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Energy Balance Calculation
Related terms:
Reactor, Biomass, Heat losses, Temperature, Cooling Water, Heat Transfer Coeﬃcient,
Cooling Requirement, Fermenter, Heat Capacity, Steam Table
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Energy Balances
Pauline M. Doran, in Bioprocess Engineering Principles (Second Edition), 2013
5.2 General Energy Balance Equations
The principle underlying all energy balance calculations is the law of conservation of energy, which states that energy can be
neither created nor destroyed. Although this law does not apply to nuclear reactions, conservation of energy remains a valid
principle for bioprocesses because nuclear rearrangements are not involved. In the followings, we will derive the equations
used for solution of energy balance problems.
The law of conservation of energy can be written as:
{energyinthroughsystemboundaries}−{energyoutthroughsystemboundaries}={energyaccumulatedwithinthesystem}
(5.4)
For practical application of this equation, consider the system depicted in Figure 5.1. Mass Mi enters the system while mass
Mo leaves. Both masses have energy associated with them in the form of internal, kinetic, and potential energies; ﬂow work
is also being done. Energy leaves the system as heat Q; shaft work Ws is performed on the system by the surroundings. We
will assume that the system is homogeneous without charge or surface energy eﬀects.
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Figure 5.1. Flow system for energy balance calculations.
To apply Eq. (5.4), we must identify the forms of energy involved in each term of the expression. If we group together the
extensive properties and express them as speciﬁc variables multiplied by mass, Eq. (5.4) can be written:
Mi(u+ek+ep+pv)i−Mo(u+ek+ep+pv)o−Q+Ws=ΔE
(5.5)
where subscripts i and o refer to inlet and outlet conditions, respectively, and ΔE represents the total change or
accumulation of energy in the system. u is speciﬁc internal energy, ek is speciﬁc kinetic energy, ep is speciﬁc potential
energy, p is pressure, and v is speciﬁc volume. All energies associated with the masses crossing the system boundary are
added together; the energy transfer terms Q and Ws are considered separately. Shaft work appears explicitly in Eq. (5.5) as
Ws; ﬂow work done by the inlet and outlet streams is represented as pv multiplied by mass.
The energy ﬂows represented by Q and Ws can be directed either into or out of the system; appropriate signs must be used
to indicate the direction of ﬂow. Because it is usual in bioprocesses that shaft work be done on the system by external
sources, in this text we will adopt the convention that work is positive when energy ﬂows from the surroundings to the
system as shown in Figure 5.1. Conversely, work will be considered negative when the system supplies work energy to the
surroundings. On the other hand, we will regard heat as positive when the surroundings receive energy from the system—
that is, when the temperature of the system is higher than that of the surroundings. Therefore, when Ws and Q are positive
quantities, Ws makes a positive contribution to the energy content of the system while Q causes a reduction. These eﬀects
are accounted for in Eq. (5.5) by the signs preceding Q and Ws. The opposite sign convention is sometimes used in
thermodynamics texts; however, the choice of sign convention is arbitrary if used consistently.
Equation (5.5) refers to a process with only one input and one output stream. A more general equation is Eq. (5.6), which
can be used for any number of separate material ﬂows:
∑inputstreamsM(u+ek+ep+pv)−∑outputstreamsM(u+ek+ep+pv)−Q+Ws=ΔE
(5.6)
The symbol ∑ means summation; the internal, kinetic, potential, and ﬂow work energies associated with all output streams
are added together and subtracted from the sum for all input streams. Equation (5.6) is a basic form of the ﬁrst law of
thermodynamics, a simple mathematical expression of the law of conservation of energy. The equation can be shortened by
substituting enthalpy h for u+pv as deﬁned by Eq. (5.3):
∑inputstreamsM(h+ek+ep)−∑outputstreamsM(h+ek+ep)−Q+Ws=ΔE
(5.7)
5.2.1 Special Cases
Equation (5.7) can be simpliﬁed considerably if the following assumptions are made:
• Kinetic energy is negligible
• Potential energy is negligible
These assumptions are acceptable for bioprocesses, in which high-velocity motion and large changes in height or
electromagnetic ﬁeld do not generally occur. Thus, the energy balance equation becomes:
∑inputstreams(Mh)−∑outputstreams(Mh)−Q+Ws=ΔE
(5.8)
Equation (5.8) can be simpliﬁed further in the following special cases:
• Steady-state ﬂow process. At steady state, all properties of the system are invariant. Therefore, there can be no
accumulation or change in the energy of the system: ΔE=0. The steady-state energy balance equation is:
∑inputstreams(Mh)−∑outputstreams(Mh)−Q+Ws=0
(5.9)
Equation (5.9) can also be applied over the entire duration of batch and fed-batch processes if there is no energy
accumulation; ‘output streams’ in this case refers to the harvesting of all mass in the system at the end of the process.
Equation (5.9) is used frequently in bioprocess energy balances.
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• Adiabatic process. A process in which no heat is transferred to or from the system is termed adiabatic; if the system has
an adiabatic wall, it cannot release or receive heat to or from the surroundings. Under these conditions Q=0 and Eq.
(5.8) becomes:
∑inputstreams(Mh)−∑outputstreams(Mh)+Ws=ΔE
(5.10)
Equations (5.8), (5.9), and (5.10) are energy balance equations that allow us to predict, for example, how much heat must be
removed from a fermenter to maintain optimum conditions, or the eﬀect of evaporation on cooling requirements. To apply
the equations we must know the speciﬁc enthalpy h of ﬂow streams entering or leaving the system. Methods for calculating
enthalpy are outlined in the followings.
Characteristics and Analysis of the Dynamic Operation of Steel
Manufacturing Process
Ruiyu Yin, in Theory and Methods of Metallurgical Process Integration, 2016
4.5.2 Research Method and Feature of Energy Flow in the Process
To research energy ﬂow in the steel manufacturing process, instead of static mass balance and energy balance calculation,
the dynamic operation model with input/output and ﬂuctuations should be proposed. By analogy to mass ﬂow study, the
concepts of “ﬂow,” “running program,” and “process network” for energy ﬂow ought to be established to study its input and
output and the conversion in the open, irreversible, and far-from-equilibrium process. It is necessary to change the massenergy balance calculation of an isolated spot into the energy ﬂow study in the network of dynamic operation of the entire
manufacturing process (Yin, 2010b).
Studies on the input and output character of “ﬂow” involve not only the nodes, connectors, and the space arrangement of
the nodes and connectors, but also the dynamic operation program, especially the time-characteristic order. The concept of
input and output of energy ﬂow involves not only the amount of energy but also the grade of energy and time-space factor
as well as the operation program of energy ﬂow. This is helpful for constructing a rational energy network containing
secondary energy utilization. This is also conducive to further improvement of the energy eﬃciency.
4.5.2.1 Input and Output Characteristics and Fluctuation Phenomena in Energy Flow of Steel Plant
There are diﬀerent types of energy carrier and input-output expressions of energy parameters including the type of energy
kind (gas, steam, self-generated power, and sensible heat), the grade of energy (gas’s kind and caloriﬁc value, steam’s
temperature and pressure, mass ﬂow’s temperature), and the amount of energy at procedure nodes in plants, in diﬀerent
spatiotemporal boundaries of the manufacturing process. These energy parameters at diﬀerent nodes in energy ﬂow
possess ﬂuctuation phenomena also. So, it is diﬃcult to describe the dynamic operation by static state separately. It is
necessary to establish the rational energy network, which will play to the comprehensive potential of the energy medium
including primary energy and secondary energy to achieve the high eﬃciency and low cost of the entire process. The
establishment of an energy ﬂow network, the rational energy recycling scheme with diﬀerent interaction coupling
mechanisms, can be achieved by combining diﬀerent amounts of gas, steam, sensible heat of matters, potential heat, etc.
within a generating spot and time.
4.5.2.2 The Limitations of Static Mass and Energy Balance Calculation for a Single Procedure
During the study on the dynamic operation of the entire steel manufacturing process, it is diﬃcult to accurately evaluate the
utilization and proﬁt of energy of the entire process by material and heat balance (mass-energy balance) of a single
procedure. When calculating static material and heat balance of the single procedure, the result can only be used for one
procedure or reactor. In the result, the kind of utilization of the secondary energy is absent, which will aﬀect the energy
conversion eﬃciency. For example, when using BOF gas as a fuel, the eﬀect of its utilization is the thermal eﬃciency and
can be simply calculated. It is also aﬀected by the types of reheating furnace and burner. However, when using BOF gas for
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the production of quality lime, there are some additional advantages like high activity of lime because of ash-free fuel, and
low sulfur in lime to increase desulfurization eﬃciency, hence, the lime consumption and temperature drop of the hot
metal will be lowered. As another example, if a gas/steam pipe network of an enterprise appears to be defective or be in an
abnormal state, the emission of gas and steam cannot be avoided. This type of energy loss can hardly be reﬂected in the
material and heat balance of the single procedure.
Therefore, the study of energy ﬂow in the steel manufacturing process should be performed by dynamic modeling of the
input/output to the open system. The dynamic modeling should be developed on the fundamentals of “ﬂow,” “running
program,” and “process networks.”
W. Fred Ramirez, in Computational Methods in Process Simulation (Second Edition), 1997
2.2.3.3 Sparse Matrices
MATLAB has extensive sparse matrix facilities. Sparse matrices arise in many engineering problems including those of
material and energy balance calculations as illustrated earlier. It is more eﬃcient to deﬁne matrices as sparse when
appropriate. If you are not sure if a matrix is sparse, then you can use the function issparse (A) which returns a value of 1 if A
is sparse and 0 if it is not sparse. To deﬁne a matrix as sparse, we use the function sparse (rowpos, colpos, val, m,n)where
rowpos are the positions of the nonzero row elements, colpos are the positions of the non–zero column elements, val are
the values of the non–zero elements, m is the number of rows, and n the number of columns. For example, if
The result is
It is important to note that matrix operations such as *, +, −, \ produce sparse results if both operands are sparse. You can
convert a full matrix to a sparse one by using the command
b=sparse(a);
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and a sparse matrix to a full one by the command
a=full(b);
There is signiﬁcant eﬃciency in properly using sparse matrix operations when appropriate.
Review of System Design and Sizing Tools
Santiago Silvestre, in Practical Handbook of Photovoltaics (Second Edition), 2012
4.1 Sizing Tools
Sizing tools allow photovoltaic systems to be dimensioned, taking into account energy requirements, site location, and
system costs (Table 3). Most of these software tools are relatively simple and help users automatically solve energy-balance
calculations considering diﬀerent combination of PV system components, including batteries, modules, and loads. These
tools are usually implemented using spreadsheets at diﬀerent level of complexity and oﬀer a ﬁrst approach for the
evaluation of speciﬁc PV system applications. In their basic form, these tools are easy to use, and some solar cell
manufacturers and vendors of PV system components oﬀer this kind of tool to potential customers (often via the Internet)
to enable customers to adapt PV system components to their products. Similar sizing tools are also available that focus on
speciﬁc studies for complete sets of modules, batteries, inverters, electronic power conditioning components, and loads
from the principal manufacturers in the photovoltaic market.
More sophisticated sizing tools are also available in the market, some oﬀering the possibility of optimising the size of each
PV system component. More detailed analysis can then be carried out of the energy ﬂows in the PV system and the
determination of critical periods along the year. Of particular interest is often the deﬁcit of energy associated with these
periods of time and minimising the ﬁnal cost of the system for a speciﬁc application.
Heat Transfer
Pauline M. Doran, in Bioprocess Engineering Principles (Second Edition), 2013
9.6 Application of the Design Equations
The equations in Sections 9.4 and 9.5 provide the essential elements for design of heat transfer systems. Figure 9.17
summarises the relationships involved. Equation (9.19) is used as the design equation; Qˆ and the inlet and outlet
temperatures are available from energy balance calculations as described in Section 9.5.3. The overall heat transfer
coeﬃcient is evaluated from correlations such as those given in Section 9.5.1; additional terms are included if the heat
transfer surfaces are fouled. The temperature-diﬀerence driving force is estimated from the fermentation and cooling water
temperatures. With these parameters at hand, the required heat transfer area can be determined.
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Figure 9.17. Summary of relationships and equations for design of a fermenter cooling coil.
Because metabolic rates, and therefore rates of heat production, vary during fermentation, the rate at which heat is
removed from the bioreactor must also be varied to maintain constant temperature. Heat transfer design is based on the
maximum heat load for the system. When the rate of heat generation drops, operating conditions can be changed to reduce
the rate of heat removal. The simplest way to achieve this is to decrease the cooling water ﬂow rate.
The procedures outlined in this chapter represent the simplest and most direct approach to heat transfer design. If several
independent variables remain unﬁxed prior to the design calculations, many diﬀerent design outcomes are possible. When
variables such as the type of ﬂuid, the mass ﬂow rates, and the terminal temperatures are unspeciﬁed, they can be
manipulated to produce an optimum design, for example, the design yielding the lowest total cost per year of operation.
Computer packages that optimise heat exchanger design are available commercially.
9.6.1 Heat Exchanger Design for Fermentation Systems
Calculating the equipment requirements for heating or cooling of fermenters can sometimes be simpliﬁed by considering
the relative importance of each heat transfer resistance.
• For large fermentation vessels containing cooling coils, the ﬂuid velocity in the vessel is generally much slower than in
the coils; accordingly, the tube-side thermal boundary layer is relatively thin and most of the heat transfer resistance is
located on the fermenter side. Especially when there is no fouling in the tubes, the heat transfer coeﬃcient for the
cooling water can often be omitted when calculating U.
• Likewise, the pipe wall resistance can sometimes be ignored as conduction of heat through metal is generally very rapid.
An exception is stainless steel, which is used widely in the fermentation industry because it does not corrode in mild
acid environments, withstands repeated exposure to clean steam, and does not have a toxic eﬀect on cells. The low
thermal conductivity of this material means that wall resistance may be important unless the pipe wall is very thin.
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The correlations used to estimate fermenter-side heat transfer coeﬃcients, such as Eqs. (9.36) and (9.37), were not
developed for fermentation systems and must not be considered to give exact values. Most of the available correlations were
developed using small-scale equipment; little information is available for industrial-size reactors.
As described in Section 8.13, aerobic fermentations are typically carried out in tall vessels using multiple impellers; however,
there have been relatively few studies of heat transfer using this vessel conﬁguration. For helical cooling coils, geometric
parameters such as the vertical separation between individual coils and the space between the coil and tank wall have been
found to aﬀect heat transfer, particularly for viscous ﬂuids. Yet these factors are not included in most commonly used heat
transfer correlations.
Equations (9.36) and (9.37) were developed for ungassed systems but are applied routinely for aerobic fermentations.
Gassing alters the value of fermenter-side heat transfer coeﬃcients, but the magnitude of the eﬀect and whether gassing
causes an increase or decrease in heat transfer cannot yet be predicted. The rate of heat transfer in gas–liquid systems
appears to depend on the distribution of bubbles in the vessel [7]; for example, accumulation of bubbles on or around the
heat transfer surface is deleterious. Taking all of the above factors into account, it is apparent that correlations such as Eqs.
(9.36) and (9.37) can provide only a starting point or rough estimate for evaluation of heat transfer coeﬃcients in
fermenters.
When estimating heat transfer coeﬃcients for non-Newtonian broths, the apparent viscosity (Section 7.5) can be
substituted for μb in the correlation equations and dimensionless groups. However, this substitution is not straightforward
when rheological parameters such as the ﬂow behaviour index n, the consistency index K, and the yield stress τ0 change
during the culture. The apparent viscosity also depends on the shear rate in the fermenter, which varies greatly throughout
the vessel. These factors make evaluation of heat transfer coeﬃcients for non-Newtonian systems diﬃcult.
Application of the heat exchanger design equations to specify a fermenter cooling system is illustrated in Example 9.6.
Example 9.6
Cooling-Coil Length in Fermenter Design
A fermenter used for antibiotic production must be kept at 35°C. After considering the oxygen demand of the
organism and the heat dissipation from the stirrer, the maximum heat transfer rate required is estimated as 550 kW.
Cooling water is available at 10°C; the exit temperature of the cooling water is calculated using an energy balance as
25°C. The heat transfer coeﬃcient for the fermentation broth is estimated from Eq. (9.36) as 2150 W m−2 °C−1. The
heat transfer coeﬃcient for the cooling water is calculated as 14 kW m−2 °C−1. It is proposed to install a helical cooling
coil inside the fermenter; the outer diameter of the pipe is 8 cm, the pipe wall thickness is 5 mm, and the thermal
conductivity of the steel is 60 W m−1 °C−1. An average internal fouling factor of 8500 W m−2 °C−1 is expected; the
fermenter-side surface of the coil is kept relatively clean. What length of cooling coil is required?
Solution
Qˆ=550×103 W. As the temperature in the fermenter is constant, ΔT is calculated from Eq. (9.39):
ΔT=(25−10)°Cln(35−1035−25)=16.4°C
U is calculated using Eq. (9.25) after omitting hfh, as there is no fouling layer on the hot side of the coil:
1U=(12150Wm−2°C−1+5×10−3m60Wm−1°C−1+114×103Wm−2°C−1+18500Wm−2°C−1)=
(4.65×10−4+8.33×10−5+7.14×10−5+1.18×10−4)m2°CW−1=7.38×10−4m2°CW−1U=1355Wm−2°C−1
Note the relative magnitudes of the four contributions to U: the cooling water ﬁlm coeﬃcient and the wall resistance
make comparatively minor contributions and can often be neglected in design calculations.
We can now apply Eq. (9.19) to evaluate the required surface area A:
A=QˆUΔT=550×103W1355Wm−2°C−1(16.4°C)=24.75m2
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Equation (9.23) for the area of a cylinder can be used to evaluate the pipe length, L. As we have information for both
the outer pipe diameter (=8 cm) and the inner pipe diameter (=outer pipe diameter−2×wall
thickness=8 cm−2×5 mm=7 cm), we can use an average pipe radius to determine L:
L=A2πR=24.75m22π(0.5(8×10−2+7×10−2)2)m=105.0m
The length of coil required is 105 m. The cost of such a length of pipe is a signiﬁcant factor in the overall cost of the
fermenter.
Mixing and heat transfer are not independent functions in bioreactors. The impeller size and stirrer speed aﬀect the value of
the heat transfer coeﬃcient in the fermentation ﬂuid; increased turbulence in the reactor decreases the thickness of the
thermal boundary layer and facilitates rapid heat transfer. However, stirring also generates heat that must be removed from
the reactor to maintain constant temperature. Although this energy contribution may be small in low-viscosity ﬂuids
because of the dominance of the heat of reaction (Section 5.10), heat removal can be a severe problem in bioreactors
containing highly viscous ﬂuids. Turbulent ﬂow and high heat transfer coeﬃcients are diﬃcult to achieve in viscous liquids
without enormous power input, which itself generates an extra heat load. The eﬀect of gas sparging on the heat load is
usually neglected for stirred bioreactors. The energy associated with sparging can be evaluated as described in Section 8.6;
however, the contribution to overall cooling requirements is minor.
Internal cooling coils typically add 15 to 25% to the cost of fermentation vessels. The length of coil that can be used is
limited by the size of the tank. Because the temperature of fermentations must be maintained within a very narrow range, if
the culture generates a large heat load, providing suﬃcient cooling can be a challenge. As discussed further in Section
9.6.2, heat transfer can be the limiting factor in fermentations. This is of particular concern for high-density cultures
growing on carbon substrates with a high degree of reduction (Section 5.9.5), as large amounts of energy are released.
Elevated broth viscosities compound the problem by dampening turbulence and preventing good mixing, thus reducing the
rate of heat transfer. Because biological reactions take place at near-ambient temperatures, the temperature of the cooling
water is always close to that of the fermentation; therefore, a relatively small driving force for heat transfer or ΔT value is
inevitable. Improving the situation by refrigerating the cooling water involves a substantial increase in capital and operating
costs and is generally not economically feasible. It may be possible to raise the cooling water ﬂow rate, but this is also
limited by equipment size and cost considerations. Although using an external heat exchanger such as that illustrated in
Figure 9.1(e) is an option for increasing the heat transfer capacity of fermenters, as described in Section 9.1.1 this
introduces extra contamination risks and also adds signiﬁcantly to the overall cost of the equipment. In some cases, the
only feasible heat transfer solution for fermentations with high heat loads is to slow down the rate of fermentation, thus
slowing down the rate of heat generation. This might be achieved, for example, by reducing the cell density, decreasing the
concentration of rate-limiting nutrients in the medium, or using a diﬀerent carbon source.
9.6.2 Relationship between Heat Transfer and Cell Concentration
The design equation, Eq. (9.19), and the steady-state energy balance equation, Eq. (9.48), allow us to derive some important
relationships for fermenter operation. Because cell metabolism is usually the largest source of heat in fermenters, the
capacity of the system for heat removal can be linked directly to the maximum cell concentration in the reactor. Assuming
that the heat dissipated from the stirrer and the cooling eﬀects of evaporation are negligible compared with the heat of
reaction, Eq. (9.48) becomes:
Qˆ=−ΔHˆrxn
(9.49)
In aerobic fermentations, the heat of reaction is related to the rate of oxygen consumption by the cells. As outlined in
Section 5.9.2, approximately 460 kJ of heat is released for each gmol of oxygen consumed. Therefore, if QO is the rate of
oxygen uptake per unit volume in the fermenter:
ΔHˆrxn=(−460kJgmol−1)QOV
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where V is the reactor volume. Typical units for QO are gmol m−3 s−1. ΔHˆrxn in Eq. (9.50) is negative because the reaction
is exothermic. Substituting this equation into Eq. (9.49) gives:
Qˆ=(460kJgmol−1)QOV
(9.51)
If qO is the speciﬁc oxygen uptake rate, or the rate of oxygen consumption per cell, QO=qOx, where x is the cell concentration.
Typical units for qO are gmol g−1 s−1. Therefore:
Qˆ=(460kJgmol−1)qOxV
(9.52)
Substituting this into Eq. (9.19) gives:
(460kJgmol−1)qOxV=UAΔT
(9.53)
The fastest rate of heat transfer occurs when the temperature diﬀerence between the fermenter contents and the cooling
water is at its maximum. This occurs when the cooling water is at its inlet temperature, that is, ΔT=(TF−Tci) where TF is the
fermentation temperature and Tci is the water inlet temperature. Therefore, assuming that the cooling water remains at
temperature Tci, we can derive from Eq. (9.53) an equation for the hypothetical maximum possible cell concentration
supported by the heat transfer system:
xmax=UA(TF−Tci)(460kJgmol−1)qOV
(9.54)
It is undesirable for the biomass concentration in fermenters to be limited by the heat transfer capacity of the cooling
system. Ideally, the extent of growth should be limited by other factors, such as the amount of substrate provided.
Therefore, if the maximum cell concentration estimated using Eq. (9.54) is lower than that desired from the process, the
heat transfer facilities must be improved. For example, the area A could be increased by installing a longer cooling coil, or
the overall heat transfer coeﬃcient could be improved by increasing the level of turbulence. Equation (9.54) was derived for
fermenters in which shaft work could be ignored; if the stirrer adds signiﬁcantly to the total heat load, xmax will be smaller
than that estimated using Eq. (9.54).
Natural Gas Conversion VI
Harry Audus, ... Samuel S. Tam, in Studies in Surface Science and Catalysis, 2001
4 Sasol-Type GTL Plant Design With and Without CO2 Abatement
A conceptual plant design for a GTL plant based on Sasol-type technology was developed as the base case which was
compared with a CO2 abatement case. Figure 1 summarizes the mass, energy, and carbon balance of the base case. Key
parameters and assumptions employed in the process simulation model are summarized in Table 2.
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Figure 1. Mass, Energy, & Carbon Balance Summary – Sasol-Type Design - Base Case
Table 2. Key Parameters and Assumptions of the Sasol-Type GTL Plant Base Case
Air Separation Unit
Conventional, single train cryogenic air separation plant
- Oxygen purity
99.5 mol% O2
Syngas Generation
Oxygen-blown, autothermal natural gas reforming
- Feed ratios:
- H2O:C, mole/mole
0.65
- CO2:C, mole/mole
0.10
- O2:C, mole/mole
0.56
- Exit conditions:
Pressure: 28 bar
- H2:CO mole ratio
2.04
Hydrogen Separation
- H2 purity
> 99.5 mol% H2
F-T Synthesis
Single SBCR reactor, cobalt catalyst in F-T synthesis derived liquid, internal heat recovery (steam raising),
recycle of part of purge gas to syngas generation, catalyst makeup/activation, catalyst recovery and
recycle
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Temperature: 1014 °C
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- Operating conditions
Pressure: 26 bar
Temperature: 220 °C
- Anderson-Schulz-Flory Several values used to ﬁt slope of carbon-number distribution for cobalt catalyst
distribution parameter
(α)
- CO conversion per
pass
76%
- Steam raising
Saturated - 13 bar, 191 °C
Mild hydrocracking of ASTM-D86 350 + °C product (wax)
- Operating conditions
Pressure: 115 bar
- Reactor LHSV
2 hr− 1
Temperature: 370 °C
The capital cost estimate was based on a factored estimating technique. The ISBL equipment was sized and materials-ofconstruction selected based on the particular process conﬁguration, heat and energy balance calculations, and the
conditions of the locally available utility streams.
Additional ﬁeld costs, bulk materials, direct labor, indirect costs, etc., were developed based on cost factors mentioned
above. Other ﬁeld costs, such as sales tax, freight costs, duties, etc., were site speciﬁc and developed separately as
percentages of the total ﬁeld cost. The oﬀsite cost estimate was developed from Bechtel in-house data for similar size and
type plants in the same site location. The IEA Financial Assessment Criteria was used to develop the costs for home oﬃce,
fees, and services and plant contingency.
The CO2 capture and compression area consisted of three plants: (1) feed gas hydrogenation and high-temperature CO
shift, (2) MDEA-based CO2 removal, and (3) CO2 compression. The intent of this design was capture, prior to emission, the
non-product carbon as a single species— CO2 in this instance—and to deliver it in a pure form and at high pressure to the
plant battery limit. This study does not address the collection, transportation, and ultimate disposal/ sequestration of this
CO2 stream.
The purge gas from the F-T synthesis section was hydrogenated to remove the trace amounts of oxygenates and the
remaining CO is converted to CO2 and hydrogen in the shift unit. A 30 wt% aqueous solution of mono-diethanolamine
(MDEA) was used to remove CO2 from the shift reactor eﬄuent gas. The CO2 from the MDEA regenerator was recovered
and compressed to 110 bar for pipeline delivery.
The Test Cell as a Thermodynamic System
A.J. Martyr, M.A. Plint, in Engine Testing (Fourth Edition), 2012
The Energy Balance of the Engine
Table 3.3 shows a possible energy balance sheet for a cell in which a gasoline engine is developing a steady power output of
100 kW.
TABLE 3.3. Simpliﬁed Energy Flows for a Test Cell Fitted with a Hydraulic Dynamometer and 100 kW Gasoline Engine
Energy Balance
In
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Out
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Energy Balance
In
Out
Fuel
300 kW
Exhaust gas
60 kW
Ventilating fan power
5 kW
Engine cooling water
90 kW
Dynamometer cooling water
95 kW
Ventilation air
70 kW
Heat loss, walls and ceiling
15 kW
Electricity for cell services
25 kW
330 kW
330 kW
The energy balance for the engine is as follows:
In
Out
Fuel
300 kW
Power
100 kW
Exhaust gas
90 kW
Engine cooling water
90 kW
20 kW
300 kW
300 kW
Note that where ﬂuids (air, water, exhaust) are concerned the energy content is referred to an arbitrary zero, the choice of
which is unimportant: we are only interested in the diﬀerence between the various energy ﬂows into and out of the cell.
Given suﬃcient detailed information on a ﬁxed engine/cell system, it is possible to carry out a very detailed
energy balance calculation (see Chapter 6 for a more detailed treatment). Alternatively, there are some commonly used
“rule-of thumb” calculations available to the cell designer; the most common of these relates to the energy balance of the
engine, which is known as the “30–30–30–10 rule”. This refers to the energy balance given in Table 3.4.
TABLE 3.4. Example of the 30–30–30–10 Rule
In Via
Out Via
Fuel 300 kW
Dynamometer 30% (90+ kW)
Exhaust system 30% (90 kW)
Engine ﬂuids 30% (90 kW)
Convection and radiation 10% (30 kW)
The key lesson to be learnt by the nonspecialist reader is that: any engine test cell has to be designed to deal with energy
ﬂows that are at least three times greater than the “headline” engine rating. To many, this will sound obvious but a
common ﬁxation on engine power and a casual familiarity with, but lack of appreciation of, the energy density of petroleum
fuels still lead people to signiﬁcantly underrate cell cooling systems.
Like any rule of thumb this is crude, but it does provide a starting point for the calculation of a full energy balance and a
datum from which we can evaluate signiﬁcant diﬀerences in balance caused by the engine itself and its mounting within the
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cell.
First, there are diﬀerences inherent in the engine design. Diesels will tend to transfer less energy into the cell than petrol
engines of equal physical size. For example, testers of rebuilt bus engines, which have both vertical and horizontal
conﬁgurations, often notice that diﬀerent models of diesels with the same nominal power output will show quite diﬀerent
distribution of heat into the test cell air and cooling water.
Second, there are diﬀerences in engine rigging in the cell that will vary the temperature and surface area of engine
ancillaries such as exhaust pipes.
Finally, there is the amount and type of equipment within the test cell, all of which makes a contribution to the convection
Specialist designers have developed their own versions of a test cell software model, based both on empirical data and
theoretical calculation, all of which is used within this book. The version developed by colleagues of the author produces the
type of energy balance shown in Figure 3.2. Table 3.5 lists just a selection, from an actual project, of the known data and
calculated energy ﬂows that such programs have to contain in order to produce Figure 3.2.
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FIGURE 3.2. Output diagram from a test cell thermal analysis and energy ﬂow program.
TABLE 3.5. A Selection of the Known, Estimated, and Calculated Data, Based on a Known Engine, Required to Produce a Complete Energy and Fluid Flow
Diagram as Shown in Figure 3.2
Engine and Fuel Data
Power output
180 kW
Engine max. power
180 kW
Fuel
Diesel
Primary energy from fuel
468 kW
Caloriﬁc value of fuel
43,000 kJ/kg
Electricity Output
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Density of fuel
Energy Balance Calculation - an overview | ScienceDirect Topics
0.830 kg/liter
Combustion Air
From AC dyno.
171 kW
Temp. intake
23 °C
Lube oil HX (N/A)
0 kW
Temp. after compressor
185 °C
Engine jacket HX
98 kW
Temp. after intercooler
55 °C
Intercooler HX
29 kW
Combustion air temp.
70 °C
Chilled Water
Exhaust Gas
Fuel cooling
1 kW
Manifold temp.
650 °C
Temp. after turbine
434 °C
Engine block
13 kW
Temp. in cell system
400 °C
Exhaust in cell
9 kW
Dilution air temp.
30 °C
Cooling water
3 kW
Temp. at cell exit
100 °C
Dynamometer
9 kW
Dilution air ratio
3
Exhaust System
Plant Cooling Water
Exhaust gas out of cell
Glycol content (%)
50%
Temperature in
22 °C
Temperature out
32 °C
Speciﬁc heat capacity
3.18 kJ/l K
Density
1.06 kg/m3
Peak Fuel Consumption
135 kW
Exhaust Dilution
Mass rate
39.1 kg/h
Ratio (kg air/kg exh.)
3
Volume rate
47.2 liter/h
Mass ﬂow at intake (air)
2519 kg/h
0.79 liter/min
Density at intake (−50 Pa)
1.16 kg/m3
0.217 kg/kWh
Volume rate at intake
2164 m3/h
Speciﬁc fuel consumption
0.60 m3/s
Combustion Air
Mass rate
800 kg/h
Total mass ﬂow (air + exh.)
3358 kg/h
Density at 1 bar abs.
1.19 kg/m3
Mixture temp. after intake
123 °C
Volume rate
672 m3/h
Mixture density out of cell
0.95 kg/m3
0.19 m3/s
Mixture ﬂow out of cell
3551 m3/h
0.99 m3/s
Exhaust Gas
Mass rate (air + fuel)
840 kg/h
Density, after turbine
0.739 kg/m3
Volume rate after turbine
1136 m3/h
Density, out of cell
0.517 kg/m3
Volume rate out
1622 m3/h
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of closed system
0.45 m3/s
These types of models are a type of “expert system”, the result of reﬁnement based on experience of many man-years.
Such tools are extremely useful but cannot be used uncritically as the ﬁnal basis of design when a range of engines need to
be tested or the design has to cover two or more cells in a facility where ﬂuid services are shared; in those cases the energy
diversity factor has to be considered.
Heat Integration: Targets and Heat Exchanger Network Design
Truls Gundersen, in Handbook of Process Integration (PI), 2013
4.3.2 Major Challenges in Data Extraction
There are two very diﬀerent types of challenges related to data extraction for a Heat Integration project:
(i) To establish the most correct set of data related to ﬂowrates and thermodynamic conditions of process streams used as
input to heat recovery analysis and design.
(ii) To represent the heating, cooling, evaporation and condensation needs of the process streams in such a way that the
degrees of freedom are kept open for network design.
While activity (i) is fairly straightforward (but involves a lot of work), activity (ii) requires skill and experience. It has often
been stated that data extraction (in particular the second part) is more art than science, and most of the attempts to provide
procedures and guidelines for this activity have failed, including the development of knowledge-based systems (also
referred to as expert systems). Some of the commercial general-purpose process simulators have features for automatic
stream data extraction on the basis of a converged steady-state mass and energy-balance calculation. While these
procedures enable easy generation of Composite and Grand Composite Curves, they do not keep the degrees of freedom
open.
Despite the importance of data extraction, the topic has not been much discussed in the literature beyond textbooks on
Process Integration, such as Linnhoﬀ et al. (1982), Smith (2005) and Kemp (2007). The topic is also thoroughly covered in
the recent book by Klemeš et al. (2010). Interestingly, rather detailed literature on data extraction has been provided in the
form of reports from research institutes (such as , CANMET 2003), software vendors (such as AspenTech, 2009) and
consulting companies (such as Linnhoﬀ March, 1998), which again illustrates the importance of proper data extraction for a
successful Heat Integration project.
For manual data extraction, the following guidelines can be useful:
(a) Do not copy all features of the conceptual ﬂowsheet or an existing design.
(b) Do not mix streams at diﬀerent temperatures.
(c) Do not include utilities as stream data.
(d) Do not accept the prejudice of colleagues against Heat Integration.
(e) Do not ignore true practical constraints.
(f ) Distinguish between soft and hard stream data.
Rule (a) refers to the issue of keeping the degrees of freedom open in order not to overlook promising solutions for heat
recovery systems. Rule (b) involves several aspects, and should be discussed in more depth. First, a mixer can act as a heat
exchanger, thus saving Capital Cost; however, mixing streams of diﬀerent compositions is only an option if the streams are
entering the same unit operation, such as a chemical reactor. Second, mixing streams at diﬀerent temperatures introduces
exergy losses and should be avoided. Third, mixing streams may eliminate potential heat recovery solutions. Finally, mixing
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streams may be required from a practical point of view, such as adding steam to hydrocarbon streams to avoid coking
inside pipes and equipment, or it may be forbidden from a safety point of view, such as mixing oxygen-rich streams with
hydrocarbon streams. Rule (c) is rather obvious, since the goal of the exercise is to establish minimum utility requirements;
however, there are cases where it is not so easy to distinguish whether a stream is a process stream or is acting as a utility.
Rule (d) relates to the common reluctance in the process industries to accept Heat Integration solutions from an operational
point of view; however, it is a fact that most industrial processes are heavily integrated, and rather than focusing on
Maximum Heat Recovery, one should focus on correct or appropriate Heat Integration. In addition, it should be mentioned
that when the economic potential of Heat Integration is established and well documented, it is often easier to get
acceptance for such projects. Rule (e) means that, even though one should try to keep the degrees of freedom open,
obviously one should not forget that some practical constraints cannot be ignored. One example is related to metal dusting,
a severe form of corrosive degradation of metals that happens in some temperature ranges when CO is present. This is a
problem in synthesis gas production, and in order to keep the metal temperature at a suﬃciently low level, the boiler is
placed upstream of the steam superheater, which is not the best solution from a thermodynamic point of view as conveyed
in Pinch Analysis.
Finally, Rule (f ) is quite important in the sense that some stream data must be considered as hard speciﬁcations, while
others can be adjusted if that improves or simpliﬁes the heat recovery system (as discussed in Chapter 2 on Basic Process
Integration Terminology). An inlet temperature to a reactor or distillation column must often be regarded as a hard
speciﬁcation, while the target temperature of a process stream going to some sort of storage is an example of soft process
data. Specifying a low target temperature for a hot product stream going to storage in order to increase the heat recovery
potential will only result in increased need for external cooling if the target temperature is below the Pinch Temperature.
Instead, this cooling could have been taken care of by nature itself through convective heat loss to the environment.
Returning to activity (i) of the data extraction exercise, there are two distinctly diﬀerent situations. For grassroots design,
there is normally a simulation model available for the process providing stream data as part of a steady-state material and
energy balance calculation. The advantage in this case is that the data are consistent. As an example, the hot and cold side
of a heat exchanger will always be in balance for a converged simulation. The quality of the data, however, depends on to
what extent the simulation models describes the behaviour of the real process.
For retroﬁt design, in addition to using a simulation model if available, one could resort to the original speciﬁcation sheets
for the process, or one could use measurements from the plant. However, the plant may have been modiﬁed several times
since its start-up, and ﬂowsheets and speciﬁcation sheets are not always updated. Regarding the use of measurements, the
typical situation is that some measurements are missing, and instruments may be either not functioning at all, or they may
give incorrect readings. In such cases, the task of data reconciliation can be enormous, and a key to success is to work very
closely with operators and plant engineers.
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