CN115290432A - Perforation erosion rate prediction and erosion damage evaluation method for perforated casing - Google Patents
Perforation erosion rate prediction and erosion damage evaluation method for perforated casing Download PDFInfo
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Abstract
The invention discloses a perforation erosion rate prediction and erosion damage evaluation method for a perforated casing, and belongs to the field of oil and gas safety engineering. The method is characterized in that: firstly, determining factors and ranges of influence on the erosion rate of the perforation of the perforated casing and formulating an erosion experimental scheme; calculating the average erosion rate of the holes according to the erosion experiment result and carrying out factor analysis; further establishing an average erosion rate prediction model under the influence of the main control factors, and combining the prediction model and the fracturing parameters on site to obtain the hole erosion expanding rate; and finally, substituting the expanding rate into the established erosion degree evaluation set membership function to evaluate the erosion damage degree of the hole. The method aims at predicting the erosion rate of the hole by erosion under the working condition of large sand fracturing, evaluates the erosion damage of the hole and provides a basis for a field fracturing scheme and the safe service of the casing.
Description
Technical Field
The invention belongs to the field of oil-gas safety engineering, and particularly relates to a perforation erosion rate prediction and erosion damage evaluation method for a perforated casing.
Background
In the development process of an unconventional oil and gas reservoir, large-scale sand fracturing has the characteristics of large discharge capacity, high pumping pressure, large sand adding amount and the like, and a propping agent and a sand-carrying liquid penetrate through a hole to enter a stratum, and the hole is continuously scoured, so that the safety of a casing is finally influenced. According to field data, the large-scale sand fracturing results in severe erosion of the hole, even cracks are formed on the casing from the channeling between the casing and the cement, and due to the fact that the underground conditions are complex and severe, the damage of the casing is accelerated by the coupling effect of the erosion, and safety problems frequently occur.
At present, numerical simulation methods such as Ansys-Fluent, CFD and the like are widely applied to erosion problems, but the numerical simulation methods still have limitations on prediction of the erosion rate of the holes, and because the mechanism of the erosion of the holes is not clear, the appearance of the erosion of the holes is complex, the hole erosion needs to be researched by designing an object model experiment and a scheme, on one hand, the erosion amount and the erosion rate of the holes can be accurately calculated, and on the other hand, the mechanism of the erosion of the holes is revealed through a corresponding characterization method.
Therefore, it is necessary to develop an experiment aiming at the borehole erosion under the sand fracturing working condition to obtain more accurate borehole erosion rate data and provide data support for field fracturing scheme design and casing safety.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a perforation erosion rate prediction and erosion damage evaluation method for a perforated casing.
The technical problem to be solved by the invention is that the method for predicting the erosion rate of the perforation of the perforated casing and evaluating the erosion damage comprises the following 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 rate is 20m/s-140m/s, the experimental range of the particle size of the propping agent is 0.1mm-0.8mm, and the viscosity range of the sand carrying liquid is 1mPa & s-50mPa & s;
step 2: 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 sand passing amount, sand concentration, flow rate, proppant particle size and viscosity of sand carrying liquid according to the design result of the erosion experimental scheme in the step 2;
(2) before experiment, the hole erosion sample is washed by film removing liquid and absolute ethyl alcohol, air dried, weighed for three times and recorded with the average value as m i ；
(3) Adding carboxymethyl cellulose into the water tank to increase the viscosity, sampling and carrying out viscosity test until the viscosity reaches the experimental parameter value of the viscosity of the group of sand carrying liquids, 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 the sand adding tank to add the propping agent into the sand adding tank, and when the sand passing amount zeta of the experiment is used i1 When the single maximum loading capacity of the sand adding tank is exceeded, the group should be 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 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) While flowingAfter the experiment requirement is met, opening a sand valve, adding the proppant in the sand tank and mixing the proppant with the sand carrying liquid, stopping timing until all the proppants are discharged, and recording the experiment time as t i (ii) a When a group of experiments are accumulated for multiple times, adding the experiment time to sum up the experiment time to the group of experiment time;
(8) after the experiment, the hole erosion sample is washed by membrane removing liquid and absolute ethyl alcohol, air-dried and weighed for three times, and the average value is 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;
fig. 2 shows a schematic diagram of an erosion experimental apparatus, which mainly comprises: a water pool, a plunger pump, a sand adding tank and a sleeve; wherein the sleeve consists of a sleeve body and an eyelet erosion sample;
and step 3: carrying out erosion experiments 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 And experimental 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 hole erosion rate 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 (not less than three times) the average mass g of the cleaned punched hole erosion sample before the i-th group of experiments; m' i End of Aperture erosion test for group i experimentWeighing the sample for multiple times (not less than three times) after cleaning, and weighing the sample for multiple times; m is i -m' i Represents mass loss after erosion test, g;
and 5: analyzing hole erosion rate main control factors; 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; ζ represents a unit i1 The sand passing amount of the ith group is kg; alpha (alpha) ("alpha") i2 Number i group sand concentration, kg/m 3 ；v i3 Is the flow velocity of the ith group, m/s; d 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 erosion rate main control factor is analyzed, the correlation coefficients of different influencing factors and the erosion rate are calculated as a formula (3);
in the formula: r is i6 The correlation coefficient of the ith factor and the erosion rate is dimensionless; r is a radical of hydrogen 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 a 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 I, sorting from large to small, selecting three factors with strongest correlation as main control factors, and selecting the three factors from large to smallRecording the size of the main control factor as a first main control factor, a second main control factor and a third main control factor;
and 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 lacked, 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 points are lost, and the erosion rate prediction plate f (x, y) under the first main control factor x and the second main control factor y is obtained by utilizing nonlinear fitting;
(c) Establishing an erosion rate prediction equation under the influence of the first, second and third 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, 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 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 process of field sand fracturing operation, when the consideration factor of the erosion rate of the perforation is two or more than two factors, and the two or more than two factors comprise a second main control factor but not comprise a 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 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 combination of the on-site fracturing time and fracturing parameters into the model selected in the step 7 to obtain the average erosion rate of the hole, 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 ratio,%; d is the wall thickness at the hole, m; t is t a Adding sand on site and fracturing for min; a, initial radius of the hole, 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 the evaluation of the erosion damage of the hole;
the equivalent expanding rate lambda obtained by the formula (5) is respectively substituted into the membership function of the formula to obtain five membership functions of
(3) According to the principle of the maximum membership degree,
the evaluation set corresponding to the medium maximum value is the evaluation result of the hole erosion damage under the equivalent expanding rate;
specifically, the hole erosion sample in step 2 needs to be processed, and as shown in the schematic diagram of the inside of the hole erosion sample in fig. 3 and the schematic diagram of the outside of the hole erosion sample in fig. 4, the hole erosion sample includes the following parts: an orifice, an inner wall erosion zone; the material of the hole erosion sample is the same as that of the field sleeve;
specifically, the geometric parameter characteristics of the hole erosion test sample in the step 2 are as shown in a front view of the hole erosion test sample in fig. 5 and a cross-sectional view of the hole erosion test sample in fig. 6, projections of an inner wall surface erosion area and a hole in the axial direction of the hole are concentric circles, the radius of the hole is a, the radius of an inner wall surface erosion area is b, and the radius of an outer wall surface is c; wherein, the radius a of the perforation is usually in the range of 4-6mm according to the parameters of field perforation; the radius b of an erosion area of the inner wall surface of an orifice erosion sample on the projection surface is 5-8 times of the radius a of the orifice, 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;
specifically, the wall thickness of the hole erosion sample in the step 2 at the hole is d, is the same as the wall thickness of an oil layer casing selected on site, and is usually within the range of 10-20mm; the inner wall surface erosion area of the hole erosion sample is a curved surface, when the hole erosion sample is arranged 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 normal range is 45-105mm;
specifically, when the radius r of the inner wall of the oil layer casing selected on site is smaller, the radius b of an erosion area of the inner wall is smaller, the minimum radius is 5 times of the radius a of the hole, and the risk of erosion exists in the hole erosion sample installation area when the radius is smaller than 5 times; when the radius of the inner wall of the oil layer casing selected on site is larger, the radius b of an erosion area of the inner wall can be properly increased, the maximum radius is 8 times of the radius a of the hole and is more than 8 times, the casing wall is a curved surface, and the thickness d of the hole needs to be kept, so that the casing is not easy to process and assemble;
further, when the experimental working conditions change, repeating the subsequent steps from step 2, wherein the experiment under the same working conditions refers to known data, so that the experimental amount is reduced to the maximum extent, and finally, the prediction model is a process which is continuously expanded; 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;
specifically, when the experimental working condition changes, the subsequent steps are repeated from step 2, and step 6 is executed, (a) the model considers a single factor, that is, under the condition of determining other factors, only 4 groups of experiments are needed at least to fit the erosion rate prediction curve; (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 experiments are required to fit the erosion rate prediction equation.
Due to the adoption of the technical scheme, the invention has the following advantages:
the method is based on an eyelet erosion physical model experiment, adopts a response surface method to carry out experiment design, predicts the average erosion rate of the eyelet under the field working condition with smaller experiment amount, particularly continuously expands the model in the using process of the method when the working condition is considered to change in the later field, and is suitable for increasing the field working condition range.
On the other hand, the method comprehensively considers the sand passing amount, the sand concentration, the flow velocity, the particle size of the propping agent and the viscosity of the sand carrying liquid, and has higher goodness of fit between the experimental parameter range and the field working condition range, thereby breaking through the limitation of average erosion rate prediction caused by small experimental range; after the perforation erosion rate is predicted according to a certain working condition, the average erosion amount of the perforation can be predicted by combining the fracturing operation time, the hole expanding rate is further predicted, the perforation erosion damage degree is evaluated, and technical bases are provided for predicting the erosion rate of the sand fracturing perforation, designing a fracturing scheme and the like.
Drawings
FIG. 1 is a flow chart of a method for predicting erosion rate of perforations in a perforated casing and evaluating erosion damage;
FIG. 2 is a schematic view of an erosion experimental apparatus;
FIG. 3 is a schematic view of the inside of an orifice erosion coupon;
FIG. 4 is a schematic view of the outside of an orifice erosion coupon;
FIG. 5 is a front view of an orifice erosion coupon;
FIG. 6 is a cross-sectional view of an orifice erosion coupon;
FIG. 7 is a plot of erosion rate prediction under the influence of a first master factor;
FIG. 8 is a graph of first and second master factors affecting an erosion rate prediction surface;
description of reference numerals: 1-a water pool; 2-a plunger pump; 3-a sand adding valve; 4-adding a sand tank; 5-sanding valve; 6-sand concentration control valve; 7-a sleeve; 8-hole erosion sample mounting area; 9-hole erosion of the sample; 10-eyelet; 11-hole erosion sample inner wall surface erosion area; 12-hole erosion of the outer wall surface of the sample; 13-inner wall of casing.
Detailed Description
The invention is described in detail below with reference to the figures and the detailed description.
Step 1: for briefly explaining the calculation method, the sand passing amount of each group is 100kg, the viscosity of the sand carrying fluid is 10mPa & s, and the sand concentration, the flow rate and the particle size of the propping agent are variables influencing the erosion rate;
and 2, step: carrying out erosion experiments on the same material eyelet erosion samples within the value range of the influence factors, wherein the geometric parameters of the eyelet erosion samples are as follows: the wall thickness d is 11.1mm, the radius r of the inner wall of the casing is 52.4mm, the radius a of the hole is 5mm, the radius b of the erosion surface of the inner wall surface is 25mm, the radius c of the outer wall surface of the hole erosion sample is 30mm, the hole erosion sample adopts TP125v which is made of the same material as the material of an on-site oil layer casing and has the density of 7900kg/m 3 ；
The experimental parameters and ranges were: the experimental range of the sand concentration is 5-20%, the experimental range of the flow rate is 20-140 m/s, the experimental range of the particle size of the proppant is 0.1-0.8 mm, and 20 groups of experiments are performed, as shown in table 1;
each set of flow design of the erosion experiment comprises 6 steps, taking the experiment set with the serial number 1 as an example:
(1) determining experimental parameter values, namely 15% of sand concentration, 40m/s of flow speed and 0.3mm of proppant particle size;
(2) before experiment, the hole erosion sample is washed by film removing liquid and absolute ethyl alcohol, air dried, weighed for three times and recorded with the average value as m i ；
(3) Adding carboxymethyl cellulose into the water tank to increase the viscosity, and sampling and testing to determine the viscosity of the sand carrying liquid to be 10mPa & s;
(4) determining the particle size of the propping agent to be 0.3mm, the maximum sand adding amount of a sand adding tank for an experiment to be 500kg and the sand adding amount of the sand adding tank for the experiment to be 100kg, opening a sand adding valve of the sand adding tank, and adding the propping agent;
(5) rotating a sand tank concentration control valve to control the sand concentration to reach 15%;
(6) starting the plunger pump, and controlling the flow rate to reach the set of flow rate experimental parameter value of 40m/s;
(7) when the flow rate meets the experimental requirements, opening a sand adding valve, mixing the proppant in a sand adding tank with a sand carrying liquid, stopping timing until all the proppant is discharged, and recording the experimental time as t i (ii) a Because the sand amount used in the experiment is less than the maximum sand adding amount of the sand adding tank, the experiment can be completed in a single time without accumulating time of multiple experiments;
(8) after the experiment, the hole erosion sample is washed by membrane removing liquid and absolute ethyl alcohol, air-dried and weighed for three times, and the average value is m' i ；
And 3, step 3: carrying out an erosion experiment according to the erosion experiment design in the step 2, wherein the experiment design and the result are shown in a table 1;
table 1: experimental protocol and experimental results
And 4, step 4: the average erosion rate of the perforations was calculated 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 |
| |
11 | 12 | 13 | 14 | 15 |
| Average erosion Rate g/min | 0.166 | 0.069 | 0.12 | 0.103 | 0.179 |
| |
16 | 17 | 18 | 19 | 20 |
| Average erosion Rate g/min | 0.135 | 0.187 | 0.342 | 0.284 | 0.243 |
And 5: according to steps 3 and 4, an erosion rate matrix a is established as follows:
in the formula: a is an erosion rate matrix; the first column is flow rate influencing factor data; the second column is sand concentration influence factor data; a third column of proppant particle size impact factor data; the 4 th column is the erosion rate experiment result under each group of flow rate, sand concentration and proppant particle size experiment;
substituting the data in the erosion rate matrix A into a correlation coefficient calculation formula (3), and calculating to obtain correlation coefficients of the three factors and the hole erosion rate as shown in a table 3;
table 3: correlation coefficient calculation result
According to the determination in table 3: the flow rate is a first main control factor, the sand content is a second main control factor, and the particle size of the proppant is a third main control factor;
step 6: establishing a prediction model of average erosion rate of the hole under the influence of main control factors;
(a) An erosion rate prediction curve under the influence of a first main control factor flow rate, namely an erosion rate prediction curve under the influence of a flow rate; setting a flow rate (m/s) interval [40,100], a step length of 15, a sand concentration of 10% and a prediction curve under the condition that the particle size of the propping agent is 0.3mm, comparing a known erosion rate matrix A, the data bit is known, and a supplementary experiment is not needed, obtaining an erosion rate prediction curve under a first main control factor by utilizing nonlinear fitting as shown in figure 7, wherein the corresponding prediction equation is as shown in a formula (12);
f＝0.00004x 2 -0.0015x+0.0319 (12)
(b) The erosion rate prediction curved surface under the influence of the first main control factor flow velocity and the second main control factor sand concentration is provided with a flow velocity (m/s) interval [40,100]]Step size 15, setting sand concentration (%) section [5, 15%]Step 5, erosion rate prediction curved surface under the condition that the particle size of the proppant is 0.3mm, compared with the known erosion rate matrix A, the supplementary experiments of the steps 2 and 3 are repeated, and the (flow rate x) is obtained through supplement i Sand concentration y i Erosion rate f i ) The discrete points 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 curves of the erosion rates under the first and second main control factors are obtained by utilizing nonlinear fitting, as shown in FIG. 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)
in the formula: f is the erosion rate, g/min; x is flow speed, m/s; y is sand concentration,%;
(c) Carrying out nonlinear fitting by using a quadratic polynomial according to an erosion rate matrix A to obtain an erosion rate prediction equation under the influence of the first, second and third main control factors, wherein the erosion rate prediction equation is as shown in formula (14) under the influence of flow rate, sand concentration and proppant particle size;
in the formula: in the formula: f is the erosion rate, g/min; x is flow speed, m/s; y is sand concentration,%; z is the proppant particle size, mm;
and 7: predicting the average erosion rate of the hole 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 fracturing operation process, if the sand concentration is considered, namely the influence of the second main control factor on the erosion rate of the holes is considered, the first main control factor needs to be considered at the same time, and the model in the step 6 (b) is selected to predict the average erosion rate of the holes;
and 8: calculating the hole erosion expanding rate and evaluating erosion damage;
evaluating the hole erosion degree when the sand concentration is 13%, the flow rate is 70m/s, the sand passing amount is 100kg, the viscosity is 10mPa & s, the propping agent is 0.3mm and the fracturing time is 90min by combining with the field fracturing parameters and the fracturing time, substituting the hole erosion degree into the model selected in the step 7 to obtain the average hole erosion rate of 0.1438g/min, further calculating the average erosion mass of 12.942g according to the formula (4), and converting the average erosion mass substitution formula (5) into the hole equivalent hole expansion formula of lambda =45.94%;
dividing the hole erosion damage degree into five types of low, medium, high and high, and establishing an evaluation set
Respectively substituting the equivalent expanding rate lambda into the membership function to obtain five membership functions of
According to the maximum membership rule, the corresponding evaluation set with the maximum value of 0.594
Namely, the evaluation result of the hole erosion damage is higher;
when the existing model cannot predict the average erosion rate of the holes under the new working condition in the step 6, the subsequent steps are repeated from the step 2, wherein the experiments under the same working condition refer to the existing data, the experiments under different working conditions are supplemented, the experiment amount is reduced to the maximum extent, and finally the prediction model is a process which is continuously expanded; step 5 is not required to be repeated in the subsequent steps, the first main control factor is still the flow rate, the second main control factor is still the sand concentration, and the third main control factor is still the proppant particle size;
for example, in the case of considering that the particle size of the proppant is 0.16mm on site, the flow rate (the first main control factor) and the sand concentration (the second main control factor) influence the average erosion rate of the lower hole, according to step 7, the prediction model is selected in step 6 (b), 5 groups of existing experimental data are referred to in table 1, and 4 groups of experiments (flow rate and sand concentration) which need to be supplemented according to step 6 (b) are (40, 5), (40, 15), (100, 5), (100, 15); although the step 6 (c) model has the highest accuracy and can be used in the situation, the reference to the step 6 (c) also needs to supplement 13 sets of experiments at least, so that the economic index is combined, and under the 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. It will be understood by those skilled in the art that while the present invention has been described in detail with reference to the preferred embodiments thereof, the present invention is susceptible to modification of part of the features of the invention and equivalents thereof without departing from the spirit and scope of the invention as defined by the appended claims. The scope of the 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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