A method for predicting fracture conductivity based on three‐dimensional spatial morphology features

The distribution of fracture clearance is an important factor that determines the conductivity of carbonate fractures. In this paper, the morphological analysis of acid fractures and the evaluation of acid fracture conductivity were carried out to test the characteristics of acid fracture clearance and the conductivity of acid fractures under the conditions of different acid rock reaction rates. Combined with the distribution rule of fracture clearance and the calculation formula of acid fracture conductivity under closure stress, the calculation formula of acid fracture conductivity of carbonate rocks is established and verified, and the influence rule of the distribution of fracture clearance on the conductivity of acid fractures is simulated and calculated. The results show that with the increase of the closure pressure, the conductivity of the fracture with a closure pressure of 60 MPa is about 94% lower than that of the fracture with a closure pressure of 10 MPa. The increase in acid dissolution rate is beneficial to improve the fracture conductivity under various closure stresses, and the acid dissolution is beneficial to reduce the influence of the closure stress on the fracture conductivity of acid dissolution. When the confining pressure is 10 MPa, the acid corrosion rate increases from 0.0001 to 0.0004 g/cm2 s, and the conductivity of the acid corrosion fracture increases from 27 to 420 μm2 cm. As the dissolution rate of acid solution increases, the proportion of large clearance on the fracture surface increases, the average value of total clearance increases, and the proportion of contact on the fracture surface decreases.


| INTRODUCTION
When the fluid flows between the two surfaces of the fracture, the size and distribution of the fracture clearance determine the fluid flow capacity, that is, the fracture conductivity.It is the great significance to explain the formation and characterization of fracture conductivity by studying the influence law of fracture clearance distribution on fracture conductivity.
There are three reasons for the clearance between fractures and fractures: The first is the relative motion of the fracture surface in the fracture surface, causing the fault surface to occur in the corresponding position.The second is that mineral particles fall off the rock surface during fracturing, creating the fracture in the rock.The third is the physical or chemical effect of the external fluid on the fracture surface, causing the fault surface to occur in the corresponding position, such as the acid fracture of the carbonate reservoir through acid fracturing.
The main means of the reconstruction of the reservoir is to make an artificial fracture in the reservoir with a certain clearance, thereby achieving the goal of improving the kinetic energy of the oil flow in the reservoir.In particular, carbonate reservoir reconstruction is usually adopted by the acid fracturing technique, and the use of acid fluid to produce nonuniform dissolution on the surface of the fracture is formed, and the tunnel is formed with a large clearance fracture.Therefore, it is necessary to study the pattern of fracture flow ability of acid dissolution fracture, and study the effect of fracture distribution on the fracture of acid dissolution fracture.
In this paper, the method of analyzing the influence of fracture clearance on the fracture of the fracture clearance was studied by using the three-dimensional (3D) contour scanner to scan the acid dissolution fracture and reconstruct the surface form of acid dissolution fracture.The fracture flow ability is obtained by using the fracture flow experiment.2][3][4][5][6][7] The surface morphology of acid dissolution fractures was characterized by the 3D morphology analyzer, and the roughness of the contact surface of the fracture was used to recognize the effect of the fracture flow ability.The surface morphology of acid dissolution fractures was obtained by Antelo et al., 8 and the acid dissolution pattern was defined by the acid dissolution morphological characteristics, and the study found that the characteristics of the dissolution fracture and the statistical parameters of the acid dissolution were analyzed.0][11][12] Rodrigues et al. found that the surface morphological parameters of the acid dissolution were used only to characterize the preflow capacity of the fracture, and conductivity of the fracture depends on the width of the fracture, 13 and the roughness and torsional effect of the fracture is less than the smaller one.Neumann et al. found that the acid dissolution pattern determines the change of the fracture flow capacity under closure stress, and the fracture roughness may be greater than or less than the original split fracture. 14Mehrjoo et al. developed three models of three different acid types.The electrical conductivity of rock after acid etching is predicted according to the injection rate, rock strength, and closure stress.Statistical and graphical analysis shows that the model has good performance. 15Tariq et al. studied the effects of rock hardness and surface roughness on the fracture conductivity. 16Shuang et al. studied the changes in the conductivity of acid corrosion fractures under different acid types and closure pressures through experiments.The results indicate that conventional acids tend to produce uniform fractures, while gelled and self-rotating acids tend to form uneven fractures. 17Mingxing et al. used the Nierod-Kruk method and indoor experiments to study the effects of acid volume, temperature, acid volume fraction, composite acids, and other factors on the corrosion fracture conductivity of long-acting acids (high-temperature gelling acids, variable viscosity acids, and self-rotating acids). 18Kamali and Pournik developed a numerical model for the contact closure of rough surfaces.The mechanical interaction between fractures is considered and its effect on fracture closure is studied. 19iawei et al. designed and introduced a physical modeling experimental device for acid fracturing, which achieved corrosion prevention and alternating injection of acid fracturing.The acid fracturing test uses hydrochloric acid, guanidine gum, and guanidine gum with acid as the fracturing fluid to analyze the characteristics of acid corrosion fractures.The results indicate that acidic fluids have corrosive effects on the surface of fractures, especially in the near wellbore area. 20Al-momin et al. studied the effects of contact time, type of acid system, and treatment temperature on the electrical conductivity of the San Andres dolomite core. 21Al-Omair et al. discussed the procedural mechanisms for the selection of stimulation techniques (acidification or proppant) in deep limestone reservoirs. 22Beg et al. studied the relationship between the acid contact time and the conductivity of fractures, and the results showed that increasing the acid contact time sometimes led to a decrease in the conductivity of fractures, and sometimes increased the conductivity of fractures. 23t present, research on the conductivity of acid corrosion fractures mainly focuses on acid fracturing design methods, testing the conductivity of different types of acid fluids, and analyzing the influencing factors of fracture conductivity.There are few reports on the relationship between crack gaps and conductivity.In this paper, the surface morphology analysis and fracture flow ability test of seven groups of acid dissolution fractures were selected by the carbonate rock.Through the distribution of acid fracture clearance and fracture conductivity under the reaction rate of different acid rocks, the calculation of the ability of carbonate acid dissolution fracture was established, and the comparison and simulation were compared.

| Experimental preparation
The experiment is composed of lime rocks, which are used to fracture and simulate artificial fractures along the length of the pipe, and test the rocks that are similar to the fracture conductivity.This article processes limestone into rock slabs according to the API standard for conductivity testing, and overlaps two rock slabs to simulate fractures.The selected material for this conductivity test experiment is limestone, which is mainly composed of calcite with a porosity of 3.8% and a permeability of 0.08 mD.The liquid in the experiment is standard brine and cross-linked acid, with the salt water formula is 5% NaCl + 3% KCl, and the cross-linked acid formula is 5%-20% HCl + 2% Coagulant + 2% Dissolution inhibitor + 1% Iron ion stabilizer + 1% Emulsion breaker + 1% cross-linking agent.The specific process of the experiment is shown in Figure 1.This experiment mainly uses an acid corrosion fracture conductivity tester and a 3D profile analyzer.

| Experimental method (1) Analysis of acid erosion surface morphology
The original fracture surface was scanned by a 3D profile analyzer, and the original fracture surface point cloud data was obtained.The core is put into the conductivity testing instrument to make the distance between the two fracture surfaces 8 mm.After heating to 120°C, the core is replaced by 10 mL standard saline and saturated for 1 h.Then 200 mL cross-linked acid is injected to react with the core fracture surface.Finally, a 3D profile analyzer is used to scan the fracture surface after acid dissolution, so as to obtain the point cloud data of the fracture surface after acid dissolution.
(2) Fracture conductivity test The core is loaded into the acidizing conductivity measuring instrument, and the confining pressure is 10, 20, 30, 40, 50, and 60 MPa, respectively.Displacement of standard brine into the core holder.When the salt water flow from the core holder is stable, the conductivity of the core fracture can be calculated by testing the pressure difference before and after the core and the salt water flow at the outlet of the holder.The acidizing conductivity measuring instrument is shown in Figure 2.
This experiment tests the fracture conductivity under different acid corrosion rates and closure pressures, and analyzes the relationship between fracture conductivity and fracture gap under different acid corrosion rates and closure pressures.

| Influence of acid rock reaction on fracture conductivity
In this paper, seven groups of fracture conductivity tests after acid dissolution are carried out, and the test results are shown in Figure 3. Figure 3 shows the variation curve of the conductivity of acid corrosion fractures with closure pressure.The horizontal axis represents the closure pressure, which represents the pressure exerted by the formation on the fracture wall. 24The vertical axis represents the conductivity of acid corrosion fractures, which represents the flow ability of fluids in acid corrosion fractures.It can be seen from Figure 3 that the fracture conductivity decreases with the increase of closure stress after acid dissolution.The decreasing range of conductivity of acid dissolution fracture is faster in the early stage, smaller in the later stage, and tends to be stable.The results show that with the increase of the closure stress, the fracture clearance closed faster in the early stage, which leads to the rapid decrease of the conductivity, and the fracture clearance change tends to be stable in the later stage, and the conductivity of acid dissolution fracture is also stable.
Figure 4 shows the situation of the fracture wall after acid corrosion.It can be seen from Figure 4 that the acid solution will form nonuniform grooves after flowing through the limestone wall, which are caused by the acid rock reaction.
Figures 5 and 6 both show the variation curves of acid corrosion fracture conductivity with acid corrosion rate.Figure 5 represents the variation curve of acid corrosion fracture conductivity with acid corrosion rate at a confining pressure of 10 MPa, and Figure 6 represents the variation curve of acid corrosion fracture conductivity with acid corrosion rate at a confining pressure of 60 MPa.The abscissa of Figures 5 and 6 shows the acid dissolution rate,  which reflects the reaction rate between acid and rock. 25he higher the acid dissolution rate, the faster the reaction rate between acid and rock.The vertical coordinates of Figures 5 and 6 represent the conductivity of acid corrosion fractures, which represents the flow ability of fluids in acid corrosion fractures.
It can be seen from Figures 5 and 6 that with the increase in acid dissolution rate, the conductivity of acid dissolution fracture under confining pressure of 10 and 60 MPa increases.This is because the increase in the dissolution rate leads to the increase of the volume of dissolution on the fracture surface and the increase of the fracture clearance, which makes more space of the clearance under the closed stress.Therefore, the increase of the acid dissolution rate is conducive to improving the fracture conductivity after acid dissolution under each closure stress.By dividing the conductivity of 60 MPa acid dissolution fracture by that of 10 MPa, the decreased range of conductivity can be obtained.The relationship between the decreased range of acid dissolution fracture conductivity and the dissolution rate (Figure 6) is made.The horizontal axis of Figure 7 shows the acid corrosion rate, while the vertical axis shows the ratio of the conductivity of acid corrosion fractures with a confining pressure of 60 MPa to that of acid corrosion fractures with a confining pressure of 10 MPa at the same acid corrosion rate.With the increase of dissolution rate, the proportion of acid dissolution fracture conductivity under 60 MPa gradually increases, which indicates that the decrease range of acid dissolution fracture conductivity decreases gradually, and acid solution dissolution is beneficial to reduce the influence of closure stress on the conductivity of acid dissolution fracture.

| Influence of acid rock reaction on fracture clearance distribution
Figure 8 shows the statistics of the ratio of each clearance on the fracture surface after acid corrosion.The horizontal axis of Figure 8 shows the acid corrosion crack gap, which was obtained through the 3D profile analyzer.The vertical axis of Figure 8 shows the proportion of fracture clearance of the same width in the entire acid corrosion fracture.The proportion of each clearance on the fracture surface is counted into a broken line diagram, as shown in Figure 8.The ratio of fracture clearance of 0 is the contact ratio of fracture surface.The clearance width on the fracture surface decreases gradually from small to large.With the increase in dissolution rate, the proportion of maximum clearance increases, which indicates that the increase of acid dissolution rate leads to the increase of large clearance between fracture surfaces.

| Influence of fracture clearance distribution on conductivity
With the increase of the closure stress, the fracture conductivity decreases gradually.The small clearance fracture is closed first, and then the large clearance fracture is closed.Therefore, there may be some relationship between the fracture clearance proportion distribution and the acid In the above formula, wk f is the conductivity of acid corrosion fracture, m and n are the coefficients, and σ is the closure stress.The m and n are the coefficients that determine the variation of conductivity of acid dissolution fractures.Previous studies have found that the m and n are related to the fracture width and rock embedding strength after dissolution.It is considered that there should be a certain relationship between the m and n coefficients and the distribution of fracture clearances.In this paper, the exponential function fitting of the fracture clearance proportion statistical chart is carried out, and the following relationship is obtained: ( In the above formula, γ is the ratio of fracture clearance and δ is the fracture clearance.The a and b are the correlation coefficients which determine the distribution of the clearances.The value of a reflects the contact ratio of fracture surface when the closing stress is 0 MPa.The larger the value of a, the greater the contact ratio of fracture surface.The value of b reflects the uniformity of clearance distribution.Generally speaking, the proportion of small clearance is higher than that of large clearance.As shown in Figure 9.When the value of b is small, it means that the proportion of large clearance is high and the distribution of clearance is relatively uniform; when the value of b is large, the proportion of large clearance is low and the distribution of clearance is relatively concentrated.The a, b, m, and n coefficients of seven groups of acid dissolution fracture conductivity experiments are counted, as shown in Table 1. As shown in Figure 10 it can be seen that the relationship between m and a is exponential, and the formula obtained by fitting is as follows: m a = −654.7 ln( ) − 183.17. (3) Similarly, the relationship between coefficients n and b in the experiments is drawn, as shown in Figure 11.It can be seen that n and b are in a linear relationship, and the formula obtained by fitting is as follows: By substituting Equations ( 3) and (4) into Equation (1), the calculation formula of acid dissolution fracture conductivity based on the fracture clearance distribution coefficient can be obtained: To verify the accuracy of the calculation formula of acid dissolution fracture conductivity established in this paper, the carbonate rock is selected for the experiment of acid dissolution fracture conductivity, and the prediction model studied by this paper is used for simulation calculation.
Comparing the predicted results of the model studied in this article with the experimental data (as shown in Figure 12), it can be seen that the predicted results of the acid soluble fracture conductivity calculation formula in this study are very close to the experimental data, and the predicted conductivity differs by approximately 11% from the experimental data.

F I G U R E 2
The acidizing conductivity measuring instrument.FEI ET AL.| 4423

F I G U R E 3
Relationship between fracture conductivity and closure stress after acid dissolution.F I G U R E 4 3D scanning image of fracture wall after acid corrosion.

F I G U R E 5
Relationship between conductivity and dissolution rate of acid dissolution fracture under 10 MPa confining pressure.

F I G U R E 6
Relationship between conductivity and dissolution rate of acid dissolution fracture under 60 MPa confining pressure.F I G U R E 7 Relationship between the decrease of conductivity and dissolution rate of acid etched fracture.F I G U R E 8 Statistics of the ratio of each clearance on the fracture surface after acid etching.FEI ET AL.| 4425 dissolution fracture conductivity.The relationship between the acid dissolution fracture conductivity and the closure stress can be fitted by the classical exponential function.26 654.7 ln( ) − 183.17)exp (−(0.0022+ 0.0583) ).f

F I G U R E 9
Fitting diagram of fracture clearance distribution.T A B L E 1 Statistics of clearance distribution coefficient and conductivity equation coefficient of acid dissolution fracture conductivity experiment.

( 1 )
With the increase of closure stress, the conductivity of acid etched fracture decreases.The conductivity of acid etched fracture decreases rapidly in the early stage, but decreases in the later stage and tends to be stable.The conductivity of the fracture with a closure pressure of 60 MPa is about 94% lower than that of the fracture with a closure pressure of 10 MPa.The increase in acid dissolution rate is beneficial to improve the fracture conductivity after acid etching under high closure stress, and moderate acid dissolution can reduce the influence of closure stress on fracture conductivity.(2)With the increase of acid dissolution rate, the proportion of large clearance on fracture surface increases, the average value of total clearance increases, and the contact ratio of fracture surface decreases.(3)On the basis of the distribution pattern of crack gaps, a formula for calculating the conductivity of acid soluble cracks was established.Compared with experimental data, this formula has higher prediction accuracy and is suitable for predicting the conductivity of acid soluble fractures in carbonate reservoirs.and the predicted conductivity differs by approximately 11% from the experimental data.

F I G U R E 10
Graph of coefficient m and a. F I G U R E 11 Graph of coefficient n and b.F G U R E 12 Comparison between prediction results of model and experimental data.