阅读说明：本技术 一种基于CPA状态方程预测NaCl水溶液中CO2溶解度的方法 (CPA state equation-based prediction of CO in NaCl aqueous solution2Method of solubility ) 是由 卞小强 何万春 于 2021-07-09 设计创作，主要内容包括：本发明提供一种基于CPA状态方程预测NaCl水溶液中CO-(2)溶解度的方法。以CPA-SRK状态方程、WS混合规则、NRTL活度系数模型、物料平衡方程、热力学平衡方程组和混相函数为基础,选用更适合CO-(2)的惰性缔合方案,建立了相态模拟逐步迭代数值计算方法。该方法计算速度快、精度高、适用范围宽泛,可指导高含CO-(2)气藏开发和碳捕集与封存,为提高天然气采收率和应对全球CO-(2)排放提供技术支持。(The invention provides a method for predicting CO in a NaCl aqueous solution based on a CPA state equation 2 Method of solubility. Based on CPA-SRK state equation, WS mixing rule, NRTL activity coefficient model, material balance equation, thermodynamic balance equation set and miscible function, selecting more suitable CO 2 The inert association scheme establishes a phase simulation step-by-step iteration numerical calculation method. The method has the advantages of high calculation speed, high precision and wide application range, and can guide high CO content 2 Gas reservoir development and carbon capture and sequestration for improving natural gas recovery and coping with global CO 2 Emissions provide technical support.)

1. CPA state equation-based prediction of CO in NaCl aqueous solution₂The solubility method comprises the following specific steps:

step 1: the equilibrium constant (K) was calculated using the Wilson equation_i) An initial value of (d);

step 2: solving a gas-liquid two-phase total material balance equation (F), and iterating the gas-phase mole number (V) by a Newton method;

and step 3: calculating the mole fraction (x, y) of each component;

and 4, step 4: calculating CPA-SRK-WS state equation parameters;

and 5: gas-liquid two-term parameter with state equation, and solving V 'by Newton iteration method'_mx、V′_my(Z_mx，Z_my)；

Step 6: respectively carrying in gas-liquid phase fugacity coefficients to calculate gas-liquid phase fugacity f of each component_i ^V、f_i ^L；

And 7: checking whether the gas-liquid phase fugacity (f) meets the condition;

and 8: if the conditions are met, outputting gas-liquid balance parameters; if not, recalculating the balance constant K and returning to the step 2.

2. The CPA equation of state based prediction of CO in aqueous NaCl solution of claim 1₂The solubility method is characterized in that in the step 1, T is calculated by adopting a contrast state principle according to input system parameters, component parameters and substance parameters_r、P_rSo that the equilibrium constant (K) is estimated by Wilson's formula_i) Initial value of (d):

in the formula, K_iIs an equilibrium constant;

T_riis a comparative temperature;

P_riis a contrast pressure;

ω is the eccentricity factor.

3. The CPA equation of state based prediction of CO in aqueous NaCl solution of claim 1₂Solubility method, characterized in that the material balance equation in step 2 is as follows:

in the formula, F is a gas-liquid two-phase total material balance equation;

v is the gas phase mole number;

n is a component number;

z is the amount of the component substance;

k is an equilibrium constant;

f' is the first derivative of F with respect to V.

4. The CPA equation of state based prediction of CO in aqueous NaCl solution of claim 1₂Solubility method, characterized in that in said step 3, the mole fraction (x) of each component is calculated using the following formula_i，y_i)：

Wherein i is the ith component;

j is the number of iterations;

y is the gas phase mole fraction;

and x is the liquid phase mole fraction.

5. The CPA equation of state based prediction of CO in aqueous NaCl solution of claim 1₂A method for solubility, characterized in that said step 4 comprises the following steps:

calculating CAP-SRK equation of state parameter a_i，b_i：

m＝0.48+1.574ω-0.176ω² (10)

Wherein R is a general gas constant of 8.314MPa cm³·mol^-1·K^-1；

v is the molar volume, cm³·mol^-1；

a and b are respectively attractive force and repulsive force parameters;

g is a radial distribution function;

α (T) is a function of temperature;

m is a function of the eccentricity factor;

omega is an eccentricity factor;

x is the liquid phase mole fraction;

i is the ith component;

j is the jth component;

is the molar fraction of i molecules that are not bonded to any other active site at association site a;

as strength of association;

ε^ABand beta^ABEnergy parameters and volume parameters of the interaction between the two points AB and AB adopt a CR-1 rule;

eta is the contrast density;

calculating excess Helmholtz free energy(or excess Gibbs free energy G)^E)：

G_ji＝b_jexp(-α_jiE_ji) (16)

G_ki＝b_kexp(-α_kiE_ki) (17)

In the formula, alpha_jiAnd alpha_kiIs a constant (alpha)_ji＝α_ij)；

E_ijIs a component i andthe interaction parameter between j;

calculating the state equation parameter a of the mixed substance_m，b_m：

In the formula (I), the compound is shown in the specification,is excess Helmholtz free energy, approximately excess Gibbs selfBy energy

C is an SRK state equation characteristic parameter and is constant (taking-ln 2);

a_m，b_mthe attractive and repulsive force parameters of the mixture, respectively;

A_m，B_mis a mixture equation of state parameter;

k_ijis a binary interaction parameter.

6. The CPA equation of state based prediction of CO in aqueous NaCl solution of claim 1₂Solubility process characterized in that the solution of V 'obtained in step 5'_mx、V′_myThe following conditions are satisfied:

|V′_mx-V_mx|/V′_mx+|V′_my-V_my|/V′_my＜10^-4 (26)

wherein V is a molar volume.

7. The CPA equation of state based prediction of CO in aqueous NaCl solution of claim 1₂A method of solubility characterized in that said step 6 comprises the steps of:

entrained gas-liquid phase fugacity coefficient:

wherein Z is a deviation coefficient;

is the fugacity coefficient;

calculating the fugacity of each component of the gas-liquid phase:

wherein f is fugacity, MPa;

v and L are gas phase and liquid phase identifiers respectively.

8. The CPA equation of state based prediction of CO in aqueous NaCl solution of claim 1₂Method for solubility, characterized in that said step 7 satisfies the following conditions:

wherein i is the ith component;

f is fugacity, MPa;

v and L are gas phase and liquid phase identifiers respectively.

9. The CPA equation of state based prediction of CO in aqueous NaCl solution of claim 1₂Method for solubility, characterized in that in step 8 the equilibrium constant K is_iCalculated using the formula:

wherein i is the ith component;

f is fugacity, MPa;

x and y are mole fractions of liquid phase and gas phase respectively.

Technical Field

The invention relates to the technical field of petroleum and natural gas exploration and development, and aims at solving the problem of high CO content₂A technology for natural gas reservoir development and Carbon Capture and Sequestration (CCS) provides a method for predicting CO in NaCl aqueous solution based on CPA state equation₂Method of solubility.

Background

As is well known, CO₂The experimental determination of solubility is time consuming and expensive. Therefore, thermodynamic models have been developed based on experimental data and phase equilibria to break through the limitations of experimental approaches. At present, the content of CO is high₂Development of gas reservoir and CO₂CO is not considered in the phase simulation research of the buried₂Influence of formation water miscibility and ion content variation, which will lead to dynamic prediction of such gas reservoir development indices and CO₂There is inaccuracy in the study of dissolution mechanism in sequestration. For CO₂Thermodynamic studies of mixed formation water systems, mainly aiming at different salt solubilities. Due to the limitation of an experimental method, the experimental data of the system is very little, so that the research of the multi-element mixed system is mainly carried out on the basis of the research of a binary system. In addition, CO₂The phase equilibrium theory of formation water mainly uses the combination of a cubic state equation and different mixing rules to calculate bubble point, dew point and flash evaporation of experimental data and fit energy and binary interaction parameters corresponding to the different mixing rules. Conventional cubic state equations (represented by SRK, RK) are widely used in the thermodynamic analysis of the petroleum industry. However, due to CO₂Extremely non-polar, and is H₂Strong hydrogen bonding exists between O, so that CO is contained₂The natural gas in the formation water has complex dissolution rule, so that the high-pressure physical property parameter calculation result is larger. Plus a polar molecule H₂The weakening chemical effect of other hydrogen bonds exists between O molecules, so that the associated molecules have two effects of self-association and cross-association, and the thermodynamic phase behavior of a solution system is difficult to describe by a conventional cubic state equation. Therefore, the equation of state containing the association is urgently needed to perform thermodynamic phase equilibrium calculation of the solution system from a microscopic angle.

Prediction of CO since 2000₂-H₂xCO in O-NaCl mixed solution system₂The method is widely concerned by a large number of scholars, and researches are mainly carried out on the conventional cubic state equation in combination with different mixing rules and considering the state equation of association. Duan and Sun (2003) established predictions of CO based on the Duan model presented in 1992 in conjunction with particle interaction theory₂Thermodynamic model of solubility in pure water and NaCl solution. Then, to improve the performance of the models for Duan and Sun, Duan et al (2006) propose a non-iterative equation. However, the model of Duan is complex, has 15 adjustable parameters, and does not consider CO₂And H₂The interaction between O. Spycher and Pruess (2005) use of a composition containing CO₂And H₂Solubility model of O activity coefficient to explain the effect of dissolved salts. Dubessy et al (2005)) CO is constructed by utilizing Redlich-Kister method₂-H₂An asymmetric thermodynamic model of activity coefficients of water and gas components in an O-NaCl system. Hassanzadeh et al (2008) propose activity coefficient-fugacity coefficient similar to the Duan modelA model of thermodynamics based on either RK or PR state equations. However, these simple equations of state do not describe CO₂And H₂Cross-associations between O and self-associations of water.

Since the rapid development of the first-order perturbation theory, the spherical state equation of the hard ball chain is widely applied to the thermodynamic phase equilibrium calculation of a solution system with stronger non-polarity. Yan and Chen (2010) propose a PC-SAFT equation of state and an activity coefficient model for determining CO at effective temperature and pressure ranges of 150MPa and 473K₂Solubility in NaCl solution. Sun and Dubessy (2012) determine CO using the SAFT-LJ model₂Solubility in sodium chloride solution below 573K. Dubacq et al (2013) constructed H₂O-CO₂The NaCl ternary system phase equilibrium activity-composition model has effective temperature and pressure ranges of 283-653K and 0.1-350 MPa. Mao et al (2015) determined CO using a Helmholtz free energy model over a broad temperature range (273-₂Solubility in NaCl solution. Xu et al (2017) use EPPR78 and the PC-SAFT equation of state for CO₂Capture was studied. However, these models have multiple adjustable parameters and are very complex. Kontogorgis et al (1996) proposed a cubic association equation of state (CPA | EOS) based on classical cubic equations of state, which is widely used to calculate the gas-liquid equilibrium and liquid-liquid equilibrium of mixed solution systems such as hydrocarbons, esters and alcohols. The equation also introduces an association term in a hard ball chain state equation to treat a solution system with extremely strong molecules on the basis of retaining the advantage that a gas state equation describes gas phase behavior. Muro-Sun et al (2008) in a water-acetic acid system, satisfactory results were obtained using the CPA-HV model at the expense of high interaction parameters. Tsivintzelis et al (2011) predicted CO using the CPA-SRK equation of state₂、CO₂-n-alkanes (n)<5) Solubility in pure water mixed solution, versus inert, 2B, 3B and 4C association schemes, consider CO₂Is a 4C association structure, and takes CO into consideration₂And H₂The prediction accuracy is highest when the cross-correlation of O is used.And Kontogoorgis (2016) studied CO₂+ quadrupole interactions of hydrocarbon mixtures with less tunable parameters than other CPA equations of state.

In summary, a single CPA equation of state has been applied to complex systems and has achieved some satisfactory results. However, there are problems such as low accuracy and narrow temperature and pressure ranges.

Disclosure of Invention

The invention aims to overcome the problems in the model and provides a method for predicting CO in a NaCl aqueous solution based on a CPA state equation₂The solubility method has the advantages of high speed, high precision and wide application range, and can provide effective reference data for practical engineering and experimental analysis.

The method firstly provides a state equation (CPA-SRK) capable of predicting liquid phase thermodynamic parameters of the polar fluid by combining a Wertheim first-order perturbation theory and adopting the SRK as a mode of combining a physical term and an association term on the basis of the SRK state equation. Secondly, the method replaces the vdW single fluid mixing rule with WS mixing rule that can describe a mixed system containing polar molecules over a wider temperature and pressure range. For CO₂-H₂The CPA-WS model provided by the method adopts a binary O system and is more suitable for CO₂The inert association scheme optimizes six adjustable parameters of the CPA-WS model in a larger temperature and pressure range; for H₂O-CO₂NaCl ternary System, believed to be in CO₂NaCl and H₂No association occurs in the O-NaCl system, the physical parameter of NaCl in the CPA-WS model is estimated by adopting an SRK state equation, and a new interaction parameter (D) is provided to replace CO₂NaCl and H₂Binary interaction parameter k in O-NaCl System_ijAnd k_ji. Finally, the overall performance of the CPA-WS model provided by the method is verified through a large amount of experimental data, aiming at CO₂-H₂Compared with a CPA-vdW model and a PRSV-WS model, the O system has better prediction performance of the CPA-WS model; for H₂O-CO₂Compared with the Duan2003, PR-HV and SRK-HV models, the NaCl element system has the same satisfactory prediction precision as the CPA-WS model.

Prediction of CO in NaCl aqueous solution based on CPA state equation₂The solubility method comprises the following specific steps:

step 1: given system parameter T, P and component parameter z_i(i-1, 2, …, N-1) and critical pressure (P) of physical property parameter of corresponding substance_c) Critical temperature (T)_c) And an eccentricity factor (ω).

Step 2: calculating T by utilizing corresponding state principle_r、P_rThereby calculating an equilibrium constant (K) by Wilson's formula_i) The initial value of (c).

In the formula, T_riIs a comparative temperature;

P_riis a contrast pressure;

p is system pressure, MPa;

t is the system temperature, K;

P_ccritical pressure, MPa;

T_ccritical temperature, K;

i is the ith component.

In the formula, K_iIs an equilibrium constant;

ω is the eccentricity factor.

And step 3: k to be estimated_iSolving the equation (F) and estimating the gas phase mole number (V) by Newton's method_j)。

In the formula, F is a gas-liquid two-phase total material balance equation;

v is the gas phase mole number;

i is the ith component;

j is the number of iterations;

y is the gas phase mole fraction;

x is the liquid phase mole fraction;

n is a component number;

z is the amount of the component substance;

k is an equilibrium constant;

f' is the first derivative of F with respect to V.

And 4, step 4: the objective function is verified to satisfy the condition.

|F(V_j+1)-F(V_j)|≤10^-3 (6)

And 5: if the detection condition is not met, returning to the step 3; and if the test condition is met, entering the step 6.

Step 6: calculating the gas-liquid phase component content mole fraction (x) of each substance_i，y_i)。

Step (ii) of7: calculating the state equation parameter a of the CAP-SRK state equation_i，b_i。

m＝0.48+1.574ω-0.176ω² (13)

Wherein R is a general gas constant of 8.314MPa cm³·mol^-1·K^-1；

v is the molar volume, cm³·mol^-1；

a and b are respectively attractive force and repulsive force parameters;

g is a radial distribution function;

α (T) is a function of temperature;

m is a function of the eccentricity factor;

omega is an eccentricity factor;

x is the liquid phase mole fraction;

i is the ith component;

j is the jth component;

is the molar fraction of i molecules that are not bonded to any other active site at association site a;

as strength of association;

ε^ABand beta^ABEnergy parameters and volume parameters of the interaction between the two points AB and AB adopt a CR-1 rule;

η is the contrast density.

And 8: calculating excess Helmholtz free energy by using Huron and Vidal improved NRTL activity coefficient model(or excess Gibbs free energy G)^E)。

G_ji＝b_jexp(-α_jiE_ji) (19)

G_ki＝b_k exp(-α_kiE_ki) (20)

In the formula, alpha_jiAnd alpha_kiIs a constant (alpha)_ji＝α_ij)；

E_ijIs the interaction parameter between components i and j.

And step 9: calculating the mixed material parameter a by using WS mixing rule_m，b_m。

In the formula (I), the compound is shown in the specification,is excess Helmholtz free energy, approximately excess Gibbs free energy

C is an SRK state equation characteristic parameter and is constant (taking-ln 2);

a_m，b_mthe attractive and repulsive force parameters of the mixture, respectively;

A_m，B_mis a mixture equation of state parameter;

k_ijis a binary interaction parameter.

Step 10: the second dimension cross term improvement published by Zhao and Lvov (2016) was chosen to improve the performance of WS-blending rules.

In the formula, k_ijFor the interaction coefficient associated with the second dimension coefficient, k_ij≠k_ji。

Step 11: in CO₂NaCl and H₂In the binary O-NaCl system, a new interaction parameter (D) is used to replace k_ijAnd k_jiAnd calculating E by changing alpha to 0_ij。

D_ij＝1-k_ij+(k_ij-k_ji)x (31)

Step 12: CO 2₂-H₂O cross-association (inert association scheme), calculating the association strength by using a combination rule with a tunable binary interaction parameter F, and calculating CO₂Mole fraction of molecules that do not form bonds with any other active site at association site A

In which i is H₂O, j is CO₂；

F is a binary interaction parameter (F)_ij＝F_ji)。

Step 13: substituting the state equation parameters of the mixed substances into the physical terms of the SRK equation, and calculating the gas-liquid two-phase molar volume V by using a Newton iteration method_mxAnd V_myAnd calculating the mixture molar density rho, the contrast density eta and the radial distribution function g (v).

In the formula, n_y、n_xThe amounts of gas and liquid substances are respectively.

Step 14: using the preceding equation of state for both gas and liquid terms a_m，b_m，X_AiEqual parameters are carried out, and the CPA-SRK is subjected to Newton iteration method to solve V'_mx、V'_myAnd V_mx、V_myAnd (4) comparing until the following conditions are met, otherwise, returning to the step 13, and recalculating the molar density rho of the mixture and the like.

|V'_mx-V_mx|/V'_mx+|V'_my-V_my|/V'_my＜10^-4 (36)

Step 15: respectively carrying in gas-liquid phase fugacity coefficients to calculate gas-liquid phase fugacity f of each component_i ^V、f_i ^L。

In the formula (I), the compound is shown in the specification,is the fugacity coefficient;

z is a deviation coefficient.

According to the adopted modified WS-mix rule:

solving the minimized Helmholtz free energy expression through Newton iteration, and simplifying the expression as follows:

calculating the fugacity of each component of the gas-liquid phase:

step 16: and (3) checking whether the gas-liquid phase fugacity (f) meets the following condition, and if the checking condition is met, obtaining a flash evaporation result: x is the number of_i，y_i，Z_mx，Z_myEta, etc.

And step 17: if the test condition is not satisfied, recalculating the balance constant K_iAnd returning to the step 3 until the condition is met, and outputting the result.

Compared with the prior art, the invention has the following advantages:

1. the calculation method provided by the invention combines the improved WS mixing rule and the NTRL activity coefficient model on the basis of considering the CPA-SRK state equation of the association term, and selects and uses the model more suitable for CO₂The inert association scheme of (1) establishes CO in the NaCl solution₂The mean absolute relative deviation of the comparative experimental data was only 3.56% in the solubility calculation model.

2. Because the invention proposes a new interaction parameter D to replace the original k_ijAnd k_jiThe proposed calculation model has only 5 adjustable parameters, and simplifies the original CPA-WS model.

3. The calculation method provided by the invention has a wide application range, the temperature and pressure ranges are 288.15-523.15K and 0.1-350.0 MPa, the accuracy is highest in the temperature and pressure ranges of 303.15-413.15K and 0.1-50 MPa, and the prediction effect is optimal.

4. The invention adopts a step-by-step iteration method, has low requirement on an initial value by calculation and has strong practicability.

5. The invention can also be used for accurately calculating gas-liquid phase density, molar content, deviation coefficient and CO-rich₂Saturated water content in phase, and the like.

Drawings

FIG. 1 is a basic process flow diagram of the present invention

FIG. 2 is CO₂-H₂AARD comparison result graph corresponding to each prediction model in O binary system

FIG. 3 is a diagram of CO prediction according to the present invention₂One of solubility in NaCl solutionExample results plot

FIG. 4 is CO₂-H₂AARD comparison result graph corresponding to each prediction model in O-NaCl ternary system

Detailed Description

The technical scheme of the invention is described in detail in the following with reference to the attached drawings:

in the embodiment, the established CPA-SRK-WS model is used for CO₂The solubility in sodium chloride solution was calculated and compared to experimental data. The CPA-SRK-WS model parameters were optimally fitted over a large temperature and pressure range using the least squares method, as shown in Table 1. The H values obtained by regression from the experimental data are listed in Table 3₂O-NaCl system and CO₂-value of the interaction parameter (D) of the NaCl system. The calculation process is summarized in FIG. 1, first inputting temperature T, pressure P and composition parameter z_i(ii) a Then calculating the contrast temperature T according to the contrast state principle_rContrast pressure P_rAnd estimating the equilibrium constant (K) by Wilson's formula_i) An initial value of (d); with K_iCalculating the mole fraction (x) of gas-liquid phase component by using material balance equation_i，y_i) (ii) a Calculating CPA-SRK state equation parameters, calculating the state equation parameters of the mixed substance according to the WS mixing rule, and calculating a deviation coefficient (gas-liquid component volume), a mixed density, a contrast density, a radial density function and the like by using a Newton iteration method; calculating the gas-liquid phase fugacity of each component, judging whether the gas-liquid phase fugacity is equal, and if so, obtaining x_i，y_i，Z_mx，Z_myAnd eta, if the results of the gas-liquid balance parameters are not equal, recalculating the balance constant (K) until the conditions are met.

TABLE 1.H₂O-CO₂CPA-WS model parameter optimization for systems

For CO₂-H₂The AARD of the O system, CPA-WS, CPA-vdW and PRSV-WS model calculation results are shown in Table 2. For H₂O-CO₂AARD of the NaCl system, CPA-WS model is shown in Table 3.

TABLE 2 AARD of CPA-WS, CPA-vdW and PRSV-WS model calculation results

TABLE 3H₂O-NaCl and CO₂CPA-WS model parameters of the NaCl System

In conclusion, the invention provides a method for predicting CO in NaCl aqueous solution based on CPA state equation₂The solubility method is a calculation method which combines an improved WS mixing rule and an NTRL activity coefficient model on the basis of considering a CPA-SRK state equation of an association term and selects a model more suitable for CO₂The inert association scheme of (1), thermodynamically theoretically for CO in NaCl solution₂The solubility was calculated. The calculation method has the characteristics of high speed, wide temperature and pressure range, high precision and the like, and the average absolute relative error with experimental data is 3.56%; by the method introduced by the invention, reliable CO is provided₂The calculation method of thermodynamic phase equilibrium theory of solubility can guide high CO content₂Gas reservoir development and carbon capture and sequestration for improving natural gas recovery and coping with global CO₂Emissions provide technical support.