chap. 3.1 mass balance single unit

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Chapter 3

Mass Balance



Contents

Process classification

Balances

Material Balance Calculations Balance on Multiple Unit Processes

Recycle and Bypass

Balances on Reactive Systems Balances on Reactive Processes

Combustion Reaction



Process Classification

Three type of process1. Batch process

Feed is charge to the process and product isremoved when the process is completed

No mass is fed or removed from the process duringthe operation

Used for small scale production Operate in unsteady state

2. Continuous process Input and output is continuously red and remove

from the process Operate in steady state Used for large scale production

3. Semibatch process

Neither batch nor continuous Durin the rocess a art of reactant can be fed or a



Operation of Process

1. Steady state

All the variables (i.e. temperatures, pressure,volume, flow rate, etc) do not change with

time

Minor fluctuation can be acceptable

2. Unsteady state or transient Process variable change with time



Test Yourself

Define type and operation of process givenbelow

A balloon is filled with air at steady rate

of 2 g/min A bottle of milk is taken from the

refrigerator and left on the kitchen

Water is boiler in open flask

Answer

Semibatch and unsteady state



Balances

General Balance

A balance on a conserved quantity (totalmass, mass of a particular species, energy,momentum) in a system ( a single processunit, a collection of units, or an entireprocess) may be written in the following

way:

INPUT + GENERATION – OUTPUT –

CONSUMPTION = ACCUMULATION



Differential vs. Integral Balances

Two types of balances may be written:1. Differential balances

balances that indicate what is happening in a systemat an instant time.

balance equation is a rate (rate of input, rate of generation, etc.) and has units of the balancedquantity unit divided by a time unit (people/yr, gSO2 /s).

usually applied to a continuous process.

2. Integral balances Balances that describe what happens between two

instants of time. balance equation is an amount of the balanced

quantity and has the corresponding unit (people, g

SO2).



Simplified Rule for Mass Balance

If the balanced quantity is TOTAL MASS,set generation = 0 and consumption = 0.Mass can neither be created nor

destroyed.

If the balanced substances is a

NONREACTIVE SPECIES (neither areactant nor a product), set generation =0 and consumption = 0.

If a system is at STEADY STATE, set



Balances on Continuous Steady State

Process

Steady state: accumulation = 0

INPUT + GENERATION – OUTPUT – CONSUMPTION = 0

If balance on nonreactive species or totalmass; balance equation become

INPUT = OUTPUT



Integral Balances on Batch Process

Ammonia is produced from nitrogen andhydrogen in a batch reactor. At time t = 0 thereare n0 mol of NH3 in the reactor, and at a latertime tf the reaction terminates and the contentsof the reactor, which include n

f

ammonia, arewithdrawn. Between t0 and tf no ammoniaenters or leaves through the reactor boundaries.

From GMBE: (input=0; output=0)Generation – Consumption = Accumulation

For batch reactor:

Accumulation = Initial input – Final output



General Procedure for Single Unit Process

Material Balance Calculation1. Choose as basis of calculation an amount or flow rate of one of

the process streams.2. Draw a flowchart and fill in all unknown variables values,

including the basis of calculation. Then label unknown streamvariables on the chart.

3. Express what the problem statement asks you to determine interms of the labeled variables.

4. If you are given mixed mass and mole units for a stream (suchas a total mass flow rate and component mole fractions or viceversa), convert all quantities to one basis.

5. Do the degree-of-freedom analysis.6. If the number of unknowns equals the number of equations

relating them (i.e., if the system has zero degree of freedom),write the equations in an efficient order (minimizingsimultaneous equations) and circle the variables for which youwill solve.

7. Solve the equations.8. Calculate the quantities requested in the problem statement if

they have not already been calculated.9. If a stream quantity or flow rate n was given in the problem



Flowcharts

When you are given process informationand asked to determine something aboutthe process, it is essential to organize the

information in a way that is convenient forsubsequent calculations.

The best way to do this is to draw a

flowchart using boxes or other symbols to represent

process units (reactors, mixers, separation

units, etc.)



Flowchart Example

An experiment on the growth rate of certainorganism requires an environment of humid airenriched in oxygen. Three input streams are fedinto an evaporation chamber to produce an output

stream with the desired composition.

A: Liquid water fed at rate of 20 cm3 /minB: Air (21% O2 and 79% N2)

C: Pure O2 with a molar flow rate one-fifth of themolar flow rate of stream B

The output gas is analyzed and is found to contain

1.5 mole% water. Draw and label the flowchart of



Flowchart Example

Evaporation

20 cm3 H2O (l)/min

mol H2O/min2n

mol O2 /min1200.0 n

mol air/min1n

mol/min3n

0.21 mol O2 /mol

0.79 mol N2 /mol

0.015 mol H2O /mol

y mol O2 /mol(0.985-y) mol N2 /mol



Flowcharts

the flowchart of a process can help getmaterial balance calculations started andkeep them moving.

flowchart must be fully labeled when it isfirst drawn, with values of known processvariables and symbols for unknownvariables being written for each input andoutput stream.

flowchart will functions as a scoreboardfor the problem solution: as each

unknown variable is determined its value



Flowcharts Labeling

Write the values and units of all knownstream variables at the locations of thestreams on the flowchart.

For example, a stream containing 21mole% O2 and 79% N2 at 320˚C and 1.4

atm flowing at a rate of 400 mol/h might

be labeled as:

400 mol/h

0.21 mol O2 /mol0.79 mol N2 /molT = 320˚C, P = 1.4 atm



Flowcharts Labeling Process stream can be given in two ways

1. As the total amount or flow rate of the stream and thefractions of each component

2. Or directly as the amount or flow rate of each component.

60 kmol N2/min40 kmol O2/min

0.6 kmol N2/kmol0.4 kmol O2/kmol

100 kmol/min

3.0 lbm CH44.0 lbm C2H43.0 lbm C2H6

0.3 lbm CH4/lbm0.4 lbm C2H4/lbm0.3 lbm C2H6/lbm

10 lbm



Flowcharts Labeling

Assign algebraic symbols to unknown streamvariables [such as m (kg solution/min), x (lbmN2 /lbm), and n (kmol C3H8)] and write thesevariable names and their associated units on the

flowchart.mol/h

0.21 mol O2 /mol0.79 mol N2 /molT = 320˚C, P = 1.4 atm

n 400 mol/h

y mol O2 /mol(1-y) mol N2 /molT = 320˚C, P = 1.4 atm



Flowcharts Labeling

If that the mass of stream 1 is half that of stream 2, label the masses of thesestreams as m and 2m rather than m1 andm2.

If you know that mass fraction of nitrogenis 3 times than oxygen, label massfractions as y g O2 /g and 3y g N2 /g rather

than y1 and y2.

When labeling component mass fraction ormole fraction, the last one must be 1

minus the sum of the others



Consistent on Notation

gasinfractionmolesy

liquidinmoles)or (massfractioncomponentx

rateflowvolumeV

volumeVrateflowmolar n

molesn

rateflowmassm

massm



Example

Two methanol-water mixture are containedin separate flask. The first mixture contains40wt% methanol and the second flask

contains 70wt% methanol. If 200g of thefirst mixture combined with 150g of thesecond, what are the mass and composition

of the product.



Example

Mixing

200 g

150 g

m g0.40 g MeOH/kg0.60 g H2O/kg

0.70 g MeOH/kg0.30 g H2O/kg

x g MeOH/kg(1-x) g H2O/kg



Solution

Batch processunit in amount

Balances:

Initial input + Generation = Final output – Consumption

But NONREACTICE process; generation=0,consumption=0

INPUT=OUTPUT



Solution

Balance on TOTAL MASS (Input=Output)200 g + 150 g = m g

m g= 350 g

Balance on MeOH (Input=Output)

x= 0.529 g MeOH/g

200 g 0.40 g MeOH + 150 g

0.70 g

MeOH =

350

g

x g

MeOH

g g g



Flowchart Example

An experiment on the growth rate of certainorganism requires an environment of humid airenriched in oxygen. Three input streams are fedinto an evaporation chamber to produce an output

stream with the desired composition.

A: Liquid water fed at rate of 20 cm3 /minB: Air (21% O2 and 79% N2)

C: Pure O2 with a molar flow rate one-fifth of themolar flow rate of stream B

The output gas is analyzed and is found to contain

1.5 mole% water. Draw and label the flowchart of



Flowchart Example

Evaporation

20 cm3 H2O (l)/min

mol H2O/min2n

mol O2 /min1200.0 n

mol air/min1n

mol/min3n

0.21 mol O2 /mol

0.79 mol N2 /mol

0.015 mol H2O /mol

y mol O2 /mol(0.985-y) mol N2 /mol



Solution

Class Discussion



TEST YOURSELF Page

93



Balancing a Process3.0 kg/min of benzene and 1.0 kg/min of toluene are mixed

Two unknown quantities – m and x, associated with process, so twoequations are needed two calculate them.For NONREACTIVE process, so input = output.3 possible balance can be written – Balance on total mass, benzene,

and toluene – any two of which provide the equations needed todetermine m and x.

For example,Total Mass Balance:3.0 kg/min + 1.0 kg/min = m kg/min = 4.0 kg/min

Benzene Balance:

m (kg/min)

x (kg C6H6 /kg)

(1- x ) (kg C7H8 /kg)

3 kg C6H6 /min

1 kg C7H8 /min



Balancing a Process

Which balance to be used when achoices exists and the order in whichthese balanced should be written?

Rules of thumb for NONREACTIVEprocess

1. The maximum number of independent

equations that can be derived by writingbalances on a nonreactive system equals thenumber of chemical species in the input andoutput streams.

2. Write balances first that involve the fewest



“ Janganlah biarkan diri anda

kecewa akibat sebarangkegagalan selagi anda telahmelakukan yang terbaik mengikut kemampuan anda”

“ Pencapaian terunggul dalamhidup ialah mampu bangkit

kembali dari kekecewaan”



Flowchart Scaling & Basis of

Calculation

Flowchart scaling – procedure of changingthe values of all stream amounts or flowrates by a proportional amount while

leaving the stream compositionsunchanged. The process would still bebalance.

Scaling-up – if final stream quantities arelarger than the original quantities.

Scaling down – if final stream quantities




Calculation1 kg C6H6

300 lbm /h

1 kg C7H8

300 kg C6H6

300 kg C7H8

300 lbm /h

2 kg

0.5 kg C6H6 /kg

0.5 kg C7H8 /kg

600 kg

0.5 kg C6H6 /kg

0.5 kg C7H8 /kg

600 lbm /h0.5 lbm C6H6 /lbm

0.5 lbm C7H8 /lbm

x 300

kg kg/hReplace kg with lbm




Calculation

Suppose you have balanced a process and theamount or flow rate of one of the processstreams is n1.You can scale the flow chart to

make the amount or flow rate of this stream n2by multiplying all stream amounts or flow rateby the ratio n1/n2.

Scaling Factor= Desired amount / Old amount

You cannot, however, scale masses or mass flowrates to molar quantities or vice versa by simple

multiplication; conversions of this type must be



Class Discussion for Example

4.3-2



Basis of Calculation

Balanced process can always be scaled.Mean that material balance calculation canbe performed on the basis of anyconvenient set of stream amount or flowrate and the results can afterward be scaledto any desired extent.

A basis of calculation is an amount (mass ormoles) of flow rate (mass or molar) of onestream or stream component in a process.

All unknown variables are determined to beconsistent with the basis.

If a stream amount or flow rate is given inproblem, choose this quantity as a basis

If no stream amount or flow rate are



Class Discussion for Example

4.3-3



TEST YOURSELF Page

98



WHAT IN NEXTCLASS?





the process streams.2. Draw a flowchart and fill in all unknown variables values,including the basis of calculation. Then label unknown streamvariables on the chart.









Chapter 2

Degree of

Freedom





the process streams.2. Draw a flowchart and fill in all unknown variables values,including the basis of calculation. Then label unknown streamvariables on the chart.









“KEGAGALAN MASA LALU

ADALAH PEDOMAN BAGIKEJAYAAN DI MASA AKANDATANG”



“SEHINGGA ANDA MENCUBA,

ANDA TIDAK TAHU APA YANGTIDAK BOLEH ANDA BUAT ”



Degree-of-Freedom

Before do any material balance calculation, usea properly drawn and labeled flowchart todetermine whether there is enough

information to solve a given problem. The procedure for doing so is referred to as

degree-of-freedom analysis.

Procedure to perform a degree-of-freedomanalysis:

a) draw and completely label a flowchart

b) count the unknown variables on the chart (n unknowns)



Number of Degree-of-Freedom Three possibilities number of degree-of-freedom (n df )

1. If ndf = 0 the problem can in principle be solved.

2. If ndf > 0 there are more unknowns than independent equations relating

to them at least ndf additional variable values must be specified before

remaining variable values can be determined. Either relations have been overlooked or the problem is

underspecified.

3. If ndf < 0 there are more independent equations than unknowns. Either the flowchart is incompletely labeled or the problem is

overspecified with redundant and possibly inconsistentrelations.

There is little point wasting time trying to solve material



6 Sources of Equation for Balance

1. Material balances. For a nonreactive process, number of independent equation can

be written is not more than number of molecules species (n ms)of the process

If benzene and toluene is involve in stream, we can writebalance on benzene, toluene, total mass, atomic carbon and

etc., but only TWO INDEPENDENT balance equation exist

2. An energy balance. If the amount of energy exchanged between the system and its

surroundings is specified or if it is one of the unknown processvariables, an energy balance provides a relationship between

inlet and outlet material flows and temperatures.

3. Process specifications The problem statement may specify how several process are

related.

i.e: Outlet flow rate is two times than flow rate stream 1 or etc.



4. Physical properties and laws Two of the unknown variables may be the mass and volume of

a stream material, in which case a tabulated specific gravity forliquids and solids or an equation of state for gases wouldprovide an equation relating the variables.

5. Physical constraints For example, if the mole fractions of the three components of a

stream labeled x A , xB, and xC, then the relation among thesevariables is x A + xB + xC = 1.

Instead label as xc, the las fraction should be 1-x A -xB

6. Stoichiometric relations If chemical reactions occur in a system, stoichiometric equation

provide a relationship between the quantities of reactant andthe product

6 Sources of Equation for Balance










relating them (i.e., if the system has zero degree of freedom),

write the equations in an efficient order (minimizingsimultaneous equations) and circle the variables for which youwill solve.





CLASS DISCUSSION

EXAMPLE 4.3-4

EXAMPLE 4.3-5



ANY QUESTIO

chap. 3.1 mass balance single unit

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