Chapter 4

FUNDAMENTALS OF MATERIAL BALANCE

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Process Classification• Chemical processes can be classified as batch,

continuous or semi-batch and as either transient or steady state

• Batch process is one in which the feed is charged into the system at the beginning of the process, and the products are removed all at once some time later

• Continuous process is when the inputs and outputs flow continuously across the boundaries throughout the duration of the process.

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• Semi-batch process is a process in which its inputs are nearly instantaneous but the outputs are continuous or vice versa

• If the values of all process variables in a process do not change with time, the process is said to be operating at steady state. If any changes with time, transient or unsteady state operation exists

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• One of the main responsibilities of chemical engineers is to create/construct/ analyse chemical processes (or, at least, to understand the existing processes)

• The layout of a chemical process is called “process flow sheet (PFS)” or “process flow diagram (PFD)” PFS or PFD can be for just a single process unit or for the whole process, either simple or complicated process.

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Examples of PFS or PFD

PFD for a water-softening by ion-exchange process

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PFD for Ammonia Synthesis Plant6Dr.Riham Hazzaa

Normally, a PFS or a PFD comprises:• All major process equipments/units• Lines entering or leaving the process/unit and/or lines

connecting two or more process equipments/units (these lines are called “streams”)

• Flow rate of each stream• Composition of each stream• operating conditions of each stream and/or

unit/equipment (e.g., T, P)• Energy/heat needed to be added to and/or removed

from any particular part of the process or the entire process

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Some important symbols of process equipments

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Material Balance Equation

• The law states that mass can neither be created nor destroyed

• Material balance equations are the manifestation of the law TOTAL MASS INPUT = TOTAL MASS OUTPUT

• The design of a new process or analysis of existing one is not complete until it is established that the inputs and outputs of the process satisfy the material balance equation.

Material balance are based on :Law of Conservation of Mass

Material Balance Equation• Suppose methane, is a component of both input and

output of a process

• If the flow rates of input and output are found to be different. Possible explanations are .…1. methane is leaking2. methane is consumed or generated in a reaction 3. methane is accumulating in the process vessel4. wrong measurement

Process unit

qin(kg CH4/h) qout(kg CH4/h)

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General Material Balance Equation

• A balance on a material in a process system may be written as:

Input + generation - output - consumption = accumulation• The equation may be written for any material that

enters or leaves any process system• It can be applied to the total mass or total moles of this

material or to any atomic species involved in the process

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EXAMPLE: The General Balance Equation• Each year 50,000 people move into a city, 75,000 people

move out, 22,000 are born, and 19,000 die. • Write a balance on the population of the city.• SOLUTION Let P denotes people:• Input + generation - output - consumption = accumulation

• Each year the city's population decreases by 22,000 people.

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• Two types of balances may be written for any system; – differential balances and – integral balances

• Differential balances indicate what is happening in a system at an instant of time. Each term is a rate and has a unit of quantity unit per time

• Integral balances describe what happens between two instant of time. Each term of the equation is an amount of the quantity with a corresponding unit

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Balances on Steady- State Processes

• The process is said to be operating at steady-state when all process variables do not change with time.

• The accumulation term in a balance must equal to zero to ensure that the amount/mass of material in the process do not change with time

STEADY STATE means ACCUMULATION = 0

Input + generation - output - consumption = 0

Input + generation = output + consumption

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• The generation and consumption terms are applied only when chemical reaction is involved

• if there is no reaction, Input =output

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• One thousand kilograms per hour of a mixture of benzene (B) and toluene (T) containing 50% benzene by mass is separated by distillation into two fractions. The mass flow rate of benzene in the top stream is 450 kg B/h and that of toluene in the bottom stream is 475 kg T/h. The operation is at steady state. Write balances on benzene and toluene to calculate the unknown component flow rates in the output streams.

Balances on Steady- State Continuous Processes (Continuous Distillation Process)

450 kg B/hrq1 (kg T/hr)

500 kg B/hr500 kg T/hr

475 kg T/hrq2 (kg B/hr)

Distillation

450 kg B/hrq1 (kg T/hr)

500 kg B/hr500 kg T/hr

475 kg T/hrq2 (kg B/hr)

Distillation

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450 kg B/hrq1 (kg T/hr)

500 kg B/hr500 kg T/hr

475 kg T/hrq2 (kg B/hr)

Distillation

450 kg B/hrq1 (kg T/hr)

500 kg B/hr500 kg T/hr

475 kg T/hrq2 (kg B/hr)

Distillation

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no reaction, rate of input = rate of output

EXAMPLE: Balances on a Batch Mixing Process• Two methanol-water mixture are contained in separate

flasks. The first mixture contains 40 wt % methanol, and the second contains 70% methanol. If 200 g of the first mixture are combined with 150 g of the second, what are the mass and composition of the product.

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• Draw a flowchart of the process, using boxes or other symbols to represent process units (reactors, mixers, separation units, etc.) and lines with arrows to represent inputs and outputs.

Flowchart

100 mols/hr C2H6

2000 mols/hr Air

0.21 mol O2/ mol

0.79 mol N2/ mol

2100 mols/hr

0.0476 mol C2H6/ mol

0.200 mol O2/ mol

0.752 mol N2/ mol

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The chart must be fully labeled with values of known variables at the locations of the streams

For example a stream containg 21 mole % O2 and 79%N2 at 320ºC and 1.4 atm flowing at a rate 400 mol/h might be labeled.

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• the total amount or flow rate of the stream and the fractions of each component,

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

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• Assign algebraic symbols to unknown streams [such as ṁ (kg solution/min), x (lbm N2/lbm), and n (kmol C3H8)] and write their associated units on the chart

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• If a volumetric flow rate of a stream is given, convert to mass or molar flow rate since balances are not normally written in volumetric quantities

• When labeling component mass or mole fractions of a stream the last one must be 1 minus the sum of the others.

• If you are given that the mass of stream 1 is half that of stream 2, label the masses of these streams m and 2m rather than ml and m2;

• if you know that there is three times as much nitrogen (by mass) in a stream as oxygen, label the mass fractions of O2 and N2 y(g O2/g) and 3y(g N2/g) rather than yl and y2.

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Degree of Freedom Analysis• Draw and label flow chart• Count the unknown variables on the flow chart, nunknowns

• Count the independent equations relating them, nindep eqns

• ndf = nunknowns - nindep eqns

– If ndf = 0, the problem is solvable– If ndf>0, the problem is underspecified, need to provide

more information/equations.– If ndf˂0, the problem is overspecified, more equations

than unknowns, redundant and possibly inconsistent information.

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• An experiment on the growth rate of certain organisms requires an environment of humid air enriched in oxygen. Three input streams are fed into an evaporation chamber to produce an output stream with the desired composition.

• A: Liquid water, fed at a rate of 20.0 cm3/min• B: Air (21 mole% O2, the balance N2)

• C: Pure oxygen, with a molar flow rate one-fifth of the molar flow rate of stream B. The output gas is analyzed and is found to contain 1.5 mole % water. Draw and label a flowchart of the process, and calculate all unknown stream variables.

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Flowchart Scaling and Basis of Calculation

• The procedure of changing the values of all stream amounts or flow rates by a proportional amount while leaving the stream compositions unchanged is referred to as scaling the flow chart.

• Scaling up: if the final stream quantities are larger than the original quantities,

• Scaling down: if they are smaller.

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• Suppose you have balanced a process and the amount or flow rate of one of the process streams is n1.

• You can scale the flowchart to make the amount or flow rate of this stream n2 by multiplying all stream amounts or flow rates by the ratio n2/n1.

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• It is desired to achieve the same separation with a continuous feed of 1250 lb-moles/h. Scale the flowchart accordingly.

• The scale factor is:

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Before scaling

After scaling

Material balance on single unit process

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General Procedure for Material Balance Calculations1. Choose as a basis of calculations an amount or flow rate of one of

the process streams2. Draw a flowchart of the process. Include all the given variables

on the chart and label the unknown stream variables on the chart 3. Write the expressions for the quantities requested in problem

statement4. Convert all mass and molar unit quantities to one basis5. Do the degree of freedom analysis. For any given information

that has not been used in labeling the flowchart, translate it into equations in terms of the unknown variables

6. If nDF = 0, write material balance equations in an order such that those involve the fewest unknowns are written first

7. Solve the equations and calculate the additional quantities requested in the problem statement

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• Example :An aqueous solution of NaOH contains 20% NaOH by mass. It is desired to produce an 8% NaOH solution by diluting a stream of 20% solution with a stream of pure water.

• Calculate the ratios (liters H2O/kg feed solution) and (kg product solution/kg feed solution).

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NaOH balance (input = output).

Total mass balance (input = output).

Ratios requested in problem statement.

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