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BATCH REACTORS

AND COMPLETELY

MIXED REACTORS

EVEN 3321 Environmental Engineering Lab

o Write & explain the general mass balance equation.

o Solve both steady-state & transient-state mass balance problems.

o Explain the meaning of hydraulic retention time.

o Describe key features of batch and completely mixed reactors.

o Explain the meaning of conservative tracer.

LEARNING

OBJECTIVES

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MASS BALANCES

Note: units are mass per unit time

o Steady-state

No accumulation of mass within “system”.

o Transient-state

(or non-steady-state, or dynamic):

Mass accumulating or disappearing from the “system”.

o Steady≠state equilibrium

STEADY-STATE VERSUS TRANSIENT STATE

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FUNDAMENTAL “REACTOR” TYPES USED TO

MODEL ENVIRONMENTAL SYSTEMS

Batch Reactors

Completely Mixed Reactors :

CFSTR-Continuous Flowing Stirred Tank Reactor

CSTR – Continuous Stirred Tank Reactors

Plug-flow Reactors (PFR)

Completely mixed reactors in series

Packed Bed Reactors

BATCH REACTORAccumulation = Inflow – Outflow + Reaction

For this reactor, no flow in or out.

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BATCH REACTORS

FOR WATER

TREATMENT

COMPLETE-MIX REACTOR (CFSTR)

Accumulation = Inflow – Outflow + Reaction

0 at steady-state

Concentrations within reactor are sameAs in effluent.

A CFSTR operated at steady-state is called a “chemostat”.

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EXAMPLE OF A CSTR IN WATER

TREATMENT

http://bluefrogsystem.com/pages/cstr.html

HYDRAULIC RETENTION TIME

o “HRT”, also called hydraulic detention time or hydraulic residence time (�H).

o Equals the average time that water molecules remain in the system.

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RESPONSE OF A CFSTR TO STEP INPUT OF

A CONSERVATIVE TRACER

0 3�H TIME

( )H

i

t

TTeCC

θ/1

−−=

RESPONSE OF CFSTR TO STEP INPUT

OF A CONSERVATIVE TRACER

∫∫ =−

tC

TT

T dtV

Q

CC

dCT

i

00

HT

TT t

C

CC

i

i

θ=

−− ln

VrQCQCVdt

dCTTT

T

i−−=

0

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( )H

i

t

TTeCC

θ/1

−−=

CONSERVATIVE TRACER VERSUS TIME

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HRRRHR kCCC

dt

dCi

θθ −−= )1( HRRHR kCC

dt

dCi

θθ +−=

( ) ∫∫ =+−

t

H

C

HRR

R dtkCC

dCR

i

00

1

1 θθ

HR

RHR

H

t

C

CkC

ki

i

θ

θ

θ=

+−

+−

)1(ln

1

1

H

tk

R

Rk

eC

C

H

H

i

θ

θθ

+

−

=

+−

1

1)1(

RESPONSE OF A CFSTR TO STEP INPUT OF A

FIRST ORDER REACTANT

VrQCQCVdt

dCRRR

R

i−−=

VkCR−

REACTANT VS TIME

o When t->0, then CR -> CRi (1-1)/(1 + k�H) and CR -> 0

o When t is large then 1/et/�H -> 0 and CR -> CRi (1-0)/(1 + k�H) CR =CRi /(1 + k�H)

o Note for example when t is about 3�H

CR = 0.95CRi /(1 + k�H)

And a large residence time will result in a lower concentration of the effluent.

H

tk

R

Rk

eC

C

H

H

i

θ

θθ

+

−

=

+−

1

1)1(

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0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

CR/C

Ri

t/θθθθH

K=0.03 per hrθH=0.5 hrs

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5

CR/C

Ri

t/θθθθH

K=0.9 per

H

tk

R

Rk

eC

C

H

H

i

θ

θθ

+

−

=

+−

1

1)1(

RESPONSE OF CFSTR TO STEP

INPUT OF A REACTANT

K=0.9 per hr

θH=0.5 hrs

K=0.03 per hr

θH=0.5 hrs

RESPONSE OF CFSTR TO STEP

INPUT OF REACTANT

0 < 3�H 3�H

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)1(0 HRR kCCi

θ+−=

DETERMINING EFFLUENT REACTANT

CONCENTRATION FOR CFSTR STEADY-STATE

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

CR/C

Ri

Detention time (θθθθH), hrs

K=0.03 per hr

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

CR/C

Ri

Detention time (θθθθH), hrs

K=0.3 per hr

STEADY-STATE EFFLUENT REACTANT

CONCENTRATIONS IN CFSTR

K=0.3 per hr

K=0.3 per hr

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MATHEMATICAL MODELS OF PHYSICAL

SYSTEMS SUMMARY

Accumulation = inflow + outflow + reaction

At steady-state: