Simple SE Reactor Model Documentation

Overview

This repository contains MATLAB scripts for simulating a simple SE (Sorption Enhanced) reactor model. The code is designed to solve a system of partial differential equations (PDEs) and ordinary differential equations (ODEs) to model the behavior of a chemical reactor. The model includes calculations for reaction kinetics, heat transfer, adsorption, and mass transfer.

Repository Structure

The repository consists of the following files:

• calculation_script.m: The main script to run the simulation. This script initializes parameters, calls the solver, and processes results.
• ODEsolver_Graaf.m: Contains the main ODE solver function that calculates the time derivatives of the system's state variables.
• dss020.m: Implements a discretization scheme for the first derivative (used for convection terms).
• dss044.m: Implements a discretization scheme for the second derivative (used for diffusion terms).
• efficiency.m: Calculates the efficiency factors for reactions and diffusion coefficients to account for the mass transfer limitations on the rate of the reactions. Calculation of efficiency factors is based on https://doi.org/10.1016/S0009-2509(00)00194-9
• equilibrium_calculation.m: Computes equilibrium constants for the reactions.
• heat_transfer.m: Calculates heat transfer coefficients and thermal conductivity. Calculation is based on https://doi.org/10.1016/0009-2509(77)80143-7
• rate_calculation_Graaf.m: Defines the reaction rate equations based on the Graaf et al. model. Rate equations are based on: https://doi.org/10.1016/0009-2509(88)85127-3
• RKS.m: Computes fugacity coefficients using the Redlich-Kwong-Soave equation of state.
• viscosity.m: Calculates the viscosity and thermal conductivity of the gas mixture.
• PSA_script.m (optional): Implements the Pressure-Swing-Absorption (PSA) logic for the SE reactor model. This script simulates the cyclic operation of the reactor, including adsorption and desorption phases.
• SERP_PDE.m (optional): Solves the system of partial differential equations (PDEs) for the SE reactor model, providing a detailed spatial and temporal resolution of the reactor's behavior.

Key Components

1. ODEsolver_Graaf.m

This is the core function of the repository. It calculates the time derivatives of the state variables, which include:

• Molar fractions of components (CO2, CO, H2, CH3OH, H2O, N2)
• Pressure
• Temperature
• Adsorbed water concentration

Key Steps:

1. Initialization: Extracts input parameters and initializes variables.
2. Momentum Balance: Calculates the velocity profile across the reactor.
3. Energy and Mass Balances: Discretizes the governing equations for pressure, temperature, and molar fractions.
4. Reaction Rates: Computes reaction rates using the Graaf et al. model.
5. Heat Transfer: Calculates heat transfer coefficients and energy balance.
6. Adsorption: Models water adsorption on the solid electrolyte.
7. Output: Returns the time derivatives of all state variables.

2. Discretization Functions

• dss020.m: Approximates the first derivative for convection terms.
• dss044.m: Approximates the second derivative for diffusion terms.

3. Reaction Kinetics

The reaction rates are based on the Graaf et al. model (1988) and include:

• CO + 2H2 → CH3OH
• CO2 + H2 → CO + H2O
• CO2 + 3H2 → CH3OH + H2O

4. Heat Transfer

The heat_transfer.m script calculates:

• Wall-to-bed heat transfer coefficient
• Effective thermal conductivity

5. Adsorption

The adsorption model includes:

• Adsorbent saturation capacity
• Mass transfer coefficients
• Adsorption rate equations

6. Physical Properties

• viscosity.m: Calculates gas mixture viscosity and thermal conductivity.
• RKS.m: Computes fugacity coefficients using the Redlich-Kwong-Soave equation of state.

7. Optional Full Cycle Simulation

• PSA_script.m: Simulates the full cycle of the SE reactor model using the Pressure-Swing-Absorption (PSA) logic. This includes adsorption and desorption phases to enhance the reactor's performance.
• SERP_PDE.m: Provides a detailed spatial and temporal resolution of the reactor's behavior by solving the system of PDEs for the SE reactor model.
• equlibria.m: Calculates equilibrium constnats for the PSA_script.m
• jacobian_SERP.m: Auxiliary file for numerical estimation of Jacobian for the ODE solver for PSA_script.m

How to Use

1. Set Up Parameters:

   • Define the reactor dimensions, operating conditions, and initial values in calculation_script.m.
   • Adjust global parameters in the ODEsolver_Graaf.m file if needed.

2. Run the Simulation:

   • Execute calculation_script.m in MATLAB.
   • The script will call the ODE solver and other functions to compute the results.

3. Analyze Results:

   • The output includes profiles of molar fractions, pressure, temperature, and other variables along the reactor length.

Dependencies

This code requires MATLAB and the following toolboxes:

• Optimization Toolbox (optional, for parameter fitting)

Contact

For questions or issues, please contact Pavel Maksimov (maksimov.ps95@gmail.com).