The following differential equation describes the steady state concentration of a substance that reacts with first-order kinetics in an axially-dispersed plug-flow reactor
Where D = the dispersion coefficient (m2/hr), c = concentration (mol/L), x = distance (m), U = the velocity (m/hr), and k = the reaction rate (/hr). The boundary conditions can be formulated as
Ucin = Uc(x = 0) = D(dc/dx) (x = 0)
dc/dx(x = L) = 0
Where cin = the concentration in the inflow (mol/L), and L = the length of the reactor (m). These are called Danckwerts boundary conditions. Use the finite-difference approach to solve for concentration as a function of distance given the following parameters:
D = 5000 m2/hr, U = 100 m/hr, k = 2/hr, L = 100 m, and cin = 100 mol/L. Employ centered finite-difference approximations with ∆x = 10 m to obtain your solutions. Compare your numerical results with the analytical solution,
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