JP2007319808A - Separation membrane simulation method, simulation device, program and computer-readable storage medium with the program recorded thereon, and separation membrane - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To estimate structure of a separation membrane having high separation performance, relating to a separation membrane simulation method, a simulation device, a program, and a computer-readable storage medium with the program recorded thereon, and a separation membrane. <P>SOLUTION: In the simulation of the structure of the separation membrane, structure data of an existing separation membrane is stored (S100), adsorption performance is found for two or more kinds of respective separation object species in the existing separation membrane structure using the grand-canonical Monte Carlo method (S106), a prediction model of the separation membrane structure is created using the multivariable regression technique based on the adsorption performance (S108), diffusion performance of the separation membrane in a plurality of micro pore networks based on the prediction model of the membrane structure is found using the dynamic Monte Carlo method (S122), the separation performance of the virtual separation membrane can be estimated. A CO<SB>2</SB>/N<SB>2</SB>separation membrane is a gas separation membrane for carbon dioxide gas and nitrogen gas, with a permeability coefficient of carbon dioxide gas of 1×10<SP>-11</SP>mol×m/m<SP>2</SP>sPa or more and a separation coefficient of 100 or more. The gas separation membrane has three-dimensional micro pore structure, including micro pores of a micro pore diameter of at least 3.2 to 4.2 Å, and a diameter Dsite of an adsorption site is 7-20 Å. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a separation membrane simulation method, a simulation apparatus, a program, a computer-readable storage medium storing the program, and a separation membrane.

  In recent years, a method has been proposed to collect and isolate carbon dioxide generated during combustion of fossil fuels after separation by membranes as a means to suppress the release of carbon dioxide into the atmosphere as global environmental problems become more serious. ing. In this carbon dioxide sequestration process, a lot of cost is required in the part of carbon dioxide separation and recovery, and reduction of this cost is indispensable for realizing the process. To that end, it is expected to synthesize a carbon dioxide separation membrane having heat resistance, pressure resistance and high separation performance.

  For example, from a mixed gas consisting of a laminated film in which a film made of a polyether copolymer is laminated on a T-type zeolite film or a mixed film made of a mixture of T-type zeolite powder and a polyether copolymer, carbon dioxide gas from a mixed gas Or the gas separation membrane which isolate | separates hydrogen gas is proposed (patent document 1).

  A polymer gas separation membrane having an asymmetric structure of cardo type polyimide with improved gas separation performance has also been proposed (Patent Document 2).

JP 2005-305371 A JP 2005-334687 A

  However, the polymer gas separation membrane has a problem that the durability of the membrane is slightly inferior to that of a conventional inorganic separation membrane. Moreover, the above-mentioned inorganic gas separation membrane is also one step ahead of the recent required separation performance level.

  The present invention has been made in view of the above-described problems, and in particular, a separation membrane simulation method, a simulation apparatus, a program, and a computer-readable computer that records the program can simulate the structure of a virtual separation membrane having a high separation performance for gas. An object is to provide a storage medium and a separation membrane.

  In order to achieve the above object, a separation membrane simulation method, a simulation apparatus, a program, a computer-readable storage medium storing the program, and a gas separation membrane of the present invention have the following characteristics.

(1) A gas separation membrane of carbon dioxide gas and nitrogen gas having a carbon dioxide gas permeability coefficient of 1 × 10 ⁻¹¹ mol · m / m ² spa or more and a carbon dioxide gas separation coefficient of 100 or more, The gas separation membrane has a three-dimensional pore structure, the pore size of the separation membrane is at least 3.2 mm to 4.2 mm, and the adsorption site diameter Dsite is from 7 mm to 20 mm. This is a characteristic CO ₂ / N ₂ separation membrane.

  By setting the pore diameters dy, dz in the permeation direction of the gas separation membrane and the diameter Dsite of the adsorption site within the above range, the permeation performance is more than one digit better than the permeation coefficient of the conventional carbon dioxide gas. A separation membrane having a separation performance superior to that of carbon dioxide gas can be obtained.

(2) In the _CO 2 / _{N 2} separation membrane according to the above (1), the _CO 2 / _{N 2} separation membrane is a _CO 2 / _{N 2} separation membrane is a separation membrane made of zeolite membrane or zeolite analogous compounds .

(3) The CO ₂ / N ₂ separation membrane according to (1) above, wherein the CO ₂ / N ₂ separation membrane is based on a skeleton made of silicon dioxide, and a part of silicon is replaced with aluminum. a zeolite separation membrane, Si / Al ratio of the Si / Al zeolite separation membrane is a _CO 2 / _{N 2} separation membrane is 20 to 99.

  Furthermore, by setting the Si / Al ratio of the Si / Al zeolite separation membrane to 20 to 99, the carbon dioxide gas has a permeation performance superior to that of the conventional carbon dioxide gas by one digit or more. A separation membrane having a separation performance superior to that of the separation factor can be obtained.

  (4) A simulation method for calculating the separation performance of a separation membrane, wherein the structure data of an existing separation membrane is stored, and at least two kinds of target separations in the existing separation membrane structure using a grand canonical Monte Carlo method The adsorption performance for the species is obtained, a prediction model for the separation membrane structure is created using a multivariable regression method based on the adsorption performance, and a plurality of pore networks are created based on the prediction model for the separation membrane structure using a dynamic Monte Carlo method. This is a separation membrane simulation method in which the diffusion performance of the separation membrane is obtained and the separation performance of the virtual separation membrane can be estimated.

  Since a prediction model of the separation membrane structure can be created and the separation performance of the virtual separation membrane structure can be estimated based on this prediction model, the same thing as conducting an experiment can be done safely in a short time and inexpensively, An optimum separation membrane structure can be obtained. Further, by combining a plurality of methods and passing through respective calculation processes, the separation performance can be screened on the virtual separation membrane structure at high speed.

  (5) The separation membrane simulation method according to (4), wherein the separation membrane simulation method further determines an optimum separation membrane structure according to the separation conditions.

  Based on the previously obtained virtual separation membrane structure and its separation performance, the optimum separation membrane structure can be obtained according to the separation conditions.

(6) In the separation membrane simulation method according to (4) or (5), the separation membrane is a separation membrane simulation method which is a zeolite membrane for CO ₂ gas separation.

  It can be applied to gas separation membranes. Furthermore, by combining the structure of the separation membrane and its separation performance using only the molecular dynamics method (MD), the Grand Canonical Ensemble and Monte Carlo method can be combined to achieve high speed in a short time. Can be screened.

  (7) A simulation device for calculating the separation performance of a separation membrane, wherein the structure data storage means stores structure data of an existing separation membrane, and at least two or more types in the existing separation membrane structure using a grand canonical Monte Carlo method An adsorption performance calculation means for obtaining adsorption performance for each target separation species, a prediction model creation means for creating a prediction model of a separation membrane structure using a multivariable regression method based on the adsorption performance, and a dynamic Monte Carlo method Diffusion performance calculation means for obtaining diffusion performance of the separation membrane in a plurality of pore networks based on the prediction model of the separation membrane structure, and a separation membrane capable of estimating the separation performance of a virtual separation membrane This is a simulation device.

  (8) The separation membrane simulation apparatus according to (7), further including a structure optimization unit that obtains an optimum separation membrane structure according to a separation condition.

(9) The separation membrane simulation apparatus according to (7) or (8), wherein the separation membrane is a separation membrane simulation method which is a zeolite membrane for CO ₂ gas separation.

  (10) Using a structure data storage means for storing the structure data of the existing separation membrane and a grand canonical Monte Carlo method, the computer calculates adsorption performance for at least two kinds of target separation species in the existing separation membrane structure. Based on the adsorption performance calculation means, a prediction model creation means for creating a prediction model of the separation membrane structure using a multivariable regression method based on the adsorption performance, and a plurality of based on the prediction model of the separation membrane structure using a dynamic Monte Carlo method This is a program for functioning as a diffusion performance calculating means for obtaining the diffusion performance of the separation membrane in the pore network and a virtual separation membrane separation performance calculating means for estimating the separation performance of the virtual separation membrane.

(11) The program according to (10), wherein the separation membrane is a zeolite membrane for CO ₂ gas separation.

  (12) A computer-readable recording medium on which the program according to (10) or (11) is recorded.

  (13) A separation membrane having a virtual separation membrane structure obtained by the separation membrane simulation method according to any one of (4) to (6) above.

  (14) A separation membrane having a virtual separation membrane structure obtained by estimation by the separation membrane simulation apparatus according to any one of (7) to (9) above.

  (15) A separation membrane having a virtual separation membrane structure obtained by reading and estimating the program according to (10) or (11) with a computer.

According to the present invention, it is possible to simulate a separation membrane structure with high separation performance. In particular, by selecting a target gas, a virtual optimum separation membrane structure can be simulated, and this virtual optimum The separation membrane performance can be screened on the separation membrane structure. Further, according to the CO 2 _/ N ₂ separation membrane, it is possible to provide a film having excellent separation performance by conventional.

  Hereinafter, a separation membrane simulation method and apparatus according to the best embodiment of the present invention will be described with reference to the drawings.

  FIG. 1 is a block diagram showing a schematic configuration of an example of a separation membrane simulation apparatus according to the present invention. FIG. 2 shows a flow of processing for carrying out an example of a numerical simulation method for calculating the separation performance of the separation membrane according to the present invention. A series of processing is performed on a computer such as a personal computer or a workstation. Is executed.

In the present embodiment, an inorganic gas separation membrane, particularly a zeolite membrane, will be described as an example of the separation membrane, and a mixed gas will be used as two or more separation target separation species. Description will be made by taking a mixed gas composed of carbon (CO ₂ ) and nitrogen (N ₂ ) as an example.

  The separation membrane simulation apparatus according to the present embodiment uses a Grand Canonical Monte Carlo (GCMC) method based on the database of the structure database 10 of the existing inorganic separation membrane structure which is a structure data storage unit. An adsorption performance calculation device 12 for obtaining adsorption performance for at least two kinds of target gases in each existing inorganic separation membrane structure and a multivariable regression method (for example, PLS (Partial Last Square) method) based on the adsorption performance are used. Based on the prediction model for the separation membrane structure and the prediction model for the separation membrane structure using the dynamic Monte Carlo method (DMC method), the diffusion performance of the separation membrane in a plurality of pore networks is obtained. Diffusion performance arithmetic unit 16 and obtained A screening membrane performance database 18 in which the inorganic separation membrane structure constituted by the predicted model and the separation performance thereof are stored in correspondence with each other. Furthermore, based on the database of the screening membrane performance database 18, it has the optimal structure prediction apparatus 20 which performs the optimal structure prediction of an inorganic type separation membrane according to separation conditions, and also the virtual structure stored in the said screening membrane performance database 18 The display device 22 displays the structure of a typical separation membrane and the optimum structure obtained by the optimum structure prediction device 20.

  The separation membrane simulation device according to the present embodiment may further include a virtual separation membrane separation performance calculation device that estimates the separation performance of the virtual inorganic separation membrane.

  In the present embodiment, the adsorption performance is evaluated using, for example, the adsorption amount and adsorption selectivity of the target separation gas with respect to the inorganic separation membrane as an index, and the diffusion performance is, for example, the target separation gas with respect to the inorganic separation membrane The separation coefficient is evaluated using the permeation coefficient and diffusion selectivity as indices, and the separation performance is evaluated using the permeation coefficient and separation coefficient of the target separation gas with respect to the inorganic separation membrane as an index, for example.

  The inorganic separation membrane structure database 10 includes existing inorganic separation membrane structures, for example, the types of atoms of the zeolite lattice in the zeolite membrane (for example, aluminum and silicon replaced by silicon in the framework of theorite silicon dioxide). Of the separation membrane structure such as the density of the zeolite membrane, the density of the zeolite membrane, the pore volume, the specific surface area, the pore diameter, and the dimension number of the pores of the adsorption site. Here, the zeolite is generally based on a skeleton made of silicon dioxide, and the entire crystal lattice is negatively charged by replacing a part of silicon with aluminum, and cations such as sodium are present in the pores of the zeolite. To balance the charge.

  In addition, the adsorption performance calculation device 12 uses a grand canonical Monte Carlo method (GCMC (Grand Canalic Monte Carlo) method), and each of the existing inorganic separation membrane structures, in this embodiment, at least two types of the existing theolite membrane structures. Adsorption ability with respect to each target gas, for example, carbon dioxide and nitrogen, for example, adsorption amount of carbon dioxide and nitrogen and adsorption selectivity of carbon dioxide and nitrogen are required.

Further, the prediction model creation device 14 predicts the separation membrane structure using, for example, a PLS (Partial Least Square) method which is a multivariable regression method based on the equilibrium adsorption amount of carbon dioxide and the adsorption selectivity of CO ₂ / N _2. Multiple models are created.

Further, the diffusion performance calculation device 16 uses a dynamic Monte Carlo method (DMC method) and based on a prediction model of the separation membrane structure, the diffusion performance of the separation membrane in a plurality of pore networks described later, for example, a carbon dioxide permeability coefficient. , CO ₂ / N ₂ diffusion selectivity is required.

  In the screening membrane performance database 18, the inorganic separation membrane structure composed of the obtained prediction model and the separation performance are stored in association with each other. Then, the optimum structure prediction device 20 performs the optimum structure prediction of the inorganic separation membrane according to the separation conditions, and the display device 20 includes the virtual separation membrane structure stored in the screening membrane performance database 18, The optimum structure obtained by the optimum structure prediction device 20 is displayed.

  In the simulation apparatus shown in FIG. 1, a separation performance calculation device may be provided between the diffusion performance calculation device 16 and the screening membrane performance database 18, and the separation performance salt storage device is obtained by the DMC method described above. From the diffusion selectivity and permeation coefficient and the adsorption selectivity and adsorption amount obtained by the GCMC method, the separation performance of a virtual inorganic separation membrane, for example, the permeation coefficient and separation coefficient of carbon dioxide and nitrogen gas are obtained.

  Next, the operation and simulation method of the separation membrane simulation apparatus of the present embodiment will be described below with reference to FIGS. In the present embodiment, as described above, a zeolite membrane is used as an example of an inorganic separation membrane, and a mixed gas of carbon dioxide and nitrogen is used as an example of a mixed gas to be separated.

  In the adsorption performance calculation device 12, the type of atoms of the zeolite lattice in the zeolite membrane stored in the structure database 10 of the inorganic separation membrane (for example, aluminum and silicon replaced by silicon in the skeleton made of theolite silicon dioxide) Ratio: Al / Si ratio), density of the zeolite membrane, pore volume, specific surface area, pore diameter, separation membrane structure characteristic data such as the number of pores of the adsorption site are read (S100). Next, adsorption simulation is performed using the GCMC method. This simulation is performed according to the following procedure.

(A) Determination of calculation conditions In this embodiment, for example, “Cerius 2” of MSI was used for calculation by the GCMC method. “Cerius 2” is very excellent in terms of Graphical Interface, and can perform complicated computer simulation relatively easily.

(B) Model of zeolite membrane The unit cell structure contained in Cerius 2 was used for the zeolite structure and Si / Al ratio used in this study. The model actually used is a unit cell expanded several times. In order to perform the calculation accurately, the larger the size of the cell, the better. However, since the calculation time is increased accordingly, in this embodiment, one side is 30 to 40 mm (3 to 4 nm). The unit cell was expanded.

(C) Handling of lattice vibration of crystal In the present embodiment, the calculation was performed with the zeolite lattice fixed. In past studies examining the diffusion mechanism of adsorbed molecules in zeolite, many zeolite lattices are fixed to shorten the calculation time. It should be noted that the effect of fixing the crystal lattice is considered to be small when a simulation is performed on a system having a small molecule with respect to the pores of zeolite or an extremely low concentration region.

(D) Number of calculation steps It is empirically known that when simulation is performed using the Monte Carlo method (MC method), the energy of the system becomes almost constant at 200,000 steps or more in many systems. Therefore, the number of trials of 200,000 steps or more is required to reach the equilibrium state. Therefore, in this embodiment, the number of simulation trials by the MC method when calculating the adsorption amount and heat of adsorption in the equilibrium state is set to 1,000,000 to 2,000,000 steps.

(E) Determination of Ensemble Since the calculation is based on the GCMC method, a μVT ensemble (grand canonical ensemble) having a constant chemical potential μ, volume V, and temperature T is used. When performing the calculation, the pressure and temperature are input as constant values (S102).

(F) CUTOFF LENGTH
In the simulation, when calculating the force and energy acting on a certain atom, calculating the interaction with all atoms results in a huge amount of calculation and requires a lot of calculation cost. The force acting between atoms converges when the distance increases to some extent. Therefore, normally, only the atoms in the sphere with radius r from the atom are considered, and the influence of the atoms outside it is ignored to speed up the calculation. The value of r is called cutoff.

  Originally, it is necessary to take a cut-off that does not change the heat of adsorption determined by the simulation by the MC method, but considering the time required for the calculation, in this study, the van der Waals cut-off was 9.8 mm, and the electrostatic interaction Cut-off of 8.2 mm.

(G) Other calculation conditions In addition to the calculation conditions as described above, various calculation conditions are set. For these, the values set in Default of “Cerius 2” are used.

(H) Potential and parameters used for calculation (i) Potential used for calculation In this embodiment, calculation was performed on the assumption that the adsorbed molecule is rigid without considering the intramolecular interaction.

The intermolecular interaction was calculated by the following formula (1).
Here, ε ₀ is bond strength and r ₀ is bond length. The Lorentz-Berthelot rules below were used as the interaction parameters between various molecules.

(Ii) Parameters used in calculation Table 1 shows the parameters used in the present embodiment. The C—O bond length was fixed at 1.18 mm. Furthermore, the parameter of the N atom was N when CO ₂ / N ₂ , and N_1 was used when N ₂ / O ₂ . N_1 and O_2 are general-purpose force field parameters “burchart1.01-DEIDING2.21” included in “Cerius2”. O_z · Si_z · Al_z is the type of atom in the zeolite lattice. The charges of Si and Al in the zeolite lattice were determined for each Si / Al ratio so as to be 4: 3 while the charge of the entire zeolite was zero (S104).

The calculation by the GCMC method described above is performed from the adsorption data of the existing zeolite membrane shown in Table 2, and the CO ₂ adsorption amount, the N ₂ adsorption amount, and the CO ₂ / N ₂ adsorption selectivity are obtained (S106). For MFIs with different Si / Al ratios, Si in silicalite was replaced with Al by hand, and Na ions were introduced using the function “Cation Locator” of “Cerius 2”. At this time, the Al atoms were randomly substituted at positions where Al—O—Al could not be formed. The number of Na indicates the number in the unit cell of MFI. The obtained results are shown in FIG.

Next, the prediction model creation device 14 uses the PLS method, which is a multivariate regression method, based on, for example, the equilibrium adsorption amount of carbon dioxide and the adsorption selectivity of CO ₂ / N ₂ obtained by the adsorption performance calculation device 12. A plurality of prediction models of the separation membrane structure are created (S108).

  Hereinafter, a process for creating a prediction model of a separation membrane structure using the PLS method and the PLS method will be described.

  First, Principal Component Analysis (PCA) is a technique for expressing features of multivariate data using an index called a principal component. By performing principal component analysis, it is possible to grasp the relationship between data and the correlation between variables.

  The PLS (Partial Least Squares) method is a multivariate regression technique that extends a PCA so that a highly predictive linear model can be constructed. In the PLS method, the explanatory variable X is not used for the regression analysis as it is, but the PLS method is optimally modeled using the principal component t which is a linear combination of the explanatory variables. On the other hand, in the PLS method, a model can be constructed even when the number of explanatory variables exceeds the number of samples. Furthermore, the problem of collinearity does not occur because the inverse matrix operation is not included. Moreover, since the information of the explanatory variable is sequentially used through the principal component, the predictability can be examined while changing the degree of freedom of the PLS model. Therefore, in the embodiment, a model of equilibrium adsorption amount / adsorption selectivity is constructed using this PLS method.

In the present embodiment, multivariate analysis was performed using only data (adsorption amount / adsorption amount ratio) with a total pressure of 100 kPa. The specific procedure of PLS modeling is shown below. In the present embodiment, in the PLS method, a linear model of Y = f (X) is constructed between the explanatory variable X and the objective variable Y. There are _two objective variables: CO ₂ adsorption amount and CO ₂ / N ₂ adsorption selectivity.
(1) Extract explanatory variables X for modeling (2) Optimize explanatory variables by GA-PLS (3) Create a PLS model using only optimized explanatory variables

First, the following explanatory variables were used.
This variable order, V _pore percentage pore volume of the zeolite, S _pore specific surface area, the AL _rate of Al atoms occupy in the T atoms of the zeolite framework, dp _-min minimum pore diameter, dp _{- max} is the maximum pore diameter, D _-min minimum adsorption sites diameter, D _-max maximum adsorption sites diameter, Frame D and TD is a variable representing the continuity of atoms taken from the database of the zeolite, P _dis the pore It represents the degree of distortion. Therefore, optimization of variables is performed by GA-PLS, and the results of creating a PLS model are shown in the following formulas (4) to (7) (models 1 to 4 in order). Model 1 is a prediction model for the equilibrium adsorption amount of CO _{2 with a} pure silica structure, Model 2 is a prediction model for adsorption selectivity (CO ₂ / N ₂ ) with a structure of pure silica, and Model 3 is a CO ₂ equilibrium adsorption structure with aluminum. The quantity prediction model, model 4, is an adsorption selectivity (CO ₂ / N ₂ ) prediction model of a structure containing aluminum.

(Equation 3)
Structure of pure silica Adsorption amount = -1.331S _pore -0.052dp _-min -0.042dp _-max -0.011D _-min +1.173 (4)
Selectivity = 21.189V _pore -171.018S _pore -2.51dp _-max -0.818D _-max +47.713 (5)
Structure containing Al Adsorption amount = 5.887 Al _rate +0.643 (6)
Selectivity = -1555.104V _pore +805.207 Al _rate + 5.129dp _-max -1.429D _-max +726.577 ・ ・ (7)

  In general, when modeling is performed, the fitting error and the prediction error vary depending on the degree of freedom of the model. When the degree of freedom of the model is small, this is called underfitting and the fitting error is large. Increasing the degree of freedom naturally reduces the fitting error and improves the fitting. In that case, however, there is a possibility of overfitting. Therefore, it is desirable to observe the prediction error while changing the degree of freedom and use the degree of freedom that minimizes the prediction error as the optimum component. The optimal number of components is determined by cross validation.

  Cross validation includes external validation and internal validation. Generally, external validation is performed when a relatively large number of samples are given.

  Internal validation is often performed using a leave-one-out method. First, assuming that there are n samples, a test set is formed by removing one sample. Considering the remaining n-1 samples as a training set, a PLS model is calculated. Thereafter, PLS models are calculated as appropriate while removing them one by one in order. Then, the correlation between the obtained n estimated values of y and measured values of y is observed. Next, an estimated value of y is obtained for all samples in the same procedure for the two-component PLS model. Further, the PLS component is increased to determine the error of the corresponding PLS component, and the number of components that minimizes the error is set as the optimal component number.

As a result of cross validation, Table 2 below shows R ² (explanation variance) and Q ² (predictive explanation variance) of each model. Further, FIG. 4 shows a comparison between the results obtained by the GCMC calculation and the results obtained by the model in the structure of pure silica.

In the structure of pure silica, R ² of the adsorption amount / adsorption selectivity was about 0.4 to 0.5, and Q ² was about 0.35 to 0.4. From this, it can be said that these two prediction accuracy is about 60%. Moreover, in the structure containing Al, high R ² and Q ² could be obtained despite the small number of data samples. The prediction accuracy here was Q ² = 0.6 to 0.9. In addition, it can be said that R ² (explanation variance) and Q ² (predictive explanation variance) are closer to 1, respectively, so that the fitness / predictability of the model is higher.

From these results, Q ² ≧ 0.35 (S110), and a prediction model with high fitness and predictability was obtained.

Next, the diffusion performance calculation device 16 uses a dynamic Monte Carlo method (DMC method) based on the obtained prediction model of the separation membrane structure shown in FIG. Diffusion performance, for example, carbon dioxide permeability coefficient, CO ₂ / N ₂ diffusion selectivity are required.

  It is necessary to model the membrane structure. The structural modeling was performed as follows. Based on the model shown in FIG. 5, the adsorption site diameter is Dsite, the x-axis direction is the transmission direction, the pore diameter is dx, the pore diameter perpendicular to the transmission direction is dy · dz, and the adjacent adsorption sites. Let the distance be L. In FIG. 5, LTA type zeolite (A type zeolite) is taken as an example. In type A, the adsorption sites are isotropically connected in the xyz direction, but not all zeolites are connected in the same way, so the connection methods between the adsorption sites were classified into seven types. The type is shown in FIG. Real zeolites almost belong to one of these seven types, and the number of pores is only slightly different. For example, when FAU type zeolite pays attention to one adsorption site, it can be said that it belongs to Type 3B because there are four isotropic adjacent sites.

The structure factor was changed as follows, and the transmission coefficient / separation coefficient was calculated by DMC calculation for all 1600 combinations of factors. The calculation conditions were such that 10 molecules were placed in the Feed cell and 10 unit cells were arranged in the transmission direction as a film model. The calculation step was 50,000,000 steps, and the transmission molecule number ratio of 40,000,000 steps to 50,000,000 steps was used as the separation factor. The following constituent factors are input (S112).
(Equation 4)
dx = 3.4, 4.2, 5.8, 7.4 [Å] (this corresponds to the pore diameter of oxygen 7-membered ring, 8-membered ring, 10-membered ring, 12-membered ring)
dy = 3.4, 4.2, 5.8, 7.4 [Å]
dz = 3.4, 4.2, 5.8, 7.4 [Å]
D _site = 9,11,13 [Å]
Si / Al ratio = ∞ (pure silica), 99, 49, 32, 24, 19 (replaced with Na ⁺ )
Adsorption site connection = 7 types (shown in Fig. 7)

Next, the hopping rate constant is calculated according to the following procedure (S114).
(A) Hopping rate constant The hopping constant is a value proportional to the probability that a molecule is selected when a moving molecule is determined, and takes a different value for each site where a molecular species / molecule exists. Therefore, the following equation is used on the assumption that the activation energy of hopping has Arrhenius dependence.
Here, k _hop is a hopping constant, ν _hop is a frequency factor, and ΔE _hop is an activation energy of hopping. Therefore, the hopping parameter can be calculated by obtaining the frequency factor and the hopping activation energy from the given structure.

(B) Activation energy of hopping About the energy by the Lennard-Jones potential between the atoms constituting the molecule and the zeolite crystal lattice, the energy when the molecule is present at the adsorption site and at the midpoint of the pore between the adsorption sites The difference was defined as the activation energy for hopping. In this case, the following assumptions shall be followed.
(I) For the zeolite lattice, the pores between the adsorption sites are assumed to be cylindrical and the adsorption sites (cage) are assumed to be spherical. Further, it is assumed that the oxygen atoms constituting the zeolite lattice are evenly distributed on the pore cross section and the adsorption site surface.
(Ii) The shape of the molecule is cylindrical when present in the pores, and the cross-sectional diameter is d _m (this is referred to as Kinetic diameter). When the molecule is at the adsorption site, it is considered to be spherical and its diameter is σ _m (this is called Lennard-Jones length constant). d _m and σ _m are generally different values.
(Iii) When a molecule is present in the pore, the center of the cross section of the molecule coincides with the center of the pore, and the axis of the molecule also coincides with the axis of the pore.
(Iv) Of the atoms constituting the zeolite lattice, only oxygen atoms contribute to the potential. This is an approximation often used in the calculation of the interatomic potential.
(V) Consider the influence between permeable molecules in the hopping parameter.
(Vi) The hopping starting direction when the target molecule comes to the adsorption site is not distinguished from other hopping directions.

(1) Calculation of molecular diameter and atomic diameter The σ _m (Lennard-Jones length constant) of a molecule is
Calculated by The eccentric factor ω _m is
Obtained by. For molecules of d _m (Kinetic diameter), use the value of the literature values [ "carbon dioxide high temperature separation and recovery and reuse technology research and development," the New Energy and Industrial Technology Development Organization commissioned business results report (1999)] It was.

(2) Activation energy of hopping The activation energy ΔE _hop of hopping was derived from the equation (11) as the difference between the energy Φ _i at the adsorption site of the molecule and the energy Φ _c at the pore.
The calculation formula for obtaining the energy Φ _c · Φ _i in the pores is described below.
Here, E (cation) is energy received from a cation existing in the adsorption site. sigma _c is the molecules in the pores - oxygen between Lennard-Jones length constant, σ _i is the distance between the centers of the O atoms is molecular oxygen between Lennard-Jones length constant, r _c in the adsorption sites constituting the center and the pores of the It is. Both units are Å, σ _c · r _c is placed constant at all O atoms constituting the pore. Therefore, equation (12) becomes
It becomes. However, n _c is the number of oxygen atoms constituting the pore. Incidentally, n _c is calculated from the following equation.
d _pore is the diameter of the _{pore and} is an equation that satisfies the following relationship.

Equation _{(13), σ c · σ} i · r c used in (14) was calculated by the equation (16) to (18).
Further, ε was obtained by the equation (19). This value is different for each set of molecules that interact.
Since there is no data on the value of ε _O / k for the O atom of the zeolite pore, the value of ε / k of the oxygen molecule was used as an approximate value. ε _m / k was calculated from the following equation (20).

The values used in this embodiment are shown in Table 5 below.

(3) Energy at the adsorption site The method for obtaining the energy Φi at the adsorption site is different from the method for obtaining the energy at the pores. A major factor is that the position where the molecules are stably changed as the adsorption site becomes larger. When the adsorption site is small, it can be assumed that the molecule is at the center of the site, similar to the energy in the pores. However, it is generally said that the position where the molecule exists stably is more than the wall than the center of the adsorption site. Therefore, in this study, the energy E (z) at the adsorption site in consideration of the stable position of the molecule, which is the left term of Equation (13), was calculated according to the following procedure.

First, the adsorption site is a sphere having a radius R, and the x-axis is determined so as to pass through the center of the sphere. Assuming that the guest molecule is at the coordinate pR (0 ≦ p ≦ 1), the interaction energy of the guest molecule with the circumference at an angle θ with the x axis from the center of the sphere is considered. The distance r between the guest molecule and this circumference is
It can be expressed as Therefore, by substituting this distance into the LJ potential distance term in the left term of equation (13) and multiplying it by a band-like area whose angle from the center of the sphere is θ to θ + dθ, the energy at that time E '
It can be expressed as Therefore, if this value is integrated from 0 to π,
Is obtained, and the unit becomes “J · m ² ”. Finally, the energy obtained by multiplying the number of oxygen atoms per unit area by F (p, R) is as shown in FIG. The number n _i0 of oxygen atoms per unit area is calculated by the following formula.
By performing the above calculation, when the size (radius R) of the adsorption site is determined, the energy and position (p) when the guest molecule is in the most stable position can be obtained. The energy E (z) at the adsorption site when not affected by

(4) Effect of cation at the adsorption site From the above, when formula (13) is simplified, formula (20) is obtained.
E (z) is as determined in (3) above. It is known that exchange cations exist at the adsorption site according to the Si / Al ratio, and the activation energy of molecules tends to increase due to the influence thereof. Therefore, the cations were fixed as Na ⁺ , and the adsorption sites in the DMC method were classified into two sites: a site affected by Na ions (strong-site) and a site not received (week-site). The value of E (Na ⁺ ) was determined by examining the increase in the heat of adsorption when Al was present by calculation using the GCMC method. Naturally, when the adsorption site is a week-site, E (Na ⁺ ) becomes zero, and only the interaction energy E (z) with zeolite needs to be considered.

Next, a frequency factor is calculated (S116). The probability that a molecule has enough energy to overcome an intersite potential barrier is generally very small, and most time molecules are considered to be near the bottom of the potential. In such a case, the molecule can be approximated by a simple vibration near the site. The frequency at this time is as shown in equation (26). This frequency was considered as a frequency factor for hopping.

Next, unit cell data is created (S118). The following three pieces of information are required to run the DMC calculation.
(I) The coordinates of each adsorption site in the unit cell (ii) Information on the connection between the adsorption sites (whether it is connected to which site, the connection across the periodic boundary, etc.)
(Iii) Hopping constant when hopping between these adsorption sites Therefore, such information is output to a file “cell.dat”, for example, and “cell.dat” is calculated in the calculation program by the DMC method. By reading the program, the program for creating the film structure information and the actual DMC calculation program are separated so as not to reduce the execution speed of the program. Here, for example, “Unitcell.cpp” was created as a program for outputting unit cell information. Not only this program, but all programs in this research use a programming language called C ⁺⁺ . “Unitcell.cpp” has the following input and output relationships.
(Equation 21)
Input: Adsorption site size Dsite, pore size dx.dy.dz in xyz direction, system temperature, number of adsorption sites in unit cell, physical properties of permeated molecule Output: data file (cell.dat )
The number of adsorption sites in the unit cell is given as 2 × 2 × 2 or 3 × 3 × 3. In the program, all the hopping rate constants k _ij for hopping from the adsorption site i to j are obtained based on the above hopping rate constant calculation method.

Next, “cell.dat” will be described. When “Unitcell.cpp” is executed, for example, “cell.dat” is obtained as shown in FIG. (Here, there are 8 examples of adsorption sites in the unit cell. Further, the hopping constant is omitted with symbols.) The first line is the length of each side of the unit cell (in units of Å). . From the second line, the state of each adsorption site is described. Each row is divided into five parts, and the first column represents the position of the adsorption site. The position is shown as a percentage of the length of each side of the unit cell with one of the intersections of the three axes as the origin. The second column shows the connection relationship, and the number of the adsorption site to which the path is connected is listed. Here, the sites that are connected by the periodic boundary conditions are also listed. The third column describes the site connected across the periodic boundary conditions. The relationship between the direction of the straddling periodic boundary condition and the value for determining it is described below.

  For example, when the periodic boundary condition is straddled in the positive direction in the X-axis direction when hopping from the site i to the site j, “10” is listed here. The 4th and 5th columns list the hopping rate constants to the adsorbed binding sites, the 4th column represents the first component of the penetrating molecular species, and the 5th column represents the second component.

  Next, a film model is created (S120). The membrane model in the DMC method is a membrane model in which ten unit cells created by the above method are connected in the transmission direction. The cells at both ends are a Feed area and a Permeate area, respectively. In the Feed area, the concentration of the penetrating molecule and the composition of the two components are not changed. In the Permeate area, the permeated molecules are counted and erased. Therefore, in this model, the eight unit cells in the center correspond to the membrane region having a concentration gradient in the transmission direction. In the present embodiment, the membrane pressure is about several hundred angstroms. Here, the transmission direction is fixed in the X-axis direction. Periodic boundary conditions are applied to hopping that jumps out of the unit cell in the Y and Z directions. When the unit cell is crossed in the X axis direction, the membrane permeates by moving to the adsorption site of the adjacent cell. It becomes possible to see the phenomenon.

Next, it calculates by DMC method. For the DMC calculation, for example, a program “DyMC10_2.cpp” was used. The relationship between the input and output of this program is as follows.
(Equation 22)
Input: "cell.dat", system temperature, number of calculation steps, number of molecules in the feed region (two components)
Output: “msd.dat”, “permeation.dat”, “file09p.dat”, transmission number, separation coefficient The following information is listed for each output file.
(Equation 23)
“Msd.dat” ・ ・ ・ Time change of mean square displacement (MSD) of permeated molecules “permeation.dat” ・ ・ ・ Time change of the number of permeated molecules “file09p.dat” ・ ・ ・ Which molecule is at each step Information on whether or not it is in position (If the results are visualized in order, the behavior of the penetrating molecule can be seen.)
Here, the transmission coefficient P and the separation coefficient α are calculated by the following equations (27) and (28), taking CO ₂ / N ₂ as an example. If it is to be obtained accurately, it is necessary to obtain it using data from where the MSD is stabilized in the above output file, but it can be solved by taking a sufficiently long number of calculation steps.

Further, hopping is performed according to the following procedure.
(1) Obtain the expected value k _expect of the hopping parameter of each site (formula (29))
(2) For all sites, use the expected value obtained in step (1) when penetrating molecules exist, and set the expected value to zero when there are no molecules (3) Weight of expected values at each site Randomly select sites based on (molecules at the selected site hopping)
(4) At the site selected in step (3), the hopping direction is stochastically determined by the ratio of the hopping constant to the adjacent adsorption site (which adsorption site is hopped).
(5) The procedure (2) to (4) is performed every step to move the penetrating molecules.

The method for _obtaining the expected value k _expect of each site's hopping parameter is as follows.
N is the number of sites that can be hopped from one adsorption site.

  Using each constituent factor, the combination of constituent factors is sequentially changed (changed to combinatorial), and the calculation by the DMC method is performed by the above-described procedure to obtain the diffusion selectivity and the transmission coefficient (S122). Next, it is determined whether or not the DMC calculation has been performed using all the constituent factors (S124). If the DMC calculation has not been completed for all the constituent factors, the process returns to S112 and the DMC calculation is completed for all the constituent factors. In this embodiment, that is, in this embodiment, 1600 patterns are further calculated, and the diffusion selectivity / permeation coefficient obtained by DMC calculation and the adsorption selectivity / adsorption amount obtained by GCMC calculation From the results, the membrane permeability coefficient / separation coefficient is calculated (S126), and each virtual separation membrane structure and its permeability coefficient / separation coefficient are output (S128). The result is shown in FIG.

Here, in the Na-Y type zeolite membrane formed by Kusakabe et al., With respect to the separation of CO ₂ / N ₂ , the separation factor 100 (300 K) · CO ₂ permeability coefficient 1.5 × 10 ⁻⁷ [mol / m ² sec Pa], KY type, separation factor 30.3 (313 K) · CO ₂ permeability coefficient 1.8 × 10 ⁻⁶ [mol / m ² sec Pa] shows the highest separation factor in the past. On the other hand, considering the results of FIG. 9, it can be seen that a virtual separation membrane structure having a membrane separation performance of the existing Y-type zeolite membrane, particularly a membrane separation performance exceeding the value of the separation coefficient, is estimated.

  A plurality of virtual separation membrane structures obtained above and their permeation coefficients / separation coefficients are linked and stored in the screening membrane property database 18, and the optimum structure prediction device 20 is used according to the separation conditions as appropriate. Then, the DMC calculation is performed as necessary, the optimum structure of the separation membrane is predicted, and displayed on the display device 22.

As mentioned above, CO ₂ / N ₂ separation was described using a mixed gas as the target separation species. Similarly, for separation of O ₂ / N ₂ , the separation membrane structure was simulated and the permeation coefficient and separation coefficient were screened. It goes without saying that it is possible. Furthermore, with respect to other gas mixtures, it is possible to screen the permeability coefficient / separation coefficient after simulating the separation membrane structure in the same manner as described above. In addition, a mixed liquid may be used as a target separation species, and as a separation membrane, an organic separation membrane or an inorganic / organic separation membrane other than the inorganic separation membrane described above is specified by simulation, and its characteristics are determined. You may screen by this invention.

Further, in the present embodiment, it has been found that a separation membrane having the following constituent factors based on FIG. 9 is useful for CO ₂ / N ₂ separation. That is, the CO ₂ / N ₂ separation membrane of the present embodiment has a carbon dioxide gas permeability coefficient of 1 × 10 ⁻¹¹ mol · m / m ² spa or more and a carbon dioxide gas separation coefficient of 100 or more. A gas separation membrane of gas and nitrogen gas, wherein the gas separation membrane has a three-dimensional pore structure, and includes pores having a pore diameter of at least 3.2 mm and no more than 4.2 mm, and adsorbing The diameter Dsite of the site is 7 to 20 mm, preferably 7 to 13 mm.

  As a result of the above simulation and screening, the permeation coefficient and the separation coefficient are increased by increasing the diameter Dsite of the adsorption site and decreasing the pore diameters dy and dz in the permeation direction at a three-dimensional pore structure. There was found. Further, the separation membrane obtained from the above results has a permeation performance that is one or more orders of magnitude higher than that of the conventional carbon dioxide gas, and superior permeation performance compared to the conventional carbon dioxide gas dispersion coefficient. Have.

  As described above, the pore structure of the separation membrane is one-dimensional, two-dimensional, and three-dimensional. A three-dimensional structure is desirable, but a structure in which at least one of the one-dimensional structure and the two-dimensional structure is incorporated in the three-dimensional structure. It may be.

The CO ₂ / N ₂ separation membrane of the present embodiment is preferably a separation membrane made of a zeolite membrane or a zeolite-related compound.

  As a membrane made of a zeolite-related compound, in the zeolite, based on a skeleton made of silicon dioxide, a part of silicon is replaced with at least one of aluminum, iron, boron, gallium, and phosphorus, so that the entire crystal lattice becomes negative. An example is a membrane that is charged and contains cations such as sodium and potassium in the pores of the zeolite.

The CO ₂ / N ₂ separation membrane of the present embodiment is a Si / Al zeolite separation membrane in which a part of silicon is replaced with aluminum on the basis of a skeleton made of silicon dioxide, and the Si / Al zeolite separation The Si / Al ratio of the film is 20-99.

  Furthermore, by setting the Si / Al ratio of the Si / Al zeolite separation membrane to 20 to 99, the carbon dioxide gas has a permeation performance superior to that of the conventional carbon dioxide gas by one digit or more. A separation membrane having a separation performance superior to that of the separation factor can be obtained.

As the separation membrane structure shown in FIG. 9, for example, the structure shown in Table 7 is preferable.

  It is particularly effective for separation applications where mixed gas separation is performed, and furthermore, it is possible to perform the same thing as an experiment in a short time, safely and inexpensively, without selecting an experiment, and to select a separation membrane structure with optimal separation performance. It is effective for.

It is a flowchart which shows the flow of a process in an example of the simulation method of the separation membrane of this invention. It is a flowchart which shows schematic structure of an example of the simulation apparatus of the separation membrane of this invention. It is a figure which shows an example of the database which added the adsorption characteristic obtained by calculation by the GCMC method to the structure data of an inorganic type separation membrane. It is a diagram illustrating the CO ₂ equilibrium adsorption and _CO 2 / _{N 2} adsorption selectivity as the comparison result of the calculated values of the predictive model by calculation results and PLS method by GCMC method. It is a figure explaining an example of modeling of a film | membrane structure, and an example of a component factor. It is a figure which shows the type of the pore network (connection of an adsorption site) of the zeolite membrane which is a structural factor used for calculation by DMC method. It is a figure explaining the calculation procedure of the energy in an adsorption site. It is a figure which shows an example of the file data in which the information used for preparation of the unit cell eater in the DMC method is stored. It is a figure which shows the result of having screened the separation performance of the inorganic type separation membrane comprised from the prediction model.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 10 Structure database of the existing inorganic separation membrane structure, 12 Adsorption performance calculation apparatus, 14 Prediction model creation apparatus, 16 Diffusion performance calculation apparatus, 18 Screening membrane performance database, 20 Optimal structure prediction apparatus, 22 Display apparatus.

Claims (15)

A gas separation membrane of carbon dioxide gas and nitrogen gas having a permeability coefficient of carbon dioxide gas of 1 × 10 ⁻¹¹ mol · m / m ² spa or more and a separation factor of carbon dioxide gas of 100 or more,
The gas separation membrane has a three-dimensional pore structure,
A CO ₂ / N ₂ separation membrane comprising pores of at least 3.2 mm or more and 4.2 mm or less as a pore diameter of the separation membrane, and an adsorption site diameter Dsite of 7 to 20 cm. The CO ₂ / N ₂ separation membrane according to claim 1,
The _CO 2 / _{N 2} separation membrane, _{CO 2} / _N 2 separation membrane which is a separating membrane composed of zeolite membrane or zeolite analogous compounds. In _CO 2 / _{N 2} separation membrane according to claim 1 or claim 2,
The CO ₂ / N ₂ separation membrane is a Si / Al zeolite separation membrane in which a part of silicon is replaced with aluminum based on a skeleton made of silicon dioxide,
A CO ₂ / N ₂ separation membrane, wherein the Si / Al zeolite separation membrane has a Si / Al ratio of 20 to 99. A simulation method for calculating the separation performance of a separation membrane,
Store the structure data of the existing separation membrane,
Using the grand canonical Monte Carlo method, the adsorption performance for at least two kinds of target separation species in the existing separation membrane structure is determined,
Create a prediction model of the separation membrane structure using a multivariable regression method based on the adsorption performance,
Based on the prediction model of the separation membrane structure using a dynamic Monte Carlo method, the diffusion performance of the separation membrane in a plurality of pore networks is determined,
A separation membrane simulation method characterized in that the separation performance of a virtual separation membrane can be estimated. The separation membrane simulation method according to claim 4,
Furthermore, a separation membrane simulation method, wherein an optimum separation membrane structure is obtained according to separation conditions. In the simulation method of the separation membrane of Claim 4 or Claim 5,
The method for simulating a separation membrane, wherein the separation membrane is a zeolite membrane for CO ₂ gas separation. A simulation device for calculating separation performance of a separation membrane,
A structure data storage means for storing structure data of an existing separation membrane;
An adsorption performance calculation means for obtaining adsorption performance for at least two kinds of target separation species in the existing separation membrane structure using a grand canonical Monte Carlo method;
A prediction model creating means for creating a prediction model of the separation membrane structure using a multivariable regression method based on the adsorption performance;
A diffusion performance calculation means for obtaining diffusion performance of the separation membrane in a plurality of pore networks based on a prediction model of the separation membrane structure using a dynamic Monte Carlo method,
A separation membrane simulation apparatus characterized in that the separation performance of a virtual separation membrane can be estimated. The separation membrane simulation apparatus according to claim 7,
Furthermore, a separation membrane simulation apparatus characterized by comprising structure optimization means for obtaining an optimum separation membrane structure according to separation conditions. The separation membrane simulation apparatus according to claim 7 or 8,
A separation membrane simulation apparatus, wherein the separation membrane is a zeolite membrane for CO ₂ gas separation. Computer
A structure data storage means for storing structure data of an existing separation membrane;
An adsorption performance calculation means for obtaining adsorption performance for at least two kinds of target separation species in the existing separation membrane structure using a grand canonical Monte Carlo method;
A prediction model creating means for creating a prediction model of the separation membrane structure using a multivariable regression method based on the adsorption performance;
Diffusion performance calculating means for obtaining diffusion performance of the separation membrane in a plurality of pore networks based on a prediction model of the separation membrane structure using a dynamic Monte Carlo method;
A program for functioning as a separation performance calculation means for a virtual separation membrane for estimating the separation performance of a virtual separation membrane. The program according to claim 10, wherein
The separation membrane is a zeolite membrane for CO ₂ gas separation.   The computer-readable recording medium which recorded the program of Claim 10 or Claim 11.   A separation membrane having a virtual separation membrane structure obtained by the separation membrane simulation method according to any one of claims 4 to 6.   A separation membrane having a virtual separation membrane structure obtained by estimation by the separation membrane simulation apparatus according to any one of claims 7 to 9.   A separation membrane having a virtual separation membrane structure obtained by reading and estimating the program according to claim 10 or 11 with a computer.