Reactor Characteristics

8/10/2019 Reactor Characteristics

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Reactor Characteristics

IntroductionChemical, biological and physical processes in nature and in engineered systems

usually take place in what we call "reactors." Reactors are defined by a real or

imaginary boundary that physically confines the processes. Lakes, segments of ariver, and settling tanks in treatment plants are examples of reactors. Most, but not all,

reactors experience continuous flow in and out!. ome reactors, experience flow

input and output! only once. #hese are called "batch" reactors. $t is important toknow the mixing level and residence time in reactors, since they both affect the

degree of process reaction that occurs while the fluid usually water! and its

components often pollutants! pass through the reactor.#racer studies can be used to determine the hydraulic characteristics of a reactor

such as the disinfection contact tanks at water treatment plants. #he results from

tracer studies are used to obtain accurate estimates of the effective contact time.

Reactor ClassificationsMixing levels give rise to three categories of reactors% completely mixed flow

CM&!, plug flow '&! and flow with dispersion &(!. #he plug flow reactor is an

ideali)ed extreme not attainable in practice. *ll realreactors fall under the category

of &( or CM&.

Reactor Modeling+oth the CM& and the '& reactors are limiting cases of the &( reactor. #herefore the&( reactor model will be developed first. -uation is the governing differential

e-uation for a conservative i.e., nonreactive! substance in a reactor that has

advective transport i.e., flow! and some mixing in the direction of flow x dimension!.

/

d /0 (

C C C

t x x

= +

C 1 concentration of a conservative substance0 1 average fluid velocity in the x direction

(d1 longitudinal dispersion coefficient

t 1 time#he dispersion coefficient is a measure of the mixing in a system.

Flow with Dispersion2ne of the easiest methods to determine the mixing dispersion! characteristics of a

reactor is to add a spike input of a conservative material and then monitor the

concentration of the material in the reactor effluent.*ssuming complete mixing in y) plane then transport occurs only in the x

direction and the concentration of tracer for any x and t after t13! the solution to

e-uation gives4


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/

Cx,t! expdd

M x

D tA D t

= 44

where M 1 mass of conservative material in the spike, (d 1 axial dispersion

coefficient 5L/6#7, x8 1 x 0t, 0 1 longitudinal advective velocity in the reactor, and

* is the crosssectional area of the reactor. * measure of dispersion can be obtaineddirectly from e-uation . &rom this e-uation we expect a maximum value of C at t 1

x60. *t this timeCx,t!d

M

A D t

=4

. $f the mass of the tracer input M! and reactor

crosssectional area *! are known, then (dcan be estimated.

#he form of e-uation is exactly like the normal distribution curve4

/

/

9 exp

xx

CA x

M

= 42

where

/ /x d

D t =

#he variance in concentration over space /

x ! is the variance in concentrations

taken from many different positions in the reactor at some single moment in time, t.

#he variance in x /

x ! has dimensions of length s-uared.

#he variance of tracer concentration versus time /

t , with dimensions of time

s-uared! can be measured by sampling at a single point in the reactor at many

different times and can be computed using the following e-uations.

/ /

/ /3 3

3 3

t

C t t t dt t C t dt t

C t dt C t dt

( )( ) ( )= =

( ) ( )

where

3

3

!

!

t C t dt

t

C t dt

=

&or discrete data points4

/

/ /3

3

n

i i

i

t n

i

i

t C t

t

C t

=

=

=

and


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3

3

n

i i

i

n

i

i

t C t

t

C t

=

=

=

$nlet and outlet boundary conditions affect the response obtained from a reactor.Closed reactors have little dispersion across their inlet and outlet boundaries whereas"open" reactors can have significant dispersion across their inlet and outlet

boundaries. #ypically open systems have no physical boundaries in the direction of

flow. *n example of an open system would be a river segment. Closed systems have

small inlets and outlets that minimi)e dispersion across the inlet and outlet regions.*n example of a closed system is a tank or a lake! with a small inlet and outlet. #he

reactors used in the lab are closed. #he t in e-uation is the measured average

residence time for the tracer in the reactor. &or ideal closed reactors the measured

residence time, t , is e-ual to the theoretical hydraulic residence time 1 reactorvolume6flow rate!.

#he above e-uations suggest that from the reactor response to a spike input we cancompute the dispersion coefficient for the reactor. :e have two options for measuring

reactor response4

9! synoptic measurements4 at a fixed time sampling many points along the axis of

the reactor will yield a ;aussian curve of concentration vs. distance. $n practicesynoptic measurements are difficult because it re-uires sampling devices that are

timecoordinated. +y combining e-uations , , and it is possible to estimate the

dispersion coefficient from synoptic measurements.

/! single point sampling4 measure the concentration at a fixed position along the x

axis of the reactor for many times. $f the reactor length is fixed at L andmeasurements are made at the effluent of the reactor observe the concentration of

a tracer at x 1 L as a function of time! then x is no longer a variable and Cx,t!

becomes Ct! only. #he response curve obtained through single point sampling isskewed. #he curve


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dispersion coefficient, the velocity in the xdirection, and the length of the reactor.

'eclet values in the range 933?'e?> result in a symmetric response curve.

Response curve skew makes the assumption of a symmetrical normal distributioncurve inappropriate and a new relationship between the variance and the dispersion

coefficient or 'e! has to be determined. +oundary conditions affect the determination

of the dispersion coefficient. #he relationship between the 'eclet number andvariance for open systems is given b4

/ /

/

/ @t

Pe Pe

= +

&or closed systems the relationship is4

( )/ /// /

9 Pe

t

Pe Pe e

=

#he term/

Pein e-uations and is dominant for 'eclet numbers much greater than

93 as is shown in rror4 Reference source not found. #he additional terms in

e-uations and are corrections for skewedness in the response curve. #hese

skewedness corrections are not very significant for 'eclet numbers greater than 93.#hus for 'eclet numbers greater than 93 the 'eclet number can be determined using

e-uation for both open and closed systems.

/

/

/

t

Pe

=

Flow through Porous Media

&low through porous media such as groundwater through soil! is a type of flowwith dispersion. #he above e-uations can be applied by recogni)ing that the relevant

10000

1000

100

10

1

0.1

0.01

0.001

1000010001001010.10.010.001

Pe

2/Pe

open

closed

2

2

&igure 9. Relationship between e-uations through


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water velocity is the pore water velocity. #he pore water velocity is 0 1Q

Awhere *

is the cross sectional area of the porous media and volume of voids6total volume! isthe porosity of the porous media.

Completely Mixed Flow Reactor$n the case of CM& reactors, there is not an analytical solution to the advective

dispersion e-uation so we revert to a simple mass balance. &or a completely mixed

reactor a mass balance on a conservative tracer yields the following differentiale-uation4

( )indC

V C C Qdt

=

where A is the volumetric flow rate and B is the volume of the reactor.

-uation can be used to predict a variety of effluent responses to tracer inputs suchas the pulse input used in this experiment. $f a mass of tracer is discharged directly

into a reactor so that the initial concentration of tracer in the reactor is C31

M

Vand

the input concentration is )ero Cin1 3! the solution to the differential e-uation is4

3

tC C exp

t

=

$f a reactor has a complete mix flow regime its response C6C3vs. time! to a pulse

input should plot as a straight line on a semilogarithmic plot. #he slope of this plot is

the negative inverse of the average hydraulic residence time, t , of the reactor.

Complete mix flow regimes can be approximated -uite closely in practice.

Plug Flow Reactor

'lug flow regimes are impossible to attain because mass transport must be by

advection alone. #here can be no differential displacement of tracer relative to the

average advective velocity. $n practice some mixing will occur due to moleculardiffusion, turbulent dispersion, and6or fluid shear. &or the case of the plug flow

reactor the advective dispersion e-uation reduces to4

C CU

t x

=


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&igure /. 'ulse and step input in a plug flow reactor.#he velocity 0 serves totransform the directional concentration gradient into a temporal concentration

gradient. $n other words, a conservative substance moves with the advective flow of

the fluid. #he solutions to this differential e-uation for a pulse input and for a step

input are shown graphically in &igure /.

Mass Conservation:hen a pulse of conservative tracer is added to a continuous flow reactor, all of the

tracer is expected to leave the reactor eventually. #he mass of a substance that has left

the reactor is given in e-uation .

3

n

i i

i

M QC t=

= where A is the flow rate and M is the mass of any substance whose concentration is

given by C. $f A and t are constant, then e-uation can be rewritten as

3

n

i

i

M Q t C=

= -uation can be used to determine if all of the tracer was measured in the reactoreffluent.

Conductivity Measurements:e will use a tracer containing salt DaCl! and red dye E F3 for visuali)ation!. #he

concentration of DaCl will be monitored using a conductivity probe. Conductivity is

the measure of a material8s ability to conduct electric current. Conductivity ismeasured by passing an electrical current between two electrodes and then measuring

the voltage. #he electrodes can be made of platinum, titanium, goldplated nickel, or

graphite. Conductivity is defined as4

IG

E=

where ; is conductivity, $ is the current, and is the measured voltage.

$f the current is held constant, as the conductivity of the solution increases the

voltage between the electrodes will decrease. &or a given current, the measuredvoltage will increase as the si)e of the electrodes decreases and as the distance

U

X

C

Co

U

X

C

Co

pulse input step input

C


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between the electrodes increases. :e are interested, however, in measuring properties

of the solution, not properties of the conductivity probeG pecific conductivity, C, is a

property of the solution.

LC G

A=

where L is the distance between the electrodes and * is the area of the electrodes. #he

termL

A

is a property of the conductivity cell and is called the cell constant. $n

practice, the cell constant is determined during calibration by measuring the

conductivity ;! of a solution with known specific conductivity C!. #he units of

specific conductivity are iemens6cm where iemens are the inverse of 2hms.&or a solution to be conductive, it must have ions that can transport the charge

between the electrodes. $n pure water, the only ions available are H Iand 2H. *dding

species that disassociate into charged ions increases both the concentration of ions

and the specific conductivity. *t low concentrations, specific conductivity increases

linearly with the concentration of ions. *t very high concentrations ionioninteractions become significant and the relationship is no longer linear. #he specific

conductivity of several common solutions is given in #able 9.

Conductivity measurements are

temperature dependent. #heconductivity of a solution will

increase as the temperature

increases. #he *ccumetJ meter that

you will use in this laboratorycompensates for this effect by also

measuring the temperature andreporting the solution specificconductivity at /KC.

$n this lab sodium chloride will

increase the specific conductivity ofthe water in the reactors. #he concentration of sodium chloride will be low enough so

that specific conductivity will be linearly related to the concentration of sodium

chloride.

Procedures* conservative tracer will be used to characteri)e each of the reactors. *

conservative tracer with /3 g DaCl6L and F g red dye E F36L will be used. #he saltwill increase the conductivity of the water and conductivity will be measured to

monitor the salt concentration. #he red dye was added to the tracer to make it possibleto see the tracer.

* common problem when using tracers is that the tracer may have a different

density than the fluid that is in the reactors. $n this case the salt and dye addsignificantly to the density of the tracer. #he tracer would tend to sink to the bottom

of the reactors. #o compensate for this problem the density of the water being pumped

#able 9. Conductivity of some common

solutions.

olution pecific Conductivity

pure water 3.3KK 6cm

distilled water 3.K 6cm

deioni)ed water 3.993 6cmtypical drinking water 3.K9.3 m6cm

wastewater 3.NN.3 m6cmmaximum drinking water 9.K m6cm

ocean water KO m6cm93P Da2H OKK m6cm

FNK mg6L DaCl 9 m6cm


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into some reactors will be increased by using a glucose solution OQ g glucose6L!.

;lucose is nonionic and thus will not increase the conductivity of the solution.

Calibrate Conductivity probe

Calibrate the conductivity probe by placing it in a FNK mg DaCl6L standard. 'ressthe conductivity button on the *ccumetJ meter if it is not already in the

conductivity mode. 'ress standardie and enter !"""6cm. 'ress enter and the

meter will calibrate and return to the normal display mode.

Measure Conductivity of tracer

'repare a calibration curve for conductivity vs. concentration of the tracerexpressed as mg6L of DaCl!. #he tracer has /3 g6L of DaCl. Measure the

conductivity of tracer diluted with distilled water so that the final concentrations ofDaCl are K33, /33, and 933 mg6L. *s a )ero point measure the conductivity of

distilled water.

Measure Reactor Response to Pulse Input

&or each reactor add a pulse input of sodium, measure conductivity vs. time in thereactor effluent and use the CompumetJ software to monitor the conductivity vs.

time see discussion below!. ave the collected data for later analysis using a

spreadsheet program. #he experimental setup is shown in &igure O. pecificinstructions for each type of reactor are detailed below.

Figure 3. Reactor schematic. Only one reactor at a time will be connected to

the peristaltic pump.Porous Media

#he porous media column is /.K cm in diameter, 3 cm long and contains 3 cm ofglass beads. #he overall porosity including headspace and underdrains is

approximately 3.F. 0se this information to estimate the volume of water in the

reactor. #he conductivity probe should be plumbed into the effluent line.

&eed

solutionglucose

solution!'eristaltic

pump

&low with

dispersion

or

Completely

mixedreactor

'lug flow

reactor

or

stirrer

$nSection port


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9! Berify that the flow rate is set to 93 mL6min.

/! $nSect 93 mg DaCl 3.K mL of tracer! into the influent line.

O! elect #et Method from the CompumetJ control palette. 0se automatic datatransmission with a timed interval of 9 second. et channel * to Conductivity and

channel + to 2ff.

F! elect Monitor #amplefrom the control palette.

K! tart the pump and press the enterkey on the keyboard to begin data ac-uisition.

! Measure the actual flow rate by collecting a timed sample from the effluent. #o

get an accurate flow rate you should collect a sample for several minutes.

Q! stimate the width of the tracer pulse when the pulse nears the top of the reactor

and record the corresponding time. #his information will be used to obtain an

estimate of the dispersion coefficient.

@! #urn off the pump when the conductivity returns to the baseline conductivity.

N! top data ac-uisition by clicking on the #top #amplingbutton.

93! ave the data to TTnviroTenviroTCoursesTFKOTreactorsTnetidUporousmedia byselecting #ave datafrom the control palette. #he data will be saved in a file tab

delimited format! that can be opened by any spreadsheet program.

Completely Mix Flow Reactor (CMFR)

9! Berify that the flow rate is set to O33 mL6min.

/! &ill the CM&R with distilled water to within about / mm of the overflow drain .

O! Measure the conductivity of the distilled water.

F! et the stirrer to the highest setting that doesn8t cause splashing setting @! and

place the conductivity probe near the stir bar.

K! *dd @33 mg DaCl F3 mL tracer! directly to the CM&R.

! elect #et Method from the CompumetJ control palette. 0se automatic data

transmission with a timed interval of 93 second. et channel * to Conductivity

and channel + to 2ff.

Q! elect Monitor #amplefrom the control palette.

@! tart the pump and press the enterkey on the keyboard to begin data ac-uisition.

N! Record the time when water begins flowing out the overflow this is your actual

time )eroG!

93! Measure the flow rate by collecting a timed sample from the effluent. #o get an

accurate flow rate you should collect a sample for several minutes.99! #urn off the pump after / residence times.

9/! top data ac-uisition by clicking on the #top #amplingbutton.

99! ave the data to TTnviroTenviroTCoursesTFKOTreactorsTnetidUCM&R by selecting

#ave datafrom the control palette. #he data will be saved in a file tab delimited

format! that can be opened by any spreadsheet program.

9O! (etermine the volume of water in the CM&R.


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a!!led "an# Reactor

#he baffled tank reactor is a simple attempt to reduce mixing and shortcircuiting.

#he channels are approximately F.K cm wide, F.@ cm deep and have a total length of@3 cm.

9! Berify that the flow rate is set to O33 mL6min.

/! (etermine the volume of water in the baffled tank.

O! &ill the baffled tank with glucose water.

F! Measure the conductivity of the glucose water.

K! elect #et Method from the CompumetJ control palette. 0se automatic data

transmission with a timed interval of 93 second. et channel * to Conductivity

and channel + to 2ff.

! elect Monitor #amplefrom the control palette.

Q! $nSect /33 mg DaCl 93 mL of tracer! into the influent line with a syringe.

@! tart the pump and press the enterkey on the keyboard to begin data ac-uisition.

N! (uring data ac-uisition, it is important to gently move the conductivity probe upand down to continually bring the probe into contact with the changing solution.

:hile moving the probe up and down, do not lift the probe so high that theplatinum contacts leave the solution

93! Measure the actual flow rate by collecting a timed sample from the effluent. #o


99! #urn off the pump when the conductivity returns to the baseline conductivity.

9/! top data ac-uisition by clicking on the #top #amplingbutton.

9O! Measure the average conductivity of the remaining solution in the baffled tank.

9/! ave the data to TTnviroTenviroTCoursesTFKOTreactorsTnetidUbaffled by selecting#ave datafrom the control palette. #he data will be saved in a file tab delimitedformat! that can be opened by any spreadsheet program.

Pipe Flow

#he pipe flow setup consists of 9K./F m of mm $( tubing.

9! Berify that the flow rate is set to K3 mL6min.

/! &ill the pipe with glucose water.

O! elect #et Method from the CompumetJ control palette. 0se automatic datatransmission with a timed interval of 9 second. et channel * to Conductivity and

channel + to 2ff.

F! elect Monitor #amplefrom the control palette.

K! $nSect 93 mg DaCl 3.K mL of tracer! into the influent line with a syringe.

! tart the pump and press the enterkey on the computer keyboard to begin dataac-uisition.

Q! Measure the actual flow rate by collecting a timed sample from the effluent. #o



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@! #urn off the pump when the conductivity returns to the baseline conductivity.

N! top data ac-uisition by clicking on the #top #amplingbutton.

9O! ave the data to TTnviroTenviroTCoursesTFKOTreactorsTnetidUpipe by selecting

#ave datafrom the control palette. #he data will be saved in a file tab delimited

format! that can be opened by any spreadsheet program.

Prelab $uestions

9! :hy is a OQ g6L glucose solution used for the plug flow reactorV :hy is the

glucose solution not needed for the completely mixed flow reactorV

/! :hy is the conductivity of pure water not )eroV

Data %nalysis0se a consistent set of units throughout your data analysis and include the units in

your spreadsheet and reportG

9! (erive an e-uation relating concentration of DaCl in the tracer to conductivity

based on the F point calibration curve. 0se the slope from the e-uation and thebaseline conductivity of each of the reactors to convert the conductivity data to

concentration of DaCl for each reactor.

/! 'erform a mass balance on the salt. :hen applicable include the measurements of

residual salt left in the reactors at the end of your experiments. 0se e-uation tocalculate the mass of DaCl measured in the effluent from each reactor and

compare with the mass of DaCl added.

O! Calculate the volume of the pipe flow and porous media reactors based on their

dimensions and porosity.

F! &rom the data determine t for each reactor use e-uation for the baffled tank,

pipe flow, and porous media column and use e-uation for the CM&R! andcompare with the hydraulic residence time 1 B6A!. (iscuss any discrepancies.

K! #he width of the plume as measured by eye for the porous media column is

approximately F standard deviations / on each side of the peak!. 0se yourmeasurement of the width of the plume and e-uation to estimate the dispersioncoefficient for the porous media reactor.

! stimate the 'eclet numbers e-uation ! and the dispersion coefficients e-uation !for the baffled tank, pipe flow, and porous media column. Compare the dispersion

coefficient for the porous media reactor with the estimate obtained in the previous

step.

Q! 'lot actual and theoretical effluent tracer concentration versus time for the threereactors. 0se the calculated dispersion coefficient e-uation ! substituted intoe-uation to model the baffled tank, pipe flow, and porous media column. 2n the

graphs also show , and t these can be added to your graph in xcel asadditional plots!. 0se the CM&R volume to obtain the theoretical value of the

initial concentration.


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@! Compare your results with theory. ;ive possible reasons for deviations from

theoretical expectations.

N! (iscuss what you learned.


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&ab Prep Notes

#able /. -uipment list

Description #upplier Catalog

number

*ccumetJ K3meter

&isher cientific 9OOKK3

floating stir bar &isher cientific 9FK99NN*

magnetic stirrer &isher cientific 99K33Q

L container &isher cientific 3OF@F//Conductivity

Cell 96cm

&isher cientific 9O/393

column &isher cientific WF/3@O3393

glass shot/NQF/3 m

unbelt$ndustries

Mil K

L container

with baffles

C shop

Oport leurmanifold

Cole 'armer H3FF@/

variable flow

digital drive

Cole 'armer H3QK/OO3

asyLoadpump head

Cole 'armer H3QK9@33

'harMed tubing

si)e 9@

Cole 'armer H3F@K9@

/3 liter H('Xerrican

&isher cientific 3/N9K3C

#able O. Reagent list

Description #upplier'#ource Catalognumber

DaCl &isher cientific +'OK@9

red dye EF3 M; Dewell 3QQ3F9

glucose *ldrich 9K,@N@9333

solution

FNK mg DaCl6L

#racer /3 g DaCl6L

F g red dye EF36Lglucose feed

solution

OQ g glucose6L

9! 'repare glucose solution for the baffled tank and pipe flow reactors in Xerricans.

/! 'repare 9 L of tracer.

O! 'repare 9 L of 9333 6cm solution conductivity standard!.

F! (istribute tracer and conductivity standard for each setup.

K! 0se E 9@ tubing for CM&R and baffled tank. 0se E9 tubing for pipe flow and

porous media reactors.

! 'lace all conductivity probes in distilled water so they are conditioned. 2therwisethe readings will drift.


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Q! 3.K mL tracer6933 mL 1 933 mg6L.#he concentration of glucose re-uired to achieve the same density as a sodium

chloride solution is 9.@F@ times as great.

NN3

9333

9393

93/3

93O3

93F3

3 /3 F3 R3 @3 933

C g6L!

densit

yg6L!

density 1 3.OQ@C I NN@./9K

&igure F. (ensity of glucose solution as a function of glucose concentration.

NNK

9333

933K

9393

939K

93/3

93/K

3 93 /3 O3

C g6L!

densityg6L!

density 1 3.RN@KC I NN@./N

&igure K. (ensity of sodium chloride solution as a function of concentration.


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Documents

Reactor Characteristics