High-temperature and ultrahigh-pressure gas reservoir deviation factor correction method

Abstract

The invention provides a high-temperature and ultrahigh-pressure gas reservoir deviation factor correction method, and belongs to the technical field of gas reservoir development. Based on the DPR relational expression, the quasi-contrast temperature, the quasi-contrast pressure and the gas contrast density are introduced, the multiple nonlinear regression method is adopted to establish functions of the high-temperature and ultrahigh-pressure gas reservoir deviation factor, the quasi-contrast temperature and the quasi-contrast pressure, and high-pressure data in the DPR relational expression are corrected, so that the high-temperature and ultrahigh-pressure gas reservoir deviation factor is obtained. And the deviation factor correction method suitable for the high-temperature and high-pressure gas reservoir is obtained. The method is suitable for different natural gas components, natural gas deviation factors under the conditions of any working temperature and any working pressure can be determined in a more targeted mode through the provided deviation factor correction method, the method is particularly suitable for ultra-deep high-temperature and high-pressure gas reservoirs, and therefore the pertinence is higher. Compared with a traditional deviation factor determination method, the method has the advantages of being simple, convenient, higher in pertinence, better in practicability and the like, and therefore the method has good application and popularization value.

Description

Technical Field

[0001] The invention relates to the technical field of gas reservoir development, and in particular to a method for correcting deviation factors of high-temperature and ultra-high-pressure gas reservoirs. Background Art

[0002] At present, the exploration and development of fossil fuels has turned to deep unconventional oil and gas reservoirs. Due to the high degree of thermal evolution, deep oil and gas resources are mainly natural gas. These gas reservoirs generally have complex characteristics such as strong geostress, strong heterogeneity, high temperature (above 150℃) and high pressure (above 70Mpa). The depth of some gas reservoirs exceeds 8000m, and the matrix is ​​low in porosity and permeability (average porosity is 6%, average permeability is 0.05×10 -3 μm 2 ). The formation temperature is as high as 190℃ (average air temperature 143℃), and the formation pressure is as high as 170MPa (average pressure 118MPa). The ground stress is as high as 180MPa (average ground stress 130MPa, stress difference 60MPa). For this type of gas reservoir, it is crucial to accurately calculate the PVT property parameters of the reservoir fluid. For example, the gas deviation factor is of great significance to the production dynamic analysis and dynamic reserve calculation during the development of oil and gas fields. The deviation factor is a dimensionless quantity with different names such as compression factor, gas supercompression coefficient, Z factor, and gas deviation factor. It indicates the degree to which the actual gas deviates from the ideal gas and is a function of temperature (T), pressure (P) and gas composition. It is generally defined as the ratio of the actual volume of a gas (at its pressure and temperature) to the ideal volume of a gas (under standard conditions) whose molecules are not attractive.

[0003] At present, the main methods for obtaining the deviation factor of high-temperature and high-pressure gas are experimental measurement method, Standing-Katz plate method and formula method.

[0004] The experimental measurement method has a long test cycle, high experimental cost, and the test temperature and pressure range are limited by experimental conditions. In well test design and interpretation, experimental measurement methods are rarely used to obtain gas deviation factors.

[0005] The Standing-Katz diagram is a relationship between the deviation factor and the pseudo-critical temperature and pseudo-critical pressure established by Standing-Katz (1942) through experiments. At the same time, the standard Standing-Katz is currently recognized by the industry as a highly reliable method for calculating the deviation factor of gases, but this method is difficult to implement through programming.

[0006] The formula method is the most common method for calculating the gas deviation factor in well testing. The formula method is convenient for computer programming, but the scope of application of different methods is different, and it is necessary to select the appropriate calculation method. Hall and Yarborough obtained a method for calculating the gas deviation factor based on the Starling-Carnahan state equation, called the HY method (1973, 1974). Based on the Benedict-Webb-Rubin (1940) state equation, Dranchuk, Purvis and Robinson (1973) obtained an eight-coefficient gas deviation factor calculation method, namely the DPR method. Dranchuk and Abu-Kassem (1975) derived an 11-coefficient gas deviation factor calculation method based on the Starling-Carnahan state equation, namely the Dranchuk-Abu-Kassem method. Beggs and Brill (1977) proposed a method for calculating the gas deviation factor, called the BB method. Londono et al. (2002) refitted the chart with an expanded data set and obtained a correction method that can be used to accurately determine the deviation factor. They provided two equations: one equation is applicable to the data set extended from the standard Standing-Katz deviation factor diagram, and the other equation contains single-component data. Li Xiangfang et al. (2012) proposed a gas deviation factor calculation method applicable to the full temperature and pressure range by fitting the Standing-Katz diagram. Unfortunately, the pressure range of these deviation factor methods is mostly below 150MPa. In addition, these relationships will produce large errors at higher gas reservoir pressures, and the errors may exceed 100%. Errors in calculating the deviation factor will lead to errors in estimating other gas properties, such as gas formation volume coefficient, gas compressibility coefficient, and dynamic reserves.

[0007] The maximum pressure range of the deviation factor calculation method in the current commercial software is 135MPa. For ultra-high pressure (above 105MPa) measured bottom hole pressure that exceeds the calculation range, and for exploration wells with estimated formation pressure above 150MPa, the use of conventional deviation factor calculation methods will produce large errors. The bottom hole pressure calculated using conventional deviation factor calculation methods will also produce large errors, which will seriously affect the calculation of on-site vertical pipe flow and the early assessment of recoverable reserves. Summary of the invention

[0008] In order to solve the low precision existing in the prior art, meet the construction requirements of high temperature and ultra-high pressure (200℃, 200MPa), and better guide the on-site production problems, the present invention provides a method for correcting the deviation factor of high temperature and ultra-high pressure gas reservoirs. Based on the Dranchuk-Purvis-Robinson (abbreviated as DPR) relationship, the pseudo-comparison temperature, pseudo-comparison pressure and gas contrast density are introduced, and the multivariate nonlinear regression method is used to establish the function of the deviation factor of the high temperature and ultra-high pressure gas reservoir with the pseudo-comparison temperature and pseudo-comparison pressure. By correcting the high pressure data in the DPR relationship, a deviation factor correction method suitable for high temperature and high pressure gas reservoirs is obtained. The deviation factor of a well under formation conditions can be predicted by using the corrected deviation factor, and the relationship between the deviation factor and pressure at different temperatures is given. The method of the present invention is applicable to different natural gas components. The proposed deviation factor correction method can be used to more specifically determine the natural gas deviation factor under any working temperature and any working pressure conditions, and is particularly suitable for ultra-deep high temperature and high pressure gas reservoirs, so it is more targeted. Compared with the traditional deviation factor determination method, the method of the present invention has the characteristics of being simple and convenient, more targeted, and better practical, and thus has a good value for promotion and use.

[0009] The present invention provides a method for correcting a deviation factor of a high-temperature and ultra-high-pressure gas reservoir, comprising the following steps:

[0010] Based on the Dranchuk-Purvis-Robinson relationship, the pseudo-comparison temperature, pseudo-comparison pressure and gas contrast density are introduced, and the coefficients related to the high-pressure data in the Dranchuk-Purvis-Robinson relationship are corrected to obtain the modified Dranchuk-Purvis-Robinson relationship. According to the modified Dranchuk-Purvis-Robinson relationship, the deviation factor calculation formula of high-temperature and ultra-high-pressure gas reservoirs is obtained, wherein the pseudo-comparison temperature is obtained according to the pseudo-critical temperature, the pseudo-comparison pressure is obtained according to the pseudo-critical pressure, and the gas contrast density is obtained according to the pseudo-comparison temperature and the pseudo-comparison pressure. The deviation factor calculation formula of high-temperature and ultra-high-pressure gas reservoirs is as follows:

[0011]

[0012] in,

[0013] Z is the deviation factor of high-temperature and ultra-high-pressure gas reservoirs, dimensionless;

[0014] ρ r is the relative density of gas, dimensionless;

[0015]

[0016]

[0017]

[0018]

[0019] T pr is the temperature to be compared, dimensionless;

[0020] A1, A2, A3, A4, A5, A6, A7, and A8 are the coefficients of the Dranchuk-Purvis-Robinson relationship.

[0021] Preferably, the relative density of a gas is the ratio of the density of a gas at a specific pressure and a specific temperature to its density at a critical pressure and a critical temperature.

[0022] Preferably, the following functional relationship is used between the quasi-comparative temperature and the quasi-critical temperature, and between the quasi-comparative pressure and the quasi-critical pressure:

[0023] Pseudo-comparative pressure = gas pressure / pseudo-critical pressure;

[0024] Pseudo-comparative temperature = gas temperature / pseudo-critical temperature.

[0025] Preferably, a sensitivity analysis is performed on the coefficients in the Dranchuk-Purvis-Robinson relationship and the deviation factor to obtain the coefficients that have an impact on the deviation factor under high pressure.

[0026] Preferably, a sensitivity analysis is performed on the coefficients and the deviation factor in the Dranchuk-Purvis-Robinson relationship by using the gas relative density to obtain the coefficients that have an impact on the deviation factor under high pressure.

[0027] Preferably, the coefficients in the Dranchuk-Purvis-Robinson relationship that affect the deviation factor beyond a preset range under high pressure are corrected to obtain a corrected deviation factor for a high-temperature and ultra-high-pressure gas reservoir.

[0028] Preferably, the coefficient A4 and the coefficient A6 in the Dranchuk-Purvis-Robinson relationship are fitted using a multivariate nonlinear regression method to obtain a corrected coefficient A4 and a new coefficient A6.

[0029] Preferably, the values ​​of coefficient A4 and coefficient A6 in the Dranchuk-Purvis-Robinson relationship are used as the initial values ​​of the nonlinear regression of coefficient A4 and coefficient A6 in the Dranchuk-Purvis-Robinson relationship in the deviation factor calculation formula, and the coefficient A4 and coefficient A6 in the Dranchuk-Purvis-Robinson relationship in the deviation factor calculation formula are corrected using least squares iteration.

[0030] Preferably, according to coefficients A4 and A6 of the modified Dranchuk-Purvis-Robinson relation, nonlinear regression of gas relative density in the prediction deviation factor calculation formula using the modified DPR relation is performed.

[0031] Preferably, according to the coefficients A4 and A6 of the modified Dranchuk-Purvis-Robinson relation, nonlinear regression of the gas relative density in the prediction deviation factor calculation formula using the modified DPR relation is performed to obtain the coefficients in the high-temperature and ultra-high-pressure gas reservoir deviation factor calculation formula, which specifically includes the following steps:

[0032] The A4 value and the A6 value in the DPR relationship are taken as the initial values ​​of A4 and A6, and the initial gas relative density is taken as the gas relative density;

[0033] Gas contrast density iterative calculation operation:

[0034] Substitute the latest A4 value, the latest A6 value and the latest gas relative density into the gas relative density equation to calculate the new gas relative density;

[0035] If the absolute value of the difference between the new gas relative density and the initial gas relative density is within the preset error range, a least squares nonlinear regression fitting operation is performed for the new A4 value and A6 value;

[0036] If the absolute value of the difference between the new gas contrast density and the initial gas contrast density exceeds the preset error range, otherwise the iterative calculation operation of the gas contrast density is continued until the absolute value of the difference between the new gas contrast density and the last calculated gas contrast density is within the preset error range, the iterative calculation operation of the gas contrast density is stopped, and the least squares nonlinear regression fitting operation of the new A4 value and A6 value is performed;

[0037] The operation of least squares nonlinear regression fitting new A4 and A6 values ​​is as follows:

[0038] According to the experimental data, new A4 and A6 values ​​are obtained by least squares nonlinear regression fitting. If the absolute value of the difference between the new A4 and A6 values ​​obtained by the previous fitting and the A4 and A6 values ​​obtained by the previous fitting exceeds the preset error range, the gas relative density iteration calculation operation will be performed. Otherwise, the new A4 and A6 values ​​obtained by the fitting will be used as the corrected A4 and A6 values, and the least squares nonlinear regression fitting operation of the new A4 and A6 values ​​will be terminated.

[0039] The gas relative density equation is as follows:

[0040]

[0041] Preferably, the corrected A4 value and A6 value are substituted into the high-temperature and ultra-high-pressure gas reservoir deviation factor calculation formula to obtain the high-temperature and ultra-high-pressure gas reservoir deviation factor;

[0042] Preferably, the following linear extrapolation method is used for feasibility analysis:

[0043] In the ultra-high pressure stage, the deviation factor is linearly related to the pressure. The deviation factor can be obtained by linearly extrapolating the high pressure stage data at different temperatures. From thermodynamics, we know that the general formula of the fluid state equation is:

[0044] P=P R -P A (1)

[0045] in,

[0046] P is the intermolecular interaction force, MPa;

[0047] P R is the intermolecular repulsion, MPa;

[0048] P A is the intermolecular attraction, MPa.

[0049] According to the above formula, the general formula of the two-parameter state equation can be written as:

[0050]

[0051] in,

[0052] R is the state equation constant, R = 8.3145;

[0053] T is temperature, K;

[0054] V is volume, m 3 ;

[0055] a and b are empirical constants of the state equation.

[0056] When u and w take different values, the above formula can be transformed into different state equations.

[0057] According to the theory of molecular motion, there is an interaction force between gas molecules. When the distance between molecules is large, the interaction force generally manifests as attraction; but when the molecules gradually get closer, the attraction gradually weakens and mainly manifests as repulsion. Under ultra-high pressure, gas molecules are in close contact with each other. Due to the mutual repulsion between electron clouds and atomic nuclei, the intermolecular force is prominently manifested as repulsion.

[0058] At this time, formula (2) can be simplified to

[0059]

[0060] Introducing the deviation factor Z

[0061]

[0062] Substituting (4) into (3), we get

[0063]

[0064] It can be seen from formula (4) that when the gas molecules are under high pressure and the intermolecular interaction is mainly manifested as repulsion, the deviation factor changes linearly with pressure and its slope is a positive number, namely b / RT.

[0065] Formula (4) is theoretically applicable to pure components, but can be extended to mixtures through the mixing rules.

[0066] By introducing the quasi-comparison pressure and quasi-comparison temperature, equation (4) is transformed into

[0067]

[0068] in,

[0069] P pr =P / P pc ,

[0070] T pr =T / T pc ,

[0071]

[0072]

[0073] P pr It is the pressure to be compared, dimensionless;

[0074] T pr is the temperature to be compared, dimensionless;

[0075] P pcis the pseudo-critical pressure, MPa;

[0076] T pc is the pseudo-critical temperature, K;

[0077] P ci is the critical pressure of component i, MPa;

[0078] T ci is the critical temperature of component i, K;

[0079] x i is the mole fraction of component i.

[0080] From formula (6), we can see that at a given temperature or quasi-comparison temperature, the deviation factor Z is related to the quasi-comparison pressure p pr There is a linear relationship.

[0081] At the same time, according to the experimental data of a certain well, when the pressure is greater than 60MPa, the deviation factor and pressure at different temperatures (such as 158.63℃, 138.63℃, 118.63℃) show a linear relationship ( Figure 1 ), and the correlation coefficients are all 1. This shows that under ultra-high pressure conditions, it is theoretically valid to obtain the deviation factor based on the linear extrapolation of the high-pressure stage data.

[0082] Preferably, the following method is used to perform sensitivity analysis of the DPR relationship coefficient to the deviation factor:

[0083] The gas contrast density is introduced to calculate the gas deviation factor, gas contrast density ρ r It is defined as the ratio of the density at a specific pressure and a specific temperature to its density at the critical pressure and critical temperature:

[0084]

[0085] Critical gas deviation factor Z c is about 0.27, and the gas relative density expression is simplified to:

[0086]

[0087] The equation for calculating the relative density of a gas is:

[0088]

[0089] in,

[0090]

[0091]

[0092]

[0093]

[0094]

[0095] A1=0.31506237; A2=-1.0467099; A3=-0.57832729; A4=0.53530771;

[0096] A5=-0.61232032; A6=-0.10488813; A7=0.68157001; A8=0.68157001;

[0097] P pr It is the pressure to be compared, dimensionless;

[0098] T pr is the temperature to be compared, dimensionless;

[0099] ρ r is the relative density of gas;

[0100] ρ in formula (9) r It needs to be solved by Newton's iteration method. Newton's iteration method is a general method. Since equation (9) is implicit, an initial value is given and substituted into equation (9) to calculate until the left side of the equation is equal to the right side, which is the comparison density value after the last iteration.

[0101] The DPR relationship contains eight coefficients, A1, A2, A3, A4, A5, A6, A7 and A8. The values ​​of these eight coefficients are analyzed for sensitivity to the deviation factor;

[0102] It is found that coefficients A4 and A6 in the DPR relationship are most sensitive to the deviation factor.

[0103] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0104] (1) The method proposed in the present invention adopts a multivariate nonlinear regression method, based on experimental data fitting, and the obtained deviation factor is more accurate and applicable to different natural gas components. The proposed deviation factor correction method can be used to more specifically determine the natural gas deviation factor under any working temperature and any working pressure conditions, and is particularly suitable for ultra-deep high-temperature and high-pressure gas reservoirs, so it is more targeted. Compared with the traditional deviation factor determination method, the method of the present invention has the characteristics of simplicity, convenience, stronger targeting, better practicality, etc., and therefore has a good value for promotion and use.

[0105] (2) The deviation factor technical method proposed in the present invention is easy to implement through programming and can be compiled into software for execution, thus providing a good pre-processing module for subsequent well test interpretation and also providing accurate guarantee for subsequent vertical pipe flow calculation and gas reservoir dynamic reserve calculation.

[0106] (3) The present invention adopts a method that combines experimental data with theoretical calculations. The principle is reliable and the operation is simple, which ensures the reliability and universality of the method. It has broad application prospects and can provide important technical support for the development of ultra-deep high-temperature and high-pressure natural gas reservoirs and natural gas storage and transportation. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 A regression curve of high pressure experimental data of a certain P1 well deviation factor according to an embodiment of the present invention;

[0108] Figure 2 In the figure, (a) is a sensitivity analysis of coefficient A1 to the deviation factor in the DPR relationship of an embodiment of the present invention, (b) is a sensitivity analysis of coefficient A2 to the deviation factor in the DPR relationship of an embodiment of the present invention, (c) is a sensitivity analysis of coefficient A3 to the deviation factor in the DPR relationship of an embodiment of the present invention, (d) is a sensitivity analysis of coefficient A4 to the deviation factor in the DPR relationship of an embodiment of the present invention, (e) is a sensitivity analysis of coefficient A5 to the deviation factor in the DPR relationship of an embodiment of the present invention, (f) is a sensitivity analysis of coefficient A6 to the deviation factor in the DPR relationship of an embodiment of the present invention, (g) is a sensitivity analysis of coefficient A7 to the deviation factor in the DPR relationship of an embodiment of the present invention, (h) is a sensitivity analysis of coefficient A8 to the deviation factor in the DPR relationship of an embodiment of the present invention;

[0109] Figure 3 is a multivariate nonlinear regression correction flow chart of an embodiment of the present invention, wherein ε is a preset error range;

[0110] Figure 4 The deviation factor after correction at 158.63°C of one embodiment of the present invention is compared with the data before correction and the experimental data;

[0111] Figure 5 In the figure, (a) is a comparison result of the deviation factor after correction and the deviation factor before correction and experimental data at 138.63°C of an embodiment of the present invention; (b) is a comparison result of the deviation factor after correction and the deviation factor before correction and experimental data at 118.63°C of an embodiment of the present invention;

[0112] Figure 6 The deviation factor experimental data of a certain well in one embodiment of the present invention;

[0113] Figure 7 This is a comparison diagram of the deviation factors of a certain well before and after correction according to an embodiment of the present invention. DETAILED DESCRIPTION

[0114] The specific implementation modes of the present invention are described in detail below in conjunction with the accompanying drawings.

[0115] The present invention provides a method for correcting a deviation factor of a high-temperature and ultra-high-pressure gas reservoir, comprising the following steps:

[0116] The present invention provides a method for correcting a deviation factor of a high-temperature and ultra-high-pressure gas reservoir, comprising the following steps:

[0117] Based on the Dranchuk-Purvis-Robinson relationship, the pseudo-comparison temperature, pseudo-comparison pressure and gas contrast density are introduced, and the coefficients related to the high-pressure data in the Dranchuk-Purvis-Robinson relationship are corrected to obtain the modified Dranchuk-Purvis-Robinson relationship. According to the modified Dranchuk-Purvis-Robinson relationship, the deviation factor calculation formula of high-temperature and ultra-high-pressure gas reservoirs is obtained, wherein the pseudo-comparison temperature is obtained according to the pseudo-critical temperature, the pseudo-comparison pressure is obtained according to the pseudo-critical pressure, and the gas contrast density is obtained according to the pseudo-comparison temperature and the pseudo-comparison pressure. The deviation factor calculation formula of high-temperature and ultra-high-pressure gas reservoirs is as follows:

[0118]

[0119] in,

[0120] Z is the deviation factor of high-temperature and ultra-high-pressure gas reservoirs, dimensionless;

[0121] ρ r is the relative density of gas, dimensionless;

[0122]

[0123]

[0124]

[0125]

[0126] T pr is the temperature to be compared, dimensionless;

[0127] A1, A2, A3, A4, A5, A6, A7, and A8 are the coefficients of the Dranchuk-Purvis-Robinson relationship.

[0128] According to a specific embodiment of the present invention, the relative density of a gas is the ratio of the density of a gas at a specific pressure and a specific temperature to the density of a gas at a critical pressure and a critical temperature.

[0129] According to a specific embodiment of the present invention, the following functional relationship is used between the pseudo-comparative temperature and the pseudo-critical temperature, and between the pseudo-comparative pressure and the pseudo-critical pressure:

[0130] Pseudo-comparative pressure = gas pressure / pseudo-critical pressure;

[0131] Pseudo-comparative temperature = gas temperature / pseudo-critical temperature.

[0132] According to a specific embodiment of the present invention, a sensitivity analysis is performed on the coefficients and the deviation factor in the Dranchuk-Purvis-Robinson relationship to obtain the coefficients that have an impact on the deviation factor under high pressure.

[0133] According to a specific embodiment of the present invention, a sensitivity analysis is performed on the coefficients and the deviation factor in the Dranchuk-Purvis-Robinson relationship by using the gas relative density to obtain the coefficients that have an impact on the deviation factor under high pressure.

[0134] According to a specific embodiment of the present invention, the coefficient of the Dranchuk-Purvis-Robinson relationship that affects the deviation factor beyond a preset range under high pressure is corrected to obtain a corrected high-temperature and ultra-high-pressure gas reservoir deviation factor.

[0135] According to a specific embodiment of the present invention, the coefficient A4 and the coefficient A6 in the Dranchuk-Purvis-Robinson relationship are fitted using a multivariate nonlinear regression method to obtain a revised coefficient A4 and a new coefficient A6.

[0136] According to a specific embodiment of the present invention, the values ​​of coefficient A4 and coefficient A6 in the Dranchuk-Purvis-Robinson relationship are used as the initial values ​​of the nonlinear regression of coefficient A4 and coefficient A6 in the Dranchuk-Purvis-Robinson relationship in the deviation factor calculation formula, and the coefficient A4 and coefficient A6 of the Dranchuk-Purvis-Robinson relationship in the deviation factor calculation formula are corrected using least squares iteration.

[0137] According to a specific embodiment of the present invention, nonlinear regression of gas relative density in the prediction deviation factor calculation formula using the modified DPR relationship is performed based on coefficients A4 and A6 of the modified Dranchuk-Purvis-Robinson relationship.

[0138] According to a specific embodiment of the present invention, according to the coefficients A4 and A6 of the modified Dranchuk-Purvis-Robinson relation, a nonlinear regression of the gas relative density in the prediction deviation factor calculation formula using the modified DPR relation is performed to obtain the coefficients in the high-temperature and ultra-high-pressure gas reservoir deviation factor calculation formula, which specifically includes the following steps:

[0139] The A4 value and the A6 value in the DPR relationship are taken as the initial values ​​of A4 and A6, and the initial gas relative density is taken as the gas relative density;

[0140] Gas contrast density iterative calculation operation:

[0141] Substitute the latest A4 value, the latest A6 value and the latest gas relative density into the gas relative density equation to calculate the new gas relative density;

[0142] If the absolute value of the difference between the new gas relative density and the initial gas relative density is within the preset error range, a least squares nonlinear regression fitting operation is performed for the new A4 value and A6 value;

[0143] If the absolute value of the difference between the new gas contrast density and the initial gas contrast density exceeds the preset error range, otherwise the iterative calculation operation of the gas contrast density is continued until the absolute value of the difference between the new gas contrast density and the last calculated gas contrast density is within the preset error range, the iterative calculation operation of the gas contrast density is stopped, and the least squares nonlinear regression fitting operation of the new A4 value and A6 value is performed;

[0144] The operation of least squares nonlinear regression fitting new A4 and A6 values ​​is as follows:

[0145] According to the experimental data, new A4 and A6 values ​​are obtained by least squares nonlinear regression fitting. If the absolute value of the difference between the new A4 and A6 values ​​obtained by the previous fitting and the A4 and A6 values ​​obtained by the previous fitting exceeds the preset error range, the gas relative density iteration calculation operation will be performed. Otherwise, the new A4 and A6 values ​​obtained by the fitting will be used as the corrected A4 and A6 values, and the least squares nonlinear regression fitting operation of the new A4 and A6 values ​​will be terminated.

[0146] The gas relative density equation is as follows:

[0147]

[0148] According to a specific embodiment of the present invention, the corrected A4 value and A6 value are substituted into the high-temperature and ultra-high-pressure gas reservoir deviation factor calculation formula to obtain the high-temperature and ultra-high-pressure gas reservoir deviation factor;

[0149] According to a specific embodiment of the present invention, the feasibility analysis is performed using the following linear extrapolation method:

[0150] In the ultra-high pressure stage, the deviation factor is linearly related to the pressure. The deviation factor can be obtained by linearly extrapolating the high pressure stage data at different temperatures. From thermodynamics, we know that the general formula of the fluid state equation is:

[0151] P=P R -P A (10)

[0152] in,

[0153] P is the intermolecular interaction force, MPa;

[0154] P R is the intermolecular repulsion, MPa;

[0155] P A is the intermolecular attraction, MPa.

[0156] According to the above formula, the general formula of the two-parameter state equation can be written as:

[0157]

[0158] in,

[0159] R is the state equation constant, R = 8.3145;

[0160] T is temperature, K;

[0161] V is volume, m 3 ;

[0162] a and b are empirical constants of the state equation.

[0163] When u and w take different values, the above formula can be transformed into different state equations.

[0164] According to the theory of molecular motion, there is an interaction force between gas molecules. When the distance between molecules is large, the interaction force generally manifests as attraction; but when the molecules gradually get closer, the attraction gradually weakens and mainly manifests as repulsion. Under ultra-high pressure, gas molecules are in close contact with each other. Due to the mutual repulsion between electron clouds and atomic nuclei, the intermolecular force is prominently manifested as repulsion.

[0165] At this time, formula (2) can be simplified to

[0166]

[0167] Introducing the deviation factor Z

[0168]

[0169] Substituting (4) into (3), we get

[0170]

[0171] It can be seen from formula (4) that when the gas molecules are under high pressure and the intermolecular interaction is mainly manifested as repulsion, the deviation factor changes linearly with pressure and its slope is a positive number, namely b / RT.

[0172] Formula (4) is theoretically applicable to pure components, but can be extended to mixtures through the mixing rules.

[0173] By introducing the quasi-comparison pressure and quasi-comparison temperature, equation (4) is transformed into

[0174]

[0175] in,

[0176] P pr =P / P pc ,

[0177] T pr =T / T pc ,

[0178]

[0179]

[0180] P pr It is the pressure to be compared, dimensionless;

[0181] T pr is the temperature to be compared, dimensionless;

[0182] P pc is the pseudo-critical pressure, MPa;

[0183] T pc is the pseudo-critical temperature, K;

[0184] P ci is the critical pressure of component i, MPa;

[0185] T ci is the critical temperature of component i, K;

[0186] x i is the mole fraction of component i.

[0187] From formula (6), we can see that at a given temperature or quasi-comparison temperature, the deviation factor Z is related to the quasi-comparison pressure p pr There is a linear relationship.

[0188] At the same time, according to the experimental data of a certain well, when the pressure is greater than 60MPa, the deviation factor and pressure at different temperatures (such as 158.63℃, 138.63℃, 118.63℃) show a linear relationship ( Figure 1 ), and the correlation coefficients are all 1. This shows that under ultra-high pressure conditions, it is theoretically valid to obtain the deviation factor based on the linear extrapolation of the high-pressure stage data.

[0189] According to a specific embodiment of the present invention, the following method is used to perform sensitivity analysis of the DPR relationship coefficient to the deviation factor:

[0190] The gas contrast density is introduced to calculate the gas deviation factor, gas contrast density ρ r It is defined as the ratio of the density at a specific pressure and a specific temperature to its density at the critical pressure and critical temperature:

[0191]

[0192] Critical gas deviation factor Z c is about 0.27, and the gas relative density expression is simplified to:

[0193]

[0194] The equation for calculating the relative density of a gas is:

[0195]

[0196] in,

[0197]

[0198]

[0199]

[0200]

[0201]

[0202] A1=0.31506237; A2=-1.0467099; A3=-0.57832729; A4=0.53530771;

[0203] A5=-0.61232032; A6=-0.10488813; A7=0.68157001; A8=0.68157001;

[0204] P pr It is the pressure to be compared, dimensionless;

[0205] T pr is the temperature to be compared, dimensionless;

[0206] ρ r is the relative density of gas;

[0207] ρ in formula (9) r It needs to be solved by Newton's iteration method. Newton's iteration method is a general method. Since equation (9) is implicit, an initial value is given and substituted into equation (9) to calculate until the left side of the equation is equal to the right side, which is the comparison density value after the last iteration.

[0208] The DPR relationship contains eight coefficients, A1, A2, A3, A4, A5, A6, A7 and A8. The values ​​of these eight coefficients are analyzed for sensitivity to the deviation factor;

[0209] It is found that coefficients A4 and A6 in the DPR relationship are most sensitive to the deviation factor.

[0210] Example 1

[0211] According to a specific embodiment of the present invention, the deviation factor correction method of the high-temperature and ultra-high-pressure gas reservoir of the present invention is described in detail below.

[0212] The present invention provides a method for correcting a deviation factor of a high-temperature and ultra-high-pressure gas reservoir, comprising the following steps:

[0213] Based on the Dranchuk-Purvis-Robinson relationship, the pseudo-comparison temperature, pseudo-comparison pressure and gas contrast density are introduced, and the coefficients related to the high-pressure data in the Dranchuk-Purvis-Robinson relationship are corrected to obtain the modified Dranchuk-Purvis-Robinson relationship. According to the modified Dranchuk-Purvis-Robinson relationship, the deviation factor calculation formula of high-temperature and ultra-high-pressure gas reservoirs is obtained, wherein the pseudo-comparison temperature is obtained according to the pseudo-critical temperature, the pseudo-comparison pressure is obtained according to the pseudo-critical pressure, and the gas contrast density is obtained according to the pseudo-comparison temperature and the pseudo-comparison pressure. The deviation factor calculation formula of high-temperature and ultra-high-pressure gas reservoirs is as follows:

[0214]

[0215] in,

[0216] Z is the deviation factor of high-temperature and ultra-high-pressure gas reservoirs, dimensionless;

[0217] ρ r is the relative density of gas, dimensionless;

[0218]

[0219]

[0220]

[0221]

[0222] T pr is the temperature to be compared, dimensionless;

[0223] A1, A2, A3, A4, A5, A6, A7, and A8 are the coefficients of the Dranchuk-Purvis-Robinson relationship.

[0224] The relative density of a gas is the ratio of the density of a gas at a specific pressure and a specific temperature to its density at a critical pressure and a critical temperature.

[0225] Among them, the following functional relationship is used between the quasi-comparative temperature and the quasi-critical temperature, and between the quasi-comparative pressure and the quasi-critical pressure:

[0226] Pseudo-comparative pressure = gas pressure / pseudo-critical pressure;

[0227] Pseudo-comparative temperature = gas temperature / pseudo-critical temperature.

[0228] Among them, the sensitivity analysis of the coefficients and deviation factors in the Dranchuk-Purvis-Robinson relationship is carried out through the gas contrast density, and the coefficients in the Dranchuk-Purvis-Robinson relationship whose influence on the deviation factor exceeds the preset range under high pressure are corrected to obtain the coefficients that have an influence on the deviation factor under high pressure.

[0229] When a value is increased or decreased by 0.02 each time, the influence range of each coefficient on the deviation factor is obtained. Figure 2 .

[0230] based on Figure 2It can be seen that as the coefficient A1 changes in value, the deviation factor changes in different degrees (large changes) in the entire pressure range (0-160MPa), which does not meet the requirements of high-pressure correction, so A1 is not considered for correction. The sensitivity analysis of A2 and A5 shows that as the value changes, Z changes in different degrees (small changes) in the entire range, and no correction is considered; the change of the deviation factor of A3, A7 and A8 is not very obvious after a small change in the coefficient value, so no correction is considered. A4 has a basically unchanged deviation factor between 0-10MPa as the coefficient value changes, but the deviation factor changes greatly with pressure after the pressure is greater than 60MPa. A4 is more sensitive to high pressure and meets the requirements of correction. Similarly, A6 has a basically unchanged Z-factor between 0-40MPa as the coefficient value changes, but the Z-factor changes greatly with pressure after the pressure is greater than 60MPa. A4 is more sensitive to high pressure and meets the requirements of correction. A6 has a strong sensitivity to parameters after 60MPa, which fully meets the needs of fitting, so the nonlinear regression method is used for fitting of A4 and A6 parameters.

[0231] According to the coefficients A4 and A6 of the modified Dranchuk-Purvis-Robinson relation, nonlinear regression of the gas relative density in the calculation formula for the prediction deviation factor using the modified DPR relation is performed to obtain the coefficients in the calculation formula for the deviation factor of the high-temperature and ultra-high-pressure gas reservoir, which specifically includes the following steps:

[0232] The A4 value and the A6 value in the DPR relationship are taken as the initial values ​​of A4 and A6, and the initial gas relative density is taken as the gas relative density;

[0233] Gas contrast density iterative calculation operation:

[0234] Substitute the latest A4 value, the latest A6 value and the latest gas relative density into the gas relative density equation to calculate the new gas relative density;

[0235] If the absolute value of the difference between the new gas relative density and the initial gas relative density is within the preset error range, a least squares nonlinear regression fitting operation is performed for the new A4 value and A6 value;

[0236] If the absolute value of the difference between the new gas contrast density and the initial gas contrast density exceeds the preset error range, otherwise the iterative calculation operation of the gas contrast density is continued until the absolute value of the difference between the new gas contrast density and the last calculated gas contrast density is within the preset error range, the iterative calculation operation of the gas contrast density is stopped, and the least squares nonlinear regression fitting operation of the new A4 value and A6 value is performed;

[0237] The operation of least squares nonlinear regression fitting new A4 and A6 values ​​is as follows:

[0238] According to the experimental data, new A4 and A6 values ​​are obtained by least squares nonlinear regression fitting. If the absolute value of the difference between the new A4 and A6 values ​​obtained by the previous fitting and the A4 and A6 values ​​obtained by the previous fitting exceeds the preset error range, the gas relative density iteration calculation operation will be performed. Otherwise, the new A4 and A6 values ​​obtained by the fitting will be used as the corrected A4 and A6 values, and the least squares nonlinear regression fitting operation of the new A4 and A6 values ​​will be terminated.

[0239] The gas relative density equation is as follows:

[0240]

[0241] Substitute the corrected A4 and A6 values ​​into the high-temperature and ultra-high-pressure gas reservoir deviation factor calculation formula to obtain the high-temperature and ultra-high-pressure gas reservoir deviation factor;

[0242] Among them, the following linear extrapolation method is used for feasibility analysis:

[0243] In the ultra-high pressure stage, the deviation factor is linearly related to the pressure. The deviation factor can be obtained by linearly extrapolating the high pressure stage data at different temperatures. From thermodynamics, we know that the general formula of the fluid state equation is:

[0244] P=P R -P A (19)

[0245] in,

[0246] P is the intermolecular interaction force, MPa;

[0247] P R is the intermolecular repulsion, MPa;

[0248] P A is the intermolecular attraction, MPa.

[0249] According to the above formula, the general formula of the two-parameter state equation can be written as:

[0250]

[0251] in,

[0252] R is the state equation constant, R = 8.3145;

[0253] T is temperature, K;

[0254] V is volume, m 3 ;

[0255] a and b are empirical constants of the state equation.

[0256] When u and w take different values, the above formula can be transformed into different state equations.

[0257] According to the theory of molecular motion, there is an interaction force between gas molecules. When the distance between molecules is large, the interaction force generally manifests as attraction; but when the molecules gradually get closer, the attraction gradually weakens and mainly manifests as repulsion. Under ultra-high pressure, gas molecules are in close contact with each other. Due to the mutual repulsion between electron clouds and atomic nuclei, the intermolecular force is prominently manifested as repulsion.

[0258] At this time, formula (2) can be simplified to

[0259]

[0260] Introducing the deviation factor Z

[0261]

[0262] Substituting (4) into (3), we get

[0263]

[0264] It can be seen from formula (4) that when the gas molecules are under high pressure and the intermolecular interaction is mainly manifested as repulsion, the deviation factor changes linearly with pressure and its slope is a positive number, namely b / RT.

[0265] Formula (4) is theoretically applicable to pure components, but can be extended to mixtures through the mixing rules.

[0266] By introducing the quasi-comparison pressure and quasi-comparison temperature, equation (4) is transformed into

[0267]

[0268] in,

[0269] P pr =P / P pc ,

[0270] T pr =T / T pc ,

[0271]

[0272]

[0273] P pr It is the pressure to be compared, dimensionless;

[0274] T pr is the temperature to be compared, dimensionless;

[0275] P pc is the pseudo-critical pressure, MPa;

[0276] T pc is the pseudo-critical temperature, K;

[0277] P ci is the critical pressure of component i, MPa;

[0278] T ci is the critical temperature of component i, K;

[0279] x i is the mole fraction of component i.

[0280] From formula (6), we can see that at a given temperature or quasi-comparison temperature, the deviation factor Z is related to the quasi-comparison pressure p pr There is a linear relationship.

[0281] At the same time, according to the experimental data of a certain well, when the pressure is greater than 60MPa, the deviation factor and pressure at different temperatures (such as 158.63℃, 138.63℃, 118.63℃) show a linear relationship ( Figure 1 ), and the correlation coefficients are all 1. This shows that under ultra-high pressure conditions, it is theoretically valid to obtain the deviation factor based on the linear extrapolation of the high-pressure stage data.

[0282] Among them, the following method is used to perform sensitivity analysis of the DPR relationship coefficient to the deviation factor:

[0283] The gas contrast density is introduced to calculate the gas deviation factor, gas contrast density ρ r It is defined as the ratio of the density at a specific pressure and a specific temperature to its density at the critical pressure and critical temperature:

[0284]

[0285] Critical gas deviation factor Z c is about 0.27, and the gas relative density expression is simplified to:

[0286]

[0287] The equation for calculating the relative density of a gas is:

[0288]

[0289] in,

[0290]

[0291]

[0292]

[0293]

[0294]

[0295] A1=0.31506237; A2=-1.0467099; A3=-0.57832729; A4=0.53530771;

[0296] A5=-0.61232032; A6=-0.10488813; A7=0.68157001; A8=0.68157001;

[0297] P pr It is the pressure to be compared, dimensionless;

[0298] T pr is the temperature to be compared, dimensionless;

[0299] ρ r is the relative density of gas;

[0300] ρ in formula (9) r It needs to be solved by Newton's iteration method. Newton's iteration method is a general method. Since equation (9) is implicit, an initial value is given and substituted into equation (9) to calculate until the left side of the equation is equal to the right side, which is the comparison density value after the last iteration.

[0301] The DPR relationship contains eight coefficients, A1, A2, A3, A4, A5, A6, A7 and A8. The values ​​of these eight coefficients are analyzed for sensitivity to the deviation factor;

[0302] It is found that coefficients A4 and A6 in the DPR relationship are most sensitive to the deviation factor.

[0303] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A method for correcting deviation factors of high temperature and ultrahigh pressure gas reservoirs, characterized in that: The steps include: Based on the Dranchuk-Purvis-Robinson relationship, the pseudo-comparison temperature, pseudo-comparison pressure and gas contrast density are introduced, and the coefficients related to the high-pressure data in the Dranchuk-Purvis-Robinson relationship are corrected to obtain the modified Dranchuk-Purvis-Robinson relationship. According to the modified Dranchuk-Purvis-Robinson relationship, the deviation factor calculation formula of high-temperature and ultra-high-pressure gas reservoirs is obtained, wherein the pseudo-comparison temperature is obtained according to the pseudo-critical temperature, the pseudo-comparison pressure is obtained according to the pseudo-critical pressure, and the gas contrast density is obtained according to the pseudo-comparison temperature and the pseudo-comparison pressure. The deviation factor calculation formula of high-temperature and ultra-high-pressure gas reservoirs is as follows: in, Z is the deviation factor of high-temperature and ultra-high-pressure gas reservoirs, dimensionless; ρ r is the relative density of gas, dimensionless; T pr is the temperature to be compared, dimensionless; A1, A2, A3, A4, A5, A6, A7 and A8 are the coefficients of the Dranchuk-Purvis-Robinson relationship.

2. The method for correcting deviation factors of high temperature and ultrahigh pressure gas reservoirs according to claim 1, characterized in that: The relative density of a gas is the ratio of the density of a gas at a specific pressure and a specific temperature to its density at its critical pressure and critical temperature.

3. The method for correcting deviation factors of high temperature and ultrahigh pressure gas reservoirs according to claim 2, characterized in that: The following functional relationship is used between the quasi-comparative temperature and the quasi-critical temperature, as well as between the quasi-comparative pressure and the quasi-critical pressure: Pseudo-comparative pressure = gas pressure / pseudo-critical pressure; Pseudo-comparative temperature = gas temperature / pseudo-critical temperature.

4. The method for correcting deviation factors of high temperature and ultrahigh pressure gas reservoirs according to claim 1, characterized in that: A sensitivity analysis was performed on the coefficients and deviation factors in the Dranchuk-Purvis-Robinson relationship, and the coefficients that affect the deviation factor under high pressure were obtained.

5. The method for correcting deviation factors of high temperature and ultrahigh pressure gas reservoirs according to claim 4, characterized in that: The coefficients and deviation factors in the Dranchuk-Purvis-Robinson relationship were subjected to sensitivity analysis based on gas contrast density, and the coefficients that affect the deviation factor under high pressure were obtained.

6. The method for correcting deviation factors of high temperature and ultrahigh pressure gas reservoirs according to claim 5, characterized in that: The coefficients in the Dranchuk-Purvis-Robinson relationship that affect the deviation factor beyond the preset range under high pressure are corrected to obtain the corrected deviation factor of high-temperature and ultra-high-pressure gas reservoirs.

7. The method for correcting deviation factors of high temperature and ultrahigh pressure gas reservoirs according to claim 6, characterized in that: The coefficients A4 and A6 in the Dranchuk-Purvis-Robinson relationship were fitted using the multivariate nonlinear regression method to obtain the revised coefficients A4 and new coefficients A6.

8. The method for correcting deviation factors of high temperature and ultrahigh pressure gas reservoirs according to claim 7, characterized in that: The values ​​of coefficient A4 and coefficient A6 in the Dranchuk-Purvis-Robinson relationship are used as the initial values ​​of the nonlinear regression of coefficient A4 and coefficient A6 in the Dranchuk-Purvis-Robinson relationship in the deviation factor calculation formula, and the coefficient A4 and coefficient A6 in the Dranchuk-Purvis-Robinson relationship in the deviation factor calculation formula are corrected using least squares iteration.

9. The method for correcting deviation factors of high temperature and ultrahigh pressure gas reservoirs according to claim 8, characterized in that: Based on coefficients A4 and A6 of the modified Dranchuk-Purvis-Robinson relation, nonlinear regression of gas relative density in the prediction deviation factor calculation formula using the modified DPR relation is performed.

10. The method for correcting deviation factors of high temperature and ultrahigh pressure gas reservoirs according to claim 9, characterized in that: According to the coefficients A4 and A6 of the modified Dranchuk-Purvis-Robinson relation, nonlinear regression of the gas relative density in the calculation formula for the prediction deviation factor using the modified DPR relation is performed to obtain the coefficients in the calculation formula for the deviation factor of the high-temperature and ultra-high-pressure gas reservoir, which specifically includes the following steps: The A4 value and the A6 value in the DPR relationship are taken as the initial values ​​of A4 and A6, and the initial gas relative density is taken as the gas relative density; Gas contrast density iterative calculation operation: Substitute the latest A4 value, the latest A6 value and the latest gas relative density into the gas relative density equation to calculate the new gas relative density; If the absolute value of the difference between the new gas relative density and the initial gas relative density is within the preset error range, a least squares nonlinear regression fitting operation is performed for the new A4 value and A6 value; If the absolute value of the difference between the new gas contrast density and the initial gas contrast density exceeds the preset error range, otherwise the iterative calculation operation of the gas contrast density is continued until the absolute value of the difference between the new gas contrast density and the last calculated gas contrast density is within the preset error range, the iterative calculation operation of the gas contrast density is stopped, and the least squares nonlinear regression fitting operation of the new A4 value and A6 value is performed; The operation of least squares nonlinear regression fitting new A4 and A6 values ​​is as follows: According to the experimental data, new A4 and A6 values ​​are obtained by least squares nonlinear regression fitting. If the absolute value of the difference between the new A4 and A6 values ​​obtained by the previous fitting and the A4 and A6 values ​​obtained by the previous fitting exceeds the preset error range, the gas relative density iteration calculation operation will be performed. Otherwise, the new A4 and A6 values ​​obtained by the fitting will be used as the corrected A4 and A6 values, and the least squares nonlinear regression fitting operation of the new A4 and A6 values ​​will be terminated. The gas relative density equation is as follows:

11. The method for correcting deviation factors of high temperature and ultrahigh pressure gas reservoirs according to claim 10, characterized in that: Substitute the corrected A4 and A6 values ​​into the calculation formula of the deviation factor of the high-temperature and ultra-high-pressure gas reservoir to obtain the deviation factor of the high-temperature and ultra-high-pressure gas reservoir.

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