You have been tasked with figuring out how to suppress changes in the supply flow rate to a reactorfor which it is desired to keep the inlet flow rate as constant as possible. You are considering designing a surgetank to place upstream of the reactor and then installing a pump on the line between that surge tank and thereactor. A surge tank is one with a weir inside it, which is a partial wall separating the tank volume into twoconnected sections allowing for flow under the weir between the two sections. The variable inlet mass flow,wi(t) flows into volume 1 and then flows due to hydrostatic pressure at a mass flow rate of w1(t) into volume 2.The weir causes a flow resistance, R1, such that w1 = (h1-h2)/R1. Fluid is then pumped out of volume 2 at thedesired constant mass flow rate of w2. Make a summary table of the three transfer functions written in standard form and their keyparameters (gains, time constants) in terms of the physical system parameters (A1, A2, , A, R…). Checkif/how surge tank T.F.’s reduce to normal tank T.F. for the relevant conditions that should lead to that. Sketch and briefly explain how each of the 3 heights would be expected to vary with time inresponse to a positive pulse change in Wi (one that returns to the nominal steady state value). What would happen if there were a step change in Wi instead of an impulse? Why? Finally, sum up the conclusions and discuss how you would go about determining whether asurge tank should be used and if so what the best split between A1 and A2 would be.

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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Question

You have been tasked with figuring out how to suppress changes in the supply flow rate to a reactor
for which it is desired to keep the inlet flow rate as constant as possible. You are considering designing a surge
tank to place upstream of the reactor and then installing a pump on the line between that surge tank and the
reactor. A surge tank is one with a weir inside it, which is a partial wall separating the tank volume into two
connected sections allowing for flow under the weir between the two sections. The variable inlet mass flow,
wi(t) flows into volume 1 and then flows due to hydrostatic pressure at a mass flow rate of w1(t) into volume 2.
The weir causes a flow resistance, R1, such that w1 = (h1-h2)/R1. Fluid is then pumped out of volume 2 at the
desired constant mass flow rate of w2.

Make a summary table of the three transfer functions written in standard form and their key
parameters (gains, time constants) in terms of the physical system parameters (A1, A2, , A, R…). Check
if/how surge tank T.F.’s reduce to normal tank T.F. for the relevant conditions that should lead to that.

Sketch and briefly explain how each of the 3 heights would be expected to vary with time in
response to a positive pulse change in Wi (one that returns to the nominal steady state value).

What would happen if there were a step change in Wi instead of an impulse? Why?

Finally, sum up the conclusions and discuss how you would go about determining whether a
surge tank should be used and if so what the best split between A1 and A2 would be.

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