Wide-temperature-pressure-domain drilling fluid rheological mode multi-parameter determination method

Abstract

The invention relates to a wide-temperature-pressure-domain drilling fluid rheological mode multi-parameter determination method which comprises the following steps: step 1, carrying out a rheological characteristic experiment, and respectively measuring rheological parameters of a drilling fluid sample at different rotating speeds at different temperatures and pressures; step 2, fitting rheological parameters of an R-S mode by using a nonlinear least square method; 3, images of different rheological parameters changing along with temperature and pressure are drawn, and a temperature and pressure correction model, suitable for the high-temperature and high-pressure conditions, of the R-S mode is obtained; and 4, predicted values of the rheological parameters at different temperatures and pressures are calculated through the temperature and pressure correction model. The method is easy to implement, the precision and efficiency are better than those of a traditional method, and good stability is shown.

Description

Technical Field

[0001] The present invention belongs to the technical fields of oil engineering drilling fluids and rheology, and specifically relates to a method for determining the R-S mode rheological parameters of high-temperature and high-pressure drilling fluids based on experimental measurements and nonlinear least-squares fitting. Background Art

[0002] Rheology is one of the most critical indicators for describing the properties of non-Newtonian fluids such as drilling fluids. It is usually quantitatively characterized by a rheological model to predict the flow characteristics of the fluid in flow spaces such as wellbores and pipelines. Physically, the rheological model of a fluid mainly characterizes the functional relationship between shear stress and shear rate. Among them, the shear stress and shear rate of Newtonian fluids are in a linear proportional relationship, while non-Newtonian fluids have a non-linear relationship. Oil drilling fluids are non-Newtonian fluids. The accurate determination of the rheological model parameters of the fluid is the basis for scientifically characterizing the flow behavior of the fluid, which is related to the efficiency and safety of oil production.

[0003] In current hydraulic analysis and friction calculation in the field of drilling engineering, such as in the Drillbench software, the commonly used drilling fluid rheological models mainly include the Newtonian model, power-law model, Casson model, Herschel-Bulkley model, and Robertson-Stiff (R-S) model. Of course, there are also some other more complex rheological models on this basis. Although they describe the shear stress-rate relationship more precisely, the introduction of more parameters means that the use of the model is more complex, limiting its versatility. Compared with other general models, the R-S model includes the functional relationships of the Newtonian, Bingham, and exponential models, can better reflect the rheological characteristics of various drilling fluids at different shear rates, can describe relatively complex rheological characteristics, especially performs well in specific types of viscous fluids, and can more accurately describe the rheological characteristics of drilling fluids. Therefore, the R-S rheological model can be widely used to describe the characteristics of non-Newtonian fluids and has good accuracy.

[0004] Under most conditions, determining rheological parameters is an overfitting problem. That is, the number of shear rate-shear stress experimental points exceeds the number of rheological parameters. Secondly, for high-temperature and high-pressure drilling fluids, their properties change greatly with temperature and pressure. Usually, it is necessary to experimentally measure the rheological experimental data under different temperature and pressure conditions and then perform parameter fitting, which means that the rheological parameters need to be fitted as functions of temperature and pressure. Although there are many general fitting and prediction methods, their accuracy and efficiency cannot meet the requirements. Therefore, fitting methods and correction models based on temperature and pressure need to be proposed for different rheological models. In addition, regarding the temperature and pressure correction models, a series of studies on rheology have been carried out at home and abroad, but the experimental data under high-temperature and high-pressure conditions are relatively few, and many of the currently proposed temperature and pressure correction models for rheological parameters are not applicable to high-temperature and high-pressure environments.

[0005] In summary, there is an urgent need to propose a rheological parameter fitting method for the R-S rheological model and a temperature and pressure correction model for rheological parameters under high temperature and high pressure conditions, so as to better analyze the fluid flow behavior and improve the efficiency and safety index of oil production. Summary of the Invention

[0006] Based on the existing fitting methods, the present invention provides a method for determining multiple parameters of the drilling fluid rheological model in a wide temperature and pressure range;

[0007] In view of the gap in rheological research under high temperature and high pressure conditions, based on the experimental measurement data of high temperature and high pressure rheology, the present invention provides a temperature and pressure correction model for the R-S model applicable to high temperature and high pressure conditions.

[0008] The technical solution of the present invention is as follows:

[0009] A method for determining multiple parameters of the drilling fluid rheological model in a wide temperature and pressure range, comprising:

[0010] Step 1: Conduct rheological characteristic experiments, and measure the rheological parameters of the drilling fluid sample at different rotation speeds under different temperatures and pressures respectively;

[0011] Step 2: Use the nonlinear least squares method to fit the rheological parameters of the R-S model;

[0012] Step 3: Plot the images of different rheological parameters changing with temperature and pressure to obtain a temperature and pressure correction model for the R-S model applicable to high temperature and high pressure conditions:

[0013] Step 4: Use the temperature and pressure correction model to calculate the predicted values of the rheological parameters at different temperatures and pressures.

[0014] Preferably according to the present invention, an OFITE high temperature and high pressure rotational viscometer is used to conduct rheological characteristic experiments, and the rheological parameters, namely shear stress, of the drilling fluid sample are measured at different rotation speeds, i.e., shear rates, under different temperatures and pressures respectively; the temperature range is 18°C - 200°C, and the pressure range is 6.89 MPa - 172.37 Mpa.

[0015] Preferably according to the present invention, the nonlinear least squares method is used to fit the rheological parameters of the R-S model; it includes:

[0016] (1) According to the least squares method, the least squares fitting objective function f for the R-S model is deduced as shown in Equation (1):

[0017]

[0018] In Equation (1), N represents a total of N pairs of shear rates and shear stresses, τ i represents the i-th shear stress, γ irepresents the i-th shear rate, A represents the consistency coefficient, B represents the flow behavior index, and C represents the initial shear rate;

[0019] (2) Respectively take the partial derivatives of the rheological parameters A, B, and C in the least squares fitting objective function f, and after sorting, obtain a system of partial derivative variances about A, B, and C, as shown in Equations (2), (3), and (4):

[0020]

[0021]

[0022] In Equations (2), (3), and (4), x is γ i , and y is τ i ;

[0023] (3) Regard Equation (3) and Equation (4) as binary functions F1(B, C) = 0 and F2(B, C) = 0 respectively, draw the binary function images, and find that the binary function F1(B, C) = 0 derived in the R-S mode, that is, the function F1 and F2(B, C) = 0, that is, the function F2, have the same rules, including:

[0024] The functions F1 and F2 have one and only one intersection point in the first quadrant;

[0025] The functions F1 and F2 both show the property of monotonically increasing;

[0026] Before the intersection point, the function image of F1 is above the function image of F2; after the intersection point, the function image of F2 is above the function image of F1;

[0027] (4) Using the discovered rules, propose a new fitting method for the R-S mode, specifically:

[0028] (4.1) Set a small positive number as the iteration step size δ, set the magnification factor η for each step size contraction, set the size of the accuracy requirement p, where p represents the calculation accuracy requirement in the iteration process, and let B1 = δ. B1 is the value of B in F1(B, C) and is also the initial value of B for iterative calculation;

[0029] (4.2) Let F1(B, C) = 0, B = B1, find the corresponding C value of B1, and then use F2(B, C) = 0 to find the corresponding B2 of C. B2 is the value of B in F2(B, C);

[0030] (4.3) If B2 > B1, it means that it is on the left side of the intersection point. Let B1 be B1 + δ, and repeat from step (4.2), continue to iterate to the right, that is, take the value of the current B1 point on the right side in the coordinate system and calculate again;

[0031] (4.4) Otherwise, it indicates that it has just passed through the intersection point and reached the right side of the intersection point. Let B1 be B1 - δ, so that B1 returns to the left side of the intersection point. At this time, the existence interval of the intersection point is [B1, B2];

[0032] (4.5) Compare the iteration step size δ and the precision p; if δ > p, it indicates that the precision requirement is not met. Let δ be δ · η, and repeat from step (4.2). If δ < p, it indicates that the precision requirement is met. Take the midpoint of B1 and B2 as the solution result of B;

[0033] (4.6) Substitute the solution result of B obtained in step (4.5) into the binary equation F1(B, C) = 0 or F2(B, C) = 0, then C can be obtained. Finally, A is obtained by using equation (2).

[0034] Further preferably, by the bisection method and the Newton iteration method, C is obtained by using the binary functions F1(B, C) = 0 and F2(B, C) = 0.

[0035] Preferably according to the present invention, the R - S mode is applicable to the temperature - pressure correction model f(P, T) under high - temperature and high - pressure conditions as shown in equation (5):

[0036] f(P, T)=a + bT + cT 2 +d(PT + exp(P)) (5);

[0037] Wherein, a, b, c, and d are characteristic constants, and P and T are pressure and temperature; for the R - S mode, f(P, T) represents the value of the consistency coefficient A, the flow behavior index B, or the initial shear rate C; exp() represents the exponential function with the base e of the natural logarithm.

[0038] Preferably according to the present invention, the predicted values of rheological parameters at different temperatures and pressures are calculated by using the temperature - pressure correction model; including:

[0039] Using the rheological parameters at different temperatures and pressures obtained in step 1, the temperature - pressure correction model applicable to high - temperature and high - pressure conditions proposed in step 3 is fitted by the least - squares method to obtain the fitted temperature - pressure correction formula. The values of each rheological parameter at different temperatures and pressures are calculated by using the fitted temperature - pressure correction formula.

[0040] A computer device, including a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, it realizes the steps of the method for determining the R - S mode rheological parameters of high - temperature and high - pressure drilling fluid.

[0041] A computer - readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it realizes the steps of the method for determining the R - S mode rheological parameters of high - temperature and high - pressure drilling fluid.

[0042] The beneficial effects of the present invention are as follows:

[0043] The present invention proposes a method for determining the rheological parameters of the R-S model of high-temperature and high-pressure drilling fluids based on experimental measurement and non-linear least squares fitting. Among them, the new method for fitting the rheological parameters of the R-S model combines the least squares method and the rheological law of the R-S model. Compared with the traditional linear regression method and other general methods, this method is simple to implement, and its accuracy and efficiency are better than the traditional methods, showing good stability. In addition, the temperature and pressure correction model of the R-S model can well predict the changes of the rheological parameters of the R-S model with temperature and pressure, and is applicable to high-temperature and high-pressure conditions. This method can better analyze the fluid flow behavior, provides a new method for calculating the rheological parameters of the R-S model under high-temperature and high-pressure conditions, helps to optimize the performance of drilling fluids, and improves the efficiency and safety index of oil production. Description of the Drawings

[0044] Figure 1 Schematic diagram of rheological parameters measured by rheological experiments Figure 1 ;

[0045] Figure 2 Schematic diagram of rheological parameters measured by rheological experiments Figure 2 ;

[0046] Figure 3 Schematic diagram of rheological parameters measured by rheological experiments Figure 3 ;

[0047] Figure 4 Schematic diagram of the iterative process of the new fitting method of the present invention;

[0048] Figure 5 Schematic diagram of the comparison of rheological parameters between linear regression and the new fitting method;

[0049] Figure 6 Schematic diagram of the comparison of the effects between linear regression and the new fitting method;

[0050] Figure 7 Schematic diagram of the fitting parameters of drilling fluids under different temperature and pressure conditions;

[0051] Figure 8 Schematic diagram of the comparison between the predicted value and the actual value of the temperature and pressure correction model Figure 1 ;

[0052] Figure 9 Schematic diagram of the comparison between the predicted value and the actual value of the temperature and pressure correction model Figure 2 . Detailed Embodiments

[0053] The present invention will be further defined below in conjunction with the accompanying drawings of the specification and embodiments, but is not limited thereto.

[0054] Example 1

[0055] A method for determining multiple parameters of the rheological model of drilling fluid in a wide temperature and pressure range, comprising:

[0056] Step 1: Conduct rheological characteristic experiments. Measure the rheological parameters of the drilling fluid sample at different rotation speeds under different temperatures and pressures respectively.

[0057] Step 2: Use the non - linear least - squares method to fit the rheological parameters of the R - S model.

[0058] Step 3: Plot the images of different rheological parameters changing with temperature and pressure. It is found that the changes of rheological parameters with temperature and pressure show similar laws, and obtain the temperature - pressure correction model applicable to high - temperature and high - pressure conditions for the R - S model:

[0059] Step 4: Use the temperature - pressure correction model to calculate the predicted values of rheological parameters at different temperatures and pressures.

[0060] Example 2

[0061] A method for determining multiple parameters of the rheological model of drilling fluid in a wide temperature and pressure range according to Example 1, wherein the difference lies in:

[0062] Use an OFITE high - temperature and high - pressure rotary viscometer to conduct rheological characteristic experiments. Measure the rheological parameters (i.e., shear stress) of the drilling fluid sample at different rotation speeds (i.e., shear rates) under different temperatures and pressures respectively. The temperature range is 18°C - 200°C, and the pressure range is 6.89 MPa - 172.37 Mpa.

[0063] The OFITE high - temperature and high - pressure rotary viscometer is a rheometer specifically manufactured by OFI Experimental Instruments Company in the United States for measuring the high - temperature and high - pressure rheological parameters of drilling fluid, completion fluid, and cement slurry. The main parameters are as follows: working pressure (206.9 MPa), working temperature (0 - 260°C), viscosity range (0 - 300 mPa·s), shear rate range (0.01 - 1700 s -1 )

[0064] The experimental system consists of a temperature control system, a pressure control system, a monitoring system, a test unit, a computer terminal, etc. The pressure control system is divided into a hydraulic part and a pneumatic part. The hydraulic part consists of an internal hydraulic oil tank, hydraulic oil pipelines, and a hydraulic pump, which is responsible for controlling the experimental pressure. The pneumatic part is supplied with gas by an external nitrogen tank and is responsible for fine-tuning the pressure to ensure the stability of the set test pressure points. The monitoring system is mainly composed of sensors. Specifically, there is a measurement hole for the temperature sensor at the bottom of the test kettle of the instrument. During the test, the temperature sensor penetrates through the small hole into the center of the kettle to accurately measure the temperature data of the sample. The test unit mainly consists of a test kettle, a rotor, and a suspension weight. After ensuring that the rotor rotates normally, the test kettle and the suspension weight need to be connected, placed into a high-temperature and high-pressure rotational viscometer, and the pressure pipeline is connected properly. The relevant parameters of the rotor and the suspension weight are shown in Table 1. The computer terminal mainly realizes automatic control by writing programs through the experimental control software ORCADA, including the control of temperature and pressure, the control of shear rate, and the saving of data.

[0065] Table 1 Relevant parameters of the rotor and the suspension weight;

[0066]

[0067]

[0068] Specifically include:

[0069] The specific experimental steps are as follows:

[0070] Prepare the drilling fluid sample used in the experiment. The formula used in this embodiment is shown in Table 2:

[0071] Table 2 Drilling fluid sample formula;

[0072]

[0073] (1) Put 155 mL of well-stirred drilling fluid into the test kettle. After checking the rotation state of the rotor, install the sealing ring and the suspension weight, apply high-temperature lubricating oil to the kettle thread, then connect the test suit with the suspension weight, tighten the thread, and then place the whole device into the high-temperature and high-pressure rotational viscometer for fixation and connect the pressure pipeline properly.

[0074] (2) Measure the rheological parameters of the drilling fluid sample at six rotation speeds of 3, 6, 100, 200, 300, and 600 r / min at different temperatures and pressures respectively.

[0075] (3) Specifically, to avoid the boiling of the drilling fluid in a high-temperature and low-pressure environment, the measurement pressure will be adjusted according to the temperature change during measurement. And based on the temperature and pressure conditions in the actual drilling process, the starting measurement pressure under high-temperature conditions will be appropriately increased.

[0076] (4) Measure the rheological properties of the drilling fluid at six different rotational speeds. Using the measurement results of the rotational viscometer at each speed point, construct the rheological property diagram of the drilling fluid to facilitate further calculation of rheological parameters. The data diagram of this embodiment is shown in Appendix Figure 1 , Appendix Figure 2 and 3 are the experimental data of the rheology of drilling fluids with other formulations. For the fitting parameters of the drilling fluid under different temperature and pressure conditions, refer to Figure 7 .

[0077] Table 3 Rheology experimental data;

[0078]

[0079]

[0080] Use the non - linear least - squares method to fit the rheological parameters of the R - S model; including:

[0081] The determination of drilling fluid parameters is essentially a least - squares fitting problem. Its basic idea is to find the best - fitting curve or line by minimizing the sum of the squares of the errors between the observed data points and the model prediction values. The general form of the R - S rheological model equation is:

[0082] τ = A(γ + C) B ;

[0083] In the formula, A, B, C are model parameters related to temperature and pressure.

[0084] Assume that the N groups of measured drilling fluid data are (γ1,τ1),(γ2,τ2),(γ3,τ3),…,(γ N ,τ N ), then the error between the predicted value and the actual value is:

[0085] ε i = τ i - A(γ i + C) B , i = 1,2,3,...,N;

[0086] Among them, ε i is the error between the predicted value and the actual value, γ i and τ i are the real data obtained by actual measurement.

[0087] The above - mentioned as the objective function of the least - squares method is as follows:

[0088]

[0089] In this way, using the least squares method, the problem of solving the rheological parameters is transformed into the problem of solving the parameters of the objective function at the minimum point.

[0090] (1) According to the least squares method, the least squares fitting objective function f for the RS mode is derived, as shown in formula (1):

[0091]

[0092] In order to solve the value of each parameter at the minimum point of the objective function, the objective function must be transformed. Here, the necessary conditions of the function extreme point are used to transform the problem of solving the parameters of the objective function at the minimum point into the problem of solving the partial derivative equation.

[0093] In formula (1), N represents the total N pairs of shear rate and shear stress, τ i represents the i-th shear stress, γ i represents the i-th shear rate, A, B, and C represent the three rheological parameters of the RS rheological mode: A represents the consistency coefficient, B represents the flow index, and C represents the initial shear rate;

[0094] (2) According to the necessary conditions for the extreme point of a multivariate function, if the function reaches an extreme value at a certain point, then the partial derivative at that point is 0. Based on this property, the partial derivatives of the rheological parameters A, B, and C in the least squares fitting objective function f are calculated respectively, and after sorting, a partial derivative variance group about A, B, and C is obtained; the problem of solving the objective function is transformed into the problem of solving the partial derivative equation group.

[0095] For the convenience of calculation, the objective function is set as:

[0096]

[0097] By taking partial derivatives of A, B, and C respectively, we can obtain equations (2), (3), and (4):

[0098]

[0099] In formula (2), formula (3) and formula (4), x is γ i , y is τ i ;

[0100] According to equations (3) and (4), after obtaining the values ​​of B and C, we can substitute them into equation (2) to obtain A. Therefore, the solution of this system of equations is actually the solution of the two-variable equation system of equations (3) and (4). However, the C parameter in equations (3) and (4) is difficult to separate, so we need to regard the system of equations as the solution problem of multivariate function equations.

[0101] Set equation (3) and equation (4) as:

[0102]

[0103]

[0104] Regarding Equation (3) and Equation (4) as the binary functions F1(B, C) = 0 and F2(B, C) = 0 respectively, and plotting the graphs of the binary functions, it is found that the binary function F1(B, C) = 0 derived in the R-S mode, that is, the function F1, and F2(B, C) = 0, that is, the function F2, both have the same rules, including:

[0105] The functions F1 and F2 have exactly one intersection point in the first quadrant;

[0106] Both the functions F1 and F2 show the property of monotonically increasing;

[0107] Before the intersection point, the graph of the function F1 is above the graph of the function F2; after the intersection point, the graph of the function F2 is above the graph of the function F1;

[0108] Obviously, the values of B and C corresponding to the intersection point of the functions F1 and F2 in the first quadrant are the best fitting results.

[0109] According to the characteristics of the function graph, a new iterative algorithm can be designed. Starting from a very small positive number and iterating backward continuously, find the approximate range [B1, B2] where the function graphs just intersect. Then, reduce the iteration step size and perform the above operations again until the range [B1, B2] meets the accuracy requirements.

[0110] (4) Utilize the discovered rules to propose a new fitting method for the R-S mode, as Figure 4 shown, specifically:

[0111] (4.1) Set a relatively small positive number as the iteration step size δ. For example, 0.1. The closer this value is to 0, the smaller the change in B during each iteration, and the more accurate the value range of B obtained in each iteration. However, the calculation time will be longer. Set the magnification factor η for shrinking the step size each time, and set the size of the accuracy requirement p. p represents the calculation accuracy requirement during the iteration process. For example, set p = 10 -10 , and the final calculation accuracy during the iteration process will reach 10 decimal places. Let B1 = δ. B1 is the value of B in F1(B, C) and also the initial value of B for iterative calculation;

[0112] (4.2) Let F1(B, C) = 0 and B = B1, and find the corresponding C value for B1. Then, use F2(B, C) = 0 to find the corresponding B2 for C. B2 is the value of B in F2(B, C);

[0113] (4.3) If B2 > B1, it indicates that on the left side of the intersection point. Let B1 be B1 + δ, and repeat from step (4.2), continue to iterate to the right, that is, take a value of the current B1 point that is more to the right on the coordinate system and calculate again;

[0114] (4.4) Otherwise, it indicates that just passed through the intersection point to reach the right side of the intersection point. Let B1 be B1 - δ, to make B1 return to the left side of the intersection point. At this time, the existence interval of the intersection point is [B1, B2];

[0115] (4.5) Compare the iteration step size δ and the precision p; if δ > p, it means that the precision requirement is not met. Let δ be δ·η, and repeat from step (4.2). If δ < p, it means that the precision requirement is met. Take the midpoint of B1 and B2 as the solution result of B;

[0116] (4.6) Substitute the solution result of B obtained in step (4.5) into the binary equation F1(B, C) = 0 or F2(B, C) = 0, then C is obtained. Finally, A is obtained using equation (2).

[0117] Through the bisection method and Newton iteration method, C is obtained using the binary functions F1(B, C) = 0 and F2(B, C) = 0. For the solution problem of the binary function, since the function is relatively complex, a series of numerical calculation methods can be adopted, such as: bisection method, Newton iteration method, quadratic interpolation method, secant method, etc. After a large number of experiments and comparisons, it is found that the bisection method and Newton iteration method are more suitable for the solution of this binary function, and the Newton iteration method has higher efficiency.

[0118] According to the function graphs of F1 and F2 in the appendix Figure 4 it can be known that both F1 and F2 are monotonically increasing functions. Therefore, the bisection method can be used for calculation. The solution steps are as follows:

[0119] (1) Set the upper bound a and the lower bound b.

[0120] (2) Take the midpoint mid of the upper and lower bounds as the initial value. Then substitute mid as the value of C or B into F1 or F2. If the function value is greater than 0, it means that the center point mid is larger. Let the upper bound a = mid, and repeat from step (2).

[0121] (3) Otherwise, it means that the center point mid is smaller. Let the lower bound b = mid, and repeat from step (2).

[0122] (4) If the length between the upper and lower bounds is less than the precision requirement, it means that a valid result is found.

[0123] In addition, the Newton iteration method can be used to improve it. Numerical calculation methods such as the central difference method can be used to approximately replace the derivative function required in the Newton iteration method, and the accuracy can still be guaranteed. Through a large number of experiments, it is found that the Newton iteration method is very suitable for solving the above two equations. The fitting results of this embodiment are shown in Table 4 below:

[0124] Table 4 Fitting results of the new method for data;

[0125]

[0126] Under a richer sample, Figures 5-6 Intuitively shows the difference between the new method and the linear regression method introducing the minimum residual. Among them, Figure 5 Shows the difference in the rheological parameter values obtained by the new method and linear regression; Figure 6 Represents the comparison of the errors (calculated value - measured value) of the two fitting methods. It can be seen that the new method has a smaller error and the calculated value does not deviate significantly from the measured value.

[0127] Using the traditional linear regression to fit the rheological parameters and comparing the performance of the new fitting method, including:

[0128] (1) Through mathematical transformation, the rheological equation in the R-S mode is transformed into a linear form. Taking the logarithm of both sides of the equation, we get:

[0129] lnτ = lnA + Bln(γ + C);

[0130] (2) Since the R-S mode is a three-parameter rheological mode, first fix the value of C, and then use the linear least squares method to further obtain A and B. To ensure the fitting effect, the C value point with the smallest fitting residual can be taken. After research, it is found that the residual image is a concave function that first decreases and then increases. Methods such as the bisection method, secant method, and golden section method can be used to solve the C value point with the smallest residual, and then further obtain the rheological parameters A and B;

[0131] (3) Using fitting evaluation indicators such as error, average error, variance, and mean to compare the performance of the new method and the linear regression method, it is found that the new method is superior to the latter in both accuracy and stability.

[0132] Let y = lnτ, x = ln(x + C), D = lnA, then equation (5) can be simplified to:

[0133] y = Bx + D;

[0134] The linear regression least squares method can be used to fit B and D, and then all rheological parameters can be obtained. However, the premise is that a C value needs to be assumed. To ensure the fitting effect, the C value point with the smallest fitting residual can be taken. After research, it is found that the residual image is a concave function that first decreases and then increases. Methods such as the bisection method, secant method, and golden section method can be used to solve the C value point with the smallest residual, and then the rheological parameters A and B can be further obtained. Here, the bisection method is used to solve the C value point with the smallest fitting residual, and A and B are further obtained.

[0135] The fitting results of the linear regression method are shown in Table 5.

[0136] Table 5 Fitting results of the linear regression method for the data;

[0137]

[0138]

[0139] The R-S model is applicable to the temperature-pressure correction model f(P, T) under high-temperature and high-pressure conditions as shown in Equation (5):

[0140] f(P, T) = a + bT + cT 2 + d(PT + exp(P)) (5);

[0141] Among them, a, b, c, and d are characteristic constants, and P and T are pressure and temperature; for the R-S model, f(P, T) represents the value of the consistency coefficient A, flow index B, or initial shear rate C; exp() represents the exponential function with the base e of the natural logarithm.

[0142] Verify the proposed temperature-pressure correction model, including:

[0143] (1) Use the nonlinear least squares method to fit the correction model to obtain the characteristic constants a, b, c, and d;

[0144] (2) Use the obtained correction formula to calculate the predicted values of the rheological parameters at different temperatures and pressures;

[0145] (3) Compare with the rheological experimental data obtained in step 1, and use the coefficient of determination (R 2 ), mean square error (MSE), mean absolute error (MAE), etc. to evaluate the regression effect to test the accuracy of the prediction model. It is found that the correction model can well predict the rheological properties of drilling fluids under different temperature and pressure conditions, and the coefficient of determination is above 0.8. For drilling fluids that are more in line with the R-S fluid characteristics, the coefficient of determination exceeds 0.95; the coefficient of determination is shown in Table 6:

[0146] Table 6 Temperature-pressure correction prediction effect for the data;

[0147]

[0148] Figure 9 The comparison between the predicted values and the measured values calculated by the calibration model for this embodiment.

[0149] (4) Using the publicly available dataset of high-temperature and high-pressure rheology experiments, the accuracy of the calibration model was further verified, and good results were obtained.

[0150] The publicly available dataset of rheology experiments is shown in Table 7 below:

[0151] Table 7 Publicly available rheology experiment data;

[0152]

[0153]

[0154] (2) Using the non-linear least squares method to fit the calibration model to obtain the characteristic constants a, b, c, and d;

[0155] (3) Using the obtained calibration formula to calculate the predicted values of the rheological parameters at different temperatures and pressures;

[0156] (4) Comparing with the publicly available data, using the coefficient of determination (R 2 ), mean square error (MSE), mean absolute error (MAE), etc. to evaluate the regression effect and to test the accuracy of the prediction model, and it was found that the calibration model can well predict the rheological properties of drilling fluids under different temperature and pressure conditions. The coefficient of determination is shown in Table 8 below;

[0157] Table 8 Coefficient of determination;

[0158]

[0159] Figure 8 The comparison between the predicted values and the measured values calculated by the calibration model for this embodiment.

[0160] Calculating the predicted values of the rheological parameters at different temperatures and pressures using the temperature-pressure calibration model; including:

[0161] Using the rheological parameters at different temperatures and pressures obtained in step 1, and using the least squares method to fit the R-S model proposed in step 3 to the temperature-pressure calibration model applicable to high-temperature and high-pressure conditions to obtain the fitted temperature-pressure calibration formula, and using the fitted temperature-pressure calibration formula to calculate the values of each rheological parameter at different temperatures and pressures.

[0162] Example 3

[0163] A computer device includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the steps of a method for determining multiple parameters of a drilling fluid rheological mode in a wide temperature and pressure range described in Embodiment 1 or 2 are implemented.

[0164] Embodiment 4

[0165] A computer-readable storage medium stores a computer program thereon. When the computer program is executed by a processor, the steps of a method for determining multiple parameters of a drilling fluid rheological mode in a wide temperature and pressure range described in Embodiment 1 or 2 are implemented.

Claims

1. A method for determining multiple parameters of the rheological model of a drilling fluid in a wide temperature and pressure range, characterized in that, Including: Step 1: Conduct rheological characteristic experiments. Measure the rheological parameters of the drilling fluid sample at different rotational speeds under different temperatures and pressures. Step 2: Use the non-linear least squares method to fit the rheological parameters of the R-S model. Step 3: Plot the images of different rheological parameters changing with temperature and pressure to obtain the temperature-pressure correction model applicable to high-temperature and high-pressure conditions for the R-S model. Step 4: Use the temperature-pressure correction model to calculate the predicted values of the rheological parameters at different temperatures and pressures.

2. The method for determining multiple parameters of the rheological model of a drilling fluid in a wide temperature and pressure range according to claim 1, wherein Use an OFITE high-temperature and high-pressure rotational viscometer to conduct rheological characteristic experiments. Measure the rheological parameters (i.e., shear stress) of the drilling fluid sample at different rotational speeds (i.e., shear rates) under different temperatures and pressures. The temperature range is 18°C - 200°C, and the pressure range is 6.89 MPa - 172.37 Mpa.

3. The multi-parameter determination method for the rheological mode of a wide-temperature and wide-pressure-range drilling fluid according to claim 1, wherein Use the non-linear least squares method to fit the rheological parameters of the R-S model, including: (1) According to the least squares method, derive the least squares fitting objective function f for the R-S model as shown in Equation (1). In Equation (1), N represents a total of N pairs of shear rate and shear stress, τ i represents the i-th shear stress, γ i represents the i-th shear rate, A represents the consistency coefficient, B represents the flow behavior index, and C represents the initial shear rate; (2) Respectively take the partial derivatives of the rheological parameters A, B, and C in the least squares fitting objective function f, and after arrangement, obtain a set of partial derivative variances about A, B, and C as shown in Equation (2), Equation (3), and Equation (4). In Formula (2), Formula (3), and Formula (4), x is γ i , and y is τ i ; (3) Regard Equation (3) and Equation (4) as the binary functions F1(B,C)=0 and F2(B,C)=0 respectively. Plot the binary function images and find that the binary functions F1(B,C)=0 (i.e., function F1) and F2(B,C)=0 (i.e., function F2) derived in the R-S model have the same rules, including: Functions F1 and F2 have and only have one intersection point in the first quadrant. Functions F1 and F2 both show the property of monotonically increasing. Before the intersection point, the function image of F1 is above the function image of F2; after the intersection point, the function image of F2 is above the function image of F1. (4) Use the discovered rules to propose a new fitting method for the R-S model, specifically: (4.1) Set a small positive number as the iteration step size δ, set the magnification factor η for each step size contraction, set the size of the precision requirement p, where p represents the calculation precision requirement in the iteration process. Let B1 = δ, and B1 is the value of B in F1(B,C) and also the initial value of B for iterative calculation. (4.2) Let F1(B,C)=0, B = B1, find the corresponding C value of B1, and then use F2(B,C)=0 to find the corresponding B2 of C, where B2 is the value of B in F2(B,C). (4.3) If B2 > B1, it means on the left side of the intersection point. Let B1 be B1 + δ, and repeat from step (4.2) to continue iterating to the right, that is, take the value of the current B1 point more on the right side in the coordinate system and calculate again. (4.4) Otherwise, it means just passing through the intersection point to reach the right side of the intersection point. Let B1 be B1 - δ to make B1 return to the left side of the intersection point. At this time, the existence interval of the intersection point is [B1, B2]. (4.5) Compare the magnitudes of the iterative step size δ and the precision p; if δ > p, it indicates that the precision requirement is not met. Let δ be δ·η, and repeat from step (4.2). If δ < p, it indicates that the precision requirement is met, and take the midpoint of B1 and B2 as the solution result of B; (4.6) Substitute the solution result of B obtained in step (4.5) into the binary equation F1(B,C) = 0 or F2(B,C) = 0, then C can be obtained. Finally, A is obtained using equation (2).

4. A method for determining multiple parameters of a rheological model of a wide-temperature and wide-pressure-range drilling fluid according to claim 3, characterized in that By the bisection method and the Newton iteration method, C is obtained using the binary functions F1(B,C) = 0 and F2(B,C) = 0.

5. A method for determining multiple parameters of a rheological model of a drilling fluid in a wide temperature and pressure range according to claim 1, characterized in that, The R-S mode is applicable to the temperature-pressure correction model f(P,T) under high temperature and high pressure conditions as shown in equation (5): f(P,T) = a + bT + cT 2 + d(PT + exp(P)) (5); Where a, b, c, and d are characteristic constants, and P and T are pressure and temperature; for the R-S mode, f(P,T) represents the value of the consistency coefficient A, the flow index B, or the initial shear rate C; exp() represents the exponential function with the base e of the natural logarithm.

6. A method for determining multiple parameters of the rheological model of a drilling fluid in a wide temperature and pressure range according to any one of claims 1-5, characterized in that, Calculate the predicted values of the rheological parameters at different temperatures and pressures using the temperature-pressure correction model; including: Using the rheological parameters at different temperatures and pressures obtained in step 1, the temperature-pressure correction model applicable to high temperature and high pressure conditions proposed in step 3 is fitted by the least squares method to obtain the fitted temperature-pressure correction formula. Using the fitted temperature-pressure correction formula, the values of each rheological parameter at different temperatures and pressures are calculated.

7. A computer device, comprising a memory and a processor, the memory storing a computer program, characterized in that, When the processor executes the computer program, it implements the steps of a method for determining multiple parameters of a wide temperature and pressure range drilling fluid rheological mode according to any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of a method for determining multiple parameters of a wide temperature and pressure range drilling fluid rheological mode according to any one of claims 1-6.

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