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Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions Determination of the kinetic constants of a chemical reaction in heterogeneous phase using parameterized metaheuristics Jos´ e Mat´ ıas Cutillas Lozano and Domingo Gim´ enez Departamento de Inform´ atica y Sistemas, University of Murcia International Conference on Computational Science - Barcelona, June 2013

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions Contents Motivation 1 Determination of kinetic constants 2 Unified shared-memory scheme 3 Results 4 Conclusions 5

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions Kinetic constants of a chemical reaction Kinetic parameters of a chemical reaction are determined with metaheuristic methods. The processes occurring in the human stomach when neutralizing the acid with an antacid tablet are simulated. It is a reaction combined with mass transfer of carbonate ions present in the solid phase upon contact with an acid solution. Solving the problem requires the calculation of the whole chemical system using the Euler numerical method.

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions Kinetic constants of a chemical reaction Kinetic parameters of a chemical reaction are determined with metaheuristic methods. The processes occurring in the human stomach when neutralizing the acid with an antacid tablet are simulated. It is a reaction combined with mass transfer of carbonate ions present in the solid phase upon contact with an acid solution. Solving the problem requires the calculation of the whole chemical system using the Euler numerical method.

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions Kinetic constants of a chemical reaction Kinetic parameters of a chemical reaction are determined with metaheuristic methods. The processes occurring in the human stomach when neutralizing the acid with an antacid tablet are simulated. It is a reaction combined with mass transfer of carbonate ions present in the solid phase upon contact with an acid solution. Solving the problem requires the calculation of the whole chemical system using the Euler numerical method.

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions Kinetic constants of a chemical reaction Kinetic parameters of a chemical reaction are determined with metaheuristic methods. The processes occurring in the human stomach when neutralizing the acid with an antacid tablet are simulated. It is a reaction combined with mass transfer of carbonate ions present in the solid phase upon contact with an acid solution. Solving the problem requires the calculation of the whole chemical system using the Euler numerical method.

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions Parallel-parameterized metaheuristics Metaheuristic calculations are carried out with various parameters and functions. Many experiments are required to select a good metaheuristic and to tune it to the problem. A large number of optimization problems will be solved. We use a unified parallel-parameterized scheme of metaheuristics: Different metaheuristics obtained from the parameterized scheme are parallelized with the parallel parameters for optimizing time execution.

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions Parallel-parameterized metaheuristics Metaheuristic calculations are carried out with various parameters and functions. Many experiments are required to select a good metaheuristic and to tune it to the problem. A large number of optimization problems will be solved. We use a unified parallel-parameterized scheme of metaheuristics: Different metaheuristics obtained from the parameterized scheme are parallelized with the parallel parameters for optimizing time execution.

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions Parallel-parameterized metaheuristics Metaheuristic calculations are carried out with various parameters and functions. Many experiments are required to select a good metaheuristic and to tune it to the problem. A large number of optimization problems will be solved. We use a unified parallel-parameterized scheme of metaheuristics: Different metaheuristics obtained from the parameterized scheme are parallelized with the parallel parameters for optimizing time execution.

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions Parallel-parameterized metaheuristics Metaheuristic calculations are carried out with various parameters and functions. Many experiments are required to select a good metaheuristic and to tune it to the problem. A large number of optimization problems will be solved. We use a unified parallel-parameterized scheme of metaheuristics: Different metaheuristics obtained from the parameterized scheme are parallelized with the parallel parameters for optimizing time execution.

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions Our search of the kinetic parameters of a chemical reaction that occurs in heterogeneous phase involves the simulation of the processes occurring on the human stomach. Depending on the value of the pH, there are three main ways in which the dissolution of calcium carbonate occurs: By reaction with acetic acid. CaCO 3 + H 3 O + ↔ Ca 2+ + HCO − 3 + H 2 O (1) By reaction with carbonic acid. CaCO 3 + H 2 CO 3 ↔ Ca 2+ + 2 · HCO − (2) 3 And by the hydrolysis reaction. CaCO 3 + H 2 O ↔ Ca 2+ + HCO − 3 + OH − (3)

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions Our search of the kinetic parameters of a chemical reaction that occurs in heterogeneous phase involves the simulation of the processes occurring on the human stomach. Depending on the value of the pH, there are three main ways in which the dissolution of calcium carbonate occurs: By reaction with acetic acid. CaCO 3 + H 3 O + ↔ Ca 2+ + HCO − 3 + H 2 O (1) By reaction with carbonic acid. CaCO 3 + H 2 CO 3 ↔ Ca 2+ + 2 · HCO − (2) 3 And by the hydrolysis reaction. CaCO 3 + H 2 O ↔ Ca 2+ + HCO − 3 + OH − (3)

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions When reaction occurs in several parallel paths independent of each other, the overall rate is simply the sum of all individual rates. So, the kinetic of dissolution of calcium carbonate is a function of the concentration of carbonic acid in the solution, the pH and the mass transfer area: 1 dN Ca 2+ H 3 O + � n 2 − k 2 a n 3 [ H 2 CO 3 ] n 4 − k 3 = − k 1 a n 1 � (4) V dt k 1 , k 2 and k 3 are the combined reaction rate constants. n 1 , n 2 , n 3 and n 4 are the reaction orders. a is the area of the tablet.

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions When reaction occurs in several parallel paths independent of each other, the overall rate is simply the sum of all individual rates. So, the kinetic of dissolution of calcium carbonate is a function of the concentration of carbonic acid in the solution, the pH and the mass transfer area: 1 dN Ca 2+ H 3 O + � n 2 − k 2 a n 3 [ H 2 CO 3 ] n 4 − k 3 = − k 1 a n 1 � (4) V dt k 1 , k 2 and k 3 are the combined reaction rate constants. n 1 , n 2 , n 3 and n 4 are the reaction orders. a is the area of the tablet.

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions Using the notation for evolutionary algorithms, an individual is represented by a real vector of size seven that is the set of kinetic constants. The ranges of values for the constants are set following empirical criteria. Every time we have to evaluate the fitness of an individual, we must solve the whole chemical system: for i = 0 → N do Calculate at instant i : Ca 2+ � , a , [ H 3 O + ] , [ HCO − ] , [ H 2 CO 3 ] , pH cal , ∆ Ca 2+ � � � , [ CH 3 COOH ] , [ CH 3 COO − ] Fitness = Fitness + ( pH exp , i − pH cal , i ) 2 end for

Motivation Determination of kinetic constants Unified shared-memory scheme Results Conclusions Using the notation for evolutionary algorithms, an individual is represented by a real vector of size seven that is the set of kinetic constants. The ranges of values for the constants are set following empirical criteria. Every time we have to evaluate the fitness of an individual, we must solve the whole chemical system: for i = 0 → N do Calculate at instant i : Ca 2+ � , a , [ H 3 O + ] , [ HCO − ] , [ H 2 CO 3 ] , pH cal , ∆ Ca 2+ � � � , [ CH 3 COOH ] , [ CH 3 COO − ] Fitness = Fitness + ( pH exp , i − pH cal , i ) 2 end for