Chapter 11 - Balances on Transient Processesteacher.buet.ac.bd/shoukat/Chapter11BalancesonTransientProcesse… · Chapter 11 Balances on Transient Processes Dr M. A. A. Shoukat Choudhury

Chapter 11 Balances on Transient Processes

Dr M. A. A. Shoukat ChoudhuryDr M. A. A. Shoukat ChoudhuryDepartment of Chemical EngineeringDepartment of Chemical Engineering

BUET, Dhaka BUET, Dhaka –– 10001000

What is Transient?

Transient: A system is said to be transient if the Transient: A system is said to be transient if the value of any system variable changes with time. value of any system variable changes with time. Example: Batch and semiExample: Batch and semi--batch processes are batch processes are always transientalways transientAt start up and shutdown, the continuous At start up and shutdown, the continuous processes are transient. They are also transient processes are transient. They are also transient d i b l it ti t dd i b l it ti t dduring an abnormal situation or unexpected during an abnormal situation or unexpected changes in operating conditions. changes in operating conditions.

Chemical Engineering, BUET Dr. M. A. A. Shoukat Choudhury

B l C ti T i t P

General Balance Equation:

Balances on Continuous Transient Process

ACCUMULATION = INPUT + GENERATION – OUTPUT – CONSUMPTION

ACCUMULATION is not equal to zeroCCU U O s ot equa to e o

Balances on Continuous Steady-State Process

Steady stateSteady stateSteady state Steady state accumulation = 0accumulation = 0

INPUT + GENERATION = OUTPUT + INPUT + GENERATION = OUTPUT +


CONSUMPTIONCONSUMPTION

General Balance Equation:

Δ t= (m + r m r ). ...

ΔM Δ t= (min + rgen – mout – rcons)ΔM

= (m + r – m – r ). ...ΔMLt

dM

= (min + rgen – mout – rcons)ΔtLt

t 0

dt = min + rgen – mout – rcons. ....dM

Differential Balance Equation One equation so you need one Boundary Condition or an initial conditionor an initial condition

Integrating the differential balance equation between initial and final conditions


between initial and final conditionswill yield the integral balance equation

Example 11.1-1

A continuous stirred tank reactor is used to produce a A continuous stirred tank reactor is used to produce a compound R in the liquid phase reaction A R. Feed enters compound R in the liquid phase reaction A R. Feed enters the reactor at a rate of vthe reactor at a rate of v (L/s); the concentration of the(L/s); the concentration of the..the reactor at a rate of vthe reactor at a rate of voo (L/s); the concentration of the (L/s); the concentration of the reactant in the feed is Creactant in the feed is CAoAo (mol A/L). The volume of the tank (mol A/L). The volume of the tank content is V (L). The vessel may be considered perfectly content is V (L). The vessel may be considered perfectly mixed so that the concentration of A in the product streammixed so that the concentration of A in the product streammixed, so that the concentration of A in the product stream mixed, so that the concentration of A in the product stream equals that in the tank. For this process the rate of equals that in the tank. For this process the rate of consumption of A equals kCconsumption of A equals kCAA [mol/s. L of reaction volume]. [mol/s. L of reaction volume]. All fluids ( the feed the tank contents and the product) mayAll fluids ( the feed the tank contents and the product) mayAll fluids ( the feed, the tank contents, and the product) may All fluids ( the feed, the tank contents, and the product) may be taken to have the same density, be taken to have the same density, ρρ (g/L).(g/L).

Write differential balances on total mass and on moles of A.Write differential balances on total mass and on moles of A.


Solution

A R rA = k CA , mol A/s.volm of liquid

VoρCAo

.

Vρ

.CA, ρ

ρCA

Example 11.1-1


11.1.1 (cont’d)



Example 11.1-2



Example 11.2-1: Mass Balance on a water storage tank

0.05


Solution to Example 11.2.1



Volume cannot be negative. Therefore,


A Problem from the Final Exam of Feb 2009

Water is added to a storage tank at a rate of 1000 kg/h and is Water is added to a storage tank at a rate of 1000 kg/h and is simulatneously withdrawn at a rate of msimulatneously withdrawn at a rate of m (t) (kg/h) that(t) (kg/h) thatsimulatneously withdrawn at a rate of msimulatneously withdrawn at a rate of mww(t) (kg/h) that (t) (kg/h) that increases linearly with time, t. At t=0, the tank contains 500 kg increases linearly with time, t. At t=0, the tank contains 500 kg water and mwater and mww=500 kg/h. Five hours later m=500 kg/h. Five hours later mww=750 kg/h. =750 kg/h. Calculate an expression for mCalculate an expression for m (t) and incorporate it into a(t) and incorporate it into aCalculate an expression for mCalculate an expression for mww(t) and incorporate it into a (t) and incorporate it into a differential mass balance equation for the system. Find the differential mass balance equation for the system. Find the expression for mass of water in the tank at any time t. What expression for mass of water in the tank at any time t. What

ill be the ma im m amo nt of ater in the tank and henill be the ma im m amo nt of ater in the tank and henwill be the maximum amount of water in the tank and when will be the maximum amount of water in the tank and when will it completely drain out?will it completely drain out?

Solution: Discuss in the class


Class Test Class Test –– 4/54/5


Documents

Chapter 11 - Balances on Transient Processesteacher.buet.ac.bd/shoukat/Chapter11BalancesonTransientProcesse… · Chapter 11 Balances on Transient Processes Dr M. A. A. Shoukat Choudhury