.TransiEnt.Producer.Gas.MethanatorSystem.EquilibriumModel.MethanatorBlock_equilibrium_L2

Information

1. Purpose of model

Equilibrium model of reactor block for methanation of hydrogen.

2. Level of detail, physical effects considered, and physical insight

The model is based on the equilibrium constants for the reaction equations of CO2-methanation, CO-methanation und CO-Shift. The gas components in the output are in an equilibrium. The model considers the heat of the exothermal reaction and therewith the temperature increase of the product gas and of the temperature increase of the reactor. A detailed description is found in [1].

3. Limits of validity

The calculation of the equilibrium is validated in [1].

4. Interfaces

gasPortIn: Input port for methanation

gasPortOut: Output port of product gas

5. Nomenclature

6. Governing Equations

The chemical balance considers the equilibrium constants. These are calculated via the following formulas:

1. equilibrium constant of CO-methanation:

2. equilibirum constant for CO-shift:

The equilibrium constant for CO2-methanation is lineraly dependent on those two equilibrium constants such that the equation can be omited.

Moreover a substance balance and an thermal balance govern the calculation. The substance balance ensures that the amount of subtance of each element entering the reactor block equals the amount of substance leaving the reactor block.

For the thermal balance a simplified model of a fixed-bed reactor is considered with the lenght L, the inner diameter di, a thickness of the reactor wall of delta_wall and an isolation layer with the thickness delta_iso. The cross section of the reactor block is shown in graphic 1.

The following differential equation is needed for the calculation of the temperature of the reactor mass T_reactor:

Here Q_flow_loss describes the heat losses towards the environment and Q_flow_inner is the heat transfer from the process gas onto the reactor mass. Q_flow_loss consists of the heat loss through radiation and convection whereby the necessary values for thermal conductivities and the heat-transfer coefficient can be defined as parameters. The formula for heat-transfer coefficient alpha_i for the heat transfer from the process gas onto the reactor mass (Q_flow_inner) is a simplified correlation which results from a more complex correlation:

The temperature increase of the process gas is calculated via the following formula:

Here F_average is the averaged molar flow between output and input, c_p,gas is the specific heat capacity of the gas, T_out and T_in are the input, respectively the output temperature of the process gas and Q_flow_reaction is the reaction heat that is released during the reaction.

Q_flow_reaction is calculated via the specific molar reaction heat:

Here F_i stands for the molar flow of the respective substance and h1 and h3 stand for the specific molar reaction heat. These specifc molar reaction heat depend on the temperature. As a simplification the reaction heat are calculated with the input temperature T_in:

specific molar reaction heat for CO-methanation:

specific molar reaction heat for CO-shift:

7. Remarks for Usage

8. Validation

Validated in [1].

9. References

[1] Schülting, Oliver - Vergleich von Power-to-Gas-Speichern mit Ziel der Rückverstromung unter derzeit gültigen technischen Restriktionen (Masterarbeit), Technische Universität Hamburg - Institut für Energietechnik, 2016

10. Version History

Model created by Oliver Schülting (oliver.schuelting@tuhh.de) in Nov 2019