2. Chemical Reaction Engineering: Please provide complete correct detailed solut

Question

2. Chemical Reaction Engineering: Please provide complete correct detailed solution. Preferentially done by hand or on paper with graphs and calculation.

2. You are given the rate equation-.-kA,, A for the liquid-phase reaction A->B. Inlet flow rates are 100 mol/s of pure A, which has a density of 1000 kg/m and a molar mass 1000 g/mol. The rate constant is 1x10°m/s. You are told the reactor has a catalyst of surface area Sg of 5 m /g, and the catalyst density in the reactor p is 25 kg/m a. To achieve 50% conversion in an isothermal steady-state C b. What volume is required for the same conversion in an isothermal steady-state, c. What is the residence time in a CSTR vs a PBR? Calculate a residence time with STR. what is the volume required? PBR? units of volumetric flowrate/catalvst weight as well as the usual volumetric flowrate/reactor volume. The former does not have the convenient units of time but physically expresses the residence time accurately in a reaction catalyzed by a solid catalyst in a reactor. Explain physically in a single sentence why the residence time for the CSTR is different from the PBR d. You decide to cut the residence time by ½ by doubling flow rates. What happens to the conversion in the PBR and CSTR above?

Explanation / Answer

I've gone to explain the problem more clearly posible without grahps so If you have some comment please write it. (the assumptions are equal in all exercises)

1. a) first step is analysis the system and the assumptions that you need to get an answer. The system is a fluid phases so in the middle of the reaction there isn't a volumetric change, the reaction is a first order and a=1 and b=1. The initial state is t0= 0min, the concentration of A0= 1mol and B0=0mol. This is a isothermal environment so T1= T2 and T=0 so the Q flow is not 0. So after this you have this equation

-ra=kCAN and this is equal to the consumint rate of the compud A so -ra=(-1/a) d(A)/dt

a is an experimental value so in this cause we assuming this like 1

using the both equation and solving the system with the value of A in one side of the equation you obtain.

d(A)/CAN=-akdt

now you only need to integrate the equiation using A0= 1mol and A1=0.1(0.1mol is because you need the 90% of conversion and the 90% of 1 is 0.1) with this value you can solve the integral and find t1= 23 min. the integrate equation is (ln(A1/A0)=-kt1).

b) the residence time in a flow reactor is calculte with this equation:

Tau=int(Ca/rA) in the time CAoand CA1

as explain before -ra=kCAN so you replace this in the equation and find that

Tau(-k)= int(Ca/Ca0) in the time CAoand CA1 and equal to (ln(A1/A0)=-ktau).

so the residence time and the reaction time are equals.

c)the reason because they're the same: the both phases are equals so the you can say that the mixing in the liquid phase are perfect.

this is a first reaction with 2 compounds (reactants and products) so there isn't middle step, limit reactant, mass transport or nay other problem.

Is a isothermal reactor so the T along the flow reactor is constant so the r doesn't change:

d)the CSTR reactor design reactor is:

Tau= CA0-CA1/-rA

and Tau is a relationship between V/V0=Tau, V0 is the volumetric flow at the beginning.

you find thevalluefor Tau= 9min then you need the V0 value in this cause you assumed l3/min ft3/min) then thesizeof the reactor is 9m3 or 9ft3

e)the CSTR reactor is better how you knowthe PFR needs 23 min and the CSTR only 9.

d) for this step the change is in the integral equation so you need to recalculate this:

dCA/CA-1=Ca2/2 evaluate in A0 and A1. Ca2/2=-kt1

e)at the end you recalculte with this integral dCA= Ca so you solve this and find the diferences.Ca= -kt1

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