Method for calculating co2 storage capacity in depleted oil reservoirs based on multi-component phase equilibrium analysis

Abstract

This invention discloses a method for calculating CO2 stockpiles in abandoned oil reservoirs based on multi-component phase equilibrium analysis, relating to the field of oil and gas field development technology. The invention first calculates the molar concentrations of non-CO2 native hydrocarbon components in the reservoir before and after CO2 injection. Then, it presets an initial value for the CO2 concentration in the reservoir mixture, determines the molar fraction of each component in the mixture under the initial state, and uses the Peng-Robinson equation of state to perform reservoir phase stability analysis under the final stockpiling pressure. This determines the molar fraction of each component in the mixture, obtains the distribution of CO2 and hydrocarbon components in the gas and liquid phases, calculates the true concentration of CO2 in the reservoir mixture, determines the solubility of CO2 in the aqueous phase, and obtains the total CO2 stockpiles in the reservoir. This invention fully considers the influence of porosity elasticity changes and complex component phase states on CO2 stockpiles in the reservoir, improving the accuracy of CO2 stockpil calculation results.

Description

Technical Field

[0001] This invention relates to the field of oil and gas field development technology, specifically to a method for calculating the CO2 burial volume of abandoned oil reservoirs based on multi-component phase equilibrium analysis. Background Technology

[0002] Currently, global warming has become a severe challenge facing humanity, and reducing greenhouse gas emissions, primarily carbon dioxide, is of paramount importance. Carbon dioxide capture and storage (CO2 capture and storage) technology, as a key pathway to achieving carbon emission reduction targets, has received widespread international attention. Utilizing depleted oil reservoirs for CO2 geological storage offers advantages such as good geological sealing, clear reservoir parameters, and well-developed infrastructure, and is considered one of the most promising large-scale storage methods. Accurately assessing the CO2 storage capacity of an oil reservoir is not only the basis for project feasibility analysis but also a prerequisite for ensuring the safety and economic viability of long-term storage.

[0003] Currently, most methods for calculating CO2 reserves in depleted oil reservoirs are based on static mass balance equations, estimating using parameters such as reservoir volume, porosity, and fluid density. However, traditional assessment models have significant limitations when dealing with complex geological conditions and fluid phases. In particular, when the mechanical deformation of the porous medium and the thermodynamic behavior of multi-component fluids are not fully coupled, the calculated results often deviate from the true values, making it difficult to meet the needs of refined assessment.

[0004] First, traditional reservoir CO2 inventory assessment models simplify the multi-component phase behavior. Considering that depleted reservoirs often contain residual methane, ethane, propane, and heavy hydrocarbons, the mixing of injected CO2 with the original multi-component fluid leads to complex interphase mass transfer and thermodynamic interactions, potentially inducing anti-condensation and forming a complex gas-liquid two-phase fluid. Existing methods typically simplify the reservoir fluid to pure CO2 or a CO2-single-component hydrocarbon binary system, without incorporating precise phase stability analysis and flash evaporation calculations. This fails to accurately describe the phase distribution and density changes of the mixed fluid under high pressure, limiting the accuracy of the calculation results.

[0005] Secondly, traditional CO2 storage assessment models neglect the dynamic changes in reservoir pore volume. Considering the significant pressure drop during long-term production, and the fact that CO2 injection is a pressurization process, the effective stress on the rock skeleton decreases as formation pressure recovers and increases. This leads to elastic rebound and expansion of reservoir pores. This physical phenomenon is often ignored in traditional CO2 storage assessment models, treated as a constant-volume process. However, pore expansion directly increases effective storage space, meaning the reservoir can hold more CO2 under the same pressure conditions. Ignoring this nonlinear change will lead to an underestimation of storage potential, thus affecting the scientific decision-making regarding injection strategies.

[0006] Therefore, there is an urgent need to propose a method for calculating CO2 reserves in abandoned oil reservoirs based on multi-component phase equilibrium analysis. This method should fully consider the impact of porosity elasticity changes and complex component phase states on CO2 reserves, significantly improve the accuracy and reliability of CO2 reserve calculation results, and provide strong technical support for CO2 geological storage engineering capacity verification, injection and production design, and risk management. Summary of the Invention

[0007] This invention aims to solve the above-mentioned problems and proposes a method for calculating CO2 storage capacity in abandoned oil reservoirs based on multi-component phase equilibrium analysis. It fully considers the impact of pore elasticity changes caused by CO2 injection and the complex phase states of components on CO2 storage capacity. By introducing the Peng-Robinson equation of state and volume translation algorithm, combined with iterative solution based on mass conservation, it dynamically captures the real-time changes in pore volume and mixed fluid properties in the reservoir, improving the accuracy of CO2 storage capacity calculation results. This provides strong technical support for capacity verification, injection-production design, and risk management in CO2 geological storage projects and has significant industrial application value.

[0008] The present invention adopts the following technical solution:

[0009] A method for calculating CO2 stockpiles in abandoned oil reservoirs based on multi-component phase equilibrium analysis, considering the influence of pore expansion and component interactions on the calculation of CO2 stockpiles in oil reservoirs, includes the following steps:

[0010] Step 1: Calculate the molar concentration of non-CO2 native hydrocarbon components in the reservoir before and after CO2 injection;

[0011] Step 2: Preset the total mass concentration of CO2 in the reservoir after CO2 injection, and use it as the initial value of the actual CO2 concentration in the reservoir mixed fluid to determine the mole fraction of each component in the reservoir mixed fluid under the initial state.

[0012] Step 3: The trial-and-error method is used to calculate the true CO2 concentration in the reservoir mixture after CO2 injection. Based on the initial value of the true CO2 concentration in the reservoir mixture, the Peng-Robinson equation of state is used to perform phase stability analysis on the reservoir under the final burial pressure condition to obtain the phase stability analysis results of the reservoir under the final burial pressure.

[0013] Step 4: Determine the mole fraction of each component in the reservoir mixed fluid based on the reservoir phase stability analysis results, obtain the distribution of CO2 and hydrocarbon components in the gas and liquid phases of the reservoir, and update the total CO2 mass concentration of the reservoir.

[0014] Step 5: Calculate the difference between the updated total CO2 mass concentration in the reservoir after step 4 and the preset total CO2 mass concentration in the reservoir during step 2. If the difference in total CO2 mass concentration in the reservoir If the error is less than the preset maximum allowable error, the update of the total CO2 mass concentration in the reservoir is terminated, and the true CO2 concentration in the reservoir mixed fluid is obtained. Otherwise, the total CO2 mass concentration in the reservoir is updated using the Newton-Raphson method and used as the initial value of the true CO2 concentration in the reservoir mixed fluid. Steps 3 to 5 are then repeated.

[0015] Step 6: Based on the actual concentration of CO2 in the reservoir mixed fluid, calculate the solubility of CO2 in the aqueous phase of the reservoir mixed fluid, and determine the total amount of CO2 buried in the reservoir.

[0016] Preferably, in step 1, considering that the formation pressure of the reservoir changes from the initial pressure during CO2 injection... Gradually rising to final burial pressure The reduction in effective stress on the rock skeleton in the reservoir leads to elastic rebound and expansion of the pores, altering the reservoir's internal storage space. The porosity of the reservoir after CO2 injection is calculated using the following formula:

[0017] ;

[0018] In the formula, Porosity of the reservoir after CO2 injection; This represents the initial porosity of the reservoir. It is an exponential function; Porosity stress sensitivity coefficient; This represents the initial pressure of the reservoir. The final burial pressure of the oil reservoir;

[0019] Considering that the volume of formation water in the reservoir remains constant during CO2 injection, the total molar number of all primary hydrocarbon components other than CO2 remains conserved, and that CO2 injection dilutes non-CO2 primary hydrocarbon components in the reservoir, based on the principle of mass conservation, the molar concentration of each non-CO2 primary hydrocarbon component in the reservoir after CO2 injection is calculated using the following formula:

[0020] ;

[0021] In the formula, After CO2 injection The molar concentration of each non-CO2 primary hydrocarbon component; For the first The initial molar concentration of each non-CO2 primary hydrocarbon component; This represents the initial water saturation of the reservoir.

[0022] Preferably, in step 2, the total CO2 mass concentration of the reservoir after CO2 injection is preset, and the reservoir mixed fluid after CO2 injection includes injected CO2 and native multi-component hydrocarbons. The mole fraction of each component in the reservoir mixed fluid is calculated using the following formula:

[0023] ;

[0024] In the formula, The first in the reservoir mixed fluid Mole fraction of each component; This represents the sum of the molar concentrations of all primary hydrocarbon components in the reservoir; The first in the reservoir mixed fluid after CO2 injection The molar concentration of each non-CO2 primary hydrocarbon component; This represents the initial value of the total CO2 mass concentration in the reservoir after CO2 injection.

[0025] Preferably, step 3 includes the following sub-steps:

[0026] Step 3.1: Based on the Peng-Robinson equation of state, establish a multi-component Peng-Robinson equation of state model to describe the relationship between pressure, volume and temperature of the mixed fluid in the reservoir.

[0027] The multi-component Peng-Robinson equation of state model is expressed as follows:

[0028] ;

[0029] In the formula, For reservoir pressure; This is the universal gas constant; For reservoir temperature; Volume is the molar volume; This is a mixture attraction parameter used to characterize the intermolecular attraction. This is a repulsive force parameter used to characterize the volume effect of the molecule itself;

[0030] Step 3.2: Transform the multi-component Peng-Robinson equation of state model into a dimensionless cubic equation, calculate the real roots of the dimensionless cubic equation, and determine the deviation factor of each phase in the reservoir mixed fluid.

[0031] The dimensionless cubic equation obtained by transforming the multi-component Peng-Robinson equation of state model is:

[0032] ;

[0033] In the formula, This is the deviation factor; , All are dimensionless coefficients. , ;

[0034] If the dimensionless cubic equation has three real roots, the largest real root corresponds to the gas phase deviation factor of the reservoir mixed fluid, and the smallest real root corresponds to the liquid phase deviation factor of the reservoir mixed fluid; if the dimensionless cubic equation has one real root, then that real root is the fluid deviation factor of the reservoir mixed fluid.

[0035] Step 3.3: The gas phase fraction is calculated by isothermal flash evaporation using the Rachford-Rice equation to determine whether anti-condensation or gas-liquid separation occurs in the reservoir mixed fluid, and to obtain the reservoir phase stability analysis results.

[0036] The Rachford-Rice equation is expressed as follows:

[0037] ;

[0038] In the formula, The total component fraction of the reservoir mixed fluid; The first in the reservoir mixed fluid Phase equilibrium constants of each component; For the gas phase fraction, when If the mixture is in a certain state, the reservoir fluid is in a two-phase state of gas and liquid coexistence; otherwise, the reservoir fluid is in a single-phase state.

[0039] Preferably, in the multi-component Peng-Robinson equation of state model, the gravitational parameters of the mixture... and repulsion parameters The calculation is based on the weighted calculation according to van der Waals' mixing rules. The calculation formula is as follows:

[0040] ;

[0041] ;

[0042] In the formula, , All are serial numbers; The first in the reservoir mixed fluid Total mole fraction of each component; The first in the reservoir mixed fluid Total mole fraction of each component; The first in the reservoir mixed fluid The components and the first Binary interaction coefficients between components; , All are single-component parameters. , ,in, , For temperature comparison, The first in the reservoir mixed fluid The critical temperature of each component; , To compare the pressure, The first in the reservoir mixed fluid The critical pressure of each component; These are characteristic parameters used to accurately characterize the vapor pressure properties of each component in a reservoir mixed fluid;

[0043] The characteristic parameters The calculation formula is:

[0044] ;

[0045] In the formula, It is the eccentricity factor.

[0046] Preferably, in step 4, based on the phase equilibrium constants and gas phase fractions of each component in the reservoir mixed fluid calculated in step 3, the mole fractions of the gas phase and liquid phase components in the reservoir mixed fluid under equilibrium conditions are calculated using the following formula:

[0047] ;

[0048] ;

[0049] In the formula, This represents the mole fraction of the liquid phase component in the reservoir mixed fluid; This represents the mole fraction of the gas phase component in the reservoir mixed fluid; The first in the reservoir mixed fluid Total mole fraction of each component; The first in the reservoir mixed fluid Phase equilibrium constants of each component; This refers to the gas phase fraction;

[0050] Based on the mole fractions of gaseous and liquid components in the reservoir mixture under equilibrium conditions, the distribution of CO2 and hydrocarbon components in the gas and liquid phases of the reservoir can be determined.

[0051] By correcting the volume shift parameter in the multi-component Peng-Robinson equation of state model for the gas phase molar volume and liquid phase molar volume, we obtain:

[0052] ;

[0053] ;

[0054] In the formula, This is the corrected molar volume of the gas phase; The molar volume of the gas phase calculated using the multi-component Peng-Robinson equation of state model; This is the corrected liquid phase molar volume; The liquid phase molar volume calculated using the multi-component Peng-Robinson equation of state model; These are the volume translation parameters;

[0055] Update the total CO2 concentration of the reservoir based on the corrected gas phase molar volume and gas phase molar volume. The calculation formula is:

[0056] ;

[0057] In the formula, Liquid phase fraction; This represents the mole fraction of CO2 in the liquid phase of the reservoir mixed fluid. It represents the mole fraction of CO2 in the gas phase of the reservoir mixed fluid.

[0058] Preferably, in step 5, when updating the total CO2 mass concentration of the reservoir using the Newton-Raphson method, a dimensionless objective function is first constructed to reflect the difference between the updated total CO2 mass concentration of the reservoir and the preset total CO2 mass concentration of the reservoir.

[0059] The dimensionless objective function is expressed as follows:

[0060] ;

[0061] In the formula, The objective function is dimensionless. The preset value for the total mass concentration of CO2 in the reservoir after CO2 injection; The total mass concentration of CO2 in the updated reservoir ;

[0062] The derivative of the dimensionless objective function with respect to the total CO2 mass concentration is calculated using the central difference method to capture the direction of gradient change, thus obtaining the reservoir's total CO2 mass concentration updated by the Newton-Raphson method. for:

[0063] ;

[0064] in,

[0065] ;

[0066] In the formula, The derivative of the dimensionless objective function; This represents the step size for small perturbations.

[0067] Preferably, step 6 includes the following sub-steps:

[0068] Step 6.1: Calculate the effective partial pressure of CO2 based on the actual concentration of CO2 in the reservoir mixed fluid. The calculation formula is as follows:

[0069] ;

[0070] In the formula, This is the effective partial pressure of CO2; This represents the mole fraction of CO2 in the free phase. This is the fugacity coefficient of CO2, used to reflect the escape tendency of CO2; The final burial pressure of the oil reservoir;

[0071] Step 6.2: Calculate the solubility of CO2 in the aqueous phase of the reservoir mixed fluid using Henry's Law, and obtain:

[0072] ;

[0073] In the formula, This represents the solubility of CO2 in the aqueous phase of the reservoir mixed fluid. It is the Henry's constant; For reservoir temperature;

[0074] Step 6.3: Calculate the total amount of CO2 buried in the reservoir based on the solubility of CO2 in the aqueous phase of the reservoir mixed fluid;

[0075] The formula for calculating the total amount of CO2 buried in the reservoir is as follows:

[0076] ;

[0077] In the formula, This represents the total amount of CO2 buried in the reservoir; This represents the molecular weight of CO2. This represents the total volume of the reservoir. Porosity of the reservoir after CO2 injection; This represents the total mass concentration of CO2 in the reservoir. This represents the water saturation of the reservoir under final burial pressure.

[0078] The present invention has the following beneficial effects:

[0079] (1) This invention proposes a method for calculating the CO2 storage capacity of abandoned oil reservoirs based on multi-component phase equilibrium analysis. By integrating an exponential porosity stress-sensitive model, it accurately quantifies the pore elastic expansion effect caused by the reduction of effective stress in reservoir rocks during gas injection pressurization. This effectively corrects the problem of underestimating the storage space of oil reservoirs by the traditional static volume method, significantly improves the assessment accuracy of CO2 storage potential in complex depleted oil reservoirs, and more realistically reflects the storage capacity of oil reservoirs.

[0080] (2) This invention proposes a method for calculating the CO2 burial volume of abandoned oil reservoirs based on multi-component phase equilibrium analysis. It breaks through the limitations of traditional methods that only target single-component or binary systems. By combining the multi-component Peng-Robinson equation of state with Rachford-Rice flash calculation, it achieves accurate characterization of the complex gas-liquid phase behavior of the mixed system of injected CO2 and native multi-component hydrocarbons in the reservoir. By introducing a volume translation algorithm to correct the high-pressure fluid density, it overcomes the inherent defect of large volume prediction deviation in the liquid phase or supercritical region of the traditional equation of state, and greatly improves the calculation accuracy of fluid physical parameters.

[0081] (3) This invention proposes a method for calculating the CO2 storage capacity of abandoned oil reservoirs based on multi-component phase equilibrium analysis. It constructs a Newton-Raphson iterative solution system based on the law of conservation of mass, which ensures the convergence and stability of the calculation of the total CO2 mass concentration of the reservoir under the conditions of multi-phase coexistence and nonlinear coupling. At the same time, when calculating the total CO2 storage capacity of the reservoir, it comprehensively considers the free phase structure storage and water phase dissolution storage mechanisms, and uses the accurate thermodynamic equilibrium fugacity to calculate the solubility, which further enhances the scientific nature of the results. It provides a more refined theoretical basis and calculation method for the geological storage of CO2 in complex oil reservoirs, which is conducive to guiding the selection of storage sites, reservoir capacity assessment and injection and production scheme design. It provides technical support for promoting the large-scale engineering application of carbon dioxide capture, utilization and storage technology and the realization of carbon neutrality goals. Attached Figure Description

[0082] Figure 1 This is a flowchart of the method for calculating CO2 storage in abandoned oil reservoirs based on multi-component phase equilibrium analysis, as described in this invention. Detailed Implementation

[0083] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0084] Example 1

[0085] This invention proposes a method for calculating CO2 storage capacity in abandoned oil reservoirs based on multi-component phase equilibrium analysis, such as... Figure 1 As shown, considering the influence of pore expansion and component effects on the calculation of reservoir carbon dioxide storage, the following steps are included:

[0086] Step 1: Calculate the molar concentration of non-CO2 native hydrocarbon components in the reservoir before and after CO2 injection.

[0087] Specifically, considering the formation pressure of the reservoir during CO2 injection, from the initial pressure... Gradually rising to final burial pressure The reduced effective stress on the rock skeleton in the reservoir leads to elastic rebound and expansion of the pores, changing the reservoir's internal storage space.

[0088] To accurately quantify the impact of CO2 injection on the internal pore space of the reservoir, the porosity of the reservoir after CO2 injection is calculated using the following formula:

[0089] ;

[0090] In the formula, Porosity of the reservoir after CO2 injection; This represents the initial porosity of the reservoir. It is an exponential function; Porosity stress sensitivity coefficient; This represents the initial pressure of the reservoir. This refers to the final burial pressure of the oil reservoir.

[0091] Considering that the volume of formation water in the reservoir remains essentially unchanged during CO2 injection, the total molar number of all primary hydrocarbon components (excluding CO2) remains conserved, and that CO2 injection dilutes non-CO2 primary hydrocarbon components in the reservoir, the molar concentration of each non-CO2 primary hydrocarbon component in the reservoir after CO2 injection is calculated using the following formula based on the principle of mass conservation:

[0092] ;

[0093] In the formula, After CO2 injection The molar concentration of each non-CO2 primary hydrocarbon component; For the first The initial molar concentration of each non-CO2 primary hydrocarbon component; This represents the initial water saturation of the reservoir.

[0094] Step 2: Since the true concentration of CO2 in the reservoir mixture after injection is unknown, the total mass concentration of CO2 in the reservoir after CO2 injection is preset and used as the initial value of the true concentration of CO2 in the reservoir mixture. The mole fraction of each component in the reservoir mixture under the initial state is then determined.

[0095] Specifically, the total CO2 mass concentration in the reservoir after CO2 injection is preset. The reservoir mixed fluid after CO2 injection includes injected CO2 and native multi-component hydrocarbons. The mole fraction of each component in the reservoir mixed fluid is calculated separately using the following formula:

[0096] ;

[0097] In the formula, The first in the reservoir mixed fluid Mole fraction of each component; This represents the sum of the molar concentrations of all primary hydrocarbon components in the reservoir; The first in the reservoir mixed fluid after CO2 injection The molar concentration of each non-CO2 primary hydrocarbon component; This represents the initial value of the total CO2 mass concentration in the reservoir after CO2 injection.

[0098] Step 3: Calculate the true CO2 concentration in the reservoir mixture after CO2 injection using the trial-and-error method. Based on the initial true CO2 concentration in the reservoir mixture, perform phase stability analysis on the reservoir under the final burial pressure using the Peng-Robinson equation of state to obtain the phase stability analysis results when the reservoir is at the final burial pressure. This step includes the following sub-steps:

[0099] Step 3.1: Considering that the ideal gas law cannot be applied to the complex multi-component hydrocarbon system in depleted reservoirs, a multi-component Peng-Robinson equation of state model is established based on the Peng-Robinson equation of state to describe the relationship between pressure, volume and temperature of the mixed fluid in the reservoir, and to accurately reflect the specific behavior of the multi-component hydrocarbon system in the reservoir under high temperature and high pressure.

[0100] The multi-component Peng-Robinson equation of state model is expressed as follows:

[0101] ;

[0102] In the formula, For reservoir pressure; This is the universal gas constant, with a value of [value missing]. ; For reservoir temperature; Volume is the molar volume; This is a mixture attraction parameter used to characterize the intermolecular attraction. This is a repulsive force parameter used to characterize the volume effect of the molecule itself.

[0103] Step 3.2, in order to solve for the compressibility of the mixed fluid in the reservoir, in this embodiment, the multi-component Peng-Robinson equation of state model is transformed into a dimensionless cubic equation, resulting in:

[0104] ;

[0105] In the formula, This is the deviation factor; , All are dimensionless coefficients. , .

[0106] The mixture attraction parameters in this embodiment and repulsion parameters It is not a simple summation of the parameters of each component, but a weighted calculation based on the van der Waals mixing rule, used to reflect the interactions between different molecules. Specifically, the attractive parameters of the mixture... and repulsion parameters The calculation formula is:

[0107] ;

[0108] ;

[0109] In the formula, , All are serial numbers; The first in the reservoir mixed fluid Total mole fraction of each component; The first in the reservoir mixed fluid Total mole fraction of each component; The first in the reservoir mixed fluid The components and the first Binary interaction coefficients between components; , All are single-component parameters. , ,in, , For temperature comparison, The first in the reservoir mixed fluid The critical temperature of each component; , To compare the pressure, The first in the reservoir mixed fluid The critical pressure of each component; These are characteristic parameters used to accurately characterize the vapor pressure properties of each component in a reservoir mixed fluid.

[0110] Specifically, the characteristic parameters The calculation formula is:

[0111] ;

[0112] In the formula, It is the eccentricity factor.

[0113] In this embodiment, the real roots of the dimensionless cubic equation are solved using existing algebraic or numerical methods. The deviation factors of each phase in the reservoir mixture are determined based on the obtained real roots. If the dimensionless cubic equation has three real roots, the largest real root corresponds to the gas phase deviation factor of the reservoir mixture, and the smallest real root corresponds to the liquid phase deviation factor of the reservoir mixture. If the dimensionless cubic equation has one real root, that real root is the fluid deviation factor of the reservoir mixture.

[0114] Step 3.3: To determine whether anti-condensation or gas-liquid separation has occurred in the reservoir mixed fluid and to obtain the reservoir phase stability analysis results, this embodiment uses the Rachford-Rice equation to calculate the gas phase fraction using isothermal flash evaporation. The calculation formula is as follows:

[0115] ;

[0116] In the formula, The total component fraction of the reservoir mixed fluid; The first in the reservoir mixed fluid Phase equilibrium constants of each component; For the gas phase fraction, when If the mixture is in a certain state, the reservoir fluid is in a two-phase state of gas and liquid coexistence; otherwise, the reservoir fluid is in a single-phase state.

[0117] Step 4: Determine the mole fraction of each component in the reservoir mixed fluid based on the reservoir phase stability analysis results, obtain the distribution of CO2 and hydrocarbon components in the gas and liquid phases of the reservoir, and update the total CO2 mass concentration of the reservoir.

[0118] Specifically, based on the phase equilibrium constants and gas phase fractions of each component in the reservoir mixed fluid calculated in step 3, the mole fractions of the gas phase and liquid phase components in the reservoir mixed fluid under equilibrium conditions are calculated using the following formula:

[0119] ;

[0120] ;

[0121] In the formula, This represents the mole fraction of the liquid phase component in the reservoir mixed fluid; This represents the mole fraction of the gas phase component in the reservoir mixed fluid; The first in the reservoir mixed fluid Total mole fraction of each component; The first in the reservoir mixed fluid Phase equilibrium constants of each component; This represents the gas phase fraction.

[0122] Based on the mole fractions of gas and liquid components in the reservoir mixture under equilibrium conditions, the distribution of CO2 and hydrocarbon components in the gas and liquid phases of the reservoir is determined. Since traditional cubic equations of state often suffer from volume bias when calculating the density of high-pressure liquids or supercritical fluids, this embodiment utilizes a volume shift parameter to correct the multi-component Peng-Robinson equation of state model to calculate the gas and liquid molar volumes, obtaining:

[0123] ;

[0124] ;

[0125] In the formula, This is the corrected molar volume of the gas phase; The molar volume of the gas phase calculated using the multi-component Peng-Robinson equation of state model; This is the corrected liquid phase molar volume; The liquid phase molar volume calculated using the multi-component Peng-Robinson equation of state model; These are the volume translation parameters.

[0126] Update the total CO2 concentration of the reservoir based on the corrected gas phase molar volume and gas phase molar volume. The calculation formula is:

[0127] ;

[0128] In the formula, Liquid phase fraction; This represents the mole fraction of CO2 in the liquid phase of the reservoir mixed fluid. It represents the mole fraction of CO2 in the gas phase of the reservoir mixed fluid.

[0129] Step 5, preset the maximum permissible error as follows: Calculate the difference between the updated total CO2 concentration in the reservoir in step 4 and the preset total CO2 concentration in the reservoir in step 2. If the difference in total CO2 mass concentration in the reservoir If the difference is less than the preset maximum allowable error, the update of the total CO2 mass concentration in the reservoir ends, and the true CO2 concentration in the reservoir mixture is obtained. Otherwise, the total CO2 mass concentration in the reservoir is updated using the Newton-Raphson method and used as the initial value of the true CO2 concentration in the reservoir mixture. Steps 3 to 5 are repeated until the difference in the total CO2 mass concentration in the reservoir is reached. Less than the preset maximum allowable error.

[0130] Furthermore, in step 5, in order to determine the total mass concentration of CO2 in the reservoir that satisfies the law of conservation of mass, a dimensionless objective function is first constructed, and the dimensionless objective function is solved using the Newton-Raphson method.

[0131] The dimensionless objective function is used to reflect the difference between the updated reservoir CO2 total mass concentration and the preset reservoir CO2 total mass concentration, and its expression is:

[0132] ;

[0133] In the formula, The objective function is dimensionless. The preset value for the total mass concentration of CO2 in the reservoir after CO2 injection; The total mass concentration of CO2 in the updated reservoir .

[0134] The derivative of the dimensionless objective function with respect to the total CO2 mass concentration is calculated using the central difference method to capture the direction of gradient change, thus obtaining the reservoir's total CO2 mass concentration updated by the Newton-Raphson method. for:

[0135] ;

[0136] in,

[0137] ;

[0138] In the formula, The derivative of the dimensionless objective function; This represents the step size for small perturbations.

[0139] Step 6: Based on the actual concentration of CO2 in the reservoir mixed fluid, calculate the solubility of CO2 in the aqueous phase of the reservoir mixed fluid, and determine the total amount of CO2 buried in the reservoir. This includes the following sub-steps:

[0140] Step 6.1: Calculate the effective partial pressure of CO2 based on the actual concentration of CO2 in the reservoir mixed fluid. The calculation formula is as follows:

[0141] ;

[0142] In the formula, This is the effective partial pressure of CO2; This represents the mole fraction of CO2 in the free phase. This is the fugacity coefficient of CO2, used to reflect the escape tendency of CO2; This refers to the final burial pressure of the oil reservoir.

[0143] Step 6.2: Calculate the solubility of CO2 in the aqueous phase of the reservoir mixture using Henry's Law, and obtain:

[0144] ;

[0145] In the formula, This represents the solubility of CO2 in the aqueous phase of the reservoir mixed fluid. It is the Henry's constant; This refers to the reservoir temperature.

[0146] Step 6.3: Based on the solubility of CO2 in the aqueous phase of the reservoir mixed fluid, and taking into account both the structural burial amount existing in the free phase and the dissolved burial amount existing in the water-soluble phase, calculate the total amount of CO2 buried in the reservoir.

[0147] The formula for calculating the total amount of CO2 buried in the reservoir is as follows:

[0148] ;

[0149] In the formula, This represents the total amount of CO2 buried in the reservoir; The molecular mass of CO2 is given by a value of [value missing]. ; This represents the total volume of the reservoir. Porosity of the reservoir after CO2 injection; This represents the total mass concentration of CO2 in the reservoir. This represents the water saturation of the reservoir under final burial pressure.

[0150] Example 2

[0151] This embodiment applies the CO2 burial capacity calculation method for abandoned oil reservoirs based on multi-component phase equilibrium analysis described in Example 1 to a target oil reservoir for which CO2 burial is planned. The initial pressure of this target oil reservoir is 3 MPa, the initial porosity is 0.20, the initial water saturation is 0.30, and the temperature is 353 K (i.e., 80 °C). The total reservoir volume of this target oil reservoir is... Porosity stress sensitivity coefficient is When CO2 storage ends, the reservoir pressure of the target oil reservoir is expected to reach 8 MPa.

[0152] The CO2 storage capacity of the target reservoir is calculated using the method for calculating CO2 storage capacity of abandoned oil reservoirs based on multi-component phase equilibrium analysis as described in Example 1. The specific steps include:

[0153] Step 1: Calculate the molar concentration of non-CO2 native hydrocarbon components in the reservoir before and after CO2 injection.

[0154] Based on the initial pressure of the target reservoir Ultimate Buried Pressure and porosity stress sensitivity coefficient Calculate the porosity of the target reservoir after CO2 injection. In this embodiment, the initial pressure of the target reservoir is... 3MPa, final burial pressure 8MPa, porosity stress sensitivity coefficient for The porosity of the target reservoir after CO2 injection was calculated. for Based on the expanded porosity and the principle of conservation of mass, the molar concentration of each non-CO2 primary hydrocarbon component in the target reservoir after CO2 injection is calculated, thus determining the initial molar concentration of each primary hydrocarbon component in the expanded pores of the target reservoir.

[0155] Step 2: Since the actual concentration of CO2 in the mixed fluid of the target reservoir after injection is unknown, the total mass concentration of CO2 in the target reservoir after CO2 injection is preset. for The initial value of the CO2 concentration in the target reservoir mixture is used as the initial value of the true CO2 concentration. Combined with the molar concentration of each non-CO2 native hydrocarbon component in the target reservoir after CO2 injection calculated in step 1, the molar fraction of each component in the target reservoir mixture is calculated respectively.

[0156] Step 3: The trial-and-error method is used to calculate the true CO2 concentration in the mixed fluid of the target reservoir after CO2 injection. Based on the initial value of the true CO2 concentration in the mixed fluid of the target reservoir, the Peng-Robinson equation of state is used to perform phase stability analysis on the reservoir under the final burial pressure condition to obtain the phase stability analysis results of the target reservoir under the final burial pressure.

[0157] In this embodiment, the mole fraction, critical physical property parameters, and binary interaction coefficients of each component in the target reservoir mixed fluid are substituted into the multi-component Peng-Robinson equation of state model for phase stability analysis, and the calculated gas-phase compressibility factor is: Liquid phase deviation factor is The system determines that there are two phases, gas and liquid, in the mixed fluid of the target reservoir, and calculates the fugacity coefficients of each component in the gas and liquid phases based on the gas phase compressibility factor and the liquid phase deviation factor.

[0158] After determining that a gas-liquid two-phase system exists in the target reservoir's mixed fluid, the phase stability analysis results of the target reservoir are substituted into the Rachford-Rice equation. The gas phase fraction is then calculated using isothermal flash evaporation based on the Rachford-Rice equation to obtain the gas phase mole fraction. The liquid phase mole fraction is 0.6633. It is 0.3367.

[0159] Step 4: Determine the mole fraction of each component in the mixed fluid of the target reservoir based on the phase stability analysis results, obtain the distribution of CO2 and hydrocarbon components in the gas and liquid phases of the target reservoir, and update the total mass concentration of CO2 in the target reservoir.

[0160] In this embodiment, the converged phase equilibrium constant is substituted into the component distribution formula to calculate the mole fraction of gas phase and liquid phase components in the target reservoir mixed fluid under the calculated equilibrium state, that is, to determine the true mole fraction distribution of CO2 in the gas phase and liquid phase under the equilibrium state.

[0161] Meanwhile, to eliminate the prediction error of the multi-component Peng-Robinson equation of state model for the high-pressure liquid phase density, the multi-component Peng-Robinson equation of state model was modified based on the volume shift parameters of each component in the target reservoir's mixed fluid, and the modified gas phase molar volume was calculated. for Corrected liquid phase molar volume for And based on the corrected gas phase molar volume and liquid phase molar volume Update the total CO2 mass concentration of the target reservoir. .

[0162] Step 5, preset the maximum permissible error as follows: Calculate the difference between the updated total CO2 concentration of the target reservoir and the preset total CO2 concentration of the target reservoir. If the difference in total CO2 mass concentration in the target reservoir If the difference is less than the preset maximum allowable error, the update of the total CO2 mass concentration of the target reservoir ends, and the true CO2 concentration in the mixed fluid of the target reservoir is obtained. Otherwise, the total CO2 mass concentration of the target reservoir is updated using the Newton-Raphson method and used as the initial value of the true CO2 concentration in the mixed fluid of the reservoir. Steps 3 to 5 are repeated until the difference in the total CO2 mass concentration of the target reservoir is reached. Less than the preset maximum allowable error.

[0163] In this embodiment, to determine the total CO2 mass concentration of the target reservoir that satisfies mass conservation, a dimensionless objective function is first constructed and solved using the Newton-Raphson method. The derivative of the dimensionless objective function with respect to the total CO2 mass concentration is calculated using the central difference method to capture the gradient change direction, thus obtaining the updated total CO2 mass concentration of the target reservoir using the Newton-Raphson method. Finally, the CO2 molar concentration at which the mixed fluid in the target reservoir reaches equilibrium was determined. for .

[0164] Step 6: Based on the actual concentration of CO2 in the mixed fluid of the target reservoir, calculate the solubility of CO2 in the aqueous phase of the mixed fluid of the target reservoir, and determine the total amount of CO2 buried in the target reservoir.

[0165] In this embodiment, the reservoir temperature of 353K, pressure of 8MPa, and equilibrium gas phase fugacity results of the target oil reservoir are substituted into the Henry's Law calculation formula, and the Henry's constant is set. for The calculated true solubility of CO2 in the formation water of the target oil reservoir is: The water saturation of the target reservoir under the final burial pressure is obtained by calculating the initial water saturation, initial porosity, and porosity after expansion of the target reservoir. for .

[0166] Finally, based on the gas phase structure burial volume, liquid phase dissolution burial volume, water phase dissolution burial volume, and reservoir parameters after expansion of the target reservoir under burial pressure, the total CO2 burial volume in the target reservoir was calculated using the formula for calculating the total CO2 burial volume in the target reservoir. The result was that the total CO2 burial volume in the target reservoir after gas injection and pressurization to 8 MPa in this embodiment was 32028.28 tons.

[0167] In summary, the method of this invention fully considers the impact of changes in porosity elasticity caused by CO2 injection and the complex phase state of components on the CO2 storage capacity of oil reservoirs, and realizes the accurate calculation of the CO2 storage capacity of abandoned oil reservoirs, providing technical support for promoting the development of CO2 geological storage technology.

[0168] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for calculating CO2 stockpiles in abandoned oil reservoirs based on multi-component phase equilibrium analysis, characterized in that, The calculation of reservoir carbon dioxide storage considers the effects of pore expansion and component interaction, including the following steps: Step 1: Calculate the molar concentration of non-CO2 native hydrocarbon components in the reservoir before and after CO2 injection; Step 2: Preset the total mass concentration of CO2 in the reservoir after CO2 injection, and use it as the initial value of the actual CO2 concentration in the reservoir mixed fluid to determine the mole fraction of each component in the reservoir mixed fluid under the initial state. Step 3: The trial-and-error method is used to calculate the true CO2 concentration in the reservoir mixture after CO2 injection. Based on the initial value of the true CO2 concentration in the reservoir mixture, the Peng-Robinson equation of state is used to perform phase stability analysis on the reservoir under the final burial pressure condition to obtain the phase stability analysis results of the reservoir under the final burial pressure. Step 4: Determine the mole fraction of each component in the reservoir mixed fluid based on the reservoir phase stability analysis results, obtain the distribution of CO2 and hydrocarbon components in the gas and liquid phases of the reservoir, and update the total CO2 mass concentration of the reservoir. Step 5: Calculate the difference between the updated total CO2 mass concentration in the reservoir after step 4 and the preset total CO2 mass concentration in the reservoir during step 2. If the difference in total CO2 mass concentration in the reservoir If the error is less than the preset maximum allowable error, the update of the total CO2 mass concentration in the reservoir is terminated, and the true CO2 concentration in the reservoir mixed fluid is obtained. Otherwise, the total CO2 mass concentration in the reservoir is updated using the Newton-Raphson method and used as the initial value of the true CO2 concentration in the reservoir mixed fluid. Steps 3 to 5 are then repeated. Step 6: Based on the actual concentration of CO2 in the reservoir mixed fluid, calculate the solubility of CO2 in the aqueous phase of the reservoir mixed fluid, and determine the total amount of CO2 buried in the reservoir. In step 4, the gas phase molar volume and liquid phase molar volume calculated by the multi-component Peng-Robinson equation of state model are corrected using volume shift parameters. Based on the corrected gas phase molar volume and liquid phase molar volume, the total CO2 mass concentration of the reservoir is updated. .

2. The method for calculating CO2 storage capacity of abandoned oil reservoirs based on multi-component phase equilibrium analysis according to claim 1, characterized in that, In step 1, considering that during CO2 injection, the formation pressure of the reservoir changes from the initial pressure... Gradually rising to final burial pressure The reduction in effective stress on the rock skeleton in the reservoir leads to elastic rebound and expansion of the pores, altering the reservoir's internal storage space. The porosity of the reservoir after CO2 injection is calculated using the following formula: ； In the formula, Porosity of the reservoir after CO2 injection; This represents the initial porosity of the reservoir. It is an exponential function; Porosity stress sensitivity coefficient; This represents the initial pressure of the reservoir. The final burial pressure of the oil reservoir; Considering that the volume of formation water in the reservoir remains constant during CO2 injection, the total molar number of all primary hydrocarbon components other than CO2 remains conserved, and that CO2 injection dilutes non-CO2 primary hydrocarbon components in the reservoir, based on the principle of mass conservation, the molar concentration of each non-CO2 primary hydrocarbon component in the reservoir after CO2 injection is calculated using the following formula: ； In the formula, After CO2 injection The molar concentration of each non-CO2 primary hydrocarbon component; For the first The initial molar concentration of each non-CO2 primary hydrocarbon component; This represents the initial water saturation of the reservoir.

3. The method for calculating CO2 storage capacity of abandoned oil reservoirs based on multi-component phase equilibrium analysis according to claim 1, characterized in that, In step 2, the total CO2 mass concentration in the reservoir after CO2 injection is preset. The reservoir mixed fluid after CO2 injection includes injected CO2 and native multi-component hydrocarbons. The mole fraction of each component in the reservoir mixed fluid is calculated using the following formula: ； In the formula, The first in the reservoir mixed fluid Mole fraction of each component; This represents the sum of the molar concentrations of all primary hydrocarbon components in the reservoir; The first in the reservoir mixed fluid after CO2 injection The molar concentration of each non-CO2 primary hydrocarbon component; This represents the initial value of the total CO2 mass concentration in the reservoir after CO2 injection.

4. The method for calculating CO2 storage capacity of abandoned oil reservoirs based on multi-component phase equilibrium analysis according to claim 1, characterized in that, Step 3 includes the following sub-steps: Step 3.1: Based on the Peng-Robinson equation of state, establish a multi-component Peng-Robinson equation of state model to describe the relationship between pressure, volume and temperature of the mixed fluid in the reservoir. The multi-component Peng-Robinson equation of state model is expressed as follows: ； In the formula, For reservoir pressure; This is the universal gas constant; For reservoir temperature; Volume is the molar volume; This is a mixture attraction parameter used to characterize the intermolecular attraction. This is a repulsive force parameter used to characterize the volume effect of the molecule itself; Step 3.2: Transform the multi-component Peng-Robinson equation of state model into a dimensionless cubic equation, calculate the real roots of the dimensionless cubic equation, and determine the deviation factor of each phase in the reservoir mixed fluid. The dimensionless cubic equation obtained by transforming the multi-component Peng-Robinson equation of state model is: ； In the formula, This is the deviation factor; , All are dimensionless coefficients. , ; If the dimensionless cubic equation has three real roots, the largest real root corresponds to the gas phase deviation factor of the reservoir mixed fluid, and the smallest real root corresponds to the liquid phase deviation factor of the reservoir mixed fluid; if the dimensionless cubic equation has one real root, then that real root is the fluid deviation factor of the reservoir mixed fluid. Step 3.3: The gas phase fraction is calculated by isothermal flash evaporation using the Rachford-Rice equation to determine whether anti-condensation or gas-liquid separation occurs in the reservoir mixed fluid, and to obtain the reservoir phase stability analysis results. The Rachford-Rice equation is expressed as follows: ； In the formula, The total component fraction of the reservoir mixed fluid; The first in the reservoir mixed fluid Phase equilibrium constants of each component; For the gas phase fraction, when If the mixture is in a certain state, the reservoir fluid is in a two-phase state of gas and liquid coexistence; otherwise, the reservoir fluid is in a single-phase state.

5. The method for calculating CO2 storage capacity of abandoned oil reservoirs based on multi-component phase equilibrium analysis according to claim 4, characterized in that, In the multi-component Peng-Robinson equation of state model, the gravitational parameters of the mixture and repulsion parameters The calculation is based on the weighted calculation according to van der Waals' mixing rules. The calculation formula is as follows: ； ； In the formula, , All are serial numbers; The first in the reservoir mixed fluid Total mole fraction of each component; The first in the reservoir mixed fluid Total mole fraction of each component; The first in the reservoir mixed fluid The components and the first Binary interaction coefficients between components; , All are single-component parameters. , ,in, , For temperature comparison, The first in the reservoir mixed fluid The critical temperature of each component; , To compare the pressure, The first in the reservoir mixed fluid The critical pressure of each component; These are characteristic parameters used to accurately characterize the vapor pressure properties of each component in a reservoir mixed fluid; The characteristic parameters The calculation formula is: ； In the formula, It is the eccentricity factor.

6. The method for calculating CO2 storage capacity of abandoned oil reservoirs based on multi-component phase equilibrium analysis according to claim 1, characterized in that, In step 4, based on the phase equilibrium constants and gas phase fractions of each component in the reservoir mixed fluid calculated in step 3, the mole fractions of the gas phase and liquid phase components in the reservoir mixed fluid under equilibrium conditions are calculated using the following formula: ； ； In the formula, This represents the mole fraction of the liquid phase component in the reservoir mixed fluid; This represents the mole fraction of the gas phase component in the reservoir mixed fluid; The first in the reservoir mixed fluid Total mole fraction of each component; The first in the reservoir mixed fluid Phase equilibrium constants of each component; This refers to the gas phase fraction; Based on the mole fractions of gaseous and liquid components in the reservoir mixture under equilibrium conditions, the distribution of CO2 and hydrocarbon components in the gas and liquid phases of the reservoir can be determined. By correcting the volume shift parameter in the multi-component Peng-Robinson equation of state model for the gas phase molar volume and liquid phase molar volume, we obtain: ； ； In the formula, This is the corrected molar volume of the gas phase; The molar volume of the gas phase calculated using the multi-component Peng-Robinson equation of state model; This is the corrected liquid phase molar volume; The liquid phase molar volume calculated using the multi-component Peng-Robinson equation of state model; These are the volume translation parameters; Update the total CO2 concentration of the reservoir based on the corrected gas phase molar volume and liquid phase molar volume. The calculation formula is: ； In the formula, Liquid phase fraction; This represents the mole fraction of CO2 in the liquid phase of the reservoir mixed fluid. It represents the mole fraction of CO2 in the gas phase of the reservoir mixed fluid.

7. The method for calculating CO2 storage capacity of abandoned oil reservoirs based on multi-component phase equilibrium analysis according to claim 1, characterized in that, In step 5, when updating the total CO2 mass concentration of the reservoir using the Newton-Raphson method, a dimensionless objective function is first constructed to reflect the difference between the updated total CO2 mass concentration of the reservoir and the preset total CO2 mass concentration of the reservoir. The dimensionless objective function is expressed as follows: ； In the formula, The objective function is dimensionless. The preset value for the total mass concentration of CO2 in the reservoir after CO2 injection; The total mass concentration of CO2 in the updated reservoir ; The derivative of the dimensionless objective function with respect to the total CO2 mass concentration is calculated using the central difference method to capture the direction of gradient change, thus obtaining the reservoir's total CO2 mass concentration updated by the Newton-Raphson method. for: ； in, ； In the formula, The derivative of the dimensionless objective function; This represents the step size for small perturbations.

8. The method for calculating CO2 storage capacity of abandoned oil reservoirs based on multi-component phase equilibrium analysis according to claim 1, characterized in that, Step 6 includes the following sub-steps: Step 6.1: Calculate the effective partial pressure of CO2 based on the actual concentration of CO2 in the reservoir mixed fluid. The calculation formula is as follows: ； In the formula, This is the effective partial pressure of CO2; This represents the mole fraction of CO2 in the free phase. This is the fugacity coefficient of CO2, used to reflect the escape tendency of CO2; The final burial pressure of the oil reservoir; Step 6.2: Calculate the solubility of CO2 in the aqueous phase of the reservoir mixed fluid using Henry's Law, and obtain: ； In the formula, This represents the solubility of CO2 in the aqueous phase of the reservoir mixed fluid. It is the Henry's constant; For reservoir temperature; Step 6.3: Calculate the total amount of CO2 buried in the reservoir based on the solubility of CO2 in the aqueous phase of the reservoir mixed fluid; The formula for calculating the total amount of CO2 buried in the reservoir is as follows: ； In the formula, This represents the total amount of CO2 buried in the reservoir; This represents the molecular weight of CO2. This represents the total volume of the reservoir. Porosity of the reservoir after CO2 injection; This represents the total mass concentration of CO2 in the reservoir. This represents the water saturation of the reservoir under final burial pressure.

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