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

Question

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

3. You are asked to select and size reactors to carry out an isothermal liquid-phase, irreversible reaction AB with the following kinetics -rA kcAn where n=1 and with k = 0.10 min Starting with a mole balance (& assumptions), calculate the time it would take for a. a batch reactor to process your feed to achieve 90% conversion Starting with a mole balance (& assumptions), calculate the residence time (reactor volume/flow rate through reactor) it would take a steady-state plug-flow reactor to process your feed to achieve 90 % conversion. Compare your results in a) and b) and explain why they are the same in a single sentence physically Starting with a mole balance (& assumptions), calculate the volume it would take for a steady-state continuously-stirred tank reactor (CSTR) to process your feed to achieve 90% conversion Compare your answer in d) to the residence time you would expect from b): which reactor will you use and why? Which reactor yields the higher conversion, given the same residence time? If the given reaction exhibited negative first order kinetic behavior (ie, n=-1) instead, how does this influence your decision in e) and why? Please redo your calculations for this case comparing steady-state plug flow reactor and CSTR for n--1. Which reactor yields the higher conversion, given the same residence time If the given reaction exhibited zero order kinetic behavior (i.e. n-0) instead, how does this influence your decision in e) and why? Please redo your calculations for this case comparing steady-state plug flow reactor and CSTR forn-0. Explain your conclusion physically in a single sentence b. c. d. e. f. g.

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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