensional fractured core acidification.

[0007] Preferably, in step S1, the grid division refers to using structured grids to divide the matrix and using the matrix grid boundaries to perform unstructured grid division on the fractures.

[0008] Preferably, in step S1, the physical parameters include the porosity and permeability of the matrix and fractures, the matrix fluid temperature, and the matrix rock temperature.

[0009] Preferably, in step S2, the process of calculating the cross - flow coefficient is as follows: The cross - flow coefficient between the matrix and the fracture:

[0010] In the formula, is the cross - flow coefficient between the matrix and the fracture, m 3 ; is the fracture area in the grid block, m 2 ; is the matrix permeability, m 2 ; is the average distance between the matrix and the fracture grid, m; The cross - flow coefficient between two intersecting fractures:

[0011]

[0012] [[ID=A5]]

[0013] In the formula, is the cross - flow coefficient between two intersecting fractures, m 3 ; and are the permeabilities of the two fractures, m 2 ; and are the widths of the two fractures, m; is the length of the intersection line of the two fractures, m; and are the average normal distances from the two fractures to the intersection line, m.

[0014] Preferably, in step S3, the matrix and fracture pressure control equations include: Matrix pressure control equation:

[0015] Fracture pressure control equation:

[0016] In the formulas, and are the matrix porosity and fracture porosity respectively, and the upper and lower subscripts and represent the matrix and fracture respectively, and the same applies hereinafter; t is time, s; is the divergence operator, dimensionless; is the gradient operator, dimensionless; and are the matrix permeability and fracture permeability respectively, m 2 ; is the acid fluid viscosity, Pa·s; and are the matrix pressure and fracture pressure respectively, Pa; and are the flux transfer functions from the matrix to the fracture and from the fracture to the matrix respectively, m 3 / s; is the flux transfer function between intersecting fractures, m 3 / s; and are the matrix grid volume and fracture grid volume respectively, m 3 ;

[0017]

[0018] In the formulas, and are the pressures of two intersecting fracture grids, Pa.

[0019] Preferably, in step S3, the calculation of the seepage velocity and the molar reaction heat includes: Calculation of the seepage velocity:

[0020]

[0021] In the formula, and are the seepage velocities in the matrix and fracture respectively, m / s; Calculation of molar reaction heat:

[0022] In the formula, represents the subscript and , representing the matrix and the fracture, and the same applies hereinafter; is the molar reaction heat of acid-rock, J / mol; is the rock temperature, K.

[0023] Preferably, in step S3, the injection pressure refers to the pressure at the boundary where the acid solution is injected, and the first recorded injection pressure is the initial injection pressure.

[0024] Preferably, in step S4, the temperature control equations for the acid solution and the rock in the matrix and the fracture include: Matrix acid solution temperature control equation:

[0025] Fracture acid solution temperature control equation:

[0026]

[0027] In the formula, is the fluid density, kg / m 3 ; is the specific heat capacity of the acid, J / (kg·K); is the thermal conductivity of the acid, W / (m·K); is the acid-rock heat transfer coefficient, W / (m 2 ·K); is 's function; is the acid-rock heat transfer coefficient, W / (m 2 ·K); and are the pore specific surface areas of the matrix and the fracture respectively, m 2 / m 3 ; and[[ID=6?]] are the acid solution temperatures in the matrix and the fracture respectively, K; and are the matrix rock temperature and the fracture wall temperature respectively, K; Matrix rock temperature control equation:

[0028] Fracture rock temperature control equation:

[0029] In the formula, is the rock density, kg / m 3 ; is the specific heat capacity of the rock, J / (kg·K); and are the molar reaction heats of acid and rock in the matrix and fracture respectively, J / mol; is the thermal conductivity of the rock, W / (m 2 ·K); and are the pore specific surface areas of the matrix and fracture respectively, m 2 / m 3 ; and are the surface reaction rates in the matrix and fracture respectively, kmol / (s·m 2 ).

[0030] Preferably, in step S4, the calculation of the effective diffusion coefficient of the acid solution, the reaction rate constant of the acid solution, and the mass transfer coefficient is as follows: Calculating the effective diffusion coefficient of the acid solution:

[0031] In the formula, is the effective diffusion coefficient in different directions, m / s, represents , and directions; is the effective diffusion coefficient, m / s; and are constants related to the pore structure, =0.5, =0.1, =0.1; is the Péclet number, expressed as ; is in magnitude, m / s; is the average pore throat radius, m; Calculating the reaction rate constant of the acid solution:

[0032] In the formula, is the reaction rate constant, m / s; and are the acid solution concentrations in the matrix and fracture respectively, kmol / m 3 ; is the gas constant, J / (mol·K); Calculating the mass transfer coefficient:

[0033] In the formula, is the mass transfer coefficient, m / s; is the asymptotic Sherwood number; is the pore Reynolds number, expressed as ; is the Schmidt number, expressed as ; is the ratio of pore length to pore diameter; is the average pore throat radius, m; Solve the surface reaction rate control equations in the matrix and fractures:

[0034] In the formula, is the surface reaction rate, kmol / (s·m 2 ); is the specific surface area of pores, m 2 / m 3 .

[0035] Preferably, in step S5, the matrix and fracture acid concentration control equations include: Matrix acid concentration control equation:

[0036] Fracture acid concentration control equation:

[0037]

[0038] In the formula, is a function of , kmol / m 3 .

[0039] Preferably, in step S5, solve the following equations to calculate the permeability, pore throat radius, specific surface area of pores, and porosity at the current time step: Permeability control equation:

[0040] Pore throat radius control equation:

[0041] Specific surface area of pores control equation:

[0042] Porosity control equation:

[0043] In the formula, and is the initial permeability and the current permeability, m 2 ; and are the initial porosity and the current porosity; and are the initial average pore throat radius and the current average pore throat radius, m; is the pore expansion parameter; are the initial pore specific surface area and the current pore specific surface area, m 2 / m 3 ; is the dissolution power of the acid, defined as the grams of dissolved solids in each mole of acid reaction, kg / kmol; is the rock density, kg / m 3 .

[0044] Compared with the prior art, the present invention has the following beneficial effects: By coupling three-dimensional fracture network modeling with non-isothermal field dynamic analysis, the present invention realizes for the first time the full-coupling numerical simulation of multi-physical fields of heat-fluid-chemistry during the acidification process of three-dimensional fractured rock cores. This model can accurately characterize the asymmetric heat exchange between fractures and the matrix, the local temperature changes caused by acid injection, and its dynamic regulation effect on the acid-rock reaction rate; by introducing temperature-sensitive acid-rock reactions, the influence of the sudden change in acid rheological properties on the wormhole expansion path when injecting low-temperature acid into high-temperature reservoirs can be quantified. Compared with the prior art, the present invention not only solves the simulation problem of the complex heat transfer path in the acidification process of three-dimensional fractured carbonates, but also significantly improves the reliability of predicting the acidification effect of heterogeneous fractured reservoirs, provides a key theoretical basis for optimizing the acid injection temperature and displacement, and has important guiding significance for the acidification process design of deep high-temperature fractured reservoirs. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0046] Figure 1 is a flowchart of a non-isothermal three-dimensional fractured rock core acidification numerical simulation method of the present invention; Figure 2 is a schematic diagram of the result of three-dimensional fractured rock core mesh division in a specific embodiment; Figure 3 is the wormhole development structure of a three-dimensional fractured rock core at the moment when the injected pore volume is 0.6 in a specific embodiment; Figure 4The wormhole development structure of a three-dimensional fractured core at a pore volume injection of 0.8 for a specific embodiment; Figure 5 The wormhole development structure of a three-dimensional fractured core at a pore volume injection of 1.0 for a specific embodiment; Figure 6 The wormhole development structure of a three-dimensional fractured core at a pore volume injection of 1.1 for a specific embodiment; Figure 7 The wormhole development structure of a three-dimensional fractured core at a pore volume injection of 1.33 for a specific embodiment; Figure 8 The temperature distribution diagram caused by the acid-rock reaction heat of a three-dimensional fractured core at a pore volume injection of 0.6 for a specific embodiment; Figure 9 The temperature distribution diagram caused by the acid-rock reaction heat of a three-dimensional fractured core at a pore volume injection of 0.8 for a specific embodiment; Figure 10 The temperature distribution diagram caused by the acid-rock reaction heat of a three-dimensional fractured core at a pore volume injection of 1.0 for a specific embodiment; Figure 11 The temperature distribution diagram caused by the acid-rock reaction heat of a three-dimensional fractured core at a pore volume injection of 1.1 for a specific embodiment; Figure 12 The temperature distribution diagram caused by the acid-rock reaction heat of a three-dimensional fractured core at a pore volume injection of 1.33 for a specific embodiment. Detailed implementation manners

[0047] The present invention will be further described below in conjunction with the accompanying drawings and embodiments. It should be noted that, without conflict, the embodiments in the present application and the technical features in the embodiments may be combined with each other. It should be pointed out that unless otherwise specified, all technical and scientific terms used in the present application have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0048] As Figure 1 shown, a non-isothermal three-dimensional fractured core acidizing numerical simulation method successively includes the following steps: S1: Construct a physical model for the numerical simulation of fractured core acidizing, divide the grid and assign physical parameters: use structured grids to divide the matrix into grids, and use the matrix grid boundaries to divide the fractures into unstructured grids; the physical parameters include the porosity and permeability of the matrix and fractures, the matrix fluid temperature and the matrix rock temperature; S2: Calculate the crossflow coefficient NNC according to the current pore permeability state; S3: Solve the matrix and fracture pressure control equations, calculate the seepage velocity and the molar heat of reaction, and record the current injection pressure. The injection pressure recorded in the first cycle is the initial injection pressure; S4: Solve the matrix and fracture acid and rock temperature control equations, and calculate the effective diffusion coefficient of the acid, the acid reaction rate constant, and the mass transfer coefficient; S5: Solve the matrix and fracture acid concentration control equations, and calculate the porosity, pore throat radius, permeability, and pore specific surface area at the current time step; S6: According to the current injection pressure, determine whether the wormhole breaks through at the current time step: If it does not break through, repeat steps S2 - S5; if it breaks through, obtain the three-dimensional fractured core acidizing numerical simulation results.

[0049] In a specific embodiment, the non-isothermal three-dimensional fractured core acidizing numerical simulation method of the present invention is adopted. As Figure 2 shown, the physical model of the fractured core acidizing numerical simulation established has a length of 0.075 m, a width of 0.025 m, and a height of 0.025 m, and 102 natural fractures are randomly and explicitly generated. Structured grids are used to divide the matrix, and unstructured grids are used to divide the fractures using the matrix grid boundaries. The number of matrix grids is 90×30×30, the number of fracture grids is 13075, and the total number of grids generated in the simulation area is 94075. The matrix grid size is 0.00083 m×0.00083 m×0.00083 m. Simulate the heat release during the acid-rock reaction in the acidizing process of carbonate rocks with complex fractures. Set the average pore volume of the matrix to 0.2, the matrix permeability to 10 mD, the fracture porosity to 0.8, the fracture permeability to 500 mD, the acid injection concentration to 15 wt% HCl (4.4178 kmol / m 3 )), the initial core temperature to 293.15 K, the initial acid solution temperature to 293.15 K, the acid injection rate to 5 ml / min, and the left side of the model is the acid injection boundary.

[0050] As Figures 3 to 7As shown, it is the wormhole structure (showing the grid with porosity greater than 0.9) at different acid injection pore volumes (dimensionless). It can be found that when the acid injection pore volume is 0.6, the wormholes only develop in a short section, and most of the acid solution is consumed in the matrix at the injection end of the core. As the acid injection pore volume gradually increases from the initial state, the wormholes start to develop from the acid injection boundary (left side) and gradually expand towards the interior of the core. The morphology evolves from a single main channel to a complex network of multi-level branches. The presence of fractures significantly affects the acid diversion path, causing the wormholes to preferentially extend along the high-permeability fractures. At the same time, the interaction with matrix dissolution forms a non-uniform expansion feature. Eventually, the amount of acid consumed by breaking through the core is only 1.33 pore volumes. The difference in the dual flow-guiding capabilities of fractures and the matrix (matrix permeability 10 mD, fracture permeability 500 mD) further exacerbates the asymmetry of wormhole branching, intuitively revealing the co-evolution mechanism of wormholes and natural fractures during the acidification process of fractured reservoirs.

[0051] As Figures 8 to 12 shown, it is the temperature distribution map caused by the acid-rock reaction heat of three-dimensional fractured core samples at different injection pore volumes. Under the initial conditions, the temperatures of the core and the acid solution are both 293.15 K. As the acid solution is injected at a speed of 5 ml / min, the heat released by the acid-rock reaction causes a significant increase in the local temperature, reaching a maximum of 299 K. The temperature field shows a decreasing trend from the acid injection boundary to the interior, and the high-temperature area coincides highly with the wormhole development area, indicating that the formation of dissolution channels accelerates the continuous reaction between the acid solution and the rock and releases heat. The fracture network, as an efficient heat transfer channel, promotes the rapid transfer of heat along the fractures, while the matrix area has a steeper temperature gradient due to its lower permeability. In addition, with the initial acid solution and the core at the same temperature, the dynamic temperature rise during the acidification process verifies the necessity of the multi-field coupling of heat-flow-fluidization in the non-isothermal model, revealing the regulatory effect of temperature changes on the acid solution viscosity, reaction rate, and wormhole branching pattern, providing a key basis for optimizing acid injection parameters.

[0052] The above description is only a preferred embodiment of the present invention and does not impose any form of limitation on the present invention. Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Any person skilled in the relevant art can make some modifications or variations equivalent to the equivalent embodiments within the scope of the technical solution of the present invention without departing from 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 still fall within the scope of the technical solution of the present invention.

Claims

1. A non-isothermal numerical simulation method for acidizing fractured core samples in three dimensions, which successively includes the following steps: S1: Construct a physical model for numerical simulation of acidizing fractured core samples, divide the grid and assign physical parameters; S2: Calculate the crossflow coefficient according to the current porosity and permeability states. The process is as follows: Crossflow coefficient between the matrix and fractures: ； Where, is the cross-flow coefficient between the matrix and the crack, m 3 ; is the crack area in the grid block, m 2 ; is the matrix permeability, m 2 ; is the average distance between the matrix and the fracture grid, m; Crossflow coefficient between two intersecting fractures: ； ； ； In the formula, is the crossflow coefficient between two intersecting fractures, m 3 ; and are the permeabilities of two fractures, m 2 ; and are the widths of two fractures, m; is the length of the intersection line of two fractures, m; and are the average normal distances from two fractures to the intersection line, m; S3: Solve the pressure control equations for the matrix and fractures, calculate the seepage velocity and molar reaction heat, and record the current injection pressure. The process is as follows: Matrix pressure control equation: ； Fracture pressure control equation: ； In the formula, and are the matrix porosity and the fracture porosity respectively. The superscripts and subscripts and represent the matrix and the fracture respectively. The same applies hereinafter. t is the time, in s; is the divergence operator, dimensionless; is the gradient operator, dimensionless; and are the matrix permeability and the fracture permeability respectively, in m 2 ; is the acid viscosity, in Pa·s; and are the matrix pressure and the fracture pressure respectively, in Pa; and are the flux transfer functions from the matrix to the fracture and from the fracture to the matrix respectively, in m 3 / s; is the flux transfer function between intersecting fractures, in m 3 / s; and are the matrix grid volume and the fracture grid volume respectively, in m 3 ; ； ； Where, and is the pressure of the two intersecting crack grids, Pa; Calculation of seepage velocity: ； ； Where, and are the seepage velocities in the matrix and fractures, m / s, respectively; Calculation of molar reaction heat: ； In the formula, represents the subscript and , representing the matrix and the fracture, and the same applies hereinafter; is the molar heat of acid-rock reaction, J / mol; is the rock temperature, K; S4: Solve the temperature control equations for the acid fluid and rock in the matrix and fractures, and calculate the effective diffusion coefficient of the acid fluid, the acid reaction rate constant, and the mass transfer coefficient. The process is as follows: Matrix acid fluid temperature control equation: ； Fracture acid fluid temperature control equation: ； ； In the formula, is the fluid density, kg / m 3 ; is the specific heat capacity of the acid, J / (kg·K); is the thermal conductivity of the acid, W / (m·K); is the acid-rock heat transfer coefficient, W / (m 2 ·K); is a function of; is the acid-rock heat transfer coefficient, W / (m 2 ·K); and are the pore specific surface areas of the matrix and the fracture respectively, m 2 / m 3 ; and are the acid solution temperatures in the matrix and the fracture respectively, K; and are the matrix rock temperature and the fracture wall temperature respectively, K; Matrix rock temperature control equation: ； Fracture rock temperature control equation: ； Wherein, is the rock density, kg / m 3 ; is the specific heat capacity of the rock, J / (kg·K); and are the acid-rock molar reaction heats in the matrix and the fracture respectively, J / mol; is the thermal conductivity of the rock, W / (m 2 ·K); and are the pore specific surface areas in the matrix and the fracture respectively, m 2 / m 3 ; and are the surface reaction rates in the matrix and the fracture respectively, kmol / (s·m 2 ); Calculate the effective diffusion coefficient of the acid fluid: ； In the formula, is the effective diffusion coefficient in different directions, m / s, represents , and directions; is the effective diffusion coefficient, m / s; and are constants related to the pore structure, = 0.5, = 0.1, = 0.1; is the Péclet number, expressed as ; is in magnitude, m / s; is the average pore throat radius, m; Calculate the acid reaction rate constant: ； In the formula, is the reaction rate constant, m / s; and are the acid solution concentrations in the matrix and the fracture respectively, kmol / m 3 ; is the gas constant, J / (mol·K); Calculate the mass transfer coefficient: ； wherein, is the mass transfer coefficient, m / s; is the asymptotic Sherwood number; is the pore Reynolds number, expressed as ; is the Schmidt number, expressed as ; is the ratio of pore length to pore diameter; is the average pore throat radius, m; Solve the surface reaction rate control equations in the matrix and fractures: ； In the formula, is the surface reaction rate, kmol / (s·m 2 ); is the specific surface area of pores, m 2 / m 3 ; S5: Solve the acid fluid concentration control equations for the matrix and fractures, and calculate the porosity, pore throat radius, permeability, and pore specific surface area at the current time step. The process is as follows: Matrix acid fluid concentration control equation: ； Fracture acid fluid concentration control equation: ； ； In the formula, is a function of, kmol / m 3 ; Calculate the permeability, pore throat radius, pore specific surface area, and porosity at the current time step: Permeability control equation: ； Pore throat radius control equation: ； Pore specific surface area control equation: ； Porosity control equation: ； In the formula, and are the initial permeability and the current permeability, m 2 ; and are the initial porosity and the current porosity; and are the initial average pore throat radius and the current average pore throat radius, m; is the reaming parameter; are the initial specific surface area of pores and the current specific surface area of pores, m 2 / m 3 ; is the dissolving power of the acid, defined as the grams of dissolved solids in each mole of acid reaction, kg / kmol; is the rock density, kg / m 3 ; S6: Determine whether the injection pressure at the current time step is greater than 1% of the initial injection pressure. If it is greater, the wormhole has not broken through the core, and repeat steps S2 - S5. Otherwise, it means the wormhole has broken through the core, and obtain the numerical simulation results of three-dimensional acidizing of fractured core samples.

2. A non-isothermal three-dimensional fractured core acidizing numerical simulation method according to claim 1, characterized in that: In step S1, the grid division refers to using structured grids to divide the matrix and unstructured grids to divide the fractures using the matrix grid boundaries.

3. A non-isothermal numerical simulation method for acidizing three-dimensional fractured core samples as described in claim 1, characterized in that, In step S1, the physical parameters include the porosity and permeability of the matrix and fractures, the matrix fluid temperature, and the matrix rock temperature.

4. A non-isothermal numerical simulation method for acidizing three-dimensional fractured core samples as claimed in claim 1, characterized in that, In step S3, the injection pressure refers to the pressure at the acid injection boundary, and the first recorded injection pressure is the initial injection pressure.

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