CN115290432B - Method for predicting erosion rate and evaluating erosion damage of perforation sleeve - Google Patents

Abstract

The invention discloses a method for predicting the erosion rate and evaluating the erosion damage of a perforation sleeve, and belongs to the field of oil gas safety engineering. The method is characterized in that: firstly, determining factors and ranges of impact rates of perforation of a perforation sleeve, and making an erosion experimental scheme; calculating the average erosion rate of the holes according to the erosion experimental result and carrying out factor analysis; further establishing an average erosion rate prediction model under the influence of a main control factor, and combining the prediction model and fracturing parameters on site to obtain the erosion expanding rate of the hole; and finally, substituting the expanding rate into the established erosion degree evaluation set membership function to evaluate the erosion damage degree of the hole. According to the method, the erosion rate of the holes is predicted by erosion under the working condition of large sand fracturing, and the erosion damage of the holes is evaluated, so that a basis is provided for an on-site fracturing scheme and safe service of the casing.

Description

A method for predicting erosion rate of perforated casing holes and evaluating erosion damage

Technical Field

The invention belongs to the field of oil and gas safety engineering, and in particular relates to a method for predicting erosion rate of perforated casing holes and evaluating erosion damage.

Background technique

In the development of unconventional oil and gas reservoirs, large-scale sand fracturing has the characteristics of large displacement, high pump pressure, and large amount of sand. The proppant and sand-carrying fluid pass through the holes into the formation, and the holes are continuously eroded, which eventually affects the safety of the casing. According to field data, large-scale sand fracturing causes severe erosion of the holes, and even cross-flow between the casing and cement forms cracks on the casing. Due to the complex and harsh downhole conditions, the coupling effect with erosion accelerates the damage of the casing, and safety problems frequently occur.

At present, numerical simulation methods such as Ansys-Fluent and CFD have been widely used in erosion problems. However, numerical simulation methods still have limitations in predicting the hole erosion rate. Since the hole erosion mechanism is still unclear and the hole erosion morphology is complex, it is necessary to design physical simulation experiments and schemes to study the hole erosion. On the one hand, the hole erosion amount and hole erosion rate can be accurately calculated, and on the other hand, the hole erosion mechanism can be revealed through corresponding characterization methods.

Therefore, it is necessary to conduct experiments on borehole erosion under sand fracturing conditions to obtain more accurate borehole erosion rate data and provide data support for field fracturing scheme design and casing safety.

Summary of the invention

In view of the shortcomings of the prior art, the present invention provides a method for predicting the erosion rate of perforated casing holes and evaluating erosion damage.

The technical problem solved by the present invention adopts the following technical solution, a method for predicting the erosion rate of perforated casing holes and evaluating erosion damage, comprising the following steps:

Step 1: Determine the factors and ranges affecting the perforation casing hole erosion rate;

The influencing factors include: ① sand flow rate, ② sand concentration, ③ flow rate, ④ proppant particle size, and ⑤ sand-carrying fluid viscosity; the experimental range of sand flow rate is 50kg-2000kg, the experimental range of sand concentration is 5%-20%, the experimental range of flow rate is 20m/s-140m/s, the experimental range of proppant particle size is 0.1mm-0.8mm, and the viscosity of sand-carrying fluid is 1mPa·s-50mPa·s;

Step 2: Perforation casing hole erosion test design, including erosion test scheme design and erosion test process design;

The erosion experiment design used the response surface methodology to conduct a multi-factor multi-level design for the five factors in step 1, with a total of n groups;

Each set of process design for erosion experiment includes 6 steps, which are:

① According to the design results of the erosion experiment scheme described in step 2, determine the values of each set of experimental parameters, namely, the amount of sand, sand concentration, flow rate, proppant particle size, and viscosity of the sand-carrying fluid;

② Before the experiment, the hole erosion sample was cleaned with film removal liquid and anhydrous ethanol, air-dried and weighed three times, and the average value was recorded as _mi ;

③ Add carboxymethyl cellulose to the water pool to increase the viscosity, take samples for viscosity testing, until the experimental parameter value of the sand-carrying fluid viscosity is reached, and the viscosity is recorded as τ _i5 ;

④ Determine the proppant particle size, recorded as d _i4 , determine the amount of sand used in this group of experiments, recorded as ζ _i1 ; open the sand adding valve of the sand adding tank to add the proppant to the sand adding tank. When the amount of sand used in the experiment ζ _i1 exceeds the maximum single load of the sand adding tank, this group should be divided into multiple sand adding processes;

⑤ Rotate the sand concentration control valve of the sand tank to control the sand concentration to reach the experimental parameter value of the sand concentration of this group, recorded as α _i2 ;

⑥ Start the plunger pump and control the flow rate to reach the flow rate experimental parameter value of this group, recorded as _vi3 ;

⑦ When the flow rate reaches the experimental requirements, open the sand valve, add the proppant in the sand tank and mix it with the sand-carrying fluid, and stop timing until all the proppant is discharged. The experimental time is recorded as _ti ; when a group of experiments is accumulated multiple times, the total experimental time is added up as the experimental time of this group;

⑧ After the experiment, the hole erosion sample was cleaned with film removal liquid and anhydrous ethanol, air-dried and weighed three times, and the average value was recorded as m′ _i ;

The main devices involved in the erosion test process include: water pool, plunger pump, sand tank, perforation casing; the casing is composed of the casing body and the perforation erosion sample;

The schematic diagram of the erosion test device is shown in Figure 2. The main devices include: a water tank, a plunger pump, a sand adding tank, and a casing; the casing is composed of a casing body and a hole erosion sample;

Step 3: Carry out erosion experiment according to the erosion experiment design in step 2, record the sand flow rate ζ _i1 , sand concentration α _i2 , flow rate v _i3 , proppant particle size d _i4 , sand-carrying fluid viscosity τ _i5 , and experimental time _{ti of} each group of experiments, weigh the hole erosion samples at least three times before and after the experiment, and calculate the average mass m _i and m′ _i ;

Step 4: Calculate the average erosion rate of the holes; using the erosion test results of step 3, based on the weight loss method, the ratio of the mass loss of the hole erosion sample before and after the experiment to the experimental time is recorded as the average erosion rate of the hole, as shown in formula (1);

Where: is the average erosion rate of the i-th group, which represents the erosion mass per unit time, g/min; _mi is the average mass of the hole erosion sample of the i-th group after cleaning and weighing multiple times (no less than three times) before the experiment, g; m′ _i is the average mass of the hole erosion sample of the i-th group after cleaning and weighing multiple times (no less than three times) after the experiment, g; _mi -m′ _i represents the mass loss after the erosion test, g;

Step 5: Analysis of the main controlling factors of hole erosion rate: According to steps 3 and 4, the erosion rate matrix is established as formula (2);

Where: A is the erosion rate matrix; ζ _i1 is the amount of sand passed by the i-th group, kg; α _i2 is the sand concentration of the i-th group, %; v _i3 is the flow rate of the i-th group, m/s; d _i4 is the particle size of the proppant of the i-th group, mesh; τ _i5 is the viscosity of the sand-carrying fluid of the i-th group, mPa·s; is the average erosion rate of the ith group of holes, g/min;

Calculate the correlation coefficients between the five influencing factors and the erosion rate. When analyzing the main controlling factors of the erosion rate, the correlation coefficients between different influencing factors and the erosion rate are calculated as shown in formula (3).

Where: _ri6 is the correlation coefficient between the i-th factor and the erosion rate, dimensionless; the larger the absolute value of _ri6 is, the stronger the correlation is and the greater the influence is; l is the total number of experimental groups, that is, the total number of rows in the erosion rate matrix A; a _ki is the data in the erosion rate matrix A, where i is 1, 2, 3, 4, and 5, respectively representing the amount of sand, sand concentration, flow rate, proppant particle size, and sand-carrying fluid viscosity, which correspond to the columns in the erosion rate matrix A in sequence; k is 1, 2…1, corresponding to the rows in the erosion rate matrix A;

The absolute values of the erosion rate correlation coefficients |r _i6 | are sorted from large to small, and the three factors with the strongest correlation are selected as the main controlling factors, and recorded as the first, second and third main controlling factors from large to small;

Step 6: Establish a prediction model for the average erosion rate of the holes under the influence of the main controlling factors;

According to the first, second and third main controlling factors analyzed from the five influencing factors of sand flow, sand concentration, flow rate, proppant particle size and sand-carrying fluid viscosity in step 5, three prediction models are established:

(a) Establishing the erosion rate prediction curve under the influence of the first main controlling factor;

Taking the first main controlling factor x as the variable, set a fixed step size within the experimental range to take discrete points x ₁ ,x ₂ ... _xi , where i≥4, and other factors are fixed values. Use the known data set in the erosion rate matrix A as much as possible. Repeat steps 3 and 4 to supplement the experiment for missing discrete points, and use nonlinear fitting to obtain the erosion rate prediction curve f(x) under the first main controlling factor x.

(b) Establishing a prediction chart of erosion rate under the influence of the first and second main controlling factors;

Taking the first main controlling factor x and the second main controlling factor y as variables, set a fixed step size within the experimental range to take discrete points (x _i ,y _j ), where i ≥ 3, j ≥ 3, and other factors are fixed values. The known data set in the erosion rate matrix A is used as much as possible. If there are missing discrete points, repeat steps 3 and 4 to supplement the experiment. Use nonlinear fitting to obtain the erosion rate prediction chart f(x, y) under the first main controlling factor x and the second main controlling factor y.

(c) Establish the erosion rate prediction equation under the influence of the first, second and third main controlling factors;

Taking the first main controlling factor x, the second main controlling factor y, and the third main controlling factor z as variables, set a fixed step size within the experimental range to take discrete points ( _xi , _yj , _zk ), where i≥3, j≥3, k≥2, and use the known data set in the erosion rate matrix A as much as possible. If there are missing discrete points, repeat steps 3 and 4 to supplement the experiment. Use nonlinear fitting to obtain the erosion rate prediction equation f(x, y, z) under the first main controlling factor x, the second main controlling factor y, and the third main controlling factor z;

Step 7: Prediction of average hole erosion rate under field conditions;

According to the three hole average erosion rate prediction models established in step 6, the model selection and calculation are carried out in combination with the field conditions;

During the on-site sand fracturing operation, the hole erosion rate is considered as a single factor. When the single factor is the first main controlling factor, the model (a) in step 6 is selected; when the single factor is the second main controlling factor, the model (b) in step 6 is selected; when the single factor is the third main controlling factor, the model (c) in step 6 is selected;

During the on-site sand fracturing operation, the factors considered for the hole erosion rate are two or more factors. When the two or more factors include the second main controlling factor but do not include the third main controlling factor, the model (b) in step 6 is selected; when the two or more factors include the third main controlling factor, the model (c) in step 6 is selected;

Step 8: Calculation of hole erosion expansion rate and evaluation of erosion damage;

After selecting an average erosion rate prediction model suitable for field conditions from step 7, the average erosion rate is obtained from the experiment in the above step and is related to one or more fracturing parameters including sand flow rate, sand concentration, flow rate, proppant particle size, and sand-carrying fluid viscosity; combining the field fracturing time and fracturing parameters, substitute the model selected in step 7 to obtain the average erosion rate of the hole, further calculate the average erosion mass as shown in formula (4), and then convert the average erosion mass into the equivalent expansion rate of the hole as shown in formula (5);

Where: is the average erosion mass, g; /> is the average erosion rate of the hole, g/min; λ is the equivalent expansion rate of the hole, %; d is the wall thickness at the hole, m; _ta is the on-site sand fracturing time, min; a is the initial radius of the hole, m; ρ is the density of the hole erosion sample, kg/m ³ ;

(1) Establishing an evaluation set: The degree of hole erosion damage is divided into five types: low, lower, medium, higher, and high.

(2) Construct the membership function corresponding to the evaluation set;

Where: They are the membership functions of the hole erosion damage evaluation set “low”, “lower”, “medium”, “higher” and “high” respectively;

Substituting the equivalent expansion rate λ obtained by formula (5) into the above membership function, we get five memberships:

(3) According to the maximum membership principle, The evaluation set corresponding to the maximum value is the evaluation result of hole erosion damage under the equivalent expansion rate;

Specifically, the hole erosion sample in step 2 needs to be processed, as shown in the schematic diagram of the inner side of the hole erosion sample in FIG3 and the schematic diagram of the outer side of the hole erosion sample in FIG4, which includes the following parts: the hole and the inner wall erosion area; the hole erosion sample material is the same as the on-site casing material;

Specifically, the geometric parameter characteristics of the hole erosion sample described in step 2 are shown in the main view of the hole erosion sample in FIG5 and the cross-sectional view of the hole erosion sample in FIG6. The projection of the inner wall erosion area and the hole along the axial direction of the hole are concentric circles. The hole radius is a, the inner wall erosion area radius is b, and the outer wall radius is c; wherein the hole radius a is based on the field perforating parameters and is usually in the range of 4-6 mm; the radius b of the inner wall erosion area of the hole erosion sample on the projection surface is 5-8 times the hole radius a, and the difference between the outer wall radius c and the inner wall erosion area radius b is 3-4 mm;

Specifically, the hole erosion sample in step 2 has a wall thickness d at the hole, which is the same as the wall thickness of the oil layer casing selected on site, usually in the range of 10-20 mm; the inner wall erosion area of the hole erosion sample is a curved surface, and when installed on the casing, the inner wall erosion area of the hole erosion sample coincides with the inner wall of the casing, and the radius of the inner wall of the casing is r, usually in the range of 45-105 mm;

Specifically, when the inner wall radius r of the oil layer casing selected on site is smaller, the radius b of the inner wall erosion zone is smaller, and the minimum is 5 times the hole radius a. When it is less than 5 times, there is a risk of erosion in the hole erosion sample installation area; when the inner wall radius of the oil layer casing selected on site is larger, the radius b of the inner wall erosion zone can be appropriately increased, and the maximum is 8 times the hole radius a. When it is greater than 8 times, it is not easy to process and assemble because the casing wall is a curved surface and the hole thickness d must be maintained;

Furthermore, when the experimental conditions change, the subsequent steps are repeated from step 2, wherein the experiments under the same conditions refer to known data to minimize the amount of experiments, and the final prediction model is a process of continuous expansion; wherein the first, second, and third main control factors will not change due to changes in the conditions, and there is no need to repeat step 5;

Specifically, when the experimental conditions change, the subsequent steps are repeated starting from step 2. When executing step 6, (a) the model considers a single factor, that is, when other factors are determined, at least 4 groups of experiments are needed to fit the erosion rate prediction curve; (b) the model requires at least 9 groups of experiments to fit the erosion rate prediction surface; (c) the model has the highest prediction accuracy, but at least 18 groups of experiments are required to fit the erosion rate prediction equation.

The present invention has the following advantages due to the adoption of the above technical solution:

The present invention provides a method for predicting the erosion rate of a perforated casing hole and evaluating erosion damage. The method is based on a hole erosion physical model experiment and adopts a response surface method for experimental design. A smaller experimental amount is used to predict the average hole erosion rate under field conditions. In particular, when changes in field conditions are considered in the later stage, the model is continuously expanded during the use of the method, and is applicable to an increase in the range of field conditions.

On the other hand, this method comprehensively considers the amount of sand passing, sand concentration, flow rate, proppant particle size, and viscosity of the sand-carrying fluid. The experimental parameter range is highly consistent with the field operating conditions, breaking through the limitations of the average erosion rate prediction caused by the small experimental range. After predicting the perforation erosion rate for a certain working condition, the average perforation erosion amount can be predicted in combination with the fracturing operation time, and the perforation expansion rate can be further predicted. The degree of perforation erosion damage is evaluated, providing a technical basis for the prediction of sand-added fracturing perforation erosion rate and the design of fracturing schemes.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a method for predicting erosion rate of perforated casing holes and evaluating erosion damage;

FIG2 is a schematic diagram of an erosion experiment device;

FIG3 is a schematic diagram of the inner side of the hole erosion specimen;

FIG4 is a schematic diagram of the outer side of the hole erosion specimen;

FIG5 is a front view of a hole erosion specimen;

FIG6 is a cross-sectional view of a hole erosion specimen;

FIG7 is a prediction curve of erosion rate under the influence of the first main controlling factor;

FIG8 is a curve surface showing the erosion rate prediction under the influence of the first and second main controlling factors;

Explanation of the reference numerals: 1-water tank; 2-plunger pump; 3-sand adding valve; 4-sand adding tank; 5-sand passing valve; 6-sand concentration control valve; 7-casing; 8-aperture erosion sample installation area; 9-aperture erosion sample; 10-aperture; 11-aperture erosion sample inner wall erosion area; 12-aperture erosion sample outer wall; 13-casing inner wall.

Detailed ways

The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

Step 1: To briefly explain the calculation method, the amount of sand passed in each group is set to 100 kg, the viscosity of the sand-carrying fluid is set to 10 mPa·s, and the sand concentration, flow rate, and proppant particle size are variables that affect the erosion rate;

Step 2: Carry out erosion test on the hole erosion sample of the same material within the value range of the above-mentioned influencing factors, wherein the geometric parameters of the hole erosion sample are: wall thickness d is 11.1mm, casing inner wall radius r is 52.4mm, hole radius a is 5mm, inner wall erosion surface radius b is 25mm, hole erosion sample outer wall radius c is 30mm, hole erosion sample adopts TP125v, the same material as the field oil layer casing, with a density of 7900kg/ ^m3 ;

The experimental parameters and ranges are as follows: the sand concentration experimental range is 5%-20%, the flow rate experimental range is 20m/s-140m/s, and the proppant particle size experimental range is 0.1mm-0.8mm, with a total of 20 groups of experiments, as shown in Table 1;

Each set of erosion test process design includes 6 steps, taking the No. 1 experimental set as an example:

① Determine the experimental parameter values, namely, sand concentration 15%, flow rate 40m/s, proppant particle size 0.3mm;

② Before the experiment, the hole erosion sample was cleaned with film removal liquid and anhydrous ethanol, air-dried, and weighed three times, and the average value was recorded as _mi ;

③ Carboxymethyl cellulose was added to the water pool to increase the viscosity, and the sand-carrying liquid viscosity was determined to be 10 mPa·s after sampling and testing;

④ Determine the proppant particle size to be 0.3 mm, the maximum sand addition amount of the sand adding tank used in the experiment is 500 kg, the sand addition amount used in the experiment is 100 kg, open the sand adding valve of the sand adding tank, and add the proppant;

⑤ Rotate the sand tank concentration control valve to control the sand concentration to 15%;

⑥ Start the plunger pump and control the flow rate to reach the experimental parameter value of this group of flow rate 40m/s;

⑦ When the flow rate reaches the experimental requirements, open the sand adding valve, and the proppant in the sand adding tank is mixed with the sand-carrying fluid until all the proppant is discharged and stop timing. The experimental time is recorded as _ti ; since the amount of sand used in the experiment is less than the maximum amount of sand added to the sand adding tank, a single experiment can be completed without the need to accumulate time for multiple experiments;

⑧ After the experiment, the hole erosion sample was cleaned with film removal liquid and anhydrous ethanol, air-dried, and weighed three times, and the average value was recorded as _mi ';

Step 3: Carry out erosion experiment according to the erosion experiment design in step 2. The experimental design and results are shown in Table 1.

Table 1: Experimental plan and experimental results

Step 4: Calculate the average erosion rate of the holes, and the results are shown in Table 2;

Table 2: Erosion rate calculation results

Serial number 1 2 3 4 5 Average erosion rate g/min 0.045 0.036 0.01 0.017 0.031 Serial number 6 7 8 9 10 Average erosion rate g/min 0.058 0.073 0.084 0.212 0.051 Serial number 11 12 13 14 15 Average erosion rate g/min 0.166 0.069 0.12 0.103 0.179 Serial number 16 17 18 19 20 Average erosion rate g/min 0.135 0.187 0.342 0.284 0.243

Step 5: According to steps 3 and 4, establish the erosion rate matrix A as follows:

Where: A is the erosion rate matrix; the first column is the data of flow rate influencing factors; the second column is the data of sand concentration influencing factors; the third column is the data of proppant particle size influencing factors; the fourth column is the erosion rate experimental results under each group of flow rate, sand concentration, and proppant particle size experiments;

Substitute the data in the erosion rate matrix A into the correlation coefficient calculation formula (3), and calculate the correlation coefficients between the three factors and the hole erosion rate as shown in Table 3;

Table 3: Correlation coefficient calculation results

According to Table 3, flow rate is the first main controlling factor, sand concentration is the second main controlling factor, and proppant particle size is the third main controlling factor.

Step 6: Establish a prediction model for the average erosion rate of the holes under the influence of the main controlling factors;

(a) Erosion rate prediction curve under the influence of the first main controlling factor, that is, the erosion rate prediction curve under the influence of flow velocity; set the flow velocity (m/s) interval [40,100], step size 15, sand concentration 10%, proppant particle size 0.3mm under the prediction curve, compared with the known erosion rate matrix A, the data is known, no additional experiments are required, and the erosion rate prediction curve under the first main controlling factor is obtained by nonlinear fitting as shown in Figure 7, and the corresponding prediction equation is as shown in Formula (12);

f＝0.00004x ² -0.0015x+0.0319 (12)

(b) Erosion rate prediction surface under the influence of the first main controlling factor flow rate and the second main controlling factor sand concentration. The flow rate (m/s) interval is set to [40, 100], the step length is 15, and the sand concentration (%) interval is set to [5, 15], the step length is 5. The erosion rate prediction surface under the proppant particle size of 0.3 mm is compared with the known erosion rate matrix A. Steps 2 and 3 need to be repeated to supplement the experiment. After supplementation, the discrete points of (flow rate x _i , sand concentration y _i , erosion rate _fi ) are (55, 15, 0.096), (55, 5, 0.033), (70, 5, 0.065), (85, 5, 0.094), and (85, 15, 0.25). The erosion rate prediction surface under the first and second main controlling factors is obtained by nonlinear fitting as shown in Figure 8, and the corresponding prediction equation is as shown in Formula (13);

f＝0.09772-0.00315x-0.01115y+0.0000262x ² +0.00006y ² +0.0003xy (13)

Where: f is the erosion rate, g/min; x is the flow rate, m/s; y is the sand concentration, %;

(c) The erosion rate prediction equation under the influence of the first, second and third main controlling factors is obtained by performing nonlinear fitting with a quadratic polynomial according to the erosion rate matrix A, and the erosion rate prediction equation under the factors of flow rate, sand concentration and proppant particle size is obtained as shown in equation (14);

In the formula: In the formula: f is the erosion rate, g/min; x is the flow rate, m/s; y is the sand concentration, %; z is the proppant particle size, mm;

Step 7: Prediction of average hole erosion rate under field conditions;

According to the three hole average erosion rate prediction models established in step 6, the model selection and calculation are carried out in combination with the field conditions;

During the on-site sand fracturing operation, if the sand concentration, i.e. the influence of the second main controlling factor on the hole erosion rate, is considered, the first main controlling factor needs to be considered at the same time, and the model (b) in step 6 is selected to predict the average hole erosion rate;

Step 8: Calculation of hole erosion expansion rate and evaluation of erosion damage;

Combined with the on-site fracturing parameters and fracturing time, the degree of hole erosion was evaluated when the sand concentration was 13%, the flow rate was 70 m/s, the sand flow was 100 kg, the viscosity was 10 mPa·s, the proppant was 0.3 mm, and the fracturing time was 90 min. The average hole erosion rate was 0.1438 g/min when substituted into the model selected in step 7. The average erosion mass was further calculated as 12.942 g according to formula (4). The average erosion mass was then substituted into formula (5) to convert it into the equivalent hole expansion, such as λ = 45.94%;

The degree of hole erosion damage is divided into five types: low, lower, medium, higher, and high.

Substituting the equivalent expansion rate λ into the membership function, we get five memberships:

According to the maximum membership principle, 0.594 is the largest value, and the corresponding evaluation set That is, the result of the hole erosion damage evaluation is "high";

When the existing model in step 6 cannot predict the average erosion rate of the perforations under the new working conditions, it is necessary to repeat the subsequent steps starting from step 2, wherein the experiments under the same working conditions refer to the existing data, and the experiments under different working conditions are supplemented to minimize the amount of experiments. The final prediction model is a process of continuous expansion; there is no need to repeat step 5 in the subsequent steps, the first main controlling factor is still the flow rate, the second main controlling factor is still the sand concentration, and the third main controlling factor is still the proppant particle size;

For example, considering the average erosion rate of the perforations under the influence of flow rate (the first main controlling factor) and sand concentration (the second main controlling factor) when the proppant particle size is 0.16 mm, according to step 7, the prediction model selects step 6(b). Referring to Table 1, serial numbers 3, 8, 10, 12 and 17 are existing experimental data, with a total of 5 groups. According to step 6(b), the 4 groups of experiments (flow rate, sand concentration) that need to be supplemented are (40, 5), (40, 15), (100, 5), and (100, 15). Although the model of step 6(c) has the highest accuracy and can also be used in this case, at least 13 groups of experiments need to be supplemented according to step 6(c). Therefore, combined with economic indicators, under this condition, the model of step 6(b) is better than the model of step 6(c).

The above describes the basic method and main features of the present invention. Those skilled in the art should understand that the embodiments describe the present invention in detail. Without departing from the spirit and scope of the present invention, the present invention may have some technical features modified or replaced by equivalents, and these modifications or replacements fall within the scope of the present invention. The scope of protection of the present invention is defined by the claims and their equivalents.

Claims (7)

1. A method for predicting the erosion rate of perforated casing holes and evaluating erosion damage, characterized in that the specific steps include: Step 1: Determine the factors and ranges affecting the perforation casing hole erosion rate; The influencing factors include: ① sand flow rate, ② sand concentration, ③ flow rate, ④ proppant particle size, and ⑤ sand-carrying fluid viscosity; the experimental range of sand flow rate is 50kg-2000kg, the experimental range of sand concentration is 5%-20%, the experimental range of flow rate is 20m/s-140m/s, the experimental range of proppant particle size is 0.1mm-0.8mm, and the viscosity of sand-carrying fluid is 1mPa·s-50mPa·s; Step 2: Perforation casing hole erosion test design, including erosion test scheme design and erosion test process design; The erosion experiment design used the response surface methodology to conduct a multi-factor multi-level design for the five factors in step 1, with a total of n groups; Each set of process design for erosion experiment includes 6 steps, which are: ① According to the design results of the erosion experiment scheme described in step 2, determine the values of each set of experimental parameters, namely, the amount of sand, sand concentration, flow rate, proppant particle size, and viscosity of the sand-carrying fluid; ② Before the experiment, the hole erosion sample was cleaned with film removal liquid and anhydrous ethanol, air-dried and weighed three times, and the average value was recorded as _mi ; ③ Add carboxymethyl cellulose to the water pool to increase the viscosity, take samples for viscosity testing, until the experimental parameter value of the sand-carrying fluid viscosity is reached, and the viscosity is recorded as τ _i5 ; ④ Determine the proppant particle size, recorded as d _i4 , determine the amount of sand used in this group of experiments, recorded as ζ _i1 ; open the sand adding valve of the sand adding tank to add the proppant to the sand adding tank. When the amount of sand used in the experiment ζ _i1 exceeds the maximum single load of the sand adding tank, this group should be divided into multiple sand adding processes; ⑤ Rotate the sand concentration control valve of the sand tank to control the sand concentration to reach the experimental parameter value of the sand concentration of this group, recorded as α _i2 ; ⑥ Start the plunger pump and control the flow rate to reach the flow rate experimental parameter value of this group, recorded as _vi3 ; ⑦ When the flow rate reaches the experimental requirements, open the sand valve, add the proppant in the sand tank and mix it with the sand-carrying fluid, and stop timing until all the proppant is discharged. The experimental time is recorded as _ti ; when a group of experiments is accumulated multiple times, the total experimental time is added up as the experimental time of this group; ⑧ After the experiment, the hole erosion sample was cleaned with film removal liquid and anhydrous ethanol, air-dried and weighed three times, and the average value was recorded as _m'i ; The main devices involved in the erosion test process include: water pool, plunger pump, sand tank, perforation casing; the casing is composed of the casing body and the perforation erosion sample; Step 3: Carry out erosion experiment according to the erosion experiment design in step 2, record the sand flow rate ζ _i1 , sand concentration α _i2 , flow rate v _i3 , proppant particle size d _i4 , sand-carrying fluid viscosity τ _i5 , and experimental time _{ti of} each group of experiments, weigh the hole erosion samples at least three times before and after the experiment, and calculate the average mass _mi and m'_i; Step 4: Calculate the average erosion rate of the holes; using the erosion test results of step 3, based on the weight loss method, the ratio of the mass loss of the hole erosion sample before and after the experiment to the experimental time is recorded as the average erosion rate of the hole, as shown in formula (1); Where: is the average erosion rate of the i-th group, which represents the erosion mass per unit time, g/min; _mi is the average mass of the hole erosion sample after cleaning before the i-th group experiment, g; _m'i is the average mass of the hole erosion sample after cleaning at the end of the i-th group experiment, g; _{mi -m'i} represents the mass loss after the erosion test, g; the number of weighings is not less than three times; Step 5: Analysis of the main controlling factors of hole erosion rate: According to steps 3 and 4, the erosion rate matrix is established as formula (2); Where: A is the erosion rate matrix; ζ _i1 is the amount of sand passed by the i-th group, kg; α _i2 is the sand concentration of the i-th group, %; v _i3 is the flow rate of the i-th group, m/s; d _i4 is the particle size of the proppant of the i-th group, mesh; τ _i5 is the viscosity of the sand-carrying fluid of the i-th group, mPa·s; is the average erosion rate of the ith group of holes, g/min; Calculate the correlation coefficients between the five influencing factors and the erosion rate. When analyzing the main controlling factors of the erosion rate, the correlation coefficients between different influencing factors and the erosion rate are calculated as shown in formula (3). Where: _ri6 is the correlation coefficient between the i-th factor and the erosion rate, dimensionless; the larger the absolute value of _ri6 is, the stronger the correlation is and the greater the influence is; l is the total number of experimental groups, that is, the total number of rows in the erosion rate matrix A; a _ki is the data in the erosion rate matrix A, where i is 1, 2, 3, 4, and 5, respectively representing the amount of sand, sand concentration, flow rate, proppant particle size, and sand-carrying fluid viscosity, which correspond to the columns in the erosion rate matrix A in sequence; k is 1, 2…1, corresponding to the rows in the erosion rate matrix A; The absolute values of the erosion rate correlation coefficients |r _i6 | are sorted from large to small, and the three factors with the strongest correlation are selected as the main controlling factors, and recorded as the first, second and third main controlling factors from large to small; Step 6: Establish a prediction model for the average erosion rate of the holes under the influence of the main controlling factors; According to the first, second and third main controlling factors analyzed from the five influencing factors of sand flow, sand concentration, flow rate, proppant particle size and sand-carrying fluid viscosity in step 5, three prediction models are established: (a) Establishing the erosion rate prediction curve under the influence of the first main controlling factor; Taking the first main controlling factor x as the variable, set a fixed step size within the experimental range to take discrete points x ₁ ,x ₂ ... _xi , where i≥4, and other factors are fixed values. Use the known data set in the erosion rate matrix A as much as possible. Repeat steps 3 and 4 to supplement the experiment for missing discrete points, and use nonlinear fitting to obtain the erosion rate prediction curve f(x) under the first main controlling factor x. (b) Establishing a prediction chart of erosion rate under the influence of the first and second main controlling factors; Taking the first main controlling factor x and the second main controlling factor y as variables, set a fixed step size within the experimental range to take discrete points (x _i ,y _j ), where i ≥ 3, j ≥ 3, and other factors are fixed values. The known data set in the erosion rate matrix A is used as much as possible. If there are missing discrete points, repeat steps 3 and 4 to supplement the experiment. Use nonlinear fitting to obtain the erosion rate prediction chart f(x, y) under the first main controlling factor x and the second main controlling factor y. (c) Establish the erosion rate prediction equation under the influence of the first, second and third main controlling factors; Taking the first main controlling factor x, the second main controlling factor y, and the third main controlling factor z as variables, set a fixed step size within the experimental range to take discrete points ( _xi , _yj , _zk ), where i≥3, j≥3, k≥2, and use the known data set in the erosion rate matrix A as much as possible. If there are missing discrete points, repeat steps 3 and 4 to supplement the experiment. Use nonlinear fitting to obtain the erosion rate prediction equation f(x, y, z) under the first main controlling factor x, the second main controlling factor y, and the third main controlling factor z; Step 7: Prediction of average hole erosion rate under field conditions; According to the three hole average erosion rate prediction models established in step 6, the model selection and calculation are carried out in combination with the field conditions; During the on-site sand fracturing operation, the hole erosion rate is considered as a single factor. When the single factor is the first main controlling factor, the model (a) in step 6 is selected; when the single factor is the second main controlling factor, the model (b) in step 6 is selected; When the single factor is the third main controlling factor, select the model (c) in step 6; During the on-site sand fracturing operation, the factors considered for the hole erosion rate are two or more factors. When the two or more factors include the second main controlling factor but do not include the third main controlling factor, the model (b) in step 6 is selected; when the two or more factors include the third main controlling factor, the model (c) in step 6 is selected; Step 8: Calculation of hole erosion expansion rate and evaluation of erosion damage; After selecting an average erosion rate prediction model suitable for field conditions from step 7, the average erosion rate is obtained from the experiment in the above step and is related to one or more fracturing parameters including sand flow rate, sand concentration, flow rate, proppant particle size, and sand-carrying fluid viscosity; combining the field fracturing time and fracturing parameters, substitute the model selected in step 7 to obtain the average erosion rate of the hole, further calculate the average erosion mass as shown in formula (4), and then convert the average erosion mass into the equivalent expansion rate of the hole as shown in formula (5); Where: m is the average erosion mass, g; v is the average erosion rate of the hole, g/min; λ is the equivalent expansion rate of the hole, %; D is the wall thickness at the hole, m; _ta is the on-site sand fracturing time, min; a is the initial radius of the hole, m; ρ is the density of the hole erosion sample, kg/m ³ ; (1) Establishing an evaluation set: The degree of hole erosion damage is divided into five types: low, lower, medium, higher, and high. (2) Construct the membership function corresponding to the evaluation set; Where: They are the membership functions of the hole erosion damage evaluation set “low”, “lower”, “medium”, “higher” and “high” respectively; Substituting the equivalent expansion rate λ obtained by formula (5) into the above membership function, we get five memberships: (3) According to the maximum membership principle, The evaluation set corresponding to the maximum value is the evaluation result of hole erosion damage under the equivalent expansion rate. 2. According to the method for predicting the erosion rate of perforated casing holes and evaluating erosion damage as described in claim 1, when the experimental conditions change, the subsequent steps are repeated starting from step 2, wherein the experiments under the same conditions refer to known data to minimize the amount of experiments, and the final prediction model is a process of continuous expansion; wherein the first, second, and third main control factors will not change due to changes in the working conditions, and there is no need to repeat step 5. 3. According to the method for predicting the erosion rate and evaluating the erosion damage of a perforated casing hole as described in claim 2, in the subsequent steps repeated from step 2, when executing step 6, (a) the model considers a single factor, that is, when other factors are determined, at least 4 groups of experiments are needed to fit the erosion rate prediction curve; (b) the model requires at least 9 groups of experiments to fit the erosion rate prediction surface; (c) the model has the highest prediction accuracy, but requires at least 18 groups of experiments to fit the erosion rate prediction equation. 4. According to the method for predicting the erosion rate and evaluating the erosion damage of a perforated casing hole according to claim 1, the inner wall erosion area of the hole erosion sample in step 2 and the projection of the hole along the axial direction of the hole are concentric circles, the hole radius is a, the inner wall erosion area radius is b, and the outer wall radius is c; wherein, the hole radius a is 4-6 mm based on the on-site perforating parameters; the inner wall erosion area radius b of the hole erosion sample on the projection surface is 5-8 times the hole radius a, and the difference between the outer wall radius c and the inner wall erosion area radius b is 3-4 mm. 5. According to the method for predicting the erosion rate and evaluating the erosion damage of a perforated casing hole as described in claim 1, the wall thickness of the hole erosion sample at the hole in step 2 is d, which is the same as the wall thickness of the oil layer casing selected on site, and is 10-20 mm; the erosion area of the inner wall of the hole erosion sample is a curved surface. When installed on the casing, the erosion area of the inner wall of the hole erosion sample coincides with the inner wall of the casing, and the radius of the inner wall of the casing is r, which is 45-105 mm. 6. According to a method for predicting the erosion rate and evaluating the erosion damage of a perforated casing according to claim 4 or 5, for the perforated erosion sample, when the inner wall radius r of the oil layer casing selected on site is smaller, the multiple of the radius b of the erosion zone on the inner wall to the hole radius a is closer to 5; when the inner wall radius of the oil layer casing selected on site is larger, the multiple of the radius b of the erosion zone on the inner wall to the hole radius a is closer to 8. 7. According to the method for predicting the erosion rate and evaluating the erosion damage of perforated casing holes as described in claim 1, the hole erosion sample in step 2 needs to be processed, and its characteristics include: hole and inner wall erosion area; the hole erosion sample material is the same as the on-site casing material.