Process Engineering for Pollution Control and Waste Minimization_5 potx

The mechanism is associated with the definition of the convective heat transfer coefficient, hW/m2 ˚C: h = A T q As the turbulent flow process carrying the heat cannot be fully described

1.1.2 Effect of Shape on Calculation of Conduction

Heat TransferEvaluation of the integral between two specific points in the direction of heattransfer allows for the calculation of the macroscopic amount of heat For anobject with constant cross-sectional area in the direction of heat flow, integration

which involves a logarithmic distance (radius) difference instead of the thickness

of the medium involved

1.1.3 Combined Resistances

A common problem in heat transfer design is the combination of several layers

of solid to provide heat insulation, or layers of solid and fluid as in heat exchangerdesign For a rectangular geometry, two combined resistances to heat transfer can

ConductivityThe values of the thermal conductivity depend on the phase of the materialconsidered:

kgas < kliquid < ksolidThus, solid materials are good heat conductors, while for heat insulation trappedgases are the best option Good electric conductor metals are the best selectionfor heat conductors The design of heat insulation follows the criteria for airentrapment in fabrics or ceramics that could be resistant to high temperatures.

1.2 Convection

Heat convection is described as heat transport in fluid eddies promoted by theflow derived from a mechanical device, a pump or fan (forced convection), or adensity difference (natural convection) The mechanism is associated with the

definition of the convective heat transfer coefficient, h(W/m2 ˚C):

h = A (T q

As the turbulent flow process carrying the heat cannot be fully described,the temperature difference is considered at two points (1) and (2) in the direction

of heat transfer It is not possible to describe this process through a differential

equation, and Eq (9) is a definition for h that is related to the specific geometry associated to the surface area, A, and the flow conditions.

The convective heat transfer coefficient can be calculated for designpurposes from experimental information gathered in the open literature Experi-ments have been carried out under geometry, flow range, and similar thermo-physical properties conditions that can be encountered in process applications.The information has been grouped in terms of flow conditions and thermophysicalproperties involved

Flow conditions are described through the Reynolds number (Re) for forcedconvection The Reynolds number relates the momentum convection associated

to the flow velocity, v, to the momentum diffusivity associated to ν, the kinematicviscosity (ν = µ/ρ), µ is Newtonian viscosity (kg/ms) At low Reynolds numbers,implying low flow velocity, momentum diffusivity dominates, and the fluiddisplacement is in the laminar flow condition When the flow velocity is highrelative to the kinematic viscosity, the Reynolds number is high, indicatingturbulent flow conditions

Gr = g β(Tw − Tinfinity)L3

Here g is the acceleration of gravity, T w is the solid wall temperature, Tinfinity is

the fluid bulk temperature, L is the heat transfer characteristic length, and β is thevolume coefficient of expansion:

β = (ρinfinity − ρ)

ρinfinity is the fluid bulk density

In natural and forced convection, the Prandtl number describes the ence of thermophysical properties in the calculation of the convective heattransfer coefficient, normally to the 1⁄3 power

The Nusselt number, Nu, is the ratio of heat convection to diffusion

associated to the heat transfer characteristic length, L:

From the exact analysis of the boundary layer between the fluid and thesolid wall transferring heat, the correlation in forced convection among Nusselt,Reynolds, and Prandtl numbers is

This theoretical correlation has very limited application, and the ence of these dimensionless numbers on the geometry makes experimentationnecessary to calculate correlations for each geometry The correlation results arenormally reported with the same mathematical formulation:

For practical conditions, radiation emitted (or received) by surface is calculated

from an equation that involves the effect of the area, A12, the emissivity, ε1, of

the emitting surface involved, and a view factor, F12, that describes the effect

of the relative positions of the two surfaces involved on the amount of radiationexchanged The formulation of the exchanged radiation is

C p (J/kg ˚C) The total amount of material that stores heat should be expressed in

the mass or molar terms used for the C p The heat stored is then a function of thetemperature change in the total mass considered:

2.2 Latent Heat

The process where a change of phase takes place requires the addition of latentheat The latent heat is used to change phase in a fluid without a change in themedium temperature The evaluation of the latent heat is necessary to measurethe amount of heat required for phase change Latent heat values and predictioncorrelations are available in Ref 1

3 EXPERIMENTAL MEASUREMENT AND PREDICTION OF

HEAT TRANSFER THERMOPHYSICAL PROPERTIES

3.1 Constant-Pressure Heat Capacity, Cp

Measurement of the C p requires the evaluation of temperature change in a fixedmass of material due to a heat flow from the surroundings according to Eq (19)

3.2 Thermal Conductivity, k

For the measurement of k, Fourier’s first law is normally used to define the

parameters involved in the evaluation The heat flux in Eq (2) is determinedfrom the heat flow and the body geometry while the temperature gradient ismeasured directly

3.3 Convective Heat Transfer, h

The convective heat transfer coefficient is experimental measured of forced- and

natural-convection conditions h is part of Nu, while flow conditions are

repre-sented by Re or Gr, and the thermophysical properties form Pr

Normally, the values of h are obtained from reported correlations If it is necessary to evaluate h for conditions not previously studied, the information is

gathered and analyzed according to Eq (16) or (17)

3.4 Thermophysical Properties of Mixtures in

Pollution Control

Mixtures of contaminated media normally require the experimental evaluation ofthe thermophysical properties In some cases, due to nonavailability of theexperimental data, correlations for calculating the thermophysical propertiesare limited

4 HEAT TRANSFER DESIGN

Process efficiency is defined at the design stage Design algorithms for heattransfer equipment can be found in several classic references (e.g., Ref 3) andare still used for designing heat transfer equipment Several software options arealso available for efficient heat transfer equipment design; software the descrip-tion can be obtained from demos downloaded from an Internet search (any searchengine) on “Heat Exchangers.”

The basic equation for heat exchange design is

where U o is the overall heat transfer coefficient and includes all the heat transferconductances around the solid wall transferring heat For a flat wall transferringheat,

where hinside is the inside convective heat transfer coefficient, G is the wall thickness, and houtside is the outside heat transfer coefficient

The driving force for heat transfer in a heat exchanger is the logarithmicmean temperature difference:

∆TLMF = [Toutlet − tinlet) − (Tinlet − toutlet)]F

ln[(Toutlet − tinlet)/(Tinlet − toutlet)] (22)

T is the hot fluid temperature, t is the cold fluid temperature, and F is the

efficiency factor adapted for each configuration of shell and tube, plate ers, and direct-contact heat exchangers (4)

exchang-From the calculation of the amount of heat transferred, including thetemperature changes involved and the overall heat transfer conductance, the areafor heat exchange is determined Several heat transfer equipment can be used toaccomplish the heat exchange between the media in a given process condition

4.1 Heat Transfer Design and Good Engineering Practices

Design defines the efficiency of the operation of a process Once the optimizeddesign is utilized, it is necessary to maintain good engineering practices Thesepractices should include pollution control and waste minimization

Heat transfer equipment is subjected to fouling and corrosion, whichare among the major hurdles for the operation Fouling increases heat transferresistance and waste of energy Good engineering practices include the use offouling suppresants in heat transfer fluids and periodic cleaning of the ex-changer walls

For water as the cooling or heating medium in industrial operations thereare several standard techniques for keeping fouling low Water in cooling-watercircuits has to be treated to keep salts and dirt content low Common treatmentsinclude the addition of coagulants for sedimentation of some salts and particles;addition of biocides, to prevent microbial growth that is another source of fouling;and the addition hardness suppresants such as polyphosphates; among others.Although the materials used in heat transfer fluids treatment are a source of solidwaste, handling its final deposition should follow normal procedures Foulingprevention is not considered a polluting operation Fouling prevention by-productscan be integrated to cement kiln operations when feasible, in order to eliminatewaste generation

Corrosion protection of heat transfer surfaces is a suggested practicefor pollution control and waste minimization In order to prevent corrosion,begin with the analysis of the appropriate combination of materials and flu-ids For the operating equipment, passive and active cathodic protection arerecommended

4.2 Innovations for Efficient Heat Use

Efficient energy use is a direct way to reduce pollution and minimize wastes fromindustrial sources The ongoing research in energy efficiency and resultinginnovations highlight the intensity of scientific activity in this field

New approaches to increase heat transfer efficiency include the following

1 Fluidized bed combustion is the choice for eliminating solids in waste management schemes In general, direct contact between thematerials increases heat transfer efficiency Direct contact reduces theheat transfer resistances due to the wall in conventional equipment, andincreases the convective heat transfer coefficients due to the highercontact velocities between the materials and fluids

solid-2 To increase the efficiency in steam generation, direct-contact heatexchangers make use of residual heat from combustion gases to preheatthe feed streams to the boiler Thermal recovery is a possibility fromdirect-contact heat exchangers and heat pumps Rotary drums recoverheat from a residual discharge in an steam generator and transport it topreheat the inlet streams to the generator

3 Heat pipes are a promising technology for increasing residual heatusage as heat pumps Heat pipes use capillary pressure as the drivingforce for condensing and evaporating the working fluid, thus elim-inating the necessity for pump and compressor in the power cycle Theunderstanding of heat pipe operation is related to the evaluation of con-vective heat transfer coefficients for change-of-phase heat transfer

4 Plate heat exchangers are now available for almost any process tion, including high-pressure and corrosivity conditions Enhanced heattransfer surfaces improve energy management, reducing wastes Im-proved surfaces increase the convective heat transfer coefficients forheating–cooling operations, and change-of-phase heat transfer

condi-5 Co-generation in chemical and petrochemical processes makes use ofthe process integration gained from the use of simulation and pinch-point techniques to increase energy usage

5 CONCLUSIONS

The understanding of heat transfer fundamentals is a basic step toward theproposition of improved industrial solutions in terms of energy wastes minimization.Clear fundamental concepts make the use of design software straight-forward This is the approach to equipment design that produces the best resultsfor waste minimization

Heat transfer innovations are improving energy handling in industrialprocesses, reducing pollution and wastes This research field is active in funda-mentals such as enhanced heat transfer or heat pipe development.

REFERENCES

1 R C Reid, J M Prausnitz and B E Poling, The Properties of Gases and Liquids, 4th

ed New York: McGraw-Hill, 1987.

2 J P Holman, Heat Transfer, 8th ed New York: McGraw-Hill, 1997.

3 D Q Kern, Process Heat Transfer New York: McGraw-Hill, 1950.

4 O Levenspiel, Engineering Flow and Heat Exchange, 2nd ed New York: Plenum

Press, 1992.

Macroscopic Balance Equations

Paul K Andersen and Sarah W Harcum

New Mexico State University, Las Cruces, New Mexico

The prevention of waste and pollution requires an understanding of numeroustechnical disciplines, including thermodynamics, heat and mass transfer, fluidmechanics, and chemical kinetics This chapter summarizes the basic equationsand concepts underlying these seemingly disparate fields

1 MACROSCOPIC BALANCE EQUATIONS

A balance equation accounts for changes in an extensive quantity (such as mass

or energy) that occur in a well-defined region of space, called the control volume

(CV) The control volume is set off from its surroundings by boundaries, called

control surfaces (CS) These surfaces may coincide with real surfaces, or they

may be mathematical abstractions, chosen for convenience of analysis If matter

can cross the control surfaces, the system is said to be open; if not, it is said to

be closed.

1.1 The General Macroscopic Balance

Balance equations have the following general form:

dt = ∑(X CS,i

where X is some extensive quantity A dot placed over a variable denotes a rate;

for example, (X⋅)i is the flow rate of X across control surface i The terms of Eq (1)

can be interpreted as follows:

Flows into the control volume are considered positive, while flows out of the

control volume are negative Likewise, a positive generation rate indicates that X

is being a created within the control volume; a negative generation rate indicates

that X is being consumed in the control volume.

The variable X in Eq (1) represents any extensive property, such as those

listed in Table 1 Extensive properties are additive: if the control volume is

T ABLE 1 Extensive Quantities

mass)

i ≡ work rate (power) at CS i

E ^ i ≡ energy per unit mass of stream i; E ~ i ≡ energy per unit mole of stream i

S ^ i ≡ entropy per unit mass of stream i; S ~ i ≡ entropy per unit mole of stream i

T i ≡ absolute temperature of CS i

F≡ net force acting on control volume

subdivided into smaller volumes, the total quantity of X in the control volume

is just the sum of the quantities in each of the smaller volumes Balance equations

are not appropriate for intensive properties such as temperature and pressure,

which may be specified from point to point in the control volume but are notadditive

It is important to note that Eq (1) accounts for overall or gross changes in

the quantity of X that is contained in a system; it gives no information about the distribution of X within the control volume A differential balance equation may

be used to describe the distribution of X (see Section 2.2).

Equation (1) may be integrated from time t1 to time t2 to show the change

in X during that time period:

∆X = ∑(X)i CS,i

1.2 Total Mass Balance

Material is conveniently measured in terms of the mass m According to Einstein’s

special theory of relativity, mass varies with the energy of the system:

Hence, the mass balance becomes

dm

dt = ∑(

CS,i

1.3 Total Material Balance

The quantity of material in the CV can be measured in moles N, a mole being

6.02 × 1023 elementary particles (atoms or molecules) The rate of change ofmoles in the control volume is given by

dN

dt = ∑(N CS,i

where (N⋅) i is the molar flow rate through control surface i and (N⋅)gen is the molar

generation rate In general, the molar generation rate is not zero; the

determina-tion of its value is the object of the science of chemical kinetics (Secdetermina-tion 4.2)

1.4 Macroscopic Species Mass Balance

A solution is a homogenous mixture of two or more chemical species Solutions

usually cannot be separated into their components by mechanical means sider a solution consisting of chemical species A, B, For each of thecomponents of the solution, a mass balance may be written:

Con-dmA

dt = ∑(

CS,i m⋅A)i + (m⋅A)gen

(m⋅A)gen + (m⋅B)gen + = 0 (conservation of mass) (8)

1.5 Macroscopic Species Mole Balance

The macroscopic species mole balances for a solution are

dNA

dt = ∑(N CS,i

⋅

A)i + (N⋅A)gen

dNB

dt = ∑(N CS,i

⋅

.

In general, moles are not conserved in chemical or nuclear reactions Hence,

(N⋅A)gen + (N⋅B)gen + = N⋅gen (10)

1.6 Macroscopic Energy Balance

Energy may be defined as the capacity of a system to do work or exchange heat

with its surroundings In general, the total energy E can expressed as the sum of

three contributions:

E = K + Φ + U (11)

where K is the kinetic energy, Φ is the potential energy, and U is the internal energy.

Energy can be transported across the control surfaces by heat, by work, and

by the flow of material Thus, the rate of energy transport across control surface

i is the sum of three terms:

where Q⋅ i is the heat transfer rate, W⋅ i is the working rate (or power), m⋅ i is the

mass flow rate, and E ^ i is the specific energy (energy per unit mass).

Energy is conserved, meaning that the energy generation rate is zero:

Therefore, the energy of the control volume varies according to

dE

dt = ∑(

CS,i Q⋅ + W⋅ + m⋅E ^

The energy flow rate can also be written in terms of the molar flow rate

N⋅ i and the molar energy E ~ i Hence, the energy balance can be written in theequivalent form

dE

dt = ∑(Q CS,i

⋅ + W⋅ + N⋅E ~

1.7 Entropy Balance

Entropy is a measure of the unavailability of energy for performing useful work.

Entropy may be transported across the system boundaries by heat and by the flow of

material Thus, the rate of entropy transport across control surface i is given by

S⋅ i = Q⋅ i

where Q⋅ i is the heat transfer rate through control surface i, T i is the absolute

temperature of the control surface, m⋅ i is the mass flow rate through the control

surface, and S ^ i is the specific entropy or entropy per unit mass In terms of the

molar flow rate and the molar entropy S ~ i, the entropy transport rate is

S⋅ i = Q⋅ T i