# Difference between revisions of "Isothermal reactor design - 2013"

Class date(s): 04 February to 14 February

• F2011: Chapter 5 and 6
• F2006: Chapter 4

### 07 February 2013 (05C)

to see the effect on pressure drop in the packed bed.

### 25 February 2013 (07A)

The example covered in class is based on example 4-8 in F2006 and example 6-2 in F2011. <rst> The 3 ODE's are:

.. math::

\dfrac{dF_A}{dV} &= r_A\\ \dfrac{dF_B}{dV} &= r_B - R_B \\ \dfrac{dF_C}{dV} &= r_C

where :math:-r_A = r_B = r_C and :math:-r_A = k\left(C_A - \dfrac{C_B C_C}{K_C} \right), and :math:R_B = k_\text{diff}C_B.

• :math:k = 0.01\,\text{s}^{-1}
• :math:k_\text{diff} = 0.005\,\text{s}^{-1}
• :math:K_C = 50\,\text{mol.m}^{-3}

We derived earlier in the course that

.. math:: C_A = C_\text{TO}\left(\dfrac{F_A}{F_T}\right)\left(\dfrac{P}{P_0}\right)\left(\dfrac{T_0}{T}\right)

Assuming isothermal and isobaric conditions in the membrane:

.. math:: C_A = C_\text{T0}\left(\dfrac{F_A}{F_T}\right)

where :math:F_T = F_A + F_B + F_C and :math:C_\text{T0} = \dfrac{P_0}{RT_0}

Using all of the above derivations, we can set up our numerical integration as shown below. </rst>

MATLAB Python

In a file called membrane.m:

sdfsdf


In a separate file (any name), for example: ode_driver.m, which will "drive" the ODE solver:

asdas

asdasd


and in Polymath:

d(FA)/d(V) = rA
d(FB)/d(V) = rB - kDiff * CB
d(FC)/d(V) = rC

FA(0) = 0.25  # mol/s
FB(0) = 0.0   # mol/s
FC(0) = 0.0   # mol/s

# Independent variable
V(0) = 0
V(f) = 0.4  #m^3

# Algebraic equations
rB = -rA
rC = -rA
rA = -k * (CA - CB * CC / KC)
CA = CT0 * FA / FT
CB = CT0 * FB / FT
CC = CT0 * FC / FT
CT0 = P0 / (R * T0)
FT = FA + FB + FC

# Constants
kDiff = 0.005  # s^{-1}
k = 0.01       # s^{-1}
KC = 50        # mol.m^{-3}
P0 = 830600    # Pa
T0 = 500       # K
R  = 8.314     # J/(mol.K)