Automatic identification

of kinetic models in

industrial reaction systems

Reoptim

J. Francisco Rodriguez

June 2016

European Conference on Mathematics for Industry

Repsol Technology Center

Oil refining

>200 Scientists and Engineers

Petrochemicals

Exploration and Production of Oil

and Gas

Reoptim. Example of teamwork

ITMATI / University of Santiago de Compostela

University of Seville

- Francisco Pena. - Gabriel Álvarez. - Jerónimo Rodriguez. - Óscar Crego. - Manuel Cremades.

- Emilio Carrizosa. - Rafael Blanquero.

- Asunción Jiménez. - Remedios Sillero

- Alfredo Bermúdez. - José Luis Ferrín - Noemí Esteban - Diego Rodríguez. - Marta Benítez. - Oana Chis

Chemical reactions (I). Stoichiometric matrix

A very simple example

5 species 2 reactions Stoichiometric matrix

Reactor

Inlet Outlet

How to define a chemical reaction system?

Chemical reactions (II). Kinetic models

A very simple example

5 species 2 reactions Stoichiometric matrix

Kinetic models. Kinetic expressions

- Concentrations of species i (yi) - Temperature (q)

How to define a chemical reaction system?

sm

kgor

sm

moles

33

6

Chemical Reactions (III). Reactors

- Complex industrial systems

- Rigorous simulation very expensive

How to define a chemical reaction system?

7

Chemical Reactions (III). Reactors

- Complex industrial systems

- Rigorous simulation very expensive

- Some data must be obtained from experiments - Usually following parameter fitting strategies

How to define a chemical reaction system?

8

Chemical Reactions (IV). Ideal Reactor Models

- Stirred Tank Reactor (STR).

- Concentrations of species (y) - Temperature (q)

Simplified reactor models for parameter fitting of the kinetic models:

independent of spatial coordinates

9

Chemical Reactions (IV). Ideal Reactor Models

- Plug Flow Reactor (PFR). - Concentrations of species (y) - Temperature (q)

Simplified reactor models for parameter fitting of kinetic models:

only dependent on axial coordinate

10

Chemical Reactions (V). Mathem. models Stirred Tank Reactor in transient state (batchSTR)

11

Chemical Reactions (V). Mathem. models Stirred Tank Reactor in transient state

Continuous Stirred Tank Reactor

12

Chemical Reactions (V). Mathem. models Stirred Tank Reactor in transient state

Continuous Stirred Tank Reactor

Plug Flow Reactor at steady state

13

Chemical Reactions (V). Mathem. models Stirred Tank Reactor in transient state

Continuous Stirred Tank Reactor

Plug Flow Reactor at steady state

Plug Flow Reactor at transient state

14

The identification problem

What do I need to identify? - First: functional forms of reaction rates: kinetic model expressions.

- Second: numerical values of the parameters in those expressions.

What do I know? What do I have? - Stoichiometric matrix. - Mathematical model of the reactor. - A “catalogue” of different kinetic models expressions. - Data (concentrations, temperature, flow) gathered from experiments at different conditions

¿ ¿

15

Common identification procedure

¿OK?

OCTAVE

EXCEL

ASPEN PLUS

HYSYS

…

Yes

No

Final Model

¿

¿

16

Reoptim procedure

¿OK?

REOPTIM

Yes Final Model

¿

¿

17

Reoptim procedure

REOPTIM

Final Model

¿

¿

18

Reoptim

A general proposal of expressions for reaction rates (catalogue):

Problem results in a large MINLP

1. No longer requires human (engineer) intervention

2. It is solved in two steps: incremental method + integral method

3. In each method we solve multiple subproblems in parallel.

Encoding chemical kinetics

19

Reoptim

1. Uses algebra to decouple the system of equations.

2. Uses the heuristic VNS hierarchically.

3. Computes the gradient of the functional by the adjoint formulation

4. Uses efficient parallelization.

How does Reoptim solve the problem?

Key ingredients

20

Reoptim.

1. Decouple the system of equations (STR) -> incremental method

We define new variables called extents as e = S · y , where matrix S must have some properties S·A = Id, S·y0 = 0

There is a functional for each reaction and kinetic model:

The ODEs are no longer coupled -> can be solved independently by reaction

We get a complete set of initial solutions to second step: integral method

Key ingredients (I)

21

Reoptim.

2. Use of Variable Neighbourhood Search heuristic.

An interval is defined for each variable where the perturbation will take place:

VNS allows us to get out of local optima by perturbing the variables

We use it in an iterative way at two levels: - First for kinetic models expressions.

- Secondly for parameters in those expressions. We use it in combination with NLP solver IPOPT.

Key ingredients (II)

22

Reoptim.

3. Fast computing of functional derivative by the adjoint state.

Instead of computing: that scales linearly with

…we discretize:

and then compute:

Requiring to compute - one linear system,

- and some derivatives that we compute analytically

Key ingredients (III)

23

Reoptim.

4. Massive parallelization.

Incremental algorithm (based on extents) VNS and Integral algorithm

Key ingredients (IV)

24

Reoptim.

Experimental data

Graphical User Interface

Chemical reactions

25

Reoptim

Graphical User Interface

Kinetic models catalogue

26

Reoptim

Graphical User Interface

- Local, sequential execution - Parallel execution

27

Reoptim.

1. Identification when there exist missing values in observed concentrations.

Additional features

28

Reoptim.

1. Identification when there exist missing values in observed concentrations.

2. Model selection. -> Aim: to provide optimal experiment for choosing the best between two models

Additional features

29

Reoptim.

3. Simulation and identification in fixed bed catalytic reactors.

Additional features

References Bermúdez, E. Carrizosa, N. Esteban. A two steps identification process in stirred tank reactors. The incremental and integral methods. In preparation A. Bermúdez, N. Esteban, J.L. Ferrín, J.F. Rodríguez-Calo, M.R. Sillero-Denamiel, Identification problem in chemical reaction systems using the adjoint method. In preparation M. Benítez, A. Bermúdez, J.F. Rodríguez Calo. Adjoint Method for Inverse Problems of chemical reaction systems. In preparation R. Blanquero, E. Carrizosa, A. Jiménez-Cordero, J.F. Rodríguez Calo, A Global Optimization Method for Model Selection in Chemical Reaction Networks. Accepted R. Blanquero, E. Carrizosa, O. Chis, N. Esteban, A. Jiménez-Cordero, J.F. Rodríguez Calo A Global Optimization Approach for Parameters Inference in Chemical Reactions Networks with Missing Data. In preparation

Automatic identification

of kinetic models in

industrial reaction systems

REOPTIM

J. Francisco Rodriguez

June 2016

European Conference on Mathematics for Industry

Thanks for your attention