A method for predicting non-equilibrium phase transition relaxation time considering pressure drop rate influence

Abstract

The application discloses a method for predicting non-equilibrium phase transition relaxation time by considering the influence of pressure drop rate, and relates to the technical field of oil and gas reservoir exploitation; by constructing a non-equilibrium characteristic parameter model and introducing a dynamic relaxation time model of the influence of pressure drop rate, the application quantitatively represents the non-equilibrium phase state characteristic parameters of the system under different pressure drop rates, and expresses the process that the non-equilibrium phase state characteristic parameters of the system gradually recover from the initial non-equilibrium state to the equilibrium state with the change of pressure; the limitation problem that the traditional model is only based on time or assumes instantaneous equilibrium is solved, and the dynamic process that the gas-liquid two phases deviate from the equilibrium and gradually recover in the rapid pressure drop process can be truly reflected; the established phase state characteristic parameter recovery model is in an analytical form, and is convenient for direct application in engineering calculation such as PVT phase state analysis and gas injection simulation, and is particularly suitable for condensate gas reservoirs, volatile oil reservoirs, gas injection systems and other complex systems with non-equilibrium phase transition behaviors.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas field development, and specifically relates to a method for predicting the non-equilibrium phase transition relaxation time considering the influence of pressure drop rate. Background Technology

[0002] In actual oil and gas reservoir development, changes in external conditions such as temperature and pressure disrupt the system's equilibrium state. The oil and gas system transitions from one equilibrium state to the next. This phase transition between the oil and gas phases is not instantaneous; it requires a certain relaxation time, known as the non-equilibrium phase transition relaxation time. The length of this relaxation time reflects, to some extent, the degree to which the system deviates from equilibrium. By calculating the relaxation time of an oil and gas reservoir, developers can predict potential non-equilibrium phase transition problems and their impact on production. Based on this, corresponding countermeasures and contingency plans can be developed in advance. This not only helps reduce development risks arising from insufficient understanding of fluid phase transition characteristics but also effectively improves the success rate and economic benefits of oil and gas development projects.

[0003] Currently, numerous scholars have conducted research on the calculation of non-equilibrium phase states in fluids. The main methods for calculating the relaxation time of non-equilibrium phase state changes in oil and gas systems include theoretical calculation, reservoir numerical simulation, and experimental testing. Regarding theoretical calculation methods, Yang Yang et al., in their paper "Calculation Methods and Systems for Non-equilibrium Phase States in Fluids" (CN112131513A), calculated the key parameter λ controlling the non-equilibrium phase behavior model by fitting historical data. λ's physical meaning is the reciprocal of the relaxation time, describing the dynamic process of fluid phase state changes over time and characterizing the dynamic process of phase equilibrium. This method is mainly applicable to two-phase oil and gas systems; for multiphase systems or complex fluid systems, corresponding improvements and extensions are needed. In terms of reservoir numerical simulation, Wu Keliu et al. explored the influence of non-equilibrium phase transition of the oil and gas system on the degassing process during reservoir development. They proposed a system weight function K(t) to characterize the degree of non-equilibrium in the phase transition of the oil and gas system, which also reflects the relaxation process. They pointed out that the process of K(t) gradually decreasing from a high value to a low value corresponds to the transition of the system from a non-equilibrium state to an equilibrium state. In actual oil reservoirs, the composition and properties of the oil and gas system are complex, and the pressure and temperature vary greatly, making it difficult to use this model for accurate calculation. (Wu Keliu, Li Xiangfang, Wang Haitao, et al. Quantitative evaluation model of the influence of non-equilibrium phase transition of volatile oil on degassing [J]. Petroleum Exploration and Development, 2012, 39(05): 597-604.) In terms of experimental testing, Kang Xiaodong et al. established a non-equilibrium phase transition model, pointing out that in the near-wellbore zone of condensate gas wells, due to high-speed flow, the condensate gas-liquid phase transition exhibits non-equilibrium characteristics. They also considered the influence of the minimum phase equilibrium time, which can be understood as the relaxation time for the system to reach equilibrium. This model is limited to the phase transition in the condensate gas anti-condensation stage and is not applicable to phase transition processes in other stages. (Kang Xiaodong, Li Xiangfang, Feng Guozhi, et al. Study on non-equilibrium phase transition model of condensate gas [J]. Daqing Petroleum Geology and Development, 2007, (06): 71-73+77.) In addition, Zhang Lei et al., in "A numerical model equivalent characterization method for non-equilibrium phase transition relaxation time of fluid in highly saturated condensate gas reservoirs" (CN118761347A), conducted a constant-volume exhaustion experiment on non-equilibrium phase transition of fluid in highly saturated condensate gas reservoirs, and statistically analyzed the pressure drop time and steady-state relaxation time of fluid phase equilibrium in different exhaustion and depressurization stages. This method establishes the correspondence between non-equilibrium phase transition relaxation time and steady-state relaxation time of phase equilibrium by correcting the parameters of the equation of state, drawing the equilibrium constants of each component in the steady-state and transient phase equilibrium of the fluid, and finally realizing the numerical model equivalent characterization of the non-equilibrium phase transition relaxation time of fluid in condensate gas reservoirs; this method is mainly for highly saturated condensate gas reservoirs, and its applicability to other types of oil and gas reservoirs needs further research.The prior art (publication number US2014343909A1), "Method and System for Dynamic Modeling of Multiphase Fluid Flows," considers modeling fluid transport in porous media at different spatial and temporal scales by solving equations related to fluid transport at each time step, and for each grid, by establishing thermodynamic and / or geochemical equilibrium in each grid during the solution process. This modeling can be particularly applied to locating sedimentary basins by simulating their geological history, predicting reservoir location, the amount and composition of hydrocarbons that can be discovered and extracted from them, and providing the possibility of predicting temporally relevant changes in petroleum sediments and optimizing the development of these sediments, and considering the reactions of non-equilibrium equations or during geothermal studies, studies managing nuclear waste, or environmental studies involving transfer in porous media with fluid composition representations.

[0004] In the aforementioned studies, existing methods for calculating non-equilibrium relaxation times still face several challenges and limitations in practical applications. These challenges include the acquisition and calibration of experimental data, model complexity and computational resource requirements, limitations in applicability, challenges in interface capture and processing, and the universality and versatility of the models. Therefore, there is an urgent need to establish a computationally simple, widely applicable method for calculating the relaxation time of non-equilibrium phase transition processes in oil and gas systems based on data fitting, providing theoretical support and practical guidance for field production. Summary of the Invention

[0005] In the development of oil and gas reservoirs, especially during gas-liquid two-phase experiments or gas injection displacement processes such as CCE and NCCE, the rapid depressurization rate often prevents the system from completing phase transitions in a timely manner, resulting in significant phase lag and deviations in phase characteristic parameters. This makes it difficult for phase equilibrium models to accurately describe the changing behavior of phase characteristic parameters, affecting the accuracy of phase analysis and development scheme design. This invention proposes a prediction method for non-equilibrium phase transition relaxation time that considers the influence of pressure drop rate. By constructing a non-equilibrium phase characteristic parameter evolution model coupled with a relaxation rate function α related to the pressure drop rate, it expresses the process by which the system's non-equilibrium phase characteristic parameters gradually recover from the initial non-equilibrium state to the equilibrium state as pressure changes. This method can not only accurately describe the lag behavior of phase characteristic parameters under rapid depressurization conditions, but also achieve unified modeling under different experimental rate conditions. The parameters are clear, easy to fit, and have good engineering applicability. Based on this, this invention provides a reliable modeling tool for gas-liquid phase evolution under complex pressure drop processes, which has important theoretical significance and engineering application value.

[0006] To achieve the above technical objectives, the present invention adopts the following technical solution, including the following steps:

[0007] Step S1: Starting from the original formation pressure, conduct equilibrium and non-phase change experiments, gradually reducing the pressure at a certain rate of pressure change dp / dt. The equilibrium phase experiment is conducted by gradually reducing the pressure, stirring, and then allowing the system to stand still. The values ​​of P and corresponding parameters under equilibrium conditions are measured. The corresponding parameter values ​​were read immediately after the pressure was reduced in the non-equilibrium phase experiment. Then continue to reduce the pressure, and record P and in, It can be a combination of one or more parameters, such as saturation, volume, and recovery rate, as tested in the corresponding experiment;

[0008] Step S2: Since there are deviations in the experimental parameters between non-equilibrium and equilibrium, the concept of characteristic parameter deviation is introduced, where... This reflects the difference between equilibrium and non-equilibrium, namely:

[0009]

[0010] Step S3: Describe the changes of the system with time during the non-equilibrium process by establishing a first-order differential equation, that is, the change of the non-equilibrium deviation is controlled by the following differential equation:

[0011]

[0012] Step S4: Solve the differential equation (2) by definite integral, and the unbalanced deviation is obtained. The dynamic behavior can be represented as:

[0013]

[0014] Step S5: The exponential function relationship of the characteristic parameters during the non-equilibrium phase transition is as follows:

[0015]

[0016] Step S6: In the phase state experiment, assuming the effect of the pressure change rate on α is nonlinear, establish the pressure change rate... The relationship between the system relaxation rate α and the system relaxation rate α is as follows:

[0017]

[0018] Step S7: Fit the experimental data using the least squares method to determine α0 and k. p and n;

[0019]

[0020] Step S8: The relaxation time of the system under different transformer speeds can be expressed as:

[0021]

[0022] In the formula: t is the system relaxation time, h.

[0023] Preferably, step S2 is performed as follows:

[0024] Step S21: Under non-equilibrium conditions, rapid pressure drop causes phase transition hysteresis in oil and gas. This manifests as a deviation between the non-equilibrium parameter values ​​after rapid pressure drop at a single pressure point P and the parameter values ​​after continuous pressure drop to reach equilibrium. This difference leads to the equilibrium phase state... Curves and non-equilibrium phases The curve exhibits a systematic deviation, namely:

[0025]

[0026] In the formula: These are the non-equilibrium characteristic parameters under pressure P; These are the equilibrium characteristic parameters under pressure P;

[0027] Step S22: During the rapid pressure drop, to describe the change of the non-equilibrium characteristic parameter with pressure, a characteristic parameter deviation is introduced, wherein, It reflects the difference between equilibrium and non-equilibrium, that is:

[0028]

[0029] In the formula: This represents the deviation value under the corresponding pressure P.

[0030] Preferably, step S3 is as follows:

[0031] Step S31: The relaxation rate α is related to the pressure drop rate, and this parameter changes with the rate of pressure change:

[0032]

[0033] Step S32: Based on the exponential form of classical relaxation dynamics, the change in non-equilibrium deviation is controlled by the following equation:

[0034]

[0035] In the formula: α is the rate of change of the non-equilibrium parameter; α is the relaxation rate, 1 / h.

[0036] Preferably, step S4 is as follows:

[0037] Step S41: Rewrite the differential equation in a separated variable form, that is... Move dt to both sides of the equation:

[0038]

[0039] Step S42: Perform a definite integral on both sides of equation (4.1); the integration interval of time t is determined by the reference pressure P. ref Reference pressure P ref The first set of P values ​​recorded in the non-equilibrium experiment. The data corresponds to the pressure value, i.e., the first pressure point at the start of the experiment after rapid depressurization; the corresponding time t(P) ref The time t(P) corresponding to P is... The integration interval is P. ref Time corresponding To P corresponding The definite integral equation can be expressed as:

[0040]

[0041] Step S43: Solve equation (4.2) by performing a definite integral, and obtain:

[0042]

[0043] Step S44: Substituting the upper and lower limits of integration, and simplifying, we get:

[0044]

[0045] Step S45: To describe the unbalanced deviation Regarding the relaxation behavior, taking the exponent on both sides of equation (4.4), we get:

[0046]

[0047] Step S46: Equation (4.5) is further simplified to:

[0048]

[0049] In the formula: P ref The initial pressure point is given in MPa; t ref The initial reference time is h.

[0050] Preferably, step S5 is as follows:

[0051] Step S51: The experimentally measured Substituting into equation (1), we obtain the expression for the unbalanced deviation:

[0052]

[0053] Step S52: Combine equations (3) and (5.1) and simplify to obtain the analytical form of the non-equilibrium characteristic parameter model:

[0054]

[0055] According to claim 1, the method for predicting the non-equilibrium phase transition relaxation time considering the influence of pressure drop rate is characterized in that step S7 is as follows:

[0056] Step S71: Substitute the relaxation rate equation (5) into the non-equilibrium volume equation (4), that is:

[0057]

[0058] In the formula: α0 is the basic relaxation rate, with units of 1 / h, which characterizes the relaxation rate of the system under slow pressure reduction or near-equilibrium conditions, and is the inherent recovery capability of the system; k p Pressure drop sensitivity coefficient, in MPa / h -n This characterizes the system's sensitivity to changes in the rate of pressure drop; The nonlinear amplification term, where n controls the nonlinear intensity, is dimensionless.

[0059] Preferably, equation (7.1) is further expressed as:

[0060]

[0061] Step S73: Prepare experimental data for equilibrium and non-equilibrium phase transitions, including: pressures at each level P1, P2, ..., P n Volume V1 determined by equilibrium experiment eq V2 eq ,...,V n eq Volume V1 determined by nonequilibrium experiment neq V2 neq ,...,V n neq ;

[0062] Step S74: Given the base rate α0 and the sensitivity coefficient k p Initial values ​​for the exponent n;

[0063] Step S75: Calculate the volume V according to equation (7.2). k neq,model The volume V is determined by the least squares method. k neq ,model Compared with the experimentally measured value V k neq If the difference between them is minimized, then output the corresponding α0,k. p and n;

[0064] Step S76: If calculating volume V k neq,modelCompared with experimental value V k neq If the difference between them is not the minimum, return to step S74 and readjust the unbalanced parameter values ​​α0 and k. p Then perform further calculations on n until the difference is minimized.

[0065] Preferably, step S8 is as follows:

[0066] Step S81: Based on step S7, the optimized non-equilibrium parameters α0 and k are... p Substituting n into equation (5), we obtain the system relaxation rate α;

[0067] Step S82: Based on the physical meaning of relaxation time, calculate the system relaxation time under different transformer speeds:

[0068]

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] This invention constructs a non-equilibrium characteristic parameter model and introduces a dynamic relaxation time model influenced by the pressure drop rate. This model quantitatively characterizes the non-equilibrium phase state characteristic parameters of the system under different pressure drop rates, expressing the process by which the system's non-equilibrium phase state characteristic parameters gradually recover to equilibrium from an initial non-equilibrium state with pressure changes. Compared with existing technologies, the advantages of this invention lie in explicitly introducing the influence mechanism of the pressure drop rate on the non-equilibrium relaxation rate, breaking through the limitations of traditional models that are only based on time or assume instantaneous equilibrium. It can realistically reflect the dynamic process of the gas-liquid two-phase deviating from equilibrium and gradually recovering during rapid pressure reduction. The established phase state characteristic parameter recovery model is in analytical form, facilitating direct application in engineering calculations such as PVT phase analysis and gas injection simulation. Simultaneously, the model structure is clear, the physical meaning of the parameters is explicit, and key parameters can be obtained through fitting multi-rate experimental data, exhibiting good operability and generalizability. It is particularly suitable for condensate gas reservoirs, volatile oil reservoirs, gas injection systems, and other complex systems exhibiting non-equilibrium phase transition behavior. Attached Figure Description

[0071] The above and other objects, features and advantages of the present invention will become more apparent from the more detailed description of exemplary embodiments of the invention in conjunction with the accompanying drawings, wherein the same reference numerals generally represent the same parts.

[0072] Figure 1 Here is a flowchart of the calculation method;

[0073] Figure 2 This is a graph showing the PV relationship during the non-equilibrium pressure reduction process;

[0074] Figure 3The variation of relaxation rate α under different pressure transformer speeds;

[0075] Figure 4 The relaxation time is given by different transformer speeds. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0077] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the system or component referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," etc., used to define components are merely for the convenience of distinguishing the aforementioned components. Unless otherwise stated, these terms have no special meaning and should not be construed as indicating or implying relative importance.

[0078] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0079] To achieve the above technical objectives, the present invention adopts the following technical solution; see the flowchart of the calculation method. Figure 1 The steps include:

[0080] Step S1: Starting from the original formation pressure, conduct equilibrium and non-phase change experiments, gradually reducing the pressure at a certain rate of pressure change dp / dt. The equilibrium phase experiment is conducted by gradually reducing the pressure, stirring, and then allowing the system to stand still. The values ​​of P and corresponding parameters under equilibrium conditions are measured. The corresponding parameter values ​​were read immediately after the pressure was reduced in the non-equilibrium phase experiment. Then continue to reduce the pressure, and record P and in, It can be a combination of one or more parameters, such as saturation, volume, and recovery rate, as tested in the corresponding experiment;

[0081] Step S2: Since there are deviations in the experimental parameters between non-equilibrium and equilibrium, the concept of characteristic parameter deviation is introduced, where... This reflects the difference between equilibrium and non-equilibrium, namely:

[0082]

[0083] Step S3: Describe the changes in the system over time during the non-equilibrium process by establishing a first-order differential equation. That is, the change in the non-equilibrium deviation is controlled by a differential equation of the following form:

[0084]

[0085] Step S4: Solve the differential equation (3) by definite integral, and the unbalanced deviation is obtained. The dynamic behavior can be represented as:

[0086]

[0087] Step S5: The exponential function relationship of the characteristic parameters during the non-equilibrium phase transition is as follows:

[0088]

[0089] Step S6: In the phase state experiment, assuming the effect of the pressure change rate on α is nonlinear, establish the pressure change rate... The relationship between the system relaxation rate α and the system relaxation rate α is as follows:

[0090]

[0091] Step S7: Fit the experimental data using the least squares method to determine α0 and k. p and n

[0092]

[0093] Step S8: The relaxation time of the system under different transformer speeds can be expressed as:

[0094]

[0095] In the formula: t is the system relaxation time, h.

[0096] Preferably, step S2 is performed as follows:

[0097] Step S21: Under non-equilibrium conditions, rapid pressure drop causes phase transition hysteresis in oil and gas. This manifests as a deviation between the non-equilibrium parameter values ​​after rapid pressure drop at a single pressure point P and the parameter values ​​after continuous pressure drop to reach equilibrium. This difference leads to the equilibrium phase state... Curves and non-equilibrium phases The curve exhibits a systematic deviation, i.e.:

[0098]

[0099] In the formula: These are the non-equilibrium characteristic parameters under pressure P; These are the equilibrium characteristic parameters under pressure P;

[0100] Step S22: During the rapid pressure drop, in order to describe the change of non-equilibrium characteristic parameters with pressure, the concept of characteristic parameter deviation is introduced, where, This reflects the difference between equilibrium and non-equilibrium, namely:

[0101]

[0102] In the formula: This represents the deviation value under the corresponding pressure P.

[0103] Preferably, step S3 is as follows:

[0104] Step S31: In actual production, the relaxation rate α is usually related to the pressure drop rate, and this parameter changes with the rate of pressure change.

[0105]

[0106] Step S32: Since Buleyko discovered in his experimental studies that typical relaxation dynamics are exponential in form, that is, the change in non-equilibrium deviation is controlled by the following equation:

[0107]

[0108] In the formula: α is the rate of change of the non-equilibrium parameter; α is the relaxation rate, 1 / h.

[0109] Preferably, step S4 is as follows:

[0110] Step S41: Rewrite the differential equation in a separated variable form, that is... Move dt to both sides of the equation:

[0111]

[0112] Step S42: Perform a definite integral on both sides of equation (4.1); the integration interval of time t is determined by the reference pressure P. ref Reference pressure P ref The first set of P values ​​recorded in the non-equilibrium experiment. The data corresponds to the pressure value, i.e., the first pressure point at the start of the experiment after rapid depressurization; the corresponding time t(P) refThe time t(P) corresponding to P is... The integration interval is P. ref Time corresponding To P corresponding The definite integral equation can be expressed as:

[0113]

[0114] Step S43: Solve equation (4.2) by performing a definite integral, and obtain:

[0115]

[0116] Step S44: Substituting the upper and lower limits of integration, and simplifying, we get:

[0117]

[0118] Step S45: To describe the unbalanced deviation Regarding the relaxation behavior, taking the exponent on both sides of equation (4.4), we get:

[0119]

[0120] Step S46: Equation (4.5) can be further simplified to:

[0121]

[0122] In the formula: P ref The initial pressure point is given in MPa; t ref The initial reference time is h.

[0123] Preferably, step S5 is as follows:

[0124] Step S51: The experimentally measured Substituting into equation (1), we can obtain the expression for the unbalanced deviation:

[0125]

[0126] Step S52: Combine equations (3) and (5.1) and simplify to obtain the analytical form of the non-equilibrium characteristic parameter model:

[0127]

[0128] Preferably, step S7 is as follows:

[0129] Step S71: Substitute the relaxation rate equation (5) into the non-equilibrium volume equation (4), that is:

[0130]

[0131] In the formula: α0 is the basic relaxation rate, with units of 1 / h, representing the relaxation rate of the system under slow pressure reduction (or near-equilibrium) conditions, and is the inherent recovery capability of the system; k p Pressure drop sensitivity coefficient, in MPa / h -n This characterizes the system's sensitivity to changes in the rate of pressure drop; The nonlinear amplification term, where n controls the nonlinear intensity, is dimensionless.

[0132] Step S72: During the rapid pressure change, the reference pressure is the first pressure point, and the time t(P) under the reference pressure is... ref If ) is 0, equation (7.1) can be further expressed as:

[0133]

[0134] Step S73: Taking the pressure and volume data obtained from the above equilibrium and non-equilibrium phase transition experiments as an example, prepare the experimental data including: pressures at each level P1, P2, ..., P n Volume V1 determined by equilibrium experiment eq V2 eq ,...,V n eq Volume V1 determined by nonequilibrium experiment neq V2 neq ,...,V n neq .

[0135] Step S74: Given the base rate α0 and the sensitivity coefficient k p Initial values ​​for the exponent n;

[0136] Step S75: Calculate the volume V according to equation (7.2). k neq,model The volume V is determined by the least squares method. k neq ,model Compared with the experimentally measured value V k neq Is the difference between them minimized? If the difference is minimized, then output the corresponding α0,k. p and n;

[0137] Step S76: If calculating volume V k neq,model Compared with experimental value V k neq If the difference between them is not the minimum, return to step S74 and readjust the unbalanced parameter values ​​α0 and k. p Then perform further calculations on n until the difference is minimized.

[0138] Preferably, step S8 is as follows:

[0139] Step S81: Based on S7, optimize the unbalanced parameters α0 and k. p Substituting n into equation (5), we obtain the system relaxation rate α;

[0140] Step S82: Based on the physical meaning of relaxation time, calculate the system relaxation time under different transformer speeds:

[0141]

[0142] Application Examples

[0143] To facilitate understanding of the solutions and effects of the embodiments of the present invention, a specific application example is given below. Those skilled in the art should understand that this example is merely for the purpose of understanding the present invention, and any specific details therein are not intended to limit the present invention in any way.

[0144] This invention takes volatile oil as an example. When the volatile oil fluid is depressurized to its bubble point pressure, gas escapes from the crude oil to form bubbles, and the system transforms from a single oil phase to a two-phase oil-gas transition. Due to the excessively rapid external pressure change, the system does not have enough time for a complete phase transition, and there is a lag effect in the interconversion between oil and gas. Starting from the initial formation pressure of 45 MPa, using the relative volume V in the characteristic parameters... eq and V neq The calculation is performed using data at 45 MPa as an example.

[0145] S1: Conduct non-equilibrium and equilibrium phase experiments to obtain the corresponding characteristic parameter experimental results. See [link to results]. Figure 2 ;

[0146] S11: Starting from the initial formation pressure of 45 MPa, an equilibrium phase transition experiment was conducted. The experiment was carried out using a staged pressure reduction and stirring method with a certain pressure change rate dp / dt, followed by static conditions. The equilibrium conditions P and relative volume V were measured. eq .

[0147] Table 1. PV data during the balanced voltage reduction process.

[0148]

[0149] S12: Conduct a phase transition experiment under non-equilibrium conditions. Rapidly reduce the pressure at a certain rate of pressure change dp / dt, and immediately read the relative volume V under the corresponding non-equilibrium conditions at pressure P. neq Then continue to reduce the pressure and record the corresponding P and V values. neq ;

[0150] Table 2 PV data during the non-equilibrium pressure reduction process

[0151]

[0152] S2: There are deviations in the experimental parameters between non-equilibrium and equilibrium, so the concept of characteristic parameter deviation is introduced;

[0153] S21: Under non-equilibrium conditions, rapid pressure drop leads to a phase transition hysteresis in oil and gas. This manifests as a deviation between the non-equilibrium relative volume after rapid pressure drop at a single pressure point P and the relative volume at equilibrium after continuous pressure drop. This difference results in a PV of the equilibrium phase. eq PV curves and non-equilibrium phases neq The curve exhibits a systematic deviation, i.e.:

[0154] V neq (P)≠V eq (P)(2.1)

[0155] S22: During rapid pressure drop, to describe the change of non-equilibrium characteristic parameters with pressure, a relative volume deviation ΔV(P) is introduced. ΔV(P) reflects the relative volume difference between equilibrium and non-equilibrium. Taking a pressure drop rate of 5 MPa / h as an example, the calculation is as follows:

[0156] ΔV(45)=V eq (45)-V neq (45) = 0.9604 - 0.9608 = 0.0004 (1)

[0157] S3: The changes of the system over time during nonequilibrium processes are described by establishing first-order differential equations.

[0158] S31: In actual production, the relaxation rate α is usually related to the pressure drop rate, and this parameter changes with the rate of pressure change.

[0159]

[0160] S32: As experimental studies have shown, typical relaxation dynamics are exponential in form, meaning that the change in non-equilibrium relative volume deviation is controlled by the following equation:

[0161]

[0162] S4: By solving the differential equation (2) by definite integral, the specific functional relationship between ΔV(P) and time t can be obtained. The dynamic behavior of the non-equilibrium relative volume deviation ΔV(P) can be expressed as:

[0163] S41: Rewrite the differential equation in a separated-variable form, that is, move ΔV(P) and dt to both sides of the equation respectively:

[0164]

[0165] S42: Perform a definite integral on both sides of equation (4.1), and the integration interval of time t is determined by the reference pressure P. ref Reference pressure P ref The first set of P and V values ​​recorded in the nonequilibrium experiment neq (P) represents the pressure value corresponding to the data, i.e., the first pressure point at the start of the experiment after rapid depressurization. The corresponding time t(P) is... ref The integral interval of ΔV(P) from time t(P) to time P is P. ref The corresponding ΔV(P) ref The definite integral equation for ΔV(P) corresponding to P can be expressed as:

[0166]

[0167] S43: Solving equation (4.2) by definite integral, we get:

[0168]

[0169] S44: Substituting the upper and lower limits of the integral and simplifying, we get:

[0170]

[0171] S465: For describing unbalanced deviations Regarding the relaxation behavior, taking the exponent on both sides of equation (4.4), we get:

[0172]

[0173] S46: Equation (4.5) can be further simplified to:

[0174]

[0175] S5: The exponential function relationship of relative volume during equilibrium phase transition.

[0176] S51: The experimentally measured V neq (P ref V eq (P ref Substituting into equation (1), we can obtain the expression for the non-equilibrium relative volume deviation:

[0177] ΔV(P ref ) = V eq (P ref )-V neq (P ref (5.1)

[0178] S52: Combining equations (3) and (5.1), and simplifying, we obtain the analytical form of the non-equilibrium relative volume model:

[0179]

[0180] S6: In actual phase state experiments, excessively rapid pressure drops can prevent the system from reaching thermodynamic phase equilibrium in time, resulting in a significant phase transition hysteresis, i.e., a non-equilibrium phenomenon. A dynamic relaxation rate α, related to the pressure drop rate, is needed to characterize the rate of change from disordered non-equilibrium to dynamic equilibrium caused by changes in external pressure. Assuming the effect of the pressure change rate on α is non-linear, a pressure change rate... The relationship between the system relaxation rate α and the system relaxation rate α is as follows:

[0181]

[0182] S7: Use the least squares method to fit the experimental data and determine α0 and k. p and n

[0183] S71: Substituting the relaxation rate equation (5) into the non-equilibrium volume equation (4), we get:

[0184]

[0185] S72: During a rapid pressure change, the reference pressure is the first pressure point, and the time t(P) under the reference pressure is... ref If ) is 0, the deviation of the non-equilibrium relative volume in equation (7.1) can be further expressed as:

[0186]

[0187] S73: Taking the pressure and volume data obtained from the above equilibrium and non-equilibrium phase transition experiments as an example, the experimental data preparation includes: pressures at various levels of 45 MPa, 40 MPa, 35 MPa, 30 MPa, 25 MPa, 20 MPa, and 15 MPa; the relative volumes measured at each pressure level in the equilibrium experiment are 0.9604, 0.9794, 1.0000, 1.0483, 1.1245, 1.2697, and 1.6954, respectively; and the non-equilibrium experiment... The relative volumes at each pressure level measured at a pressure drop rate of 5 MPa / h were 0.9608, 0.9815, 1.0129, 1.0807, 1.1703, 1.3605, and 1.6722, respectively; the relative volumes at each pressure level measured at a pressure drop rate of 10 MPa / h in the non-equilibrium experiment were 0.9611, 0.9807, 1.0072, 1.0755, 1.1617, 1.3305, and 1.6633, respectively.

[0188] S74: Given initial values: base rate α0 = 0.1, sensitivity coefficient k p =0.5 and the exponent n=1.5;

[0189] S75: Calculate the volume V according to equation (7.2). k neq,model The volume V is determined by the least squares method. k neq,model Compared with the experimentally measured value V k neq Check if the difference between them is minimized; if the difference is minimized, output the corresponding α0,k. p and n;

[0190] S76: If calculating volume V k neq,model Compared with experimental value V k neq If the difference between them is not the minimum, return to step S74 and readjust the unbalanced parameter values ​​α0 and k. p Then, calculate n and continue the calculations until the difference is minimized.

[0191] The non-equilibrium parameters α0 and k obtained through fitting are... p The values ​​of n are 0.50002, -0.46966, and 0.14763, respectively.

[0192] S8: The physical meaning of the α value is the reciprocal of the characteristic relaxation time, which essentially reflects the system's response rate characteristics to changes in external pressure.

[0193] S81: Based on S7, the optimized non-equilibrium parameters α0 and k p Substituting α and β into equation (5) respectively, we obtain the system relaxation rate α. See the results below. Figure 3 ;

[0194] When the pressure drop rate is 5 MPa / h and 10 MPa / h respectively, the pressure change rate The relationship between the system relaxation rate α and the system relaxation rate α is expressed as follows:

[0195]

[0196] S82: Based on the physical meaning of relaxation time, calculate the system relaxation time at different transformer speeds when the pressure drop rate is 5 MPa / h and 10 MPa / h, respectively. See the results below. Figure 4 ;

[0197] When the pressure drop rate is 5 MPa / h:

[0198]

[0199] When the pressure drop rate is 10 MPa / h:

[0200]

[0201] Those skilled in the art should understand that the above description of the embodiments of the present invention is only intended to illustrate the beneficial effects of the embodiments of the present invention, and is not intended to limit the embodiments of the present invention to any of the examples given.

[0202] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A method for predicting the relaxation time of a non-equilibrium phase transition considering the influence of pressure drop rate, characterized in that, Includes the following steps: Step S1: Starting from the original formation pressure, conduct equilibrium and non-phase change experiments. Pressure is gradually reduced in stages at a certain rate of change dp / dt. The equilibrium phase experiment is conducted using a staged pressure reduction and stirring method followed by static conditions. The values ​​of P and corresponding parameters under equilibrium conditions are measured. The corresponding parameter values ​​were read immediately after the pressure was reduced in the non-equilibrium phase experiment. Then continue to reduce the pressure, and record P and in, It can be a combination of one or more parameters, such as saturation, volume, and recovery rate, as tested in the corresponding experiment; Step S2: Since there are deviations in the experimental parameters between non-equilibrium and equilibrium, the concept of characteristic parameter deviation is introduced, where... This reflects the difference between equilibrium and non-equilibrium, namely: Step S3: Describe the changes of the system with time during the non-equilibrium process by establishing a first-order differential equation, that is, the change of the non-equilibrium deviation is controlled by the following differential equation: Step S4: Solve the differential equation (2) by definite integral, and the unbalanced deviation is obtained. The dynamic behavior can be represented as: Step S5: The exponential function relationship of the characteristic parameters during the non-equilibrium phase transition is as follows: Step S6: In the phase state experiment, assuming the effect of the pressure change rate on α is nonlinear, establish the pressure change rate... The relationship between the system relaxation rate α and the system relaxation rate α is as follows: Step S7: Fit the experimental data using the least squares method to determine α0 and k. p and n; Step S8: The relaxation time of the system under different transformer speeds can be expressed as: In the formula: t is the system relaxation time, h.

2. The method for predicting the non-equilibrium phase transition relaxation time considering the influence of pressure drop rate according to claim 1, characterized in that, The process of step S2 is as follows: Step S21: Under non-equilibrium conditions, rapid pressure drop causes phase transition hysteresis in oil and gas. This manifests as a deviation between the non-equilibrium parameter values ​​after rapid pressure reduction at a single pressure point P and the parameter values ​​after continuous pressure reduction to reach equilibrium. This difference leads to the equilibrium phase state... Curves and non-equilibrium phases The curve exhibits a systematic deviation, namely: In the formula: These are the non-equilibrium characteristic parameters under pressure P; These are the equilibrium characteristic parameters under pressure P; Step S22: During the rapid pressure drop, to describe the change of the non-equilibrium characteristic parameter with pressure, a characteristic parameter deviation is introduced, wherein, It reflects the difference between equilibrium and non-equilibrium, that is: In the formula: This represents the deviation value under the corresponding pressure P.

3. The method for predicting the non-equilibrium phase transition relaxation time considering the influence of pressure drop rate according to claim 1, characterized in that, The process of step S3 is as follows: Step S31: The relaxation rate α is related to the pressure drop rate, and this parameter changes with the rate of pressure change: Step S32: Based on the exponential form of classical relaxation dynamics, the change in non-equilibrium deviation is controlled by the following equation: In the formula: α is the rate of change of the non-equilibrium parameter; α is the relaxation rate, 1 / h.

4. The method for predicting the non-equilibrium phase transition relaxation time considering the influence of pressure drop rate according to claim 1, characterized in that, The process of step S4 is as follows: Step S41: Rewrite the differential equation in a separated variable form, that is... Move dt to both sides of the equation: Step S42: Perform a definite integral on both sides of equation (4.1); the integration interval of time t is determined by the reference pressure P. ref Reference pressure P ref The first set of P values ​​recorded in the non-equilibrium experiment. The data corresponds to the pressure value, i.e., the first pressure point at the start of the experiment after rapid depressurization; the corresponding time t(P) ref The time t(P) corresponding to P is... The integration interval is P. ref Time corresponding To P corresponding The definite integral equation can be expressed as: Step S43: Solve equation (4.2) by performing a definite integral, and obtain: Step S44: Substituting the upper and lower limits of integration, and simplifying, we get: Step S45: To describe the unbalanced deviation Regarding the relaxation behavior, taking the exponent on both sides of equation (4.4), we get: Step S46: Equation (4.5) is further simplified to: In the formula: P ref The initial pressure point is given in MPa; t ref The initial reference time is h.

5. The method for predicting the non-equilibrium phase transition relaxation time considering the influence of pressure drop rate according to claim 1, characterized in that, The process of step S5 is as follows: Step S51: The experimentally measured Substituting into equation (1), we obtain the expression for the unbalanced deviation: Step S52: Combine equations (3) and (5.1) and simplify to obtain the analytical form of the non-equilibrium characteristic parameter model: 。 6. The method for predicting the non-equilibrium phase transition relaxation time considering the influence of pressure drop rate according to claim 1, characterized in that, The process of step S7 is as follows: Step S71: Substitute the relaxation rate equation (5) into the non-equilibrium volume equation (4), that is: In the formula: α0 is the basic relaxation rate, with units of 1 / h, which characterizes the relaxation rate of the system under slow pressure reduction or near-equilibrium conditions, and is the inherent recovery capability of the system; k p Pressure drop sensitivity coefficient, in MPa / h -n This characterizes the system's sensitivity to changes in the rate of pressure drop; The nonlinear amplification term, where n controls the nonlinear intensity, is dimensionless. Step S72: During the rapid pressure change, the reference pressure is the first pressure point, and the time t(P) under the reference pressure is... ref If ) is 0, equation (7.1) can be further expressed as: Step S73: Prepare experimental data for equilibrium and non-equilibrium phase transitions, including: pressures at each level P1, P2, ..., P n Volume V1 determined by equilibrium experiment eq V2 eq ,...,V n eq Volume V1 determined by nonequilibrium experiment neq V2 neq ,...,V n neq ; Step S74: Given the base rate α0 and the sensitivity coefficient k p Initial values ​​for the exponent n; Step S75: Calculate volume V according to equation (7.2). k neq,model The volume V is determined by the least squares method. k neq,model Compared with the experimentally measured value V k neq If the difference between them is minimized, then output the corresponding α. 0， k p and n; Step S76: If calculating volume V k neq,model Compared with experimental value V k neq If the difference between them is not the minimum, return to step S74 and readjust the unbalanced parameter values ​​α0 and k. p Then perform further calculations on n until the difference is minimized.

7. The method for predicting the non-equilibrium phase transition relaxation time considering the influence of pressure drop rate according to claim 1, characterized in that, The process of step S8 is as follows: Step S81: Based on step S7, the optimized non-equilibrium parameters α0 and k are... p Substituting n into equation (5), we obtain the system relaxation rate α; Step S82: Based on the physical meaning of relaxation time, calculate the system relaxation time under different transformer speeds: 。

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