CN109871612A - In conjunction with the heterogeneous catalysis surface coverage acquisition methods of ODE integral and Newton iterative method - Google Patents
In conjunction with the heterogeneous catalysis surface coverage acquisition methods of ODE integral and Newton iterative method Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 54
- 238000007210 heterogeneous catalysis Methods 0.000 title claims abstract description 17
- 238000006243 chemical reaction Methods 0.000 claims abstract description 27
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 21
- 230000010354 integration Effects 0.000 claims abstract description 20
- 239000003054 catalyst Substances 0.000 claims abstract description 11
- 238000004088 simulation Methods 0.000 claims abstract description 9
- 239000002156 adsorbate Substances 0.000 claims description 6
- 230000008901 benefit Effects 0.000 abstract description 4
- 238000006555 catalytic reaction Methods 0.000 abstract description 2
- 230000008859 change Effects 0.000 description 4
- 230000008569 process Effects 0.000 description 3
- 230000003197 catalytic effect Effects 0.000 description 2
- 238000009903 catalytic hydrogenation reaction Methods 0.000 description 2
- 239000002352 surface water Substances 0.000 description 2
- ORILYTVJVMAKLC-UHFFFAOYSA-N Adamantane Natural products C1C(C2)CC3CC1CC2C3 ORILYTVJVMAKLC-UHFFFAOYSA-N 0.000 description 1
- 102100021164 Vasodilator-stimulated phosphoprotein Human genes 0.000 description 1
- 230000009471 action Effects 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000006870 function Effects 0.000 description 1
- 238000012804 iterative process Methods 0.000 description 1
- 238000009790 rate-determining step (RDS) Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000002441 reversible effect Effects 0.000 description 1
Abstract
The present invention relates to a kind of heterogeneous catalysis surface coverage acquisition methods of combination ODE integral and Newton iterative method, comprising the following steps: 1) starts catalysis simulation；2) one surface coverage of random initializtion, and construct micro kinetics steady-state equation；3) using the coverage of initialization as starting point, steady-state equation is integrated using ODE numerical integration algorithm；4) it after integral reaches specified time, obtains current solving in the initial value feeding Newton iteration device as Newton iteration and carries out Newton iteration；5) if coverage changes with time rate less than convergence precision, it then obtains steady state solution and carries out step 6), if not converged, return step 3) using current solution as the starting point of ODE numerical integration algorithm, continue ODE integral, and repeat step 3) -5)；6) catalyst system reaction rate is obtained according to steady state solution.Compared with prior art, the present invention has many advantages, such as not depend on unduly that initial value, to save memory, raising efficiency, flexibility high.
Description
Technical field
The present invention relates to heterogeneous catalysis micro kinetics simulation fields, more particularly, to a kind of combination ODE integral and newton
The heterogeneous catalysis surface coverage acquisition methods of method iteration.
Background technique
Micro kinetics simulate (Microkinetic simulation) connection micro-scale first-principles calculations with
Vital role is played in macrodynamics phenomenon, this method has been applied extensively and successfully at present multiple
In the various researchs of miscellaneous surface heterogeneous catalysis.Researcher can calculate catalytic body by the quantum chemistry software of business at present
The thermodynamics and kinetics energy datum of each possible elementary reaction in system, based on this data and based on the micro- of mean field approximation
Seeing dynamic method can be used the reaction rate of the prediction catalyst system of computer rapidly and efficiently and some other macro
Property is seen, such as surface composition and the reversible degree of elementary reaction, rate determining step is rapid etc..
Micro kinetics method is a kind of chemical reaction system based on mean field approximation in physical chemistry and steady state approximation
The method for numerical simulation of kinetic property.The catalytic cycle that one heterogeneous catalytic reaction system is made of multiple elementary reactions.
Wherein each elementary reaction can be indicated by a kind of general reaction equation:
Wherein AiAdsorbate, meteorological molecule or surface vacancy are represented,Indicate AiCoefficient in elementary reaction e,It is that just/back reaction rate of entire elementary reaction can write out the reaction of the elementary reaction by the law of mass action
Rate:
Wherein,Indicate adsorbate AiSurface coverage in certain elementary reactions,Meteorological point can also be used
The partial pressure of sonIt replaces, for some adsorbing species, can derive that species surface coverage becomes at any time according to above formula
The expression formula of rate:
For multiple species, entire catalyst system will obtain one group of ordinary differential system:
According to steady state approximation, when entire catalyst system reaches stable state, the species coverage on surface should keep stable state,
That is the coverage rate that changes with time is 0, therefore can convert above-mentioned ordinary differential system to one group of Nonlinear System of Equations:
Entire catalyst system just can be obtained in stable state by solving above-mentioned Nonlinear System of Equations or ordinary differential system
The coverage of surface species under state, and then predict the reaction rate and other macroscopic properties of whole system.
It is at present Newton method for the common method for solving micro kinetics equation, Newton method needs at the beginning of previously given one
Initial value (initial coverage), is then iterated by Newton iterative, when all species coverages change over time rate
Close to 0, at the same be less than some precision (such as 10e-50) when can consider that whole system has reached stable state,
Terminate iteration.However, whether the effect of the method iterative solution (can converge to enough precision and reach the solution after precision
Whether with reasonable physical significance) depend critically upon iteration initial value value, if the value " unreasonable " of initial value
When, Newton iterative method hardly results in final correctly solution.A kind of situation is that iterative algorithm is difficult error convergence to specified essence
Degree, and there is the coverage that the convergence of low precision obtains very big error can not use as a result；Second situation is ox
The solution that the method for pausing can converge to designated precision, but obtain not is the final reasonable solution with physical significance, such as is solved
The coverage of negative out, or it is unsatisfactory for the coverage etc. of conservation of mass relationship.Especially when needing to carry out micro kinetics simulation
Catalyst system very complicated (include many elementary reactions) when, the stability and accuracy for solving steady-state equation can be more difficult to ensure
Card.
Summary of the invention
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and provide a kind of combination ODE integral and
The heterogeneous catalysis surface coverage acquisition methods of Newton iterative method.
The purpose of the present invention can be achieved through the following technical solutions:
A kind of heterogeneous catalysis surface coverage acquisition methods of combination ODE integral and Newton iterative method, comprising the following steps:
1) start the micro kinetics simulation of heterogeneous catalysis；
2) one surface coverage of random initializtion, and construct micro kinetics steady-state equation；
3) using the coverage of initialization as starting point, steady-state equation is integrated using ODE numerical integration algorithm；
4) after integral reaches specified time, ODE numerical integration is terminated, and obtains current solution as the first of Newton iteration
Initial value is sent into Newton iteration device and carries out Newton iteration；
5) if coverage changes with time rate less than convergence precision, iteration is terminated, steady state solution is obtained and carries out step
6), if not converged, return step 3) using current solution as the starting point of ODE numerical integration algorithm, continue ODE numerical integration,
And repeat step 3) -5)；
6) catalyst system reaction rate is obtained according to steady state solution.
In the step 2), micro kinetics steady-state equation are as follows:
Wherein,For adsorbate AnCoverage on surface,For adsorbate AnCoefficient in elementary reaction e, re
For the reaction rate of elementary reaction.
Convergence precision in the step 5) is 10e-50.
In the step 4), wherein the time span and time step of ODE numerical integration, carry out automatic with hydridization iteration
It adjusts, then has:
α × 10 T=N
I=10-(N+2)
Wherein, T is the time span of integral, and I is time step, and α is an adjustable value, and size is between 0~1, N
For the number of current hydridization iteration.
In the step 3), ODE numerical integration algorithm uses real value variable coefficient ODE Integration Solving device.
The step 4) specifically includes the following steps:
41) using the solution of ODE numerical integration as initial coverage Θ0；
42) iteration direction d is obtained:
43) by iterative rate constant λ=0.5i-1As iteration step length, wherein i is the step number of current Newton iteration；
44) after obtaining iteration direction and step-length, pass through Θk+1=Θk+ λ d updates coverage；
45) iteration is terminated when iteration convergence, otherwise return step 42) until convergence.
Compared with prior art, the invention has the following advantages that
One, the input present invention employs ODE integrated value as Newton method initial value reduces total algorithm for initial
Value value is depended on unduly.
Two, ODE integral use low precision numerical value indicate, relative good accuracy floating number indicate, have save memory with
And the advantages such as raising efficiency.
Three, ODE integral, can also will be under the process record of surface evolution in addition to can be using integrated value as Newton method input
Come, than the information that pure Newton iterative method has more also physical significances.
Four, change hydridization iterative algorithm use multiple hydridization iteration strategy, even if an iteration can not obtain it is convergent
Steady state solution, algorithm will continue to repeat ODE/Newton integral handoff procedure, and can be dynamic to adjust integral according to switching times
Parameter improves higher flexibility.
Detailed description of the invention
Fig. 1 is flow chart of the method for the present invention.
Fig. 2 is iteration error evolution curve.
Specific embodiment
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.
As shown in Figure 1, present invention employs the hydridization of a kind of low precision ODE integral of combination and high-precision Newton iterative method to change
Come for algorithm so that the micro kinetics of heterogeneous catalysis simulates to overcome and depends on initial value unduly and be unable to get steady state solution
It is difficult.The ODE integral of low precision can be integrated since arbitrary initial value, to will not depend upon taking for initial coverage
Value, when integrating to a certain extent, the coverage of surface species can gradually develop with the time, terminate at a time point of setting
ODE integral obtains the current species covering angle value initial point rough as one and is brought into high-precision Newton iteration solution
In device, high-precision steady state solution is obtained using Newton method.If Newton method can not still restrain, it is switched in ODE integrator and continues
ODE algorithm will be used to carry out solution integral, and repeat to switch between two kinds of algorithms, until the change rate of coverage converges to
The standard of holding back obtains steady state solution.
The brief process of the algorithm is as follows:
1) simulation starts；
2) it is randomized an initial surface coverage, constructs micro kinetics steady-state equation；
3) using the coverage of initialization as starting point, steady-state equation is integrated using ODE numerical integration algorithm, the product
Usually using real value variable coefficient ODE Integration Solving device in point, which has used fixed-leading-coefficient real
It is existing, so as to automatically be switched between implicit Adam method and method based on backward difference formula (BDF)；
4) it is integrated to specified time, terminates ODE integral, and obtain current solution and bring into as initial value (initial coverage)
High-precision Newton iteration is carried out in Newton iteration device, specially；
It being indicated used here as vector function F and coverage vector theta, such steady-state equation group can be expressed as, wherein
Θ * is final steady state solution, and wherein iterative process is as follows:
A) initial coverage Θ 0 (i.e. back ODE integral result) is given；
B) iteration direction d is obtained by solving following formula；
C) iterative rate constant λ=0.5i-1 is calculated as iteration step length, and wherein i is the step number of current Newton iteration；
D) after obtaining iteration direction and step-length, pass through Θi+1=Θi+ λ d updates coverage vector, while making k=k+1；
If e) F (Θ 0) < ε, illustrate iteration convergence, terminates iteration；It is opposite then return b) repeat above procedure；
5) if coverage changes with time rate less than convergence, iteration is terminated；If not converged, return step 3)
Using current solution as starting point, integrates, repeat the above steps into ODE；
6) Data Post, based on other macroscopic properties such as steady state solution prediction catalyst system reaction rates.
Embodiment:
The present invention is to assist CO2 catalytic hydrogenation micro kinetics simulative example in Cu (211) surface water
Table 1 show the elementary reaction expression formula in certain paths of Cu (211) surface water auxiliary CO2 catalytic hydrogenation
And energy datum, data are calculated by quantum chemistry software VASP and are obtained.Event of whole process can be updated to not with this
Dynamics simulation is carried out in same micro kinetics method for solving and in this, as comparison.
The elementary reaction expression formula and energy datum that table 1 is likely to occur
It is compared to compare, uses standard random starting values Newton method and improved ODE/Newton method hydridization respectively
Iterative algorithm is solved to above catalyst system progress micro kinetics model, and obtained Newton iterative method error develops bent
Line is as shown in Figure 2.
From fig. 2 it can be seen that hydridization iterative algorithm, has just converged to 10e-100 by an ODE/Newton iteration
Power, and it is the last solution with reasonable physical significance that finally obtained result is verified.And the standard ox of random initializtion
Pause iterative algorithm, is still difficult to converge to correct solution by the iteration of multiple initial values immediately, even if iteration can all be received every time
The solution holding back lower error amount, but obtaining but includes negative value (can not have negative value when coverage).As it can be seen that multiple
In miscellaneous catalyst system, hydridization iterative algorithm has more acurrate and stable convergence advantage than traditional Newton iterative method.
Claims (6)
1. a kind of heterogeneous catalysis surface coverage acquisition methods of combination ODE integral and Newton iterative method, which is characterized in that including
Following steps:
1) start the micro kinetics simulation of heterogeneous catalysis；
2) one surface coverage of random initializtion, and construct micro kinetics steady-state equation；
3) using the coverage of initialization as starting point, steady-state equation is integrated using ODE numerical integration algorithm；
4) after integral reaches specified time, ODE numerical integration is terminated, and obtains initial value of the current solution as Newton iteration
It is sent into Newton iteration device and carries out Newton iteration；
5) if coverage changes with time rate less than convergence precision, iteration is terminated, steady state solution is obtained and carries out step 6), if
It is not converged, then return step 3) starting point of ODE numerical integration algorithm is used as using current solution, continue ODE numerical integration, and repeatedly
Step 3) -5)；
6) catalyst system reaction rate is obtained according to steady state solution.
2. the heterogeneous catalysis surface coverage of a kind of combination ODE integral according to claim 1 and Newton iterative method obtains
Method, which is characterized in that in the step 2), micro kinetics steady-state equation are as follows:
Wherein,For adsorbate AnCoverage on surface,For adsorbate AnCoefficient in elementary reaction e, reFor primitive
The reaction rate of reaction.
3. the heterogeneous catalysis surface coverage of a kind of combination ODE integral according to claim 1 and Newton iterative method obtains
Method, which is characterized in that the convergence precision in the step 5) is 10e-50.
4. the heterogeneous catalysis surface coverage of a kind of combination ODE integral according to claim 1 and Newton iterative method obtains
Method, which is characterized in that in the step 4), the wherein time span and time step of ODE numerical integration, with hydridization iteration
It automatically adjusts, then has:
α × 10 T=N
I=10-(N+2)
Wherein, T is the time span of integral, and I is time step, and α is an adjustable value, and for size between 0~1, N is to work as
The number of preceding hydridization iteration.
5. the heterogeneous catalysis surface coverage of a kind of combination ODE integral according to claim 1 and Newton iterative method obtains
Method, which is characterized in that in the step 3), ODE numerical integration algorithm uses real value variable coefficient ODE Integration Solving device.
6. the heterogeneous catalysis surface coverage of a kind of combination ODE integral according to claim 1 and Newton iterative method obtains
Method, which is characterized in that the step 4) specifically includes the following steps:
41) using the solution of ODE numerical integration as initial coverage Θ0；
42) iteration direction d is obtained:
43) by iterative rate constant λ=0.5i-1As iteration step length, wherein i is the step number of current Newton iteration；
44) after obtaining iteration direction and step-length, pass through Θi+1=Θi+ λ d updates coverage；
45) iteration is terminated when iteration convergence, otherwise return step 42) until convergence.
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