Tag Archives: Material balance planning


This section is a general discussion of the techniques used for the preparation of flowsheets from manual calculations. The stream flows and compositions are calculated from material balances; combined with the design equations that arise from the process and equipment design constraints.There will be two kinds of design constraints:

External constraints: not directly under the control of the designer, and which cannot normally be relaxed. Examples of this kind of constraint are:
(i) Product specifications, possibly set by customer requirements.
(ii) Major safety considerations, such as flammability limits.
(iii) Effluent specifications, set by government agencies.
Internal constraints: determined by the nature of the process and the equipment functions. These would include:
(i) The process stoichiometry, reactor conversions and yields.
(ii) Chemical equilibria.
(iii) Physical equilibria, involved in liquid-liquid and gas/vapour-liquid separations.
(iv) Azeotropes and other fixed compositions.
(v) Energy-balance constraints. Where the energy and material balance interact, as for example in flash distillation.
(vi) Any general limitations on equipment design.

The flow-sheet is usually drawn up at an early stage in the development of the project. A preliminary flow-sheet will help clarify the designer’s concept of the process; and serve as basis for discussions with other members of the design team.

The extent to which the flow-sheet can be drawn up before any work is done on the detailed design of the equipment will depend on the complexity of the process and the information available. If the design is largely a duplication of an existing process, though possibly for a different capacity, the equipment performance will be known and the stream flows and compositions can be readily calculated. For new processes, and for
major modifications of existing processes, it will only be possible to calculate some of the flows independently of the equipment design considerations; other stream flows and compositions will be dependent on the equipment design and performance. To draw up the flow-sheet the designer must use his judgement in deciding which flows can be calculated
directly; which are only weakly dependent on the equipment design; and which are determined by the equipment design.

By weakly dependent is meant those streams associated with equipment whose performance can be assumed, or approximated, without introducing significant errors in the flow-sheet. The detailed design of these items can be carried out later, to match the performance then specified by the flow-sheet. These will be items which in the designer’s estimation do not introduce any serious cost penalty if not designed for their optimum
performance. For example, in a phase separator, such as a decanter, if equilibrium between the phases is assumed the outlet stream compositions can be often calculated directly, independent of the separator design. The separator would be designed later, to give sufficient residence time for the streams to approach the equilibrium condition assumed in the flow-sheet calculation.

Strong interaction will occur where the stream flows and compositions are principally determined by the equipment design and performance. For example, the optimum conversion in a reactor system with recycle of the unreacted reagents will be determined by the performance of the separation stage, and reactor material balance cannot be made
without considering the design of the separation equipment. To determine the stream flows and compositions it would be necessary to set up a mathematical model of the reactor-separator system, including costing.

To handle the manual calculations arising from complex processes, with strong interactions between the material balance calculations and the equipment design, and where physical recycle streams are present, it will be necessary to sub-divide the process into manageable sub-systems. With judgement, the designer can isolate those systems with strong interactions, or recycle, and calculate the flows sequentially, from sub-system to sub-system, making approximations as and where required.

Each sub-system can be considered separately, if necessary, and the calculations repeatedly revised till a satisfactory flow-sheet for the complete process is obtained. To attempt to model a complex process without subdivision and approximation would involve too many variables and design equations to be handled manually. Computer flow-sheeting programs should be used if available.

When sub-dividing the process and approximating equipment performance to produce a flow-sheet, the designer must appreciate that the resulting design for the complete process, as defined by the flow-sheet, will be an approximation to the optimum design. He must continually be aware of, and check, the effect of his approximations on the performance of the complete process.

Scaling factor
It is usually easiest to carry out the sequence of flow-sheet calculations in the same order as the process steps; starting with the raw-material feeds and progressing stage by stage, where possible, through the process to the final product flow. The required production rate will usually be specified in terms of the product, not the raw-material feeds, so it will be necessary to select an arbitrary basis for the calculations, say 100 kmol/h of the principal raw material. The actual flows required can then be calculated by multiplying each flow by a scaling factor determined from the actual production rate required.

Scaling factor = mols product per hour specified/ mols product produced per 100 kmol of the principal raw material



As the process flow-sheet is the definitive document on the process, the presentation must be clear, comprehensive, accurate and complete. The various types of flow-sheet are discussed below.

Block diagrams

A block diagram is the simplest form of presentation. Each block can represent a single piece of equipment or a complete stage in the process.
With complex processes, their use is limited to showing the overall process.
Block diagrams are useful for representing a process in a simplified form in reports and textbooks, but have only a limited use as engineering documents.
The stream flow-rates and compositions can be shown on the diagram adjacent to the stream lines, when only a small amount of information is to be shown, or tabulated separately. The blocks can be of any shape, but it is usually convenient to use a mixture of squares and circles, drawn with a template.

Pictorial representation

On the detailed flow-sheets used for design and operation, the equipment is normally drawn in a stylised pictorial form. For tender documents or company brochures, actual scale drawings of the equipment are sometimes used, but it is more usual to use a simplified representation. The symbols given in British Standard, BS 1553 (1977) “Graphical Symbols for General Engineering” Part 1, “Piping Systems and Plant” are recommended; though most design offices use their own standard symbols. The American National Standards Institute (ANSI) has also published a set of symbols for use on flow-sheets. Austin (1979) has compared the British Standard, ANSI, and some proprietary flow-sheet symbols.
In Europe, the German standards organisation has published a set of guide rules and symbols for flow-sheet presentation, DIN 28004 (1988). This is available in an English translation from the British Standards Institution.

Presentation of stream flow-rates

The data on the flow-rate of each individual component, on the total stream flow-rate, and the percentage composition, can be shown on the flow-sheet in various ways. The simplest method, suitable for simple processes with few equipment pieces, is to tabulate the data in blocks alongside the process stream lines. Only a limited amount of information can be shown in this way, and it is difficult to make neat alterations or to add additional data.
In another method each stream line is numbered and the data tabulated at the bottom of the sheet. Alterations and additions can be easily made. This is the method generally used by professional design offices.

New Picture

Information to be included

The amount of information shown on a flow-sheet will depend on the custom and practice of the particular design office. The list given below has therefore been divided into essential items and optional items. The essential items must always be shown, the optional items add to the usefulness of the flow-sheet but are not always included.
1. Stream composition, either:
(i) the flow-rate of each individual component, kg/h, which is preferred, or
(ii) the stream composition as a weight fraction.
2. Total stream flow-rate, kg/h.
3. Stream temperature, degrees Celsius preferred.
4. Nominal operating pressure (the required operating pressure).

Optional information
1. Molar percentages composition.
2. Physical property data, mean values for the stream, such as:
(i) density, kg/m3,
(ii) viscosity, mN s/m2.
3. Stream name, a brief, one or two-word, description of the nature of the stream, for example “ACETONE COLUMN BOTTOMS”.
4. Stream enthalpy, kJ/h.

New Picture (1)
The stream physical properties are best estimated by the process engineer responsible for the flow-sheet. If they are then shown on the flow-sheet, they are available for use by the specialist design groups responsible for the subsequent detailed design. It is best that each group use the same estimates, rather than each decide its own values.

Multistage Compressors & Unsteady State Energy Balance

Multistage compressors
Single-stage compressors can only be used for low pressure ratios. At high pressure ratios, the temperature rise will be too high for efficient operation.
To cope with the need for high pressure generation, the compression is split into a number of separate stages, with intercoolers between each stage. The interstage pressures are normally selected to give equal work in each stage.
For a two-stage compressor the interstage pressure is given by:

New Picture (2)

where Pi is the intermediate-stage pressure.

Electrical drives
The electrical power required to drive a compressor (or pump) can be calculated from a knowledge of the motor efficiency:

New Picture

where W = work of compression per unit mass
Ee = electric motor efficiency.
The efficiency of the drive motor will depend on the type, speed and size. The values can be used to make a rough estimate of the power required.

New Picture (1)

All the examples of energy balances considered previously have been for steady-state processes; where the rate of energy generation or consumption did not vary with time and the accumulation term in the general energy balance equation was taken as zero.
If a batch process is being considered, or if the rate of energy generation or removal varies with time, it will be necessary to set up a differential energy balance, similar to the differential material balance . For batch processes the total energy requirements can usually be estimated by taking as the time basis for the calculation 1 batch; but the maximum rate of heat generation will also have to be estimated to size any
heat-transfer equipment needed.



The best way to tackle a problem will depend on the information given; the information required from the balance; and the constraints that arise from the nature of the problem. No all embracing, best method of solution can be given to cover all possible problems. The following step-by-step procedure is given as an aid to the efficient solution of material balance problems. The same general approach can be usefully employed to organise the solution of energy balance, and other design problems.
Step 1. Draw a block diagram of the process. Show each significant step as a block, linked by lines and arrows to show the
stream connections and flow direction.
Step 2. List all the available data. Show on the block diagram the known flows (or quantities) and stream compositions.
Step 3. List all the information required from the balance.
Step 4. Decide the system boundaries.
Step 5. Write out all the chemical reactions involved for the main products and byproducts.
Step 6. Note any other constraints, such as: specified stream compositions, azeotropes, phase equilibria, tie substances.
The use of phase equilibrium relationships and other constraints in determining stream compositions and flows is discussed later
Step 7. Note any stream compositions and flows that can be approximated.
Step 8. Check the number of conservation (and other) equations that can be written, and compare with the number of unknowns. Decide which variables are to be design variables; This step would be used only for complex problems.
Step 9. Decide the basis of the calculation; The order in which the steps are taken may be varied to suit the problem.

Material Balance (Step 13,14,15,16)


Processes in which a flow stream is returned (recycled) to an earlier stage in the processing sequence are frequently used. If the conversion of a valuable reagent in a reaction process is appreciably less than 100 per cent, the unreacted material is usually separated and recycled. The return of reflux to the top of a distillation column is an example of a recycle process in which there is no reaction. In mass balance calculations the presence of recycle streams makes the calculations more difficult.
Without recycle, the material balances on a series of processing steps can be carried out sequentially, taking each unit in turn; the calculated flows out of one unit become the feeds to the next. If a recycle stream is present, then at the point where the recycle
is returned the flow will not be known as it will depend on downstream flows not yet calculated. Without knowing the recycle flow, the sequence of calculations cannot be continued to the point where the recycle flow can be determined.
Two approaches to the solution of recycle problems are possible:
1. The cut and try method. The recycle stream flows can be estimated and the calculations continued to the point where the recycle is calculated. The estimated flows are then compared with the calculated and a better estimate made. The procedure is continued until the difference between the estimated and the calculated flows is within acceptable limits.
2. The formal, algebraic, method. The presence of recycle implies that some of the mass balance equations will have to be solved simultaneously. The equations are set up with the recycle flows as unknowns and solved using standard methods for the solution of simultaneous equations. With simple problems, with only one or two recycle loops, the calculation can often be simplified by the careful selection of the basis of calculation and the system boundaries.

14 – PURGE

It is usually necessary to bleed off a portion of a recycle stream to prevent the build-up of unwanted material. For example, if a reactor feed contains inert components that are not separated from the recycle stream in the separation units these inerts would accumulate in the recycle stream until the stream eventually consisted entirely of inerts. Some portion of the stream would have to be purged to keep the inert level within acceptable limits. A continuous purge would normally be used. Under steady-state conditions:

Loss of inert in the purge = Rate of feed of inerts into the system

The concentration of any component in the purge stream will be the same as that in the recycle stream at the point where the purge is taken off. So the required purge rate can be determined from the following relationship:

[Feed stream flow-rate] x [Feed stream inert concentration] =
[Purge stream flow-rate] x [Specified (desired) recycle inert concentration]

15 – BY-PASS

A flow stream may be divided and some part diverted (by-passed) around some units. This procedure is often used to control stream composition or temperature. Material balance calculations on processes with by-pass streams are similar to those
involving recycle, except that the stream is fed forward instead of backward. This usually makes the calculations easier than with recycle.


All the previous material balance examples have been steady-state balances. The accumulation term was taken as zero, and the stream flow-rates and compositions did not vary with time. If these conditions are not met the calculations are more complex. Steady state calculations are usually sufficient for the calculations of the process flow-sheet. The unsteady-state behaviour of a process is important when considering the process start-up and shut-down, and the response to process upsets.
Batch processes are also examples of unsteady-state operation; though the total material requirements can be calculated by taking one batch as the basis for the calculation. The procedure for the solution of unsteady-state balances is to set up balances over
a small increment of time, which will give a series of differential equations describing the process. For simple problems these equations can be solved analytically. For more complex problems computer methods would be used.
The behaviour of processes under non-steady-state conditions is a complex and specialised subject and beyond the scope of this book. It can be important in process design when assessing the behaviour of a process from the point of view of safety and control.
The use of material balances in the modelling of complex unsteady-state processes is discussed in the books by Myers and Seider (1976) and Henley and Rosen (1969).

Material Balance (Step 1,2,3)

Einstein showed that mass and energy are equivalent. Energy can be converted into mass,and mass into energy. They are related by Einstein’s equation:

E = mc2 

where E = energy, J,
m = mass, kg,
c = the speed of light in vacuo, 300000000 m/s.
The loss of mass associated with the production of energy is significant only in nuclear reactions. Energy and matter are always considered to be separately conserved in chemical reactions.

The general conservation equation for any process system can be written as: Material out D Material in C Generation  Consumption  Accumulation
For a steady-state process the accumulation term will be zero. Except in nuclear processes, mass is neither generated nor consumed; but if a chemical reaction takes place a particular chemical species may be formed or consumed in the process. If there is no chemical reaction the steady-state balance reduces to

Material out = Material in

A balance equation can be written for each separately identifiable species present, elements, compounds or radicals; and for the total material.

When specifying a composition as a percentage it is important to state clearly the basis: weight, molar or volume. The abbreviations w/w and v/v are used to designate weight basis and volume basis.

Fundamental Of Material Balance


Material balances are the basis of process design. A material balance taken over the complete process will determine the quantities of raw materials required and products produced. Balances over individual process units set the process stream flows and compositions.
A good understanding of material balance calculations is essential in process design.  Practice is needed to develop expertise in handling what can often become very involved calculations. More examples and a more detailed discussion of the subject can be found in the numerous specialist books written on material and energy balance computations. Several suitable texts are listed under the heading of “Further
Reading” at the end of this category.
The application of material balances to more complex problems is discussed in “Flowsheeting”, Material balances are also useful tools for the study of plant operation and trouble shooting. They can be used to check performance against design; to extend the often limited data available from the plant instrumentation; to check instrument calibrations; and to locate sources of material loss.