Uppal, Ray, and Poore provide the following system of differential equations describing irreversible, first-order, exothermic reactions in a CSTR:

where x₁ and x₂ are dimensionless concentration and temperature variables respectively, and Da, γ , B, and β are dimensionless parameters that describe the dynamic behavior of the CSTR. Write a MATLAB function that will create phase planes for each of the following cases. Briefly explain the result of each phase plane.

(a) Use the parameters Da = 0.085, B = 22.0, and β = 3.0 with an initial condition of x₁ = 0.8, x₂ = 4.25.

(b) Use the parameters Da = 0.150, B = 19.0, and β = 3.0 with an initial condition of x₁ = 0.9, x₂ = 6.25.

(c) Use the parameters Da = 0.320, B = 11.2, and β = 3.0 with initial conditions of x₁ = 0.95, x₂ = 2.5, and x₁ = 0.7, x2 = 1.8.

Transcribed Image Text:

dx2 dt dx1 dt = -x₁ + Da(1-x₁) exp = -x2 + BDa(1-x₁) exp 1+ X2 X2 1 + X2 Y X2 Y - Bx2