che 126 last exam

ChE 126 Reference: Fundamentals of Chemical Reaction Engineering, Davis and Davis. California Institute of Technology Library. a. Energy balance: For a spherical pellet, the energy balance (as adapted from Bird, Stewart and Lightfoot, p. 275 of first edition) of a spherical shell of thickness ∆r Thermal energy in at r Thermal energy out at Thermal energy produc ed From The te rms above are summed and divided by Dividing by and simplifying the limit as r approaches 0 into the derivative, Note that q is actually Fourier’s law of thermal conductivity, Where is the effective thermal conductivity of the pellet. is given as 0 at r = 0 and T = Ts at r = R. Concentration profile The c oncentration profile for a spheric al particle for a first o rder reaction is given by the following equation:

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8/2/2019 ChE 126 Last Exam

http://slidepdf.com/reader/full/che-126-last-exam 1/4

ChE 126

Reference:Fundamentals of Chemical Reaction Engineering, Davis and Davis. California Instituteof Technology Library.

a.Energy balance:

For a spherical pellet, the energy balance (as adapted from Bird, Stewart andLightfoot, p. 275 of first edition) of a spherical shell of thickness ∆r

Thermal energy in at r

Thermal energy out at

Thermal energy produced

From

The terms above are summed and divided by

Dividing by and simplifying the limit as r approaches 0 into the derivative,

Note that q is actually Fourier’s law of thermal conductivity,

Where is the effective thermal conductivity of the pellet. is given as 0 at r = 0and T = Ts at r = R.

Concentration profile

The concentration profile for a spherical particle for a first order reaction is given bythe following equation:

8/2/2019 ChE 126 Last Exam

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The concentration profile and temperature profile were evaluated using Maple. Seenext page for the code and the final equations.

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Another boundary condition is that at r =0, the derivative of T(r) is 0. However, avalue of 0 at the denominator is not allowed. In order for equation 9 to be valid, _C2should also be equal to Ts. The equation for T(r) simplifies to:

Simplifying this equation we arrive at

Given the boundary condition that at Tmax, Ca = 0

b. Representative values of the parameters and graph for the temperature andconcentration profile when the reaction is carried out adiabatically.

When the reaction is carried out adiabatically, no heat is transferred to thesurroundings and all energy generated (or consumed) by the reaction goes to heat(or cool) the pellet. The temperature difference between the surface and the pelletinterior is directly related to the concentration difference. The relation forconcentration and temperature is given in equation 5 of the Maple derivations.

Thus, the equations previously derived are suitable for use in an adiabatic system.Setting the parameters for our system as:

Parameter Value

R 0.01 metersSa 530 square meters per gramk1 4.42 * 10e-10 cubic meters/square

meters-sDe 10e-1 cm^2/sΡ 2800 kg/cubic meter or 2.8*10e6 g/cubic

meterCs (surface concentration) 4e-5 mol/cm^3∆Hreaction +/- 80000 Joules/molkt (thermal conductivity) 1.6e-3 J/(cm-sec-C)Ts 200 degrees Celsius