A continuous stirred tank reactor is used to break down a chemical in an irreversible first-order reaction. The reactor has a volume of 10 m3 and nominal inlet and outlet concentrations of the chemical of 5 kg m-3 and 0.1 kg m-3 respectively. The flowrate through the reactor is perfectly controlled at 0.5 m3 h -1 .a) Derive a dynamic model for the reactor.b) By considering steady state, calculate the reaction rate constant.c) Using deviation variables, derive the response when the inlet concentration increase in a step by 1 kg m-3 ONLY PART C PLEASE AND DONT COPY AND PASTE FROM OTHER ANSWERED QUESTIONS AS THEY ARE WRONG!SHOW WORKING ON HOW TO REACH ANSWER FOR PART C asnwerrs and feedback attached 1. Most managed this question well:a) Derive a dynamic model for the reactor.The model is the same as the one we found during the lecture.b) By considering steady state, calculate the reaction rate constant.Set the accumulation term to zero for steady-state. Sub in the steady-statevalues of concentration that were provided and rearrange for k. Pay attentionthat the units of k are consistent with the order of reaction.V0 ==20 h k =Fc* (t)=1 Cin - Css0 Cssc) Using deviation variables, derive the response when the inlet concentrationincrease in a step by 1 kg m-³.1=Again the solution is the one we obtained during the lecture, although in this casewith specific numerical values for the time constant and steady-state gain.504.90.1 × 20= 2.45 h-¹[1 - exp(-2.5t)] Deviation Variables• We use the following notation for these:CA* (t)= C₁ (t) - CASSCA,in (t)=CA,in (t) - CA, inss• At the nominal steady state (at t=0), both of theseare zeroSubstituting into our model rate equation we relatechanges in CA* (t) to changes in CA,in* (t)• Often we deal with a step-change in the inputDeviation VariablesFrom previously:Substitute in the deviation variables:d(C₁* + CA₂)dtCA (t)=CA (t) - CassCA,in' (t)= CA,in (t) - CA,inssTdC₁dtdcdtdC₁KCAIR - CAdCAdtDeviation Variables=KCA,in - CA2 = K (Cain" + Gina) - CA + CrisIn fact, for a linear system an equivalent cancellation is alwayspossible, so we can take deviation variables directlydt= [²4/1/T0=KCAin - CACA"(t)= KCA,in (1-expl= KCA.in - CAxp (--))0=(residence time)1K = 1+k@T=1=1+kQ²Cancel since: CA = KCA,ings0 ==(residence time)11+k@T=01+k@'K=Thus, we have a solution that deals only with the changes in theinput and output of the system

Irreversible first-order reaction is taking place in CSTRVolume of reactor = 10 m3 Inlet…

Answered: Using deviation variables, derive the…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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A continuous stirred tank reactor is used to break down a chemical in an irreversible first-order reaction. The reactor has a volume of 10 m3 and nominal inlet and outlet concentrations of the chemical of 5 kg m-3 and 0.1 kg m-3 respectively. The flowrate through the reactor is perfectly controlled at 0.5 m3 h -1 .

a) Derive a dynamic model for the reactor.

b) By considering steady state, calculate the reaction rate constant.

c) Using deviation variables, derive the response when the inlet concentration increase in a step by 1 kg m-3

ONLY PART C PLEASE AND DONT COPY AND PASTE FROM OTHER ANSWERED QUESTIONS AS THEY ARE WRONG!

SHOW WORKING ON HOW TO REACH ANSWER FOR PART C

asnwerrs and feedback attached