EG2002: Process Engineering Rev 4H by JC on 06/10/2011 Page | 1 1. Introduction My name is John Cavanagh - your tutor for the next three weeks over which I will be introducing the concept of material balances. I am providing course notes and will be making recommendations for further reading so will use my lectures simply to introduce and discuss key concepts whilst hopefully providing a different perspective on some of the material. You will be expected to take notes during lectures as I will not be providing copies of my lecture slides. 2. Overview of the lecture series The course notes are divided into six sessions but will be delivered in nine lectures over the next three weeks. Session 1 - Introduction to material balances Session 2 - Material balances involving change of composition Session 3 - Degrees of freedom and problems involving multiple processes Session 4 - Material balances involving chemical reaction Session 5 - Material balances at the molecular level and problems involving recycles and purges Session 6 – Solution of complex material balances 3. Recommended reading Whilst course notes are provided students are still expected to undertake additional reading in order to more fully understand the subject. However, as everyone learns in different ways it is important to find a reference book that meets your own personal needs. That said, I highly recommend that you consult the following two well established text books both of which are cited extensively throughout these course notes. Sinnott, R and Towler, G. eds., 2009. Chemical Engineering Design 5th ed. Elsevier Ltd. (ISBN 978-0-7506-8551-1) Felder, R and Rousseau, R., 2005. Elementary Principles of Chemical Processes 3rd ed. John Wiley and sons, Inc. (ISBN 978-0-471-37587-6) Introduction to Material Balances (Material Balances - Session 1 of 6)
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EG2002: Process Engineering Rev 4H by JC on 06/10/2011
Page | 1
1. Introduction
My name is John Cavanagh - your tutor for the next three weeks over which I will be introducing
the concept of material balances.
I am providing course notes and will be making recommendations for further reading so will use
my lectures simply to introduce and discuss key concepts whilst hopefully providing a different
perspective on some of the material. You will be expected to take notes during lectures as I will
not be providing copies of my lecture slides.
2. Overview of the lecture series
The course notes are divided into six sessions but will be delivered in nine lectures over the next
three weeks.
Session 1 - Introduction to material balances
Session 2 - Material balances involving change of composition
Session 3 - Degrees of freedom and problems involving multiple processes
Session 4 - Material balances involving chemical reaction
Session 5 - Material balances at the molecular level and problems involving recycles and purges
Session 6 – Solution of complex material balances
3. Recommended reading
Whilst course notes are provided students are still expected to undertake additional reading in
order to more fully understand the subject. However, as everyone learns in different ways it is
important to find a reference book that meets your own personal needs. That said, I highly
recommend that you consult the following two well established text books both of which are
cited extensively throughout these course notes.
Sinnott, R and Towler, G. eds., 2009. Chemical Engineering Design 5th ed. Elsevier Ltd.
(ISBN 978-0-7506-8551-1)
Felder, R and Rousseau, R., 2005. Elementary Principles of Chemical Processes 3rd ed. John Wiley
and sons, Inc. (ISBN 978-0-471-37587-6)
Introduction to Material Balances
(Material Balances - Session 1 of 6)
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4. Learning Outcomes
As this is the first session it is appropriate to begin by outlining the learning outcomes for all six
sessions.
Having completed this course you should understand the importance and key concepts of
material balances. Presented with a suitable problem you should be able to draw and mark-up
simple flow diagram, select a basis of calculation, select suitable system boundary(s), analyse the
degrees of freedom, write down the material balance equations to describe the process and solve
these equations to determine any unknowns. Having done all this you should be able to present
your results professionally in the form of a stream list.
It is recognised that not everyone studying this course will have a background in chemistry but
such students should leave with understanding of how to write down and balance an equation
describing a simple chemical reaction. They should also understand and be able to make use of
the concept of a ‘mole’.
At the end of this first session you should understand what a material balance is and why they
are so important within the process industries. You should also understand and be able to write
down the general equation for conservation of mass.
5. Why are mass (and energy) balances so important to Process /Chemical Engineers?
Imagine you are CEO of a company wishing to design and build a new process.
In all likelihood you will only be considering such an investment because you hope to make a
healthy profit that will pay back the initial investment in the shortest possible time.
What do you need to know in order to make the right decision? A decision that could potentially
make or break your organisation.
Clearly you need to know what you are going to make and where you are going to make it so it
might be useful, albeit outside the scope of this course, for you to spend a few moments thinking
about what things that might influence your choice?
What else do you need to know?
The production rate of the new facility is important as it not only sets the scale of the investment
and infrastructure requirements but also determines the quantities of products you will need to
sell and raw materials you will need to purchase.
OK, so you know the ‘what’, the ‘where’ and the ‘how much’ but what else do you need to know?
You need to be sure that you can you make whatever it is safely without damaging the
environment but you also need to know what it will cost you to make as only then can you value
the investment and decide whether or not to go ahead.
Questions you may have might include…..
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What raw materials are required? At what rate?
What by-products and/or waste streams are there?
What are the energy requirements?
What will it cost to build?
What inventories and process conditions are required and what hazards do they present.
What intermittent and continuous effluents are there to air, land and water?
All reasonable questions but how will you answer these?
If what you are proposing is very similar to something you (or someone else) have done before it
may be possible to start by making comparisons then scaling up or down for factors such as size
or complexity. However, you will rapidly need to get into more detail, initially to provide better
estimates of capital expenditure (CAPEX) and operating expenditure (OPEX) but then to actually
specify and build the equipment. Without material and energy balances it would be very difficult
if not impossible to answer many of these questions.
Material and Energy balances are the starting point and fundamental building blocks of most, if
not all, process designs. Most projects are aborted based solely on initial material balances and
the associated economic case. For the few that continue material and energy balances are the
starting point for pretty much every aspect of the design, be it process, mechanical, civil or
electrical in nature. Even once a process is operational the material and energy balance is the
basis for production monitoring systems and any troubleshooting that is required to resolve
emergent process issues.
This is something that engineers from all disciplines will need to grasp in order to function
effectively in the process industries be it oil and gas, chemicals, petrochemicals, pharmaceuticals,
food and drink, utilities or waste treatment.
6. Mass and Energy
According to Sinnott and Towler (page 52) the loss of mass associated with the production of
energy, as described by Einstein’s equation E=mC2, is only significant in nuclear reactions. In fact
whilst Einstein proposed the concept of mass-energy equivalence he also proposed that both
total mass and total energy are in fact conserved separately.
This, albeit a very interesting discussion, is only mentioned here in this context as justification for
why the conservation of mass and that of energy are always, with the possible exception of the
nuclear industry, dealt with separately. That said, in reality, it is almost always necessary to carry
out a material balance in order to carry out an energy balance as the latter is usually reliant on
data generated by the former.
In this series of lectures we deal exclusively with material balances but return to discuss energy
balances later in the course.
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7. Material, Mass and Weight
Material is anything made of matter( a somewhat poorly defined concept), Mass is a property of
matter and weight is the force exerted by a mass on earth as a consequence of it mass and
acceleration due to gravity.
In studying this area and in industry you will come across references to material balances, mass
balances and less commonly weight balances. However, unless there is some specific reason to
believe otherwise you can generally consider these terms as equivalent and interchangeable. In
the case of mass and weight the fact that both sides of the ‘balance’ are subject to the same
force of due to gravity mean that this term can be cancelled making any disambiguation rather
pointless.
8. What do we mean by Mass Balance?
8.1 Conservation of Mass
Imagine you are inside a bubble which has permeable membrane such that material can enter
and/or leave as necessary. Now consider the fate of a molecule of oxygen which passes through
the membrane in to the bubble. There are a number of different things that might happen next.
The molecule can
pass back through the membrane and out of the bubble back to whence it came
remain within the bubble (accumulate)
be used up by your breathing perhaps (consumed)
Now consider the fate of a molecule of carbon dioxide which also enters the bubble
It can also course pass back out of the bubble or accumulate within it and whilst it cannot
realistically be consumed by the human body it could be consumed if you happened to be holding
your favourite potted plant. On the other hand it could gain a friend as carbon dioxide is made
(generated) by the same process which consumed the oxygen.
If we had knowledge of the material entering the bubble, the capability of the human body to
convert oxygen to carbon dioxide and the capacity for the bubble to accumulate gases we could
perhaps predict both the quantity and composition of the air leaving the bubble. In doing so we
would in effect be conducting a simple material balance over the bubbles membrane.
It has already been said that mass can neither be created nor destroyed (other than in a nuclear
process) and based on the above, albeit rather simplistic example, it is possible to write the
following expression to describe this conservation of mass.
Material Out = Material In + Generation – Consumption – Accumulation
(Sinnott & Towler, 2009 page 53)
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Where, ‘Material Out’ refers to material leaving the system boundary whilst ‘Material In’ refers to
material entering the system boundary. ‘Generation’ and ‘Consumption’ refer to material
generated and consumed within the system and ‘Accumulation’ refers to an increase of material
within the system although this can also decrease (usually expressed as ‘negative accumulation’).
The above expression known as the general mass balance equation can be applied (and holds
true) across any given boundary whether considering overall flows, component flows or flows of
individual elements. It no doubt holds true even at the subatomic level although this is not
considered within this course since modelling at this level would serve no useful purpose in the
context of industrial processes.elder and Rousseau (page 86) define two types of balances;
1. Differential balances indicate what is happening at an instant of time where each term of
the balance equation has a rate such as kg/hr. - usually applied to continuous processes.
2. Integral balances indicate what happens between two instants in time where each term
of the balance equation may be stated as some given quantity per batch or per day or
even per hour provided it is recognised that the flow throughout the period being studied
may well not be uniform- usually applied to batch processes
Felder and Rousseau correctly obverse that differential balances are generally applied to
continuous processes whilst integral balances are generally applied to batch processes. However,
it is worth noting that integral balances can be (and are) easily derived from differential balances
produced for continuous processes in order to produce balances showing such things as annual
production figures. This information can be far more useful than instantaneous balances for
evaluating the financial performance of a particular unit as they take into account on stream time
(the proportion of the year the process is running) and the proportion of maximum capacity that
the process is operating at which may be limited by technical or commercial constraints.
Differential balances are often more useful for design and troubleshooting of continuous
processes as they provide information about what is happening at a particular period of time
which may well be masked by the averaging which can result from integration over time.
Having introduced the general mass balance equation it is worthwhile pausing to examine it in
more detail. This expression is the foundation on which the next five lectures are built so it is
essential that everyone has a clear understanding before we take the next step.
8.2. Material OUT = Material IN
Consider a simple pipe, just like the copper ones in figure 1 (overleaf) which most of you will have
supplying water to your bathroom at home.
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Fig. 1: Selection of Copper Pipes
Imagine you are filling your bath and water is flowing through such a pipe. This can be
represented diagrammatically as in figure 2, with the arrow indicating the direction of flow.
Fig. 2: Cross-section of a pipe with water flowing through it
As you we see over the coming sessions we ALWAYS start by converting a written problem into a
process flow diagram. A good process diagram is clear and concise showing all relevant items of
equipment and direction of material flows. All streams should be labelled and information such
as flow rate and/or process conditions marked (although the same information could be
presented in a stream list as we will see later). This helps in clarifying the problem, structuring
your calculations and (importantly) communicating your approach and findings to the reader.
This is regarded as a critical part of any mass balance calculation for which marks will always be
awarded. Expectations will become clearer over the next few lectures as we cover some
examples.
Having drawn our diagram the next step is always to mark on the boundary(s) over which we will
be conducting our material balance. In this example it is rather obvious but it is best to develop
good habits right from the start.
So let’s draw our ‘boundary’ as shown in figure 3, marked in red where M1 and M2 represent the
mass of material entering and leaving the chosen boundary in any given time. This boundary is
analogous to the permeable skin of the bubble we discussed earlier. You should also note that
the streams have been given numbers to uniquely identify them and arrows to indicate the
direction of flow.
Bath Supply
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Fig. 3: Cross-section of a pipe with water flowing through it showing mass balance envelope and
stream numbers
The rate water enters and leaves the boundary in fig 3 should be the same (unless we have a
leak!) or in other words;
Mass of water leaving per unit time= Mass of water entering per unit time
(Interestingly this still applies even in the case of a leak although the mass of water leaving
through both the end of the pipe and the leak would then equal the mass of water entering)
Or expressing this more generally we have
Material OUT = Material IN
This is a material balance in its simplest form although if you compare this formula with the
generalised mass balance formula described earlier there are some other terms (shown in
brackets below) which are missing.
Material Out = Material In (+ Generation – Consumption – Accumulation)
We will now go on to discuss the ‘missing’ terms in turn.
8.3. Accumulation
In this context accumulation is essentially the ‘build-up of material’
In order to investigate this concept let us return to the previous example but this time consider a
situation where the copper pipe is initially empty (and to simplify things) oriented vertically with
water entering from the bottom as in figure 4 (overleaf)
1 2
M1 M2
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fig.4: Cross-section of a pipe with water flowing through it showing mass balance envelope with
inlet marked as stream ‘1’ and outlet marked as stream ‘2’
So does ‘material OUT = material IN’ still hold true in this example? What do you think?
In order to answer this question we should consider what happens over time. This is shown in
Figure 5 (below) which assumes that the pipe holds 20kg of water when full and water is entering
at the rate of 10kg/hr.
Time = 0hr Time = 1hr Time = 2hr Time = 3hrs
Figure 5: Mass balance after 0, 1, 2 and 3 hours where ṁn = mass flowrate of stream n
ṁ1= 10kg/hr
ṁ2= 0kg/hr
ṁ1= 10kg/hr
ṁ2= 0kg/hr
ṁ1= 10kg/hr ṁ1= 10kg/hr
ṁ2= 0kg/hr ṁ2= 10kg/hr
System
boundary for
Mass balance
purposes
2 2 2 2
1 1 1 1
2
1
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To start with the pipe is empty and must be filled. After 1hr the pipe is half filled but nothing has
left the system boundary at this point. After 2hrs the pipe is completely full but again nothing has
actually left the system boundary. Clearly, up until the point when the pipe is full
Material OUT ≠ Material IN
But rather
Material OUT = Material IN - Accumulation
This type of situation where flows can change with time is known as an ‘un-steady state’. The
modelling of such is often described as dynamic modelling.
However from 2hrs onwards water cannot enter without displacing an equal amount of water
out the other end. Once the pipe is full it is again true to say that
Material OUT = Material IN
The process is now said to be in ‘steady-state’
In real life situations a process is always in unsteady state to some degree especially during start-
up and turn down. However, due primarily to the difficulties associated with modelling the steady
state the vast majority of process modelling has to date been done on a steady state basis with
appropriate design margins and the assumption that appropriately specified control systems will
keep us at least close to steady state for the vast majority of the time. In reality the use of steady
state modelling has proven itself successful over the years when linked with good engineering
judgement and input from experienced plant managers and control engineers as required. Only
occasionally do we get caught out but when it happens it tends to happen ‘big-time’ causing
major operating difficulties and/or delaying plant start-up by weeks or even months whilst
appropriate modifications are made to equipment and control systems.
In most, though not all, problems encountered it will normally be safe to ignore accumulation
but you will be expected to state the assumption of ‘steady-state’ at the start of any calculations
as part of simplifying general mass balance equation.
In order to further illustrate this concept let us consider a cylindrical vessel similar to the one
shown below.
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We can represent such a vessel, which we can assume is partially full, as shown in the diagram
below.
In steady state the level remains constant and material OUT = material IN
ṁ2= ṁ1
However, if we increase the flowrate of stream 1, whilst holding that of stream 2 constant, we
will observe the level in the drum will start to rise and we will no longer be in steady state. The
vessel will continue to fill until the excess flow spills out of the vent at the top unless or until the
flowrate of stream 1 is reduced or conversely that of stream 2 is increased to the point where the
flows again balance. Steady state is restored but it should be noted that the level in the vessel is
now higher than it was before. In order to restore the level to its original position one would have
to temporarily reduce the flowrate of stream 1 or increase that of stream 2 until the level
returned to its original position.
8.4. Generation and Consumption
Returning to the full material balance equation
Material OUT = Material IN + Generation- Consumption – Accumulation.
From an either overall or an elemental material balance perspective both Generation and
Consumption are always zero. This is because mass can neither be created nor destroyed, other
than in a nuclear reaction.
However if a chemical reaction takes place one chemical species can of course be converted to
another chemical species. When we burn methane, for example, it ‘reacts’ with oxygen to
produce carbon dioxide and water. In effect methane and oxygen are consumed whilst carbon
dioxide and water are generated. The overall mass and elemental balance is of course still
preserved but we exchange one molecule for another so if we are looking only at a balance on a
ṁ1
ṁ2
Vent
1
2
F
F
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particular molecule we can have both generation and consumption. Only if we have no chemical
reaction, are ignoring changes in composition or are balancing down at the elemental level can
we cancel out these terms from the general mass balance equation.
As always it is essential that all assumptions are stated when carrying out calculations. Marks will
be awarded for assumptions and conversely deducted where they are either lacking or not
explicitly stated.
9. Example Problems
The following examples are rather simplistic but are intended to get you thinking along the right
lines and for you to start to develop a structured methodology for answering such questions.
Mass balance problems can get very complicated and if you want to have any chance at solving
them you should try to develop a standard approach that works and stick with it. You will note
that Sinnott and Towler tend to prefer a more ad hoc approach to solving their examples and
whilst this can be an effective way of solving simple problems it is suggested that you try to adopt
a more structured approach even when, as will often be the case to start with, the examples
seem to have an intuitive solution.
In going through the following example try not worry too much about the nomenclature as we
will standardise this at the start of the next lecture.
[PTO]
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Example 1
Question
The flowrate into and out of a 1m3 vessel is 10kg/day and 5 kg/day respectively calculate how
long it will take to fill the vessel if it is initially empty. Density of water = 1000kg/m3
Solution
As always, start with a flowsheet.
Flowsheet
Basis: Differential, Mass kg/day
General Equation
Material OUT = Material IN + Generation- Consumption – Accumulation.
But assume no chemical reactions (Generation and Consumption = 0) reducing the above formula