CN115290432A - Perforation erosion rate prediction and erosion damage evaluation method for perforated casing - Google Patents

Abstract

The invention discloses a method for predicting the erosion rate of perforation casing holes and evaluating erosion damage, and belongs to the field of oil and gas safety engineering. It is characterized in that: first determine the influencing factors and scope of the perforation casing hole erosion rate, and formulate the erosion experiment plan; calculate the average erosion rate of the hole according to the erosion experiment results and conduct factor analysis; further establish the average erosion rate under the influence of the main control factors. The erosion rate prediction model can be combined with the prediction model and fracturing parameters in the field to obtain the hole erosion and expansion rate; finally, the expansion rate is substituted into the established erosion degree evaluation set membership function to evaluate the degree of hole erosion damage. Aiming at the large-scale sand fracturing condition, the invention predicts the hole erosion rate through erosion, and evaluates the hole erosion damage, so as to provide the basis for the field fracturing plan and the safe service of the casing.

Description

A Method for Prediction of Perforated Casing Hole Erosion Rate and Evaluation of Erosion Damage

technical field

The invention belongs to the field of oil and gas safety engineering, and in particular relates to a perforation casing perforation erosion rate prediction and erosion damage evaluation method.

Background technique

During the development of unconventional oil and gas reservoirs, large-scale sand fracturing has the characteristics of large displacement, high pump pressure, and large sand volume. Casing safety. According to field data, large-scale sand fracturing causes severe hole erosion, and even cracks are formed on the casing from the channeling between the casing and cement. Due to the complex and harsh downhole conditions, the coupling effect with erosion accelerates casing erosion. The pipe is damaged, and safety problems occur frequently.

At present, numerical simulation methods such as Ansys-Fluent and CFD have been widely used in the erosion problem, but the numerical simulation method still has limitations in the prediction of hole erosion rate. The shape is complex, and it is necessary to design physical model experiments and plans to study 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 carry out experiments on hole erosion under sand fracturing conditions to obtain more accurate hole erosion rate data and provide data support for field fracturing scheme design and casing safety.

Contents of the invention

Aiming at the deficiencies of the prior art, the invention provides a method for predicting the erosion rate of perforated casing holes and evaluating the erosion damage.

The technical problem solved by the present invention adopts the following technical scheme, and the perforation casing perforation erosion rate prediction and erosion damage evaluation method includes the following steps:

Step 1: Determine the influencing factors and scope of perforation casing perforation erosion rate;

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

Step 2: Perforated casing perforation erosion experiment design, including erosion experiment scheme design and erosion experiment process design;

The design of the erosion experiment scheme adopts the response surface method to carry out multi-factor and multi-level design for the five factors in step 1, with a total of n groups;

The process design of each set of erosion experiments includes 6 steps, which are as follows:

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

②Before the experiment, wash the perforation erosion sample with film remover and absolute ethanol, air-dry it, weigh it three times and record the average value as m _i ;

3. add carboxymethyl cellulose to the pool to increase the viscosity, take samples and carry out the viscosity test until reaching the experimental parameter value of the viscosity of the sand-carrying liquid, record the viscosity as τ _i5 ;

④Determine the particle size of the proppant, denoted as d _i4 , determine the amount of sand used in this group of experiments, denoted as ζ _i1 ; open the valve of the sand adding tank to add proppant to the sand adding tank, when the amount of sand used in the experiment ζ _i1 exceeds When the single maximum load of the sand tank is used, this group should be divided into multiple sand filling 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 group of sand concentration, denoted as α _i2 ;

⑥Start the plunger pump, and control the flow rate to reach the experimental parameter value of the group of flow rate, denoted as v _i3 ;

⑦When the flow rate reaches the experimental requirements, open the sand valve, mix the proppant and the sand-carrying liquid in the sand tank, and stop timing until all the proppant is discharged. The experimental time is recorded as t _i ; , the sum of the experimental time is the experimental time of this group;

⑧ After the experiment, the perforation erosion sample is cleaned with film-removing solution and absolute ethanol, air-dried, and weighed three times to record the average value as m'_i;

The main equipment involved in the erosion test process includes: water pool, plunger pump, sand tank, perforated casing; the casing is composed of the casing body and the hole erosion sample;

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

Step 3: Carry out erosion experiments according to the erosion experiment design in step 2, and record the sand passing volume ζ _i1 , sand concentration α _i2 , flow velocity v _i3 , proppant particle size d _i4 , sand-carrying fluid viscosity τ _i5 , The test time is t _i , the perforation erosion sample is weighed no less than three times before and after the test, and the average mass m _i and m' _i are calculated;

Step 4: Calculating the average erosion rate of the hole; using the results of the erosion experiment in 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 experiment time is recorded as the average erosion rate of the hole, as shown in formula (1) ;

为第i组平均冲蚀速率，表示单位时间内的冲蚀质量，g/min；m_i为第i组实验前孔眼冲蚀试样清洗后多次称重(不少于三次)平均质量，g；m'_i为第i组实验结束孔眼冲蚀试样清洗后多次称重(不少于三次)平均质量，g；m_i-m'_i表示冲蚀试验后质量损失，g；In the formula:

is the average erosion rate of group _i , which represents the erosion mass per unit time, g/min; g; m' _i is the average mass of the perforation erosion sample after repeated weighing (not less than three times) after the test of group i is completed, g; m _i -m' _i represents the mass loss after the erosion test, g;

Step 5: Analysis of main controlling factors of hole erosion rate; according to steps 3 and 4, establish erosion rate matrix such as formula (2);

为第i组孔眼平均冲蚀速率，g/min；In the formula: A is the erosion rate matrix; ζ _i1 is the amount of sand passing through the i group, kg; α _i2 is the sand concentration of the i group, kg/m ³ ; v _i3 is the flow velocity of the i group, m/s; d _i4 is the particle size of proppant in group i, mesh; _τi5 is the viscosity of sand-carrying fluid in group i, mPa·s;

is the average erosion rate of holes in group i, 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 formula (3);

In the formula: r _i6 is the correlation coefficient between the i-th factor and the erosion rate, dimensionless; the greater the absolute value of r _i6 , the stronger the correlation and the greater the influence; l is the total number of experimental groups, that is, the corresponding erosion rate matrix The total number of rows in A; a _ki is the data in the erosion rate matrix A, where i takes 1, 2, 3, 4, and 5 to represent the amount of sand passing, sand concentration, flow rate, proppant particle size, viscosity of sand-carrying fluid, and hole The average erosion rate corresponds to the columns in the erosion rate matrix A in turn, and k takes 1, 2...l to correspond to the rows in the erosion rate matrix A;

Sort the absolute value |r _i6 | control factor;

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

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

(a) establish the erosion rate prediction curve under the influence of the first main control factor;

Take the first main control factor x as a variable, set a fixed step size within the experimental range to take discrete points x ₁ , x ₂ ... x _i (i≥4), other factors are fixed values, and the maximum possible use of the obtained erosion For the known data set in the rate matrix A, missing discrete points need to repeat steps 3 and 4 for supplementary experiments, and use nonlinear fitting to obtain the erosion rate prediction curve f(x) under the first main control factor x;

(b) establish the erosion rate prediction chart under the influence of the first and second main control factors;

Take the first main control factor x and the second main control factor y as variables, set a fixed step size within the experimental range to take discrete points ( _xi , y _j ) (i≥3, j≥3), and other factors are fixed values , use the known data set in the erosion rate matrix A that has been obtained to the greatest possible extent. If the missing discrete points need to repeat steps 3 and 4 to supplement the experiment, use nonlinear fitting to obtain the first main control factor x and the second main control factor y. Erosion rate prediction plate f(x,y);

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

Taking the first main control factor x, the second main control factor y, and the third main control factor z as variables, set a fixed step size within the experimental range and take discrete points ( _xi , y _j , z _k ) (i≥3, j ≥ 3, k ≥ 2), use the known data set in the erosion rate matrix A as far as possible, and repeat steps 3 and 4 for supplementary experiments if missing discrete points, and use nonlinear fitting to obtain the first main control factor x , the erosion rate prediction equation f(x,y,z) under the second main control factor y and the third main control factor z;

Step 7: Predict the average erosion rate of holes under field conditions;

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

During the on-site sand fracturing operation, the hole erosion rate consideration is a single factor, and when the single factor is the first main controlling factor, the model (a) in step 6 is selected; the single factor is the second main controlling factor , select (b) model in step 6; when described single factor is the third main control factor, select (c) model in step 6;

During the on-site sand fracturing operation, the hole erosion rate is considered to be two or more factors, and when the two or more factors include the second main control factor but not the third main control factor, choose (b) model in step 6; When said two or more factors include the third main control factor, select (c) model in step 6;

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

After selecting an average erosion rate prediction model suitable for field conditions in step 7, the average erosion rate is obtained from the above-mentioned step experiment, and the amount of sand passing, sand concentration, flow velocity, and proppant particle size It is related to one or more fracturing parameters in the diameter and viscosity of sand-carrying fluid; combined with the fracturing time and fracturing parameters on site, substituting the model selected in step 7 to obtain the average erosion rate of holes, and further calculating the average erosion quality as follows: (4), and then convert the average erosion mass into the equivalent diameter expansion rate of the hole as shown in formula (5);

为平均冲蚀质量，g；

为孔眼平均冲蚀速率，g/min；λ孔眼等效扩径率，％；d为孔眼处壁厚，m；t_a为现场加砂压裂时间，min；a孔眼初始半径，m；ρ为孔眼冲蚀试样密度，kg/m³；In the formula:

is the average erosion mass, g;

λ is the average erosion rate of the hole, g/min; λ is the equivalent diameter expansion rate of the hole, %; d is the wall thickness of the hole, m; t _a is the sand fracturing time on site, min; is the density of hole erosion sample, kg/m ³ ;

(1) Establish an evaluation set: divide the degree of perforation erosion damage into five types: low, low, medium, high, and high, and establish an evaluation set

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

分别为孔眼冲蚀损伤评价集“低”“较低”“中”“较高”“高”的隶属度函数；In the formula:

Respectively, the membership function of the perforation erosion damage evaluation set "low", "low", "medium", "high" and "high";

Putting the equivalent diameter expansion rate λ obtained by formula (5) into the membership degree function of the above formula, the five membership degrees are obtained as

中最大值对应的评价集为该等效扩径率下的孔眼冲蚀损伤评价结果；(3) According to the principle of maximum membership degree,

The evaluation set corresponding to the medium maximum value is the evaluation result of hole erosion damage under the equivalent diameter expansion ratio;

Specifically, the hole erosion sample described in step 2 needs to be processed, as shown in Figure 3, the schematic diagram of the inside of the hole erosion sample and the schematic diagram of the outside of the hole erosion sample shown in Figure 4, which includes the following parts: , Inner wall surface erosion area; the hole erosion sample material is the same as that of the on-site casing;

Specifically, the geometric parameter characteristics of the hole erosion sample described in step 2 are shown in Figure 5, the front view of the hole erosion sample and Figure 6, the cross-sectional view of the hole erosion sample, the inner wall erosion area and the hole along the hole axis The projection of the direction is a concentric circle, the radius of the hole is a, the radius of the erosion area on the inner wall is b, and the radius of the outer wall is c; among them, the radius a of the hole is based on the field perforation parameters, usually in the range of 4-6mm; The radius b of the erosion area on the inner wall of the corrosion sample is 5-8 times the radius a of the hole, and the difference between the radius c of the outer wall and the radius b of the erosion area on the inner wall is 3-4mm;

Specifically, the wall thickness of the perforation erosion sample in step 2 is d at the perforation, which is the same as the wall thickness of the oil layer casing selected on site, usually in the range of 10-20mm; the erosion area of the inner wall surface of the perforation erosion sample It 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. The radius of the inner wall of the casing is r, usually in the range of 45-105mm;

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

Further, when the experimental working conditions change, repeat the subsequent steps from step 2, in which the experiments of the same working conditions refer to known data to minimize the amount of experiments, and the final prediction model is a process of continuous expansion; among them, the first, The second and third main control factors will not change due to changes in working conditions, so there is no need to repeat step 5;

Specifically, when the experimental conditions change, the subsequent steps are repeated from step 2, and when step 6 is performed, (a) the model considers a single factor, that is, when other factors are determined, at least only 4 sets of experiments are needed to simulate (b) The model needs at least 9 sets of experiments to fit the erosion rate prediction surface; (c) The model has the highest prediction accuracy, but it needs at least 18 sets of experiments to fit the erosion rate prediction equation.

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

The invention provides a perforation casing hole erosion rate prediction and erosion damage evaluation method. The method is based on the hole erosion model experiment, and adopts the response surface method for experimental design, and predicts the field work with a small amount of experiments. The average erosion rate of the hole under the condition, especially when the working conditions are considered to change in the later stage, the model is continuously expanded during the use of this method, and the scope of the applicable field working conditions increases.

On the other hand, this method comprehensively considers the amount of sand passing, sand concentration, flow velocity, proppant particle size, and viscosity of the sand-carrying fluid. The limitation of erosion rate prediction; after the perforation erosion rate is predicted for a certain working condition, the average erosion amount of the perforation can be predicted in combination with the fracturing operation time, and the diameter expansion rate of the perforation can be further predicted to evaluate the degree of perforation erosion damage. It provides a technical basis for the prediction of the erosion rate of sand-filled fracturing holes and the design of fracturing schemes.

Description of drawings

Fig. 1 is a flow chart of a method for predicting erosion rate of perforated casing holes and evaluating erosion damage;

Figure 2 is a schematic diagram of the erosion test device;

Figure 3 is a schematic diagram of the inner side of the hole erosion sample;

Figure 4 is a schematic diagram of the outside of the perforation erosion sample;

Fig. 5 is the front view of the hole erosion sample;

Fig. 6 is a cross-sectional view of a hole erosion sample;

Fig. 7 is the erosion rate prediction curve under the influence of the first main controlling factor;

Fig. 8 is the erosion rate prediction surface under the influence of the first and second main control factors;

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

Detailed ways

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

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

Step 2: Conduct erosion experiments on hole erosion samples of the same material within the value range of the above-mentioned influencing factors. The geometric parameters of the hole erosion samples are: wall thickness d is 11.1mm, casing inner wall radius r is 52.4mm, The hole radius a is 5mm, the radius b of the inner wall erosion surface is 25mm, the outer wall surface radius c of the hole erosion sample is 30mm, and the hole erosion sample is made of TP125v, which is the same material as the field oil layer casing, and the density is 7900kg/m ³ ;

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

The process design of each group of erosion experiments includes 6 steps, taking the experimental group No. 1 as an example:

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

②Before the experiment, wash the perforation erosion sample with film remover and absolute ethanol, air-dry it, weigh it three times and record the average value as m _i ;

③ Add carboxymethyl cellulose to the pool to increase the viscosity, take samples for testing, and the viscosity of the sand-carrying fluid is set at 10mPa·s;

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

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

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

⑦When the flow rate reaches the experimental requirement, open the sand adding valve, and the proppant in the sand adding tank is mixed with the sand-carrying liquid until all the proppant is discharged, then stop timing, and record the experiment time as t _i ; The maximum amount of sand added to the tank can be completed in a single experiment, without the need to accumulate time for multiple experiments;

⑧ After the experiment, the perforation erosion sample is cleaned with film-removing solution and absolute ethanol, air-dried, and weighed three times to record the average value as m'_i;

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

Table 1: Experimental scheme and experimental results

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

Table 2: Calculation results of erosion rate

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, the erosion rate matrix A is established as follows:

In the formula: A is the erosion rate matrix; the first column is the data of factors affecting flow velocity; the second column is the data of factors affecting sand concentration; the third column is the data of factors affecting particle size of proppant; the fourth column is the data of each group of flow velocity and sand concentration . Experimental results of erosion rate under proppant particle size experiment;

Put 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 perforation erosion rate as shown in Table 3;

Table 3: Calculation results of correlation coefficient

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

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

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

f＝0.00004x2-0.0015x ⁺ 0.0319 (12)

(b) The erosion rate prediction surface under the influence of the first main control factor, flow velocity, and the second main control factor, sand concentration, set the flow velocity (m/s) interval [40,100], step size 15, and set the sand concentration (%) interval [ 5,15], step length 5, the erosion rate prediction surface under the proppant particle size of 0.3mm, compared with the known erosion rate matrix A, it is necessary to repeat steps 2 and 3 for supplementary experiments, and the supplementary obtained (flow rate x _i , The discrete points of sand concentration y _i , erosion rate f _i ) are (55,15,0.096), (55,5,0.033), (70,5,0.065), (85,5,0.094), (85,15 ,0.25), using nonlinear fitting to obtain the erosion rate prediction surface under the first and second main control factors as shown in Figure 8, and the corresponding prediction equation is as in formula (13);

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

In the formula: 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, according to the erosion rate matrix A, is fitted with a quadratic polynomial to obtain the flow rate, sand concentration, and proppant particle size factors The prediction equation of lower erosion rate is as formula (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: Predict the average erosion rate of holes under field conditions;

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

During the on-site sand fracturing operation, if the sand concentration, that is, the influence of the second main control factor on the hole erosion rate, needs to be considered at the same time as the first main control factor, select the model in step 6 (b) to calculate the average hole erosion rate speed prediction;

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

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

Divide the degree of perforation erosion damage into five types: low, low, medium, high, and high, and establish an evaluation set

Substituting the equivalent diameter expansion rate λ into the membership function respectively, the five membership degrees are obtained as

即孔眼冲蚀损伤评价结果为“较高”；According to the principle of maximum membership degree, the value of 0.594 is the largest, and the corresponding evaluation set

That is, the evaluation result of perforation erosion damage is "higher";

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

For example, considering the proppant particle size of 0.16 mm on site, the average erosion rate of holes is affected by the flow rate (the first main control factor) and the sand concentration (the second main control factor). According to step 7, the prediction model is selected in step 6 (b ), with reference to Table 1, serial numbers 3, 8, 10, 12 and 17 are existing experimental data, 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), (100, 15); although step 6(c) has the highest model accuracy and can also be used in this case, refer to step 6(c) and need to add at least 13 groups Experiment, so combined with economic indicators, under this working condition, the step 6(b) model is better than the step 6(c) model.

The basic method and main features of the present invention have been described above. Those skilled in the art should understand that the embodiment has described the present invention in detail, and on the premise of not departing from the spirit and scope of the present invention, the present invention also has modifications or equivalent replacements of some technical features, and these modifications or replacements fall within the scope of the present invention. within the scope of the claimed invention. The protection scope of the present invention is defined by the claims and their equivalents.

Claims (7)

1. A perforation erosion rate prediction and erosion damage evaluation method for a perforated casing is characterized by comprising the following specific steps:

step 1: determining factors and ranges of the influence of the erosion rate of the perforation of the perforated casing;

the influencing factors include: (1) sand passing amount, (2) sand concentration, (3) flow rate, (4) proppant particle size, and (5) viscosity of sand carrying liquid; wherein the experimental range of the sand passing amount is 50kg-2000kg, the experimental range of the sand concentration is 5% -20%, the experimental range of the flow velocity is 20m/s-140m/s, the experimental range of the proppant particle size is 0.1mm-0.8mm, and the viscosity range of the sand carrying liquid is 1mPa & s-50mPa & s;

and 2, step: the method comprises the following steps of designing an erosion experiment design of a perforation sleeve, wherein the erosion experiment design comprises an erosion experiment scheme design and an erosion experiment process design;

designing an erosion experiment scheme by adopting a response surface method to carry out multi-factor multi-level design aiming at the five factors in the step 1, wherein n groups are counted;

each group of flow design of the erosion experiment comprises 6 steps which are sequentially as follows:

(1) determining each group of experimental parameter values, namely the sand passing amount, the sand concentration, the flow velocity, the proppant particle size and the viscosity of the sand carrying fluid according to the design result of the erosion experimental scheme in the step 2;

(2) before experiment, the hole erosion sample is cleaned by membrane removing liquid and absolute ethyl alcohol, air-dried and weighed for three times, and the average value is recorded as m _i ；

(3) Adding carboxymethyl cellulose into water pool to increase viscositySampling and carrying out viscosity test until the viscosity test parameter value of the group of sand carrying fluids is reached, and recording the viscosity as tau _i5 ；

(4) Determining the proppant particle size, denoted d _i4 Determining the amount of sand used in the set of experiments and recording as zeta _i1 (ii) a Opening a sand adding valve of a sand adding tank to add the propping agent into the sand adding tank, and when the sand passing amount zeta used in the experiment _i1 When the single maximum loading capacity of the sand adding tank is exceeded, the component is subjected to a sand adding process for multiple times;

(5) rotating the sand concentration control valve of the sand tank to control the sand concentration to reach the experimental parameter value of the sand concentration, and recording the experimental parameter value as alpha _i2 ；

(6) Starting the plunger pump, controlling the flow rate to reach the set of flow rate experimental parameter values, and recording as v _i3 ；

(7) When the flow rate meets the experimental requirements, opening a sand valve, mixing the proppant in the sand adding tank with the sand carrying liquid, stopping timing until all the proppant is discharged, and recording the experimental time as t _i (ii) a When a group of experiments are accumulated for multiple times, adding up the experiment time to obtain the group of experiment time;

(8) after the experiment, the eyelet erosion sample is cleaned by membrane removing liquid and absolute ethyl alcohol, air-dried and weighed for three times, and the average value is recorded as m _i '；

The erosion experiment process relates to the main device and includes: the device comprises a water pool, a plunger pump, a sand adding tank and a perforation sleeve; wherein the sleeve consists of a sleeve body and an eyelet erosion sample;

and 3, step 3: carrying out the erosion experiment according to the erosion experiment design in the step 2, and recording the sand passing amount zeta of each group of experiments _i1 Sand concentration alpha _i2 Flow velocity v _i3 Particle diameter d of proppant _i4 Viscosity tau of sand-carrying fluid _i5 Experiment time t _i The weight of the hole erosion sample is not less than three times before and after the experiment, and the average mass m is obtained by calculation _i 、m′ _i ；

And 4, step 4: calculating the average erosion rate of the holes; recording the ratio of the mass loss of the hole erosion sample before and after the experiment to the experiment time as the average erosion rate of the hole as shown in the formula (1) by utilizing the erosion experiment result in the step 3 and based on a weight loss method;

in the formula:

the average erosion rate of the ith group represents the erosion mass in unit time, g/min; m is _i Weighing average mass g for a plurality of times after cleaning the hole erosion sample before the ith group of experiments; m' _i Weighing the average mass g for a plurality of times after the hole erosion sample is cleaned after the experiment of the i group is finished; m is _i -m′ _i Represents the mass loss after the erosion test, g; wherein the weighing times are not less than three;

and 5: analyzing main control factors of the erosion rate of the holes; establishing an erosion rate matrix according to the steps 3 and 4 as shown in the formula (2);

in the formula: a is an erosion rate matrix; zeta _i1 The sand passing amount of the ith group is kg; alpha is alpha _i2 The sand concentration of the ith group is kg/m ³ ；v _i3 Is the flow velocity of the ith group, m/s; d is a radical of _i4 Is the particle size of the i-th group of propping agents; tau is _i5 The viscosity of the i group sand carrying liquid is mPa.s;

the average erosion rate of the i group of holes is g/min;

calculating the correlation coefficients of the 5 influencing factors and the erosion rate respectively; when the main control factors of the erosion rate are analyzed, the correlation coefficients of different influencing factors and the erosion rate are calculated as a formula (3);

in the formula: r is _i6 Is the ith factor and erosionCorrelation coefficient of rate, dimensionless; r is _i6 The larger the absolute value is, the stronger the correlation is, and the larger the influence is; l is the total number of groups in the experiment, namely the total number of rows of the corresponding erosion rate matrix A; a is _ki The data in the erosion rate matrix A is shown, wherein i is 1, 2, 3, 4 and 5 which respectively represent the sand passing amount, the sand concentration, the flow, the particle size of a propping agent, the viscosity of a sand carrying liquid and the average erosion rate of pores, namely the data sequentially correspond to columns in the erosion rate matrix A, and k is 1, 2 \8230l, | corresponds to rows in the erosion rate matrix A;

absolute value | r of correlation coefficient of erosion rate _i6 Sorting from large to small, selecting three factors with strongest correlation as main control factors, and marking as a first main control factor, a second main control factor and a third main control factor from large to small;

step 6: establishing a prediction model of average erosion rate of the hole under the influence of main control factors;

establishing three prediction models according to a first main control factor, a second main control factor and a third main control factor which are analyzed from five influencing factors of the sand passing amount, the sand concentration, the flow rate, the proppant particle size and the sand carrying fluid viscosity in the step 5:

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

setting a fixed step length and taking a discrete point x in an experimental range by taking a first main control factor x as a variable ₁ ,x ₂ ...x _i (i is more than or equal to 4), other factors are fixed values, the known data set in the obtained erosion rate matrix A can be used to the maximum extent, the supplementary experiments of the steps 3 and 4 are repeated when discrete points are lost, and a first main control factor x lower erosion rate prediction curve f (x) is obtained by utilizing nonlinear fitting;

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

setting a fixed step length and taking discrete points (x) in an experimental range by taking a first main control factor x and a second main control factor y as variables _i ,y _j ) (i is more than or equal to 3, j is more than or equal to 3), other factors are fixed values, the known data group in the obtained erosion rate matrix A can be used to the maximum extent, the supplementary experiments of the steps 3 and 4 are repeated when the discrete point is lost, and the erosion rate prediction plate under the first main control factor x and the second main control factor y is obtained by utilizing nonlinear fittingf(x,y)；

(c) Establishing an erosion rate prediction equation under the influence of the first, second and third main control factors;

setting a fixed step length to take a discrete point (x) in an experimental range by taking a first main control factor x, a second main control factor y and a third main control factor z as variables _i ,y _j ,z _k ) (i is more than or equal to 3, j is more than or equal to 3, k is more than or equal to 2), the known data set in the obtained erosion rate matrix A is used as much as possible, the supplementary experiments of the steps 3 and 4 are repeated when discrete points are lacked, and the erosion rate prediction equation f (x, y, z) under the first main control factor x, the second main control factor y and the third main control factor z is obtained by utilizing nonlinear fitting;

and 7: predicting the average erosion rate of the holes under the field working condition;

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

in the field sand adding fracturing operation process, considering the erosion rate of the holes as a single factor, and selecting the model in the step 6 (a) when the single factor is a first main control factor; when the single factor is a second main control factor, selecting the model in the step 6 (b);

when the single factor is a third main control factor, selecting the model in the step 6 (c);

in the field sand fracturing operation process, when the factors of the erosion rate of the holes are two or more factors, and the two or more factors comprise the second main control factor but not comprise the third main control factor, selecting the model in the step 6; selecting the model of step 6 (c) when the two or more factors include a third master factor;

and step 8: calculating the hole erosion expanding rate and evaluating erosion damage;

after selecting an average erosion rate prediction model suitable for the field working condition from the step 7, the average erosion rate is obtained from the experiment of the step and is related to one or more fracturing parameters of sand passing amount, sand concentration, flow rate, proppant particle size and sand carrying fluid viscosity; substituting the obtained average erosion rate of the hole into the model selected in the step 7 by combining the on-site fracturing time and fracturing parameters, further calculating the average erosion quality as shown in the formula (4), and converting the average erosion quality into the equivalent hole expansion rate as shown in the formula (5);

in the formula:

average erosion mass, g;

the average erosion rate of the holes is g/min; lambda eyelet equivalent hole enlargement rate,%; d is the wall thickness at the position of the hole, m; t is t _a Adding sand on site and fracturing for min; a, initial radius of an eyelet, m; rho is density of hole erosion sample, kg/m ³ ；

(1) Establishing an evaluation set: dividing the hole erosion damage degree into five types of low, medium, high and high, and establishing an evaluation set

(2) Constructing a membership function corresponding to the evaluation set;

in the formula:

respectively collecting membership functions of 'low', 'lower', 'middle', 'higher' and 'high' for evaluation of the erosion damage of the perforation;

the equivalent expanding rate lambda obtained by the formula (5) is respectively substituted into the membership function of the formula to obtain five membership degrees which are respectively

(3) According to the principle of the maximum membership degree,

and the evaluation set corresponding to the medium maximum value is the evaluation result of the hole erosion damage under the equivalent expanding rate.

2. The method for predicting the erosion rate and evaluating the erosion damage of the perforation of the perforated casing according to claim 1, when the experimental working conditions are changed, repeating the subsequent steps from step 2, wherein the experiment under the same working conditions refers to known data, the experimental amount is reduced to the maximum extent, and finally the prediction model is a continuously expanded process; the first, second and third main control factors can not change due to the change of working conditions, and the step 5 does not need to be repeated.

3. The method of claim 2 wherein the subsequent steps are repeated starting from step 2, and when step 6 is performed, (a) the model takes into account a single factor, i.e. a minimum of 4 sets of experiments are required to fit the erosion rate prediction curve, with the other factors being determined; (b) The model needs at least 9 groups of experiments to fit the erosion rate prediction curved surface; (c) The prediction accuracy of the model is the highest, but a minimum of 18 sets of experiments are required to fit the erosion rate prediction equation.

4. The method for predicting the erosion rate of the perforation and evaluating the erosion damage of the perforation casing according to claim 1, wherein the projections of the erosion area of the inner wall surface of the perforation erosion sample and the perforation along the axial direction of the perforation in the step 2 are concentric circles, the radius of the perforation is a, the radius of the erosion area of the inner wall surface is b, and the radius of the outer wall surface is c; wherein, the radius a of the perforation is 4-6mm according to the on-site perforation parameters; the radius b of an erosion area of the inner wall surface of the hole erosion sample on the projection surface is 5-8 times of the radius a of the hole, and the difference between the radius c of the outer wall surface and the radius b of the erosion area of the inner wall surface is 3-4mm.

5. The method for predicting the erosion rate of the perforation of the perforated casing and evaluating the erosion damage according to claim 1, wherein the wall thickness of the erosion sample at the perforation in the step 2 is d, is the same as the wall thickness of an oil layer casing selected on site, and is 10-20mm; the inner wall surface erosion area of the hole erosion sample is a curved surface, when the hole erosion sample is installed on the sleeve, the inner wall surface erosion area of the hole erosion sample is superposed with the inner wall surface of the sleeve, the radius of the inner wall of the sleeve is r, and the radius is 45-105mm.

6. The method for predicting the erosion rate and evaluating the erosion damage of the perforation of the perforated casing according to claim 4 or 5, wherein the radius r of the inner wall surface of the selected reservoir casing is smaller, and the multiple of the radius b of the erosion area of the inner wall surface to the radius a of the perforation is closer to 5; when the radius of the inner wall of the oil layer casing selected on site is larger, the radius b of the erosion area of the inner wall surface is closer to 8 than the multiple of the radius a of the hole.

7. The method for predicting the erosion rate and evaluating the erosion damage of the perforation of the perforated casing according to claim 1, wherein the perforation erosion sample is processed in step 2, and the method comprises the following steps: an orifice, an inner wall erosion zone; the material of the hole erosion sample is the same as that of the field sleeve.

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