Example: Variable Volume Reactor

This example shows how to model a reactor where the phase volume changes during reaction. Density parameters are required when you enable this option.
You may import the Bio-Diesel.rex file from the Optience Corporation\REX Suite\REX Examples folder to view the model.

Vegetable oil is a mixture of triglycerides (TG) and free fatty acids; the overall transesterification reaction to biodiesel (BD) can be simplified to:

TG + 3 Alcohol → 3 BD + Glycerol

where a tri-ester (TG) is converted to three individual esters.
Using Methanol, the above reaction actually proceeds in three steps:

R1: TG + MeOH → DG + BD
R2: DG + MeOH → MG + BD
R3: MG + MeOH → G + BD

where DG, MG and G represents diglycerides, monoglycerides and glycerol respectively.

This base catalyzed reaction is performed with the addition of either KOH or NaOH which provides the OH^- active ions. They react with alcohol producing the respective alkoxide by the following equilibrated reaction:

R-starter : MeOH + OH^- ⇔ H2O + Alkoxide

Reactions R1 to R3 are first order with respect to the alkoxide concentration in both forward and reverse directions. For example, Rate(R1_forward) = k_R1-f [TG] [MeOH] [Alkoxide]. They also have their forward and reverse kinetic parameters constrained to their equilibrium constant: K_eq(R_n) = k_Rn-f / k_Rn-r

OH- ions are also a reactant in competing saponification reactions, where the catalyst OH- and the BD, TG, DG and MG are consumed:

Sap1: BD + OH^- → MeOH + Soap
Sap2: TG + OH^- → DG + Soap
Sap3: DG + OH^- → MG + Soap
Sap4: MG + OH^- → G + Soap

All these reactions take place in a batch reactor, where the liquid phase volume is calculated using compound density values provided in the Compounds → Properties node. You may review the entry of the compounds and reactions in the provided rex file. Note that the reaction R-starter is marked as a quasi-equilibrium reaction in the Reactions node.

In order to allow for phase volume calculation, density parameters must be defined. In general multiphase reactors, you must provide the density parameters in the liquid and solid phases. No density calculation is done for gas phase. Gas volume is obtained by subtracting the liquid and solid phase volumes from the total reactor volume.

We have only one liquid phase, so the density correlation parameters must be entered for liquid. This example uses constant density:




In the Reactor node, the Use Density option is chosen to enable calculation of phase volumes as the reaction proceeds:

The available measurements are for a liquid phase batch reactor, where measurements are taken along reaction time for a single experimental set. All data are at the same temperature of 55C, thus only pre-exponentials are to be estimated from this data, while activation energies will stay fixed to zero. You may view the data in the Measurements→Set1 node of REX, which is partially shown below:

The reactions to be estimated in REX are R1, R2, R3 and R-starter as marked in the Estimation node. The saponification reactions have their parameter fixed to the values in [Ref 1]. In the Weights node, we specify the compounds whose predicted values are to be reconciled with their data:



The weights for these measurements are generated with the Hybrid method. After executing the run, we can view the solution in the Results tree.
The optimized kinetics parameters are shown in Results → Parameters node. You can visualize the rate equations and other model information in the Results → Rate Equations node:



The following charts from Results → Model-Data Comparison node show the comparison between experimental and calculated values:













The calculated reactor volume shows minor change during the reaction. Thus, the model may be simplified by using constant volume without much compromise on accuracy.

1. Turner, T.L., 2005, Modeling and Simulation of Reaction Kinetics for Biodiesel Production, M.S thesis, North Carolina State University. Webpage: http://repository.lib.ncsu.edu/ir/bitstream/1840.16/1037/1/etd.pdf