11

CE 548

Introduction to Process Analysis and Selection

22

Reactors used for the treatmentReactors used for the treatmentWastewater treatment involving physical, chemical or biological

activities are carried out in vessels or tanks commonly known as “reactors”.

Types of reactors:

• Batch reactor: The flow enters, is treated and then is discharged and the cycle repeats. Once the processing commences flow does not enter or leave the vessel. Used for small operations.

33

Reactors used for the treatmentReactors used for the treatmentTypes of reactors:

• Complete mix reactor: Complete mixing occurs instantaneously and uniformly throughout the reactor as fluid enters the reactor. Usually squar tanks, L~W. Used with most newer systems.

44

Reactors used for the treatmentReactors used for the treatmentTypes of reactors:

• Plug-flow reactor: Fluid passes through the reactor with little or no longitudinal mixing and exit the reactor in the same sequence as they entered. Long rectangular tanks L>>W. Used in most older systems.

55

Reactors used for the treatmentReactors used for the treatmentTypes of reactors:

• Complete-mix reactors in series (e)

• Packed-Bed reactors (f), (g)

• Fluidized-Bed reactors (h)

66

Reactors used for the treatmentReactors used for the treatmentApplications of the reactors:

• The principle applications of reactors types used for the treatment of wastewater are reported in Table 4-1

• Operational factors that are considered in the selection of the type of reactor to be used:

The nature of the wastewater to be treated

The nature of the reaction

The reaction kinetics

The process performance requirements

77

Table 4-1

88

Reactors used for the treatmentReactors used for the treatmentHydraulic characteristics of reactors:

Ideal flow in complete-mix and plug-flow reactors for pulse (slug-dose)

= V/Q

Where;

= hydraulic detention time, T

V = volume of reactor, L3

Q = flowrate, L3

99

Reactors used for the treatmentReactors used for the treatmentHydraulic characteristics of reactors:

Ideal flow in complete-mix and plug-flow reactors for step inputs (continuous injection)

= V/Q

Where;

= hydraulic detention time, T

V = volume of reactor, L3

Q = flowrate, L3

1010

Mass-Balance AnalysisMass-Balance Analysis Principle: conservation of

mass; mass neither created nor destroyed.

Rate of accumulation of

reactant within the system boundary

=

Rate of flow of reactant into the system boundary

-

Rate of flow of reactant out of

the system boundary

+

Rate of generation of reactant within

the system boundary

(1) (2) (3) (4)

1111

Mass-Balance AnalysisMass-Balance Analysis Preparation of Mass Balances

• Schematic

• Control volume

• List all data and assumptions

• List all rate expressions

• Select a basis for calculation

Application of mass-balance analysis

• Assumptions: Constant flowrate into and out of control volume No evaporation (constant volume) Complete mixing Reaction occurs within reactor

Rate of reaction is first-order (rc = -kC)

1212

Mass-Balance AnalysisMass-Balance Analysis Formulation of mass balance:

Accumulation = Inflow – outflow + generation

if the reaction is steady state, there is no accumulation (dC/dt = 0), Thus equation (4-6) can be written as:

VrQCQCVdt

dCco

kCrc

6)-(4 eq VkCQCQCVdt

dCo )(

VrQCQC co 0

)( oc CCV

Qr

1313

Modeling Ideal Flow in ReactorsModeling Ideal Flow in ReactorsModeling of the hydraulic characteristics of reactors is important because the results can be used to determine the actual amount of time a given volume of water will remain in the reactor.

Complete Mix Reactor:

Accumulation = Inflow – outflow + generation

Using tracer, nothing is being generated; generation = 0

For pulse (slug) input:

Integrating with limits C=Co to C=C, and t=0 to t= t yields:

QCQCVdt

dCo

CV

Q

dt

dc

0oC

eCeCeCC ot

oVQt

o/)/(

1414

Modeling Ideal Flow in ReactorsModeling Ideal Flow in ReactorsComplete Mix Reactor:

Accumulation = Inflow – outflow + generation

Using tracer, nothing is being generated; generation = 0

For step input:

Integrating with limits C=C to C=Co, and t=0 to t= t yields:

dtV

Q

CC

dC

CCV

Q

dt

dC

QCQCVdt

dC

o

o

o

)(

)(

)1()1()1( /)/( eCeCeCC ot

oVQt

o

1515

Modeling Ideal Flow in ReactorsModeling Ideal Flow in ReactorsPlug-flow Reactor:

Accumulation = Inflow – outflow + generation (generation = 0)

xxx QCQCVt

C

xx

CCQQCV

t

C

xx

CQxA

t

C

x

C

A

Q

t

C

x

C

x

C

A

Q

t

C

1616

Nonideal Flow in ReactorsNonideal Flow in Reactors Factors leading to nonideal flow in reactors: (Fig 4-6)

1717

Nonideal Flow in ReactorsNonideal Flow in Reactors Need for tracer analysis:

• Tracer analysis is used to assess the hydraulic performance of the reactor by measuring the residence time.

• Application of tracer studies include:

Assessment of short circuiting in sedimentation tanks and biological reactors

Assessment of contact time in chlorine contact basins

Assessment of the hydraulic approach conditions in UV reactors

Assessment of flow patterns in constructed wetlands and other natural treatment systems

Example 4-1 Page 236

1818

Reactions, Rates, and Coefficients Reactions, Rates, and Coefficients Types of reactions:

• Homogenous: the reactants are distributed uniformly throughout the fluid. (batch, complete-mix, plug-flow)

Rate of reaction;

• Heterogeneous: reaction occur at a specific site. (packed and fluidized bed reactors)

Rate of reaction;

dt

dCr

timearea

moles

dt

Nd

Sr

1

1919

Reactions, Rates, and Coefficients Reactions, Rates, and Coefficients Types of rate expressions:

• Typical rate expressions for selected processes: Table 4-6

• Integration and differential methods used to determine reaction rate coefficients: Table 4-7

• Example 4-5.

order)-mixed or n(saturatio

order)-(second

order)-(second

order)-(first

order)-(first

order)-(zero

CK

kCr

CkCr

kCr

CCkr

kCr

kr

BA

s

2

)(

2020

2121

2222

Modeling treatment process kineticsModeling treatment process kineticsBatch reactor:

kt

o

C

C

Co

eC

C

kCr

rdt

dC

Q

VrQCQCVdt

dC

0

2323

Modeling treatment process kineticsModeling treatment process kineticsComplete mix-reactor:

• Graphical solution: Example 4-6

no

no

oo

C

Co

nk

C

nQkV

CC

n

k

C

QVk

CC

kCr

VrQCQCVdt

dC

)/(1)/(1

1)/(1

:is expression the searies, in reactors for

:by given is 0) (dC/dt

conditions statesteady under 93)-(4 Eq to solution The

93)-(4

2424

Modeling treatment process kineticsModeling treatment process kineticsPlug-flow:

kQ

Vk

o

C

C

xx

Cxxx

eeC

C

kCr

Vrxx

CCQQCV

dt

dC

QC

VrQCQCVdt

dC

:by given is solution the 0), (dC/dt conditions statesteady under

:gives for form aldifferenti the ngSubstituti

2525

Modeling treatment process kineticsModeling treatment process kineticsPlug-flow with axial dispersion:

120-4 eq of use the facilitate to used be can 26-4 Figure

velocity fluid

dispersion axial of tcoefficien

factor dispersion

where;

120)-(4

:equation following theby given is solution The

u

D

uLDd

dka

daadaa

da

C

C

o

/

41

)2/exp()1()2/exp()1(

)2/1exp(422

2626