Mathematical Methods for Modeling Chemical Reaction Networks

Numerical modeling for nonlinear biochemical reaction networks

Nowadays, numerical models have great importance in every field of science, especially for solving the nonlinear differential equations, partial differential equations, biochemical reactions, etc. The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by the Runge-Kutta of order four (RK4) and by nonstandard finite difference (NSFD) method. A...

Mathematical Modeling of Fluorination Reaction of Uranium Dioxide and Evaluation of Existing Gas-Solid Reaction Models

Mathematical modeling of a fixed bed chromatographic reactor for Fischer Tropsch synthesis

In this research, Fischer Tropsch synthesis (FTS) has been modeled in the fixed bed chromatographic reactor for the first time by applying a rather complex dispersed plug flow model for fluid phase and linear driving force (LDF) model for adsorbent. Model equations are dynamic, multi-component, non-linear and heterogeneous including reaction and adsorption simultaneously Complex kinetics fo...

Kinetic Mechanism Reduction Using Genetic Algorithms, Case Study on H2/O2 Reaction

For large and complex reacting systems, computational efficiency becomes a critical issue in process simulation, optimization and model-based control. Mechanism simplification is often a necessity to improve computational speed. We present a novel approach to simplification of reaction networks that formulates the model reduction problem as an optimization problem and solves it using geneti...

Comparison of Simulated Annealing, Genetic, and Tabu Search Algorithms for Fracture Network Modeling

The mathematical modeling of fracture networks is critical for the exploration and development of natural resources. Fractures can help the production of petroleum, water, and geothermal energy. They also greatly influence the drainage and production of methane gas from coal beds. Orientation and spatial distribution of fractures in rocks are important factors in controlling fluid flow. The obj...