CO2 Hydrogenation to Methanol and Formic Acid in Competition with Hydrogen Evolution: A Spreadsheet Model for Use in Capstone Design Courses
Authors: Adler Stuart B. , Stuve Eric M. 
Published: February 2020

Electrochemical reactors (ECR), such as fuel cells and electrolyzers, are ideal systems to include in chemical engineering design courses. Electrochemistry and electrochemical reaction engineering are not normally required in the chemical engineering curriculum, so use of an ECR in a capstone design course requires a brief introduction of the topic and a working model to assist the students in ECR design.
Here, we focus on CO2 hydrogenation to make methanol and formic acid in competition with the hydrogen evolution reaction. This project was used in the Spring 2019 Process Design II class in Chemical Engineering at the University of Washington. A spreadsheet model was developed that estimates current densities of the three reactions occurring simultaneously. The model was derived from earlier versions that simulated H2/O2 fuel cells, in proton exchange membrane fuel cell (PEM) and solid oxide fuel cell (SOFC) configurations; and CH4-fed SOFCs with water gas shift and coking.
The cathode reactions included in the model were:
CO2+ 6 H++ 6 e
− → CH3OH + H2O
CO2+ 2 H++ 2 e
− → HCOOH
2 H++ 2 e
− → H2

and were coupled with the oxygen evolution anode reaction:
H2O → 2 H++ 2 e
− + 1/2 O2

Reactions are represented by a matrix of stoichiometric coefficients and physical properties of all species and reactions including molecular weight, gas and liquid phase viscosities, gas and liquid phase heat capacities, and heats and entropies of reaction. Activities are given by partial pressure for gaseous species and mole fraction for liquid species, under the assumptions of ideal gas and ideal solution. Reversible electrode potentials for non-unity species activities are calculated by the Nernst equation.
The spreadsheet is a one-dimensional, along-the-channel model solved step-wise by the Eulerian method. The channel, in parallel or serpentine pattern, is divided into 100 segments and each segment solved by a double (outer and inner) iteration loop. Each segment is assumed to be gradientless, which makes the model a series of CSTRs. Iteration is by the Newton-Raphson method, and both iterations are open-loop. Five iterations are sufficient to achieve convergence in most cases. The outer iteration begins with a guessed initial current density, from which the model solves for the overpotentials of electrolyte resistance, mass transfer limitation, and anode kinetics. The single term (Tafel) form of the Butler-Volmer equation is sufficient for CO2 hydrogenation due to the high overpotentials involved.
Individual reaction current densities are determined by the inner iteration, consisting of a guessed current density for methanol synthesis, from which the overpotential of that reaction is determined. Together with the reversible potentials of all three reactions, the cathode potential vs. RHE and the other cathode overpotentials can be determined. The inner iteration continues until the sum of all three reaction current densities equals the originally guessed current density. The outer iteration then proceeds until the outer-iterated cell potential agrees with the input cell potential. At this point, the total current density and individual reaction current densities are known, and the Faradaic efficiency can be determined. The mass balance is updated according to the extents of each reaction, and the solution procedure is repeated for the next segment.
Modeling inputs are cell potential; temperature; and inlet pressures, flow rates, compositions, exchange current densities, and limiting current densities for cathode and anode. Physical parameters include cell dimensions (length x width), channel dimensions (width, height, rib), and choice of serpentine (single or multiple pass) or parallel flow fields.
The screen shot in Fig. 1 shows a small portion of the control panel at left along with plots of CO2 and H2O conversion, current density, pressure, and species fluxes for the cell operating at −1.9 V cell potential and 70 °C. Serpentine flow fields are used for both cathode and anode with 1 and 2 passes, respectively. The average current density is 0.5 A/cm2, which is almost entirely due to methanol production, with a Faradaic efficiency of essentially 1. Current densities for formic acid and hydrogen evolution are less than 1 μA/cm2 in this case.
The model enables solution of a complex, real-world problem with tools readily available and understandable by senior chemical engineering students. It can be adapted for a variety of electrochemical reactions making it a powerful tool in electrochemistry education.

Figure 1