In case you missed part 1, you can view it here. In this part, I tried to recreate the examples in section A.2.2 of the computational appendix in the reaction engineering book by Rawlings and Ekerdt.

## Solving a nonlinear system of equations

This example involves determining reaction equilibrium conditions by solving the following system of nonlinear equations.

The relation between the variables and extent of reactions are:

Here I have used R package rootSolve for solving the above set of equations to determine and . The library is loaded and the functions to be solved are defined in the R function fns.

# load library rootSolve library(rootSolve) # function defining F(x)=0 fns=function(x){ K1=108; K2=284; P=2.5 yI0=0.5; yB0=0.5; yP10=0; yP20=0; d=1-x[1]-x[2] yI=(yI0-x[1]-x[2])/d yB=(yB0-x[1]-x[2])/d yP1=(yP10+x[1])/d yP2=(yP20+x[2])/d F1=P*K1*yI*yB-yP1 F2=P*K2*yI*yB-yP2 c(F1=F1,F2=F2) }

Next, an initial guess of (0.2,0.2) is set for the variables and the equations are solved using the function multiroot (from package rootSolve)

# initial guess for x xinit=c(0.2,0.2) # solve the equations xans=multiroot(f=fns,start=xinit) # object returned by multiroot > xans $root [1] 0.1333569 0.3506793 $f.root F1 F2 6.161738e-15 1.620926e-14 $iter [1] 7 $estim.precis [1] 1.11855e-14 # solution to the equations > xans$root [1] 0.1333569 0.3506793 >

The solution to the equations is accessed from the variable xans$root which in this case is (0.1334,0.3507)

MATLAB/Octave functions for solving nonlinear equations (fsolve) have been used in Chemical Engineering computations for a long time and are robust. R has traditionally not been used in this domain. So it is hard to say how the functions I have used in this blog will perform across the range of problems encountered in Reaction Engineering.

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