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

Uc_in = Uc(x = 0) = D(dc/dx) (x = 0)

dc/dx(x = L) = 0

Where c_in = 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 c_in = 100 mol/L. Employ centered finite-difference approximations with ∆x = 10 m to obtain your solutions. Compare your numerical results with the analytical solution, 

Transcribed Image Text:

diUe 0 Ucin where AKNX U2 λο 2D