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The economics of heat pump assisted distillation systems—I. A design and economic model
Heat Recorerv Systems"Vol 4, No, 3. pp, 187 200. 1984
0198-7593 84 53,0(I ~ 0.00 Pergamon Press Lid
Printed in Great Britain.
THE ECONOMICS OF HEAT P U M P ASSISTED DISTILLATION S Y S T E M S - - I . A D E S I G N A N D ECONOMIC M O D E L T. O. OMIDEYI, J. KASPRZYCKI a n d F. A . WATSON Department of Chemical and Gas Engineering, University of Salford, Salford M5 4WT, U K . Abstract--Several factors may be expected to influence the overall economics of heat pump assisted distillation systems. Some of these are design and operational, while others are purely economic factors. Economic analyses of such systems so far reported in the literature have not adequately investigated the importance of these factors. A design and economic model is presented in this paper which can be used for a preliminary economic analysis of heat pump assisted distillation systems. Two important points of consideration in the design, notably, the problem of matching the heat loads between the heat pump and the distillation sections, and the selection of the heat pump working fluid. are discussed. The major design equations used in the model are presented. A design algorithm as well as a flowchart for the computer programme of the model are given.
NOMENCLATURE a
A~c A MARC~X A ~,r b B c
cc cE cn
Crc (COP)~ (COP) c (COP)R (CR) d D Di e fa fL
fu~ f~ts f~r
fen fsr frr F h H (HPE) R i M n N
NMt,s N, Nr P
Pco PEr (PBP) Q QB Q~
empirical constant in equation 22 annual equivalent of fixed capital cost annual marginal cost between alternative systems annual utilities cost empirical constant in equation 22 flow rate of bottom product empirical constant in equation 22 unit cost of coolant to absorb heat unit cost of primary energy source unit cost of heating medium capital cost actual coefficient of performance of heat pump Carnot coefficient of performance of heat pump Rankine coefficient of performance of heat pump compression ratio of heat pump constant in equation 26 flow rate of top product internal diameter of column shell constant in equation 26 discount factor [1- i) -" base factor relating installed equipment cost to fixed capital cost material of construction factor for shell and tube exchangers material of construction factor for column shell material of construction factor for distillation trays pressure factor for column shell factor for tray spacing factor for tray construction type flow rate of feed to column individual boiling or condensing film heat transfer coefficient enthalpy Rankine heat pump effectiveness factor fractional annual cost of capital mass flowrate of working fluid number of years since plant startup number of trays required in the column minimum number of trays required in the column compressor speed theoretical number of trays required in the column saturation vapour pressure saturation vapour pressure of condensing working fluid saturation vapour pressure of evaporating working fluid payback period of marginal investment heat transfer rate heat transfer rate in the reboiler or heat pump condenser maximum heat transfer rate acceptable by the reboiler 187
[dimensionless] [£ yr -l] [£ yr -~] [£ yr- ~] [K] [kmol s- ~] [K[ [£ kW- k h - ~] [£ kW-~ h ~] [£ kW th-~[ [£] [dimensionless] [dimensionless] ]dimensionless] [dimensionless[ [dimensionless] [kmol s- ~} [m] [dimensionless] ]dimensionless[ [dimensionless] [dimensionless[ [dimensionless] [dimensionless] [dimensionless] [dimensionless] [dimensionless[ [kmol s -~] [kW m-2K t] [kJ kmol ~] [dimensionless] [dimensionless] [kg s t] [dimensionless] [dimensionless[ [dimensionless] [rev s- J] ]dimensionless] [bar] [bar] [bar] [yr] [kW] [kW] [kW]
188
T.O. OMIOEWet al. Qn Q~ QLoss z R RMt.~ S (SV) T TB Too TD Try (TF) U v L V W Wa X y z ATco ATrv 2o rlov r/r rlvo,
heat transfer rate in the condenser or heat pump evaporator maximum heat transfer rate available from the condenser heat loss from the total system ratio defined by equation 17 reflux ratio minimum reflux ratio for given separation heat transfer area compressor swept volume temperature boiling temperature of distillation mixture in reboiler condensing temperature of working fluid m reboiler condensing temperature of distillation mtxture m condenser evaporating temperature of working fluid in condenser temperaturefactor defined by equation 19 overall heat transfer coefficient permissible vapour velocity specific volume of vapour volumetric vapour rate in the column energy supplied to compressor shaft energy supplied to the prime mover of the compressor ratio defined by equation 16 operating time tray spacing temperaturedriving force in reboiler temperaturedriving force in condenser latent heat of condensation of overhead product overall efficiencyof motor and compressor overall tray efficiency in column volumetric efficiency of compressor
[kW1 [kW} [kW] [dimensionless] [dimensionless] [dimensionless] [m2] [m~re', j [K or C] [K] [K] [K] [K] [dimensionless] [kW m- ~'K- ~] [m s ~] [m3kg 11 [m3s-~] [kW] [kW] [dimensionless] [h yr ~] [m] [K] [K] [kJ kmol-~] [dimensionless] [dimensionless] [dimensionless]
INTRODUCTION Distillation is a widely used, but energy intensive, method o f separating liquid mixtures into relatively pure components. It is c o m m o n to the chemical and allied industries where certain mixtures such as crude petroleum, alcohols and other organic intermediates and products are refined on a very large scale. It was estimated [1] that in 1976, distillation systems accounted for almost 60% o f the energy consumption in the US chemical industry, costing some $5000 million that year. A conventional distillation system, as shown in Fig. 1, would typically include a steam heated reboiler, a fractionating column and a water cooled condenser. Although it is customary to exchange heat between the incoming feed and the outgoing bottom product, in most industrial distillation systems between 80 and 90% o f the total heat supplied is removed in the condenser. In general, the temperature o f the outlet coolant is too low to be useful and this heat is wasted. While energy costs were a relatively small fraction of the product cost. the wastage o f this energy caused no concern. Since it is believed that energy costs will continue to escalate over the long term, several shemes for reducing the energy demands of distillation systems are being investigated. Such schemes include tray internal retrofit, control retrofit, heat exchange retrofit, heat cascading, inter-heat exchangers, double effect distillation and heat pumps. Some of these schemes cost little to implement and consequently have shown attractive payback periods (PBP), but in terms of saving energy, the heat pump is potentially the most promising. The heat integration method [2] attempts to integrate the heat demand of a column within the heat network for the overall process of which the column is only a part. The general impression given is that with the heat integration method fully adopted, there will be a rather limited need for other methods such as heat pumping. This o f course presumes that the chemical and allied industries will be prepared to abandon their age old tradition of general caution towards integration. The problem with integration is that it often reduces flexibility m addition to complexing the controls. A heat pump operates on the same principle as the domestic refrigerator and is capable, therefore, of absorbing heat from a cold source and of rejecting an augmented amount of heat to a higher temperature sink. The simplest way of introducing a heat pump into a distillation system is to replace the coolant in the column condenser by a working fluid evaporating at a relatively low temperature and pressure. In this alternative arrangement, which is shown schematica:lly in Fig. 2, the reboiler becomes the condenser of a heat pump system and the condenser becomes the
Heat pump assisted distillation systems--I
TotoL
/
~
CooLant
reflux D overhead product F feed
CoLumn
__.____..,=_
Steam
ReboiLer(~)
'B bottom product Fig. 1. Conventional distillation system.
ro(~ r~v
%riser
_I5 ~ R o
reflux D overhead product
F feed
=-CoLumn
;ompressor
ReboiLer
~ Heat pump ; condenser
T~o RecircuLating working fluid B
bottom product Fig. 2. Heat pump assisted distillation system with an external working fluid.
189
190
T.O. OMIDe','l er al.
evaporator of the heat pump system. After evaporation, the working fluid is compressed and gives up latent heat at a higher temperature in the heat pump condenser. The condensed working fluid is then expanded through an expansion valve and returned to the heat pump evaporator to complete the cycle. As the distillation process is unaffected by the method used to maintain the temperatures at the top and the bottom of the column, the incorporation of a heat pump in this way should have no effect on the column operation. Consequently the heat pump working fluid can be selected independently of the composition of the distillation mixture. Such a combined system, therefore, presents the minimum technical risk and is the obvious first choice for economic assessment. An alternative arrangement, commonly referred to as the vapour recompression system, is when the overhead vapour from the column is used directly as the heat pump working fluid. After compression, this vapour is condensed by indirect heat exchange in the reboiler and the condensate cooled by indirect interchange with the incoming feed. Part of the condensate is removed as product and the remainder returned to the column as reflux. The relative simplicity of this arrangement is obvious, although it has the disadvantage of interfering with the distillation process. This disadvantage limits its potential application. Practical application of such systems has been limited. This is partly because technological innovation would be required in a welt established and competitive industry and partly because previous economic reviews have indicated that specific applications examined might not be attractive. However, such analyses have not been thorough. Several factors may be expected to influence the overall economic viability of the process. Some of these are system design variables while others are economic factors. Such economic analyses as have been reported have not adequately investigated the importance of these variables in the o~erall economics. What is needed for such detailed analysis is a simple but realistic model for preliminary design and economic assessment of the system, compared with a conventional design.
HEAT PUMP ASSISTED DISTILLATION SYSTEM In an ideal system as shown in Fig. 2, the working fluid extracts an amount of heat energy Qo from the column condenser. An amount of high grade energy W is added to the shaft o f the compressor or its equivalent. The amount of heat energy Qm delivered to the high temperature sink is related to W by the coefficient of performance (COP)A of the heat pump system defined by (COP)A = Q--y W"
(1)
In an ideal system with no heat losses, and with perfect heat matching between the distillation subsystem and the heat pump subsystem, Qs = QD + W.
(2)
The coefficient of performance (COP)~ is, in effect, the factor by which the energy demand of the system can be reduced. The maximum possible coefficient of performance could only be obtained if compression were to be carried out reversibly according to the Carnot cycle. The Carnot coefficient of performance (COP)c for the theoretically limiting case can be defined in terms of the condensing temperature Tco and evaporating temperature TEv of the working fluid (COP)c =
Too
(3)
/ ' c o - T~v where Too = Ts + ATco
(4)
Tev = T~ - ATev.
(5)
and
Ts is the boiling temperature of the bottom product and To is the condensing temperature of the distillate. Practical systems will require finite temperature driving forces ATco across the reboiler
Heat pump assisted distillation systems--I
191
and ATEv across the condenser. In practical systems the inclusion of the inherently irreversible expansion valve means that the heat pump cycle corresponds more closely to the Rankine heat pump cycle. The corresponding theoretical Rankine coefficients of performance (COP)R depend, in addition, on the thermodynamic properties of the working fluid chosen. Values of (COP)R for twenty-one working fluids capable of delivering heat in the temperature range 80-200 C have been published for various temperature lifts and condensing temperatures [5]. The same publication includes design graphs which simplify the selection of potentially useful working fluids for a particular duty. A real heat pump system will have an even lower actual coefficient of performance (COP)4 since the compressor is not operated reversibly and because of pressure drops in the system. A heat pump effectiveness factor (HPE) R may be defined by (COP)A (HPE)R - (COP)~
(6)
Experiments on a number of different working fluids in a water-to-water heat pump have shown that values of (HPE)R in the range 75-92~o can be obtained [6].
DESIGN CONSIDERATIONS It is important to highlight some of the various factors which would need to be considered in producing a model for the preliminary design and economic analysis of the heat pump assisted distillation systems. The selection of a possible heat pump working fluid is made on the basis of the compositions of the distillation products which in turn determine the bubble and dew points.
Selection of workingfluid The choice of the working fluid will influence the design of the system and the economics of its operation. The optimum selection requires a critical appraisal of the following factors [7]. (a) The critical temperature of the working fluid must be significantly greater than the boiling temperature of the mixture in the reboiler so that the latent heat of condensation of the working fluid is sufficiently large to avoid excessive heat transfer areas in the major heat exchangers. (b) The condensing and boiling film heat transfer coefficients of the working fluid should be high in order to reduce the size of the major heat exchangers. (c) The working fluid should be chemically and thermally stable at the maximum temperature encountered in the heat pump to reduce down time for maintenance and cleaning. The working fluid should not react excessively with the materials of construction or with the lubricant used in the compressor. (d) The pressure range corresponding to the temperature range of the heat pump system should be within the capability of the compressor chosen. (e) The vapour volumetric flow rates of the working fluid should be as near optimal as possible for the compressor chosen. (f) The viscosity of the vapour of the working fluid should be low to minimize pressure losses in the heat exchangers and transfer lines. (g) The working fluid should have as high a theoretical Rankine coefficient of performance as possible for the temperature range involved. (h) The working fluid should be nontoxic. (i) The working fluid should be cheap and readily available. Vapour compression heat pumps can now be designed to deliver heat at temperatures in the region of 180°C. This means that it is now technically possible to apply heat pumps on distillation systems ranging from light hydrocarbons to water and oxygenated hydrocarbons such as alcohols. At the lower end of this temperature range the common refrigerants RI2 (dichlorodifluoromethane) and R22 (monochlorodifluoromethane) are often suitable working fluids. At intermediate temperatures of 80°C to a little over 100°C, R114 (dichiorotetrafluoroethane), is the common choice.
192
T.O. OMIDEYIet aL
At the higher temperature end. R I 1 Itrichlorofluoromethane}, R! 13 (trichlorotrifluoroethane~ and R718 (water) can be considered. The (COP)R for most of these working fluids can be related to the condensing temperature Too and the (COP)c by equauons of the type (COP)R --- A (COP)c + B
(7)
A = AI Too + A2 Too + A3
[8)
B = B l Tc~ -,- B~
¢9~
where A~, A 2, A3, BI and B2 are constants to be determined for each working fluid. General design strategy
The first step is to decide on possible heat pump working fluids in the context of the temperatures demanded by the distillation process. The materials of construction can now be established in the context of the temperatures, pressures and chemical nature of the distillation mixture and of the working fluid. The required thickness of heat exchanger tubes can then be determined, which in turn establishes the minimum resistance to heat transfer obtainable. The likelihood of the distillation mixture or decomposition products causing fouling of the heat transfer surfaces can be assessed and a fouling resistance established which will permit an adequate on-stream life between cleanings. Values of heat transfer coefficients can be calculated by standard methods and hence minimum values of ATco and AT~v can be estimated. Maximum values of (COP)A and hence of energy saving can be established. If these seem reasonable then the effect of increasing ATco and A T e v and hence of reducing the size and cost of heat transfer areas on (COP)4 can be assessed, This will rapidly define the practical range of the variables. For a pure working fluid only two factors may be decided independently. As discussed above. these will be the condensing temperature Tco and the gross temperature lift ( T o o - T~v). This automatically determines all other variables of the heat pump including the theoretical coefficient of performance (COP)k, the latent heat per unit volume of the working fluid and. in particular. the compression ratio required. The last two factors, together with the known heat demand of the reboiler, will establish if a compressor is available in the chosen materials of construction and of the size and type required by the heat demand. The compression ratio (CR) actually achieved will be determined by the size and adjustment of the throttling device used as the expansion valve, which is usually manually adjusted. The heat exchangers may then be designed. In practical systems, it is unlikely that the heat energy match will be obtained between the two subsystems, so that a choice must be made as to which heat exchanger shall be the limiting unit Of the system. H e a t balances
In the conventional arrangement shown in Fig. l the heat removed in the overhead condensate is given by equation l0 Qo = D ( R + 1)2o.
I10)
The overall heat balance on the arrangement is given by Qn - Qo - QLoss + F H r - D H o - BHn = 0
( 1 1)
where F, B and D are the mass flow rates of the feed, bottom product and top product respectively and the enthalpies are measured above an appropriate datum level. Heat losses QLoss, in typical industrial distillation systems average about 10~o of Qn. If the heat supply can be matched exactly, the energy supplied at the shaft of the compressor is given by equation 2. It follows therefore from equation 1, that (COP)A =
Qn
-.
QB- Qo
( 12
For assumed values of ATco and A T e v , Tco and TEv are fixed, and from the thermodynamics of the working fluid (COP)R is fixed. Normally one would attempt to design the system for an (HPE)R value approaching 1.0. In choosing a realistic (HPE)R value as target, it follows from
Heat pump assisted distillation systems--I (a}
To
193
{b)
rEv
To
(e)
TEv
To
TEv
..IRD
ra
Tco
B
- ~
I"".
Fig. 3. Some alternative arrangements of heat pump assisted distillation systems with an external working fluid.
equation 6 that the corresponding actual coefficient of performance (COP)] becomes fixed. When (COP)] is equal to (COP)A, the whole system is well matched, and no additional heat transfer equipment will be needed, except perhaps for purposes of control. For systems where (COP)] is less than (COP)A, the system will produce excess heat which will have to be removed. Excess heat removal can be done in either of two ways. (i) On the distillation side, an auxiliary water condenser may be located at the top of the column as in Fig. 3a. (ii) Alternatively, on the heat pump side, an auxiliary condenser may be located at the outlet from the heat pump compressor as in Fig. 3b. Some of this excess heat, which will be available at a much higher temperature than in the column, can be used for preheating the feed as shown in Fig. 3c. In other systems (COP)] will be higher than (COP)A. This situation is most desirable, as it offers greater flexibility in design, particularly in choosing ATco and ATEv. It is clear that the design of heat pump assisted distillation systems should be considered as a unit and not as an add-on retrofit. Design equations
Three main items of equipment are considered in this model, the column, the heat exchangers and the compressor. (i) The fractionating column. The actual number of trays N required is estimated from equation 13. N = Nr/rl r (13) where N r is the number of trays theoretically required to effect the given separation and r/r is the overall tray efficiency, based on tray type and flow characteristics in the column. The calculation of N r has been exhaustively covered in the literature and for present purposes has been reduced to two alternatives suitable for binary or pseudo-binary distillation mixtures. For mixtures with fairly constant relative volatility, the Gilliland's short cut method is adequately represented [8] by equations 14-17. z = 0.5039 - 0.5968X - 0.0908 logt0X for 0.0078 < X < 0.125 (14) r = 0.6257- 0.986X +0.5160X 2-0.1738X 3 for
T
H R . S 4/3--E
0.125 < X < 1
(15)
X = (R - R,.~.)/(R + 1)
(16)
(Nr + 1) -- (N.,,. + l) (NT+ 1)+ 1
(17)
--
194
T.O. OMU)EYIet al
Rmin, the minimum reflux ratio is estimated by Underwood's method, and the minimum number of trays Nm,n may be estimated by Fenske's method. For systems where the relative volatility can adequately be represented by an equation, an analytical equivalent of McCabe-Thiele method is used. The equations for estimating the relative volatility may be simple or complex. For instance, the relative volatility could be estimated indirectly from Wilson equations, for mixtures with peculiar equilibrium curves such as ethanol-water. The column diameter is estimated using equation 18:
.~_(4V) 05 Di
\n--~/
(18)
where D, = internal diameter of column: V = volumetric vapour rate: and v = linear velocity appropriate to the contacting device. (ii) The heat exchangers. In the design of conventional distillation systems, the temperature difference driving forces across the condenser and reboiler are determined by the temperature of the available coolant and heating medium respectively. In the design of heat pump assisted distillation systems, ATco and ATEv may be fixed arbitrarily, but this increases the risk of worse matching in the heat balance. In some circumstances it may be more convenient to estimate them indirectly from the temperature factor. (TF), defined by equation 19: (TF) =
(COP)R (COP)~ .....
it9)
(COP)~.~ is the maximum value of (COP)R which occurs when there is zero thermal resistance in the heat exchangers and, hence, when the temperature lift has the minimum value of ( T s - To). The choice of a value of (TF) in the range of zero to unity determines the sum of the temperature difference driving forces for the two main heat exchangers for a given heat pump working fluid. This sum may be split into equal values of ATco and ATEv, or in inverse ratio to the expected heat transfer coefficients U, or otherwise as judgement dictates. It should be noted that since the temperatures on either side of each heat exchanger are almost constant, these values are the same as the log mean temperature differences. Heat transfer areas are then estimated from the relationship S=
Q
(20)
UAT"
The values of U may be estimated with reasonable accuracy from equation 21 l
1
l
1
V-h where h~ is the boiling heat transfer coefficient on one side of the heat exchanger and h, is the condensing heat transfer coefficient on the other side of the same heat exchanger, and hd is a combined coefficient for the wall and fouling chosen to g~ve adequate on-stream time. (iii) The compressor. The compressor type and size is determined by the absolute pressures at the inlet and outlet and the required volumetric throughput of the working fluid. The pressures can be estimated, with sufficient accuracy, by empirical vapour pressure-temperature relationships such as: P=exp a+
(22)
where P and T are saturation values and a, b and c are constants specific to the working fluid. The compression ratio of the compressor may be obtained from equations 22 and 23 since Too and Tev are calculated from equations 4 and 5 (CR) = Pco
PEV"
~23)
For a given compressor and motor the overall efficiency Nov and work required W vary with
Heat pump assisted distillation systems--I
195
compression ratio, and may be obtained from manufacturers data. The actual power supplied by the prime mover to the compressor shaft is given by equation 24 (24)
WA = W h l o v .
The total energy supplied to the shaft also requires a knowledge of the energy conversion efficiency of the prime mover and of any gear train which may be needed to adjust the volumetric displacement rate of the compressor to that required by the distillation system. The volumetric efficiency can in theory be estimated for some types of compressors from the relationship given by My,
(25)
~IvoL- ( S V ) N ,
where: v, = specific volume of vapour at inlet conditions to compressor; M = flow rate of working fluid in the system; ( S V ) = compressor swept volume; and N, = compressor speed. The volumetric efficiency for reciprocating type compressors has been related [9] to the compression ratio by correlations of the type given by (CR) = (d - rlvoL)/e
(26)
where d, e = constants specific to individual compressors. ECONOMIC CONSIDERATIONS Ultimately, the overriding factor in the adoption of a heat pump assisted distillation system is the economics. With so many parameters involved in .its design, the need for some form of optimisation is obvious. In the economic optimisation of the conventional system the reflux ratio
PLant Qfe : 20 yr
Annual total cost { ,d~F-C~r AUT)
t~ 3 - '~0
Annual utilities COSt, AUT
8 u 5 c <~
Annual fixed copJtal COSt, A FC
,
0
i
1
I
5 ~0 15 20 25 Temperature difference driving forces z~Tco end /kTEv(*C)
Fig. 4. Effect of the temperature difference driving forces across heat pump main heat exchangers on the total annual costs for a typical ethanol-water distillation system.
T. O, OMIDEYI Cl aL
196
has long been recognised and well accepted as a crucial factor. An obvious parameter for optimisation in the heat pump assisted distillation system is the differential temperature driving forces in the two main heat exchangers. Increasing ATco and ATev would, as expected, mean a reduction in the fixed capital cost of the heat exchangers, and hence the whole system. On the other hand, increasing ATco and ATEv would, as expected, mean a reduction in the fixed capital cost of the heat exchangers, and hence the whole system. On the other hand, increasing Too and TLv increases the required gross temperature lift on the heat pump side (Tco - Tev). This in turn reduces the coefficient of performance (COP), for the system, which reduces the potential tor energy saving, and hence an increase in the annual cost of utilities, A~r. As an example, the total annual costs (Arc + Aur) is shown in Fig. 4 against the differential temperature driving forces for a typical ethanol-water distillation system, where R 114 is the heat pump working fluid. In this example the system capacity is taken as 50 000 kg/day of 96 wt°, ethanol strength. The Rankine heat pump effectiveness factor for the heat pump side is assumed as 0.8. For a distillation system the number of yr n for which the system will operate is likely to be determined by the life of the column rather than by the heating and cooling system adopted. The number of plant items q and the annual fixed and utilities costs of each of those items will depend on the items chosen. Considering the marginal cost difference between the conventional distillation system l and an alternative system 2, the financial advantage of system 2 in any year may be expressed symbolically by ql
q2
AM~mm = ~ (AFc + Aur), -- ~ (Am + Avr):~.
(27)
I
The annual equivalent of the fixed capital cost Am is related to the fixed capital cost Cvc, the number of years since the project started n and the interest rate i demanded on invested capital by equation 28:
AFC = Cm i l -fa
(28)
where .)ra = (1 + i)-". The annual utilities cost Aer for gas, electricity, water steam, sewage, etc. is a revenue item and depending on the accountancy practice adopted by the company may be accepted as it is or reduced by the discount factorfu. The former will be assumed for the purposes of the present presentation, in which case the marginal playback period (PBP) is given by
(PBP)
=
q2
ql
Z C~.~-
Z C~c.,
I
ql
J
q2
(29)
A.T , - Y. ART.: I
I
In the context of high interest and inflation rates and of business uncertainty it is customary to demand relatively short payback periods. This criterion will, therefore, be adopted here and comparisons will be made on the basis of equation 29. If it is desired to make comparisons on the basis of net present value or of discounted cash flow rate of return, then equation 27 is appropriate and the modification required will be obvious.
Capital cost estimation (1) The capital costs for the column have been estimated from the graphical correlation of Guthrie [10] corrected for the change in the CE cost index from 119 in 1969 to 300 at the end of 1981. The relevant capital costs of the column shell and of tray type vapour-liquid contactors with tray spacing z are given by Crc (shell) = 1278 fzfMsfesDj(zN) °'"ts2
(30)
Cm (trays) = 19.4ftzu (3.28 D~)t'~ (fsr + frr + f Mr).
( 31 )
The various cost factors are defined in the nomenclature and were obtained from Guthrie [10].
Heat pump assisted distillation systems--I
197
(2) The capital costs of heat exchangers were estimated from the graphical correlation presented by Hall et al. [11] corrected from capital installation costs to fixed capital costs by appropriate fL values. The resulting relationship is given by Crc (heat exchanger)
=
0.625fMnfL [l 0 (0.65logs + 2648)].
(32)
Estimates made in this way were found to lie within the range of accuracy given by Guthrie [10] in his correlation for the capital costs of heat exchangers. (3) The capital costs of compressors were obtained from graphical correlations of Hall et al. [1 1] for compressors to obtain
CFC(compressors)
=
278.5fL W °94.
(33)
Utility cost estimation (1) The utility costs of conventional condensers or coolers is given by
Aur (coolers) = Qycc.
(34)
This equation is also used for the utility cost of any auxiliary cooler which may be needed in a heat pump assisted system.
Specify distiLtotion requirements
Heat and mass balances and equilibrium caLcuLations to estimate N, Di, OB, 0 o
Or
I
i
SeLect design option
I i
I
I
OPTION I Conventional system
I
I
Heat pump assisted I system
I
' SeLect working fluid
I
and assume (TIC) or L~Tco8 ATEv
Estimate heat.exchange areas for steam reboiLer
I
and water condenser
J
I
I
I
Assess whether perfect heat matching is possible i.e. (HPE)• < a*
SeLect.another workingfluid or assume different (TF)
EsUmate exchange areas for feed preheaters
I
~
I NO
*o-desirabLe value of (HPEIp. The ideal value is I. VaLueof up to 0.9 is attainable in practice , re{ 6)
~
OR Excess heat to be E:m~)TalchboYnge;,L,ary
Fig. 5. Design algorithm for a heat pump assisted distillation system.
198
T.O. OMIDEYIeta/,
?
? ]
OPTION 2 Heat p u m p wltn perfect neat matcn=ng
Select oot~on for removing excess heat ,~ the system
I
I
I
4
I
OPTION 3 Add)t=onoL C O L u m n overhead water
OPTION Add=t)ona[ heat pump water
OPTIOI'4 5 2nd stage feed
condenser
condenser
(see FIg. 3c)
(see Fig,
(see F)g.3b;
3ol I
preheoter
I
)
]
I
I I f Z~Tcoand Z~TFvare g,venthen est)mctte Tcc and TEv. and (COP),~, (COP) c
I f (TF) s g,ven, est,mate Tco and ~ v from (COPIo ar~d
Hence determ)ne
(COP) c
&Tea ana A ~
I Use appro~ote heat transfer coefficients to estimate heat exchange areas for all heat exchangers
. Size compressors
J
Fig. 5. (continued). Design algorithm for a heat pump assisted distillation system.
(2) The utility cost of conventional reboilers and heaters is given by
ArT (heaters) = QycH.
(35)
This equation is also used for the utility cost of any auxiliary heater which may be needed in a heat pump assisted system. (3) The utility cost of the compressor of the heat pump is given by
AuT (compressor) = WycL..
(36)
In these equations y is the operational period in h yr-~, Cc, cn and cE the unit costs of coolant, heating medium and primary power energy per kWh.
DESIGN A N D ECONOMIC
MODEL
A model was developed to incorporate the various points discussed above, using the relevant equations outlined. The main steps in the alogorithm evolved are given in Fig. 5. These can be summarised as follows. (i) Specify the distillation requirements. (ii) Estimate the distillation design parameters such as the number of trays. (iii) Estimate the sizes of all the main equipment items in the conventional design. (iv) Cost these main items and estimate the annual cost of utilities.
Heat pump assisted distillation systems--I
190
I Input data 70 variabLes ( Xo, XF, X e . . . . . )
/
CALL EDIST. Moss, heat balances and equilibrium caLcuLations. CoLumn size specification.
CALL DESIGN Estimate areas for all heat exchangers in the arrangement ( / = I, (/ = 2, (
conventional system) heat pump system) size compressor)
Use equations t9 and 20
I
CaLcuLate costs
]
~'Crc.,, ]rZlrc.,, ~Aur, /
CaLcuLate economic factors (PBP) and ZIMARG,N from equations 24 and 26
//
CALLEOOT
I
Output subroutine
I
I /
I ( stop ) Fig. 6. Main flowchart for the computer programme for assessing economics of heat pump assisted distillation systems.
(v) Select a suitable working fluid for the heat pump assisted distillation system. (vi) Perform a heat balance on this system and establish possible imbalance in heat load. (vii) Depending on the answers to step (vi), decide on the optional use of the excess heat, or the means of supplementing recycled heat. (viii) Assign a value to the one variable in the model to be investigated, having fixed all others. (ix) Estimate the sizes of all main equipment items in the system. (x) Cost these equipment items and estimate the annual cost of utilities. (xi) Estimate the payback period (PBP) for the additional capital investment on the heat pump assisted distillation system, over that for the conventional system. (xii) Assign a new value to the vairable being investigated and return to step (viii). Observe the effect on the payback period. A computer programme of the model has been written in Fortran 77 and consists of a main programme and three sub-programmes. The flowchart for the main programme is presented in Fig. 6. The economic evaluations are carried out by the main programme and the design calculations are performed by the sub-programmes EDIST and DESIGN. The third-sub-
200
T.O.
OMIDEYI el t//.
p r o g r a m m e E O U T is a n o u t p u t s u b r o u t i n e . In all, a b o u t seventy i n p u t variables are r e q u i r e d bv the p r o g r a m m e . T h e influence o f a n y o f these seventy v a r i a b l e s on the p a y b a c k p e r i o d can be investigated by v a r y i n g o n l y o n e at a time. T h e p a y b a c k p e r i o d will o b v i o u s l y be m o r e sensitive to s o m e v a r i a b l e s t h a n others. A careful e x a m i n a t i o n o f the seventy s h o u l d highlight t h o s e which are m o r e likely to be o f i m p o r t a n c e . A s m e n t i o n e d a b o v e , the choice o f the differential t e m p e r a t u r e driving forces in the m a i n h e a t e x c h a n g e r s will be m o s t i m p o r t a n t . A s in c o n v e n t i o n a l distillation, the o p e r a t i n g reflux ratio, the feed s t r e n g t h a n d c o l u m n c a p a c i t y m u s t be c o n s i d e r e d . F r o m an o p e r a t i o n a l viewpoint, the r u n n i n g time o f the e q u i p m e n t will certainly influence the p a y b a c k period. T h e unit costs o f utilities will v a r y f r o m o n e c o u n t r y to a n o t h e r a n d m u s t t h e r e f o r e be c o n s i d e r e d appropriately. Acknowledgement Authors wish to thank Professor F. A. Holland and Dr. S. Devotta for their valuable contribution towards the preparation of this paper.
REFERENCES 1. J. T. Mix, J. S. Dwec,k, R. C. Weinberg and R. C. Armstrong, Energy conservation in distillation. Chem. Engng Prog. 74, 49-55 (1978). 2. B. Linnhoff, H. Dunford and R. Smith, Heat integration of distillation columns into overall processes. Chem. Engng Sci. (in press). 3. H. R. Null, Heat pumps in distillation, Chem. Engng Prog. 72, 58-64 (1976). 4. B. D. Tyreus and W. L. Luyben, Two towers cheaper than one?, Hydrocarbon Processing 54, 93-96 ~1975). 5. F. A. Holland, F. A. Watson and S. Dcvotta, Thermodynamic Design Data for Heat Pump Sy~tems, Pergamon Press. Oxford (1982). 6. A. (3. Gutierrez, S. A. K. EI-Meniawy, F. A. Watson and F. A. Holland, Operating characteristics of a water-water heat pump system using RI2, Indian Chem. Engr 21, 16-26 (1979). 7. S. Devotta and P. J. Diggory, D~isa and theoretical aspects of heat pump systems, Applied Energy 11, 125-150 (1982). 8. A. W o i n ~ y and S. gmigeh~-dli,Relationships for calculation ofoptimal reflux in rectifying towers. Revta Chimie 32, 541-547 (1981). 9. P. Welsby and S. I~votta, Private communication. Department of Chemical and Gas Engincenng, University of Salford. 10. A. Guthric, Data and techniques for preliminary capital cost estimating, Chem. Engng. 76, 114-121 (1969). 11. R. S. Hall, J. Matlcy and K. J. MeNaughton, Current costs of process equipment, Chem~ Engng. 89, 80-116 (1982).
0198-7593 84 53,0(I ~ 0.00 Pergamon Press Lid
Printed in Great Britain.
THE ECONOMICS OF HEAT P U M P ASSISTED DISTILLATION S Y S T E M S - - I . A D E S I G N A N D ECONOMIC M O D E L T. O. OMIDEYI, J. KASPRZYCKI a n d F. A . WATSON Department of Chemical and Gas Engineering, University of Salford, Salford M5 4WT, U K . Abstract--Several factors may be expected to influence the overall economics of heat pump assisted distillation systems. Some of these are design and operational, while others are purely economic factors. Economic analyses of such systems so far reported in the literature have not adequately investigated the importance of these factors. A design and economic model is presented in this paper which can be used for a preliminary economic analysis of heat pump assisted distillation systems. Two important points of consideration in the design, notably, the problem of matching the heat loads between the heat pump and the distillation sections, and the selection of the heat pump working fluid. are discussed. The major design equations used in the model are presented. A design algorithm as well as a flowchart for the computer programme of the model are given.
NOMENCLATURE a
A~c A MARC~X A ~,r b B c
cc cE cn
Crc (COP)~ (COP) c (COP)R (CR) d D Di e fa fL
fu~ f~ts f~r
fen fsr frr F h H (HPE) R i M n N
NMt,s N, Nr P
Pco PEr (PBP) Q QB Q~
empirical constant in equation 22 annual equivalent of fixed capital cost annual marginal cost between alternative systems annual utilities cost empirical constant in equation 22 flow rate of bottom product empirical constant in equation 22 unit cost of coolant to absorb heat unit cost of primary energy source unit cost of heating medium capital cost actual coefficient of performance of heat pump Carnot coefficient of performance of heat pump Rankine coefficient of performance of heat pump compression ratio of heat pump constant in equation 26 flow rate of top product internal diameter of column shell constant in equation 26 discount factor [1- i) -" base factor relating installed equipment cost to fixed capital cost material of construction factor for shell and tube exchangers material of construction factor for column shell material of construction factor for distillation trays pressure factor for column shell factor for tray spacing factor for tray construction type flow rate of feed to column individual boiling or condensing film heat transfer coefficient enthalpy Rankine heat pump effectiveness factor fractional annual cost of capital mass flowrate of working fluid number of years since plant startup number of trays required in the column minimum number of trays required in the column compressor speed theoretical number of trays required in the column saturation vapour pressure saturation vapour pressure of condensing working fluid saturation vapour pressure of evaporating working fluid payback period of marginal investment heat transfer rate heat transfer rate in the reboiler or heat pump condenser maximum heat transfer rate acceptable by the reboiler 187
[dimensionless] [£ yr -l] [£ yr -~] [£ yr- ~] [K] [kmol s- ~] [K[ [£ kW- k h - ~] [£ kW-~ h ~] [£ kW th-~[ [£] [dimensionless] [dimensionless] ]dimensionless] [dimensionless[ [dimensionless] [kmol s- ~} [m] [dimensionless] ]dimensionless[ [dimensionless] [dimensionless[ [dimensionless] [dimensionless] [dimensionless] [dimensionless] [dimensionless[ [kmol s -~] [kW m-2K t] [kJ kmol ~] [dimensionless] [dimensionless] [kg s t] [dimensionless] [dimensionless[ [dimensionless] [rev s- J] ]dimensionless] [bar] [bar] [bar] [yr] [kW] [kW] [kW]
188
T.O. OMIOEWet al. Qn Q~ QLoss z R RMt.~ S (SV) T TB Too TD Try (TF) U v L V W Wa X y z ATco ATrv 2o rlov r/r rlvo,
heat transfer rate in the condenser or heat pump evaporator maximum heat transfer rate available from the condenser heat loss from the total system ratio defined by equation 17 reflux ratio minimum reflux ratio for given separation heat transfer area compressor swept volume temperature boiling temperature of distillation mixture in reboiler condensing temperature of working fluid m reboiler condensing temperature of distillation mtxture m condenser evaporating temperature of working fluid in condenser temperaturefactor defined by equation 19 overall heat transfer coefficient permissible vapour velocity specific volume of vapour volumetric vapour rate in the column energy supplied to compressor shaft energy supplied to the prime mover of the compressor ratio defined by equation 16 operating time tray spacing temperaturedriving force in reboiler temperaturedriving force in condenser latent heat of condensation of overhead product overall efficiencyof motor and compressor overall tray efficiency in column volumetric efficiency of compressor
[kW1 [kW} [kW] [dimensionless] [dimensionless] [dimensionless] [m2] [m~re', j [K or C] [K] [K] [K] [K] [dimensionless] [kW m- ~'K- ~] [m s ~] [m3kg 11 [m3s-~] [kW] [kW] [dimensionless] [h yr ~] [m] [K] [K] [kJ kmol-~] [dimensionless] [dimensionless] [dimensionless]
INTRODUCTION Distillation is a widely used, but energy intensive, method o f separating liquid mixtures into relatively pure components. It is c o m m o n to the chemical and allied industries where certain mixtures such as crude petroleum, alcohols and other organic intermediates and products are refined on a very large scale. It was estimated [1] that in 1976, distillation systems accounted for almost 60% o f the energy consumption in the US chemical industry, costing some $5000 million that year. A conventional distillation system, as shown in Fig. 1, would typically include a steam heated reboiler, a fractionating column and a water cooled condenser. Although it is customary to exchange heat between the incoming feed and the outgoing bottom product, in most industrial distillation systems between 80 and 90% o f the total heat supplied is removed in the condenser. In general, the temperature o f the outlet coolant is too low to be useful and this heat is wasted. While energy costs were a relatively small fraction of the product cost. the wastage o f this energy caused no concern. Since it is believed that energy costs will continue to escalate over the long term, several shemes for reducing the energy demands of distillation systems are being investigated. Such schemes include tray internal retrofit, control retrofit, heat exchange retrofit, heat cascading, inter-heat exchangers, double effect distillation and heat pumps. Some of these schemes cost little to implement and consequently have shown attractive payback periods (PBP), but in terms of saving energy, the heat pump is potentially the most promising. The heat integration method [2] attempts to integrate the heat demand of a column within the heat network for the overall process of which the column is only a part. The general impression given is that with the heat integration method fully adopted, there will be a rather limited need for other methods such as heat pumping. This o f course presumes that the chemical and allied industries will be prepared to abandon their age old tradition of general caution towards integration. The problem with integration is that it often reduces flexibility m addition to complexing the controls. A heat pump operates on the same principle as the domestic refrigerator and is capable, therefore, of absorbing heat from a cold source and of rejecting an augmented amount of heat to a higher temperature sink. The simplest way of introducing a heat pump into a distillation system is to replace the coolant in the column condenser by a working fluid evaporating at a relatively low temperature and pressure. In this alternative arrangement, which is shown schematica:lly in Fig. 2, the reboiler becomes the condenser of a heat pump system and the condenser becomes the
Heat pump assisted distillation systems--I
TotoL
/
~
CooLant
reflux D overhead product F feed
CoLumn
__.____..,=_
Steam
ReboiLer(~)
'B bottom product Fig. 1. Conventional distillation system.
ro(~ r~v
%riser
_I5 ~ R o
reflux D overhead product
F feed
=-CoLumn
;ompressor
ReboiLer
~ Heat pump ; condenser
T~o RecircuLating working fluid B
bottom product Fig. 2. Heat pump assisted distillation system with an external working fluid.
189
190
T.O. OMIDe','l er al.
evaporator of the heat pump system. After evaporation, the working fluid is compressed and gives up latent heat at a higher temperature in the heat pump condenser. The condensed working fluid is then expanded through an expansion valve and returned to the heat pump evaporator to complete the cycle. As the distillation process is unaffected by the method used to maintain the temperatures at the top and the bottom of the column, the incorporation of a heat pump in this way should have no effect on the column operation. Consequently the heat pump working fluid can be selected independently of the composition of the distillation mixture. Such a combined system, therefore, presents the minimum technical risk and is the obvious first choice for economic assessment. An alternative arrangement, commonly referred to as the vapour recompression system, is when the overhead vapour from the column is used directly as the heat pump working fluid. After compression, this vapour is condensed by indirect heat exchange in the reboiler and the condensate cooled by indirect interchange with the incoming feed. Part of the condensate is removed as product and the remainder returned to the column as reflux. The relative simplicity of this arrangement is obvious, although it has the disadvantage of interfering with the distillation process. This disadvantage limits its potential application. Practical application of such systems has been limited. This is partly because technological innovation would be required in a welt established and competitive industry and partly because previous economic reviews have indicated that specific applications examined might not be attractive. However, such analyses have not been thorough. Several factors may be expected to influence the overall economic viability of the process. Some of these are system design variables while others are economic factors. Such economic analyses as have been reported have not adequately investigated the importance of these variables in the o~erall economics. What is needed for such detailed analysis is a simple but realistic model for preliminary design and economic assessment of the system, compared with a conventional design.
HEAT PUMP ASSISTED DISTILLATION SYSTEM In an ideal system as shown in Fig. 2, the working fluid extracts an amount of heat energy Qo from the column condenser. An amount of high grade energy W is added to the shaft o f the compressor or its equivalent. The amount of heat energy Qm delivered to the high temperature sink is related to W by the coefficient of performance (COP)A of the heat pump system defined by (COP)A = Q--y W"
(1)
In an ideal system with no heat losses, and with perfect heat matching between the distillation subsystem and the heat pump subsystem, Qs = QD + W.
(2)
The coefficient of performance (COP)~ is, in effect, the factor by which the energy demand of the system can be reduced. The maximum possible coefficient of performance could only be obtained if compression were to be carried out reversibly according to the Carnot cycle. The Carnot coefficient of performance (COP)c for the theoretically limiting case can be defined in terms of the condensing temperature Tco and evaporating temperature TEv of the working fluid (COP)c =
Too
(3)
/ ' c o - T~v where Too = Ts + ATco
(4)
Tev = T~ - ATev.
(5)
and
Ts is the boiling temperature of the bottom product and To is the condensing temperature of the distillate. Practical systems will require finite temperature driving forces ATco across the reboiler
Heat pump assisted distillation systems--I
191
and ATEv across the condenser. In practical systems the inclusion of the inherently irreversible expansion valve means that the heat pump cycle corresponds more closely to the Rankine heat pump cycle. The corresponding theoretical Rankine coefficients of performance (COP)R depend, in addition, on the thermodynamic properties of the working fluid chosen. Values of (COP)R for twenty-one working fluids capable of delivering heat in the temperature range 80-200 C have been published for various temperature lifts and condensing temperatures [5]. The same publication includes design graphs which simplify the selection of potentially useful working fluids for a particular duty. A real heat pump system will have an even lower actual coefficient of performance (COP)4 since the compressor is not operated reversibly and because of pressure drops in the system. A heat pump effectiveness factor (HPE) R may be defined by (COP)A (HPE)R - (COP)~
(6)
Experiments on a number of different working fluids in a water-to-water heat pump have shown that values of (HPE)R in the range 75-92~o can be obtained [6].
DESIGN CONSIDERATIONS It is important to highlight some of the various factors which would need to be considered in producing a model for the preliminary design and economic analysis of the heat pump assisted distillation systems. The selection of a possible heat pump working fluid is made on the basis of the compositions of the distillation products which in turn determine the bubble and dew points.
Selection of workingfluid The choice of the working fluid will influence the design of the system and the economics of its operation. The optimum selection requires a critical appraisal of the following factors [7]. (a) The critical temperature of the working fluid must be significantly greater than the boiling temperature of the mixture in the reboiler so that the latent heat of condensation of the working fluid is sufficiently large to avoid excessive heat transfer areas in the major heat exchangers. (b) The condensing and boiling film heat transfer coefficients of the working fluid should be high in order to reduce the size of the major heat exchangers. (c) The working fluid should be chemically and thermally stable at the maximum temperature encountered in the heat pump to reduce down time for maintenance and cleaning. The working fluid should not react excessively with the materials of construction or with the lubricant used in the compressor. (d) The pressure range corresponding to the temperature range of the heat pump system should be within the capability of the compressor chosen. (e) The vapour volumetric flow rates of the working fluid should be as near optimal as possible for the compressor chosen. (f) The viscosity of the vapour of the working fluid should be low to minimize pressure losses in the heat exchangers and transfer lines. (g) The working fluid should have as high a theoretical Rankine coefficient of performance as possible for the temperature range involved. (h) The working fluid should be nontoxic. (i) The working fluid should be cheap and readily available. Vapour compression heat pumps can now be designed to deliver heat at temperatures in the region of 180°C. This means that it is now technically possible to apply heat pumps on distillation systems ranging from light hydrocarbons to water and oxygenated hydrocarbons such as alcohols. At the lower end of this temperature range the common refrigerants RI2 (dichlorodifluoromethane) and R22 (monochlorodifluoromethane) are often suitable working fluids. At intermediate temperatures of 80°C to a little over 100°C, R114 (dichiorotetrafluoroethane), is the common choice.
192
T.O. OMIDEYIet aL
At the higher temperature end. R I 1 Itrichlorofluoromethane}, R! 13 (trichlorotrifluoroethane~ and R718 (water) can be considered. The (COP)R for most of these working fluids can be related to the condensing temperature Too and the (COP)c by equauons of the type (COP)R --- A (COP)c + B
(7)
A = AI Too + A2 Too + A3
[8)
B = B l Tc~ -,- B~
¢9~
where A~, A 2, A3, BI and B2 are constants to be determined for each working fluid. General design strategy
The first step is to decide on possible heat pump working fluids in the context of the temperatures demanded by the distillation process. The materials of construction can now be established in the context of the temperatures, pressures and chemical nature of the distillation mixture and of the working fluid. The required thickness of heat exchanger tubes can then be determined, which in turn establishes the minimum resistance to heat transfer obtainable. The likelihood of the distillation mixture or decomposition products causing fouling of the heat transfer surfaces can be assessed and a fouling resistance established which will permit an adequate on-stream life between cleanings. Values of heat transfer coefficients can be calculated by standard methods and hence minimum values of ATco and AT~v can be estimated. Maximum values of (COP)A and hence of energy saving can be established. If these seem reasonable then the effect of increasing ATco and A T e v and hence of reducing the size and cost of heat transfer areas on (COP)4 can be assessed, This will rapidly define the practical range of the variables. For a pure working fluid only two factors may be decided independently. As discussed above. these will be the condensing temperature Tco and the gross temperature lift ( T o o - T~v). This automatically determines all other variables of the heat pump including the theoretical coefficient of performance (COP)k, the latent heat per unit volume of the working fluid and. in particular. the compression ratio required. The last two factors, together with the known heat demand of the reboiler, will establish if a compressor is available in the chosen materials of construction and of the size and type required by the heat demand. The compression ratio (CR) actually achieved will be determined by the size and adjustment of the throttling device used as the expansion valve, which is usually manually adjusted. The heat exchangers may then be designed. In practical systems, it is unlikely that the heat energy match will be obtained between the two subsystems, so that a choice must be made as to which heat exchanger shall be the limiting unit Of the system. H e a t balances
In the conventional arrangement shown in Fig. l the heat removed in the overhead condensate is given by equation l0 Qo = D ( R + 1)2o.
I10)
The overall heat balance on the arrangement is given by Qn - Qo - QLoss + F H r - D H o - BHn = 0
( 1 1)
where F, B and D are the mass flow rates of the feed, bottom product and top product respectively and the enthalpies are measured above an appropriate datum level. Heat losses QLoss, in typical industrial distillation systems average about 10~o of Qn. If the heat supply can be matched exactly, the energy supplied at the shaft of the compressor is given by equation 2. It follows therefore from equation 1, that (COP)A =
Qn
-.
QB- Qo
( 12
For assumed values of ATco and A T e v , Tco and TEv are fixed, and from the thermodynamics of the working fluid (COP)R is fixed. Normally one would attempt to design the system for an (HPE)R value approaching 1.0. In choosing a realistic (HPE)R value as target, it follows from
Heat pump assisted distillation systems--I (a}
To
193
{b)
rEv
To
(e)
TEv
To
TEv
..IRD
ra
Tco
B
- ~
I"".
Fig. 3. Some alternative arrangements of heat pump assisted distillation systems with an external working fluid.
equation 6 that the corresponding actual coefficient of performance (COP)] becomes fixed. When (COP)] is equal to (COP)A, the whole system is well matched, and no additional heat transfer equipment will be needed, except perhaps for purposes of control. For systems where (COP)] is less than (COP)A, the system will produce excess heat which will have to be removed. Excess heat removal can be done in either of two ways. (i) On the distillation side, an auxiliary water condenser may be located at the top of the column as in Fig. 3a. (ii) Alternatively, on the heat pump side, an auxiliary condenser may be located at the outlet from the heat pump compressor as in Fig. 3b. Some of this excess heat, which will be available at a much higher temperature than in the column, can be used for preheating the feed as shown in Fig. 3c. In other systems (COP)] will be higher than (COP)A. This situation is most desirable, as it offers greater flexibility in design, particularly in choosing ATco and ATEv. It is clear that the design of heat pump assisted distillation systems should be considered as a unit and not as an add-on retrofit. Design equations
Three main items of equipment are considered in this model, the column, the heat exchangers and the compressor. (i) The fractionating column. The actual number of trays N required is estimated from equation 13. N = Nr/rl r (13) where N r is the number of trays theoretically required to effect the given separation and r/r is the overall tray efficiency, based on tray type and flow characteristics in the column. The calculation of N r has been exhaustively covered in the literature and for present purposes has been reduced to two alternatives suitable for binary or pseudo-binary distillation mixtures. For mixtures with fairly constant relative volatility, the Gilliland's short cut method is adequately represented [8] by equations 14-17. z = 0.5039 - 0.5968X - 0.0908 logt0X for 0.0078 < X < 0.125 (14) r = 0.6257- 0.986X +0.5160X 2-0.1738X 3 for
T
H R . S 4/3--E
0.125 < X < 1
(15)
X = (R - R,.~.)/(R + 1)
(16)
(Nr + 1) -- (N.,,. + l) (NT+ 1)+ 1
(17)
--
194
T.O. OMU)EYIet al
Rmin, the minimum reflux ratio is estimated by Underwood's method, and the minimum number of trays Nm,n may be estimated by Fenske's method. For systems where the relative volatility can adequately be represented by an equation, an analytical equivalent of McCabe-Thiele method is used. The equations for estimating the relative volatility may be simple or complex. For instance, the relative volatility could be estimated indirectly from Wilson equations, for mixtures with peculiar equilibrium curves such as ethanol-water. The column diameter is estimated using equation 18:
.~_(4V) 05 Di
\n--~/
(18)
where D, = internal diameter of column: V = volumetric vapour rate: and v = linear velocity appropriate to the contacting device. (ii) The heat exchangers. In the design of conventional distillation systems, the temperature difference driving forces across the condenser and reboiler are determined by the temperature of the available coolant and heating medium respectively. In the design of heat pump assisted distillation systems, ATco and ATEv may be fixed arbitrarily, but this increases the risk of worse matching in the heat balance. In some circumstances it may be more convenient to estimate them indirectly from the temperature factor. (TF), defined by equation 19: (TF) =
(COP)R (COP)~ .....
it9)
(COP)~.~ is the maximum value of (COP)R which occurs when there is zero thermal resistance in the heat exchangers and, hence, when the temperature lift has the minimum value of ( T s - To). The choice of a value of (TF) in the range of zero to unity determines the sum of the temperature difference driving forces for the two main heat exchangers for a given heat pump working fluid. This sum may be split into equal values of ATco and ATEv, or in inverse ratio to the expected heat transfer coefficients U, or otherwise as judgement dictates. It should be noted that since the temperatures on either side of each heat exchanger are almost constant, these values are the same as the log mean temperature differences. Heat transfer areas are then estimated from the relationship S=
Q
(20)
UAT"
The values of U may be estimated with reasonable accuracy from equation 21 l
1
l
1
V-h where h~ is the boiling heat transfer coefficient on one side of the heat exchanger and h, is the condensing heat transfer coefficient on the other side of the same heat exchanger, and hd is a combined coefficient for the wall and fouling chosen to g~ve adequate on-stream time. (iii) The compressor. The compressor type and size is determined by the absolute pressures at the inlet and outlet and the required volumetric throughput of the working fluid. The pressures can be estimated, with sufficient accuracy, by empirical vapour pressure-temperature relationships such as: P=exp a+
(22)
where P and T are saturation values and a, b and c are constants specific to the working fluid. The compression ratio of the compressor may be obtained from equations 22 and 23 since Too and Tev are calculated from equations 4 and 5 (CR) = Pco
PEV"
~23)
For a given compressor and motor the overall efficiency Nov and work required W vary with
Heat pump assisted distillation systems--I
195
compression ratio, and may be obtained from manufacturers data. The actual power supplied by the prime mover to the compressor shaft is given by equation 24 (24)
WA = W h l o v .
The total energy supplied to the shaft also requires a knowledge of the energy conversion efficiency of the prime mover and of any gear train which may be needed to adjust the volumetric displacement rate of the compressor to that required by the distillation system. The volumetric efficiency can in theory be estimated for some types of compressors from the relationship given by My,
(25)
~IvoL- ( S V ) N ,
where: v, = specific volume of vapour at inlet conditions to compressor; M = flow rate of working fluid in the system; ( S V ) = compressor swept volume; and N, = compressor speed. The volumetric efficiency for reciprocating type compressors has been related [9] to the compression ratio by correlations of the type given by (CR) = (d - rlvoL)/e
(26)
where d, e = constants specific to individual compressors. ECONOMIC CONSIDERATIONS Ultimately, the overriding factor in the adoption of a heat pump assisted distillation system is the economics. With so many parameters involved in .its design, the need for some form of optimisation is obvious. In the economic optimisation of the conventional system the reflux ratio
PLant Qfe : 20 yr
Annual total cost { ,d~F-C~r AUT)
t~ 3 - '~0
Annual utilities COSt, AUT
8 u 5 c <~
Annual fixed copJtal COSt, A FC
,
0
i
1
I
5 ~0 15 20 25 Temperature difference driving forces z~Tco end /kTEv(*C)
Fig. 4. Effect of the temperature difference driving forces across heat pump main heat exchangers on the total annual costs for a typical ethanol-water distillation system.
T. O, OMIDEYI Cl aL
196
has long been recognised and well accepted as a crucial factor. An obvious parameter for optimisation in the heat pump assisted distillation system is the differential temperature driving forces in the two main heat exchangers. Increasing ATco and ATev would, as expected, mean a reduction in the fixed capital cost of the heat exchangers, and hence the whole system. On the other hand, increasing ATco and ATEv would, as expected, mean a reduction in the fixed capital cost of the heat exchangers, and hence the whole system. On the other hand, increasing Too and TLv increases the required gross temperature lift on the heat pump side (Tco - Tev). This in turn reduces the coefficient of performance (COP), for the system, which reduces the potential tor energy saving, and hence an increase in the annual cost of utilities, A~r. As an example, the total annual costs (Arc + Aur) is shown in Fig. 4 against the differential temperature driving forces for a typical ethanol-water distillation system, where R 114 is the heat pump working fluid. In this example the system capacity is taken as 50 000 kg/day of 96 wt°, ethanol strength. The Rankine heat pump effectiveness factor for the heat pump side is assumed as 0.8. For a distillation system the number of yr n for which the system will operate is likely to be determined by the life of the column rather than by the heating and cooling system adopted. The number of plant items q and the annual fixed and utilities costs of each of those items will depend on the items chosen. Considering the marginal cost difference between the conventional distillation system l and an alternative system 2, the financial advantage of system 2 in any year may be expressed symbolically by ql
q2
AM~mm = ~ (AFc + Aur), -- ~ (Am + Avr):~.
(27)
I
The annual equivalent of the fixed capital cost Am is related to the fixed capital cost Cvc, the number of years since the project started n and the interest rate i demanded on invested capital by equation 28:
AFC = Cm i l -fa
(28)
where .)ra = (1 + i)-". The annual utilities cost Aer for gas, electricity, water steam, sewage, etc. is a revenue item and depending on the accountancy practice adopted by the company may be accepted as it is or reduced by the discount factorfu. The former will be assumed for the purposes of the present presentation, in which case the marginal playback period (PBP) is given by
(PBP)
=
q2
ql
Z C~.~-
Z C~c.,
I
ql
J
q2
(29)
A.T , - Y. ART.: I
I
In the context of high interest and inflation rates and of business uncertainty it is customary to demand relatively short payback periods. This criterion will, therefore, be adopted here and comparisons will be made on the basis of equation 29. If it is desired to make comparisons on the basis of net present value or of discounted cash flow rate of return, then equation 27 is appropriate and the modification required will be obvious.
Capital cost estimation (1) The capital costs for the column have been estimated from the graphical correlation of Guthrie [10] corrected for the change in the CE cost index from 119 in 1969 to 300 at the end of 1981. The relevant capital costs of the column shell and of tray type vapour-liquid contactors with tray spacing z are given by Crc (shell) = 1278 fzfMsfesDj(zN) °'"ts2
(30)
Cm (trays) = 19.4ftzu (3.28 D~)t'~ (fsr + frr + f Mr).
( 31 )
The various cost factors are defined in the nomenclature and were obtained from Guthrie [10].
Heat pump assisted distillation systems--I
197
(2) The capital costs of heat exchangers were estimated from the graphical correlation presented by Hall et al. [11] corrected from capital installation costs to fixed capital costs by appropriate fL values. The resulting relationship is given by Crc (heat exchanger)
=
0.625fMnfL [l 0 (0.65logs + 2648)].
(32)
Estimates made in this way were found to lie within the range of accuracy given by Guthrie [10] in his correlation for the capital costs of heat exchangers. (3) The capital costs of compressors were obtained from graphical correlations of Hall et al. [1 1] for compressors to obtain
CFC(compressors)
=
278.5fL W °94.
(33)
Utility cost estimation (1) The utility costs of conventional condensers or coolers is given by
Aur (coolers) = Qycc.
(34)
This equation is also used for the utility cost of any auxiliary cooler which may be needed in a heat pump assisted system.
Specify distiLtotion requirements
Heat and mass balances and equilibrium caLcuLations to estimate N, Di, OB, 0 o
Or
I
i
SeLect design option
I i
I
I
OPTION I Conventional system
I
I
Heat pump assisted I system
I
' SeLect working fluid
I
and assume (TIC) or L~Tco8 ATEv
Estimate heat.exchange areas for steam reboiLer
I
and water condenser
J
I
I
I
Assess whether perfect heat matching is possible i.e. (HPE)• < a*
SeLect.another workingfluid or assume different (TF)
EsUmate exchange areas for feed preheaters
I
~
I NO
*o-desirabLe value of (HPEIp. The ideal value is I. VaLueof up to 0.9 is attainable in practice , re{ 6)
~
OR Excess heat to be E:m~)TalchboYnge;,L,ary
Fig. 5. Design algorithm for a heat pump assisted distillation system.
198
T.O. OMIDEYIeta/,
?
? ]
OPTION 2 Heat p u m p wltn perfect neat matcn=ng
Select oot~on for removing excess heat ,~ the system
I
I
I
4
I
OPTION 3 Add)t=onoL C O L u m n overhead water
OPTION Add=t)ona[ heat pump water
OPTIOI'4 5 2nd stage feed
condenser
condenser
(see FIg. 3c)
(see Fig,
(see F)g.3b;
3ol I
preheoter
I
)
]
I
I I f Z~Tcoand Z~TFvare g,venthen est)mctte Tcc and TEv. and (COP),~, (COP) c
I f (TF) s g,ven, est,mate Tco and ~ v from (COPIo ar~d
Hence determ)ne
(COP) c
&Tea ana A ~
I Use appro~ote heat transfer coefficients to estimate heat exchange areas for all heat exchangers
. Size compressors
J
Fig. 5. (continued). Design algorithm for a heat pump assisted distillation system.
(2) The utility cost of conventional reboilers and heaters is given by
ArT (heaters) = QycH.
(35)
This equation is also used for the utility cost of any auxiliary heater which may be needed in a heat pump assisted system. (3) The utility cost of the compressor of the heat pump is given by
AuT (compressor) = WycL..
(36)
In these equations y is the operational period in h yr-~, Cc, cn and cE the unit costs of coolant, heating medium and primary power energy per kWh.
DESIGN A N D ECONOMIC
MODEL
A model was developed to incorporate the various points discussed above, using the relevant equations outlined. The main steps in the alogorithm evolved are given in Fig. 5. These can be summarised as follows. (i) Specify the distillation requirements. (ii) Estimate the distillation design parameters such as the number of trays. (iii) Estimate the sizes of all the main equipment items in the conventional design. (iv) Cost these main items and estimate the annual cost of utilities.
Heat pump assisted distillation systems--I
190
I Input data 70 variabLes ( Xo, XF, X e . . . . . )
/
CALL EDIST. Moss, heat balances and equilibrium caLcuLations. CoLumn size specification.
CALL DESIGN Estimate areas for all heat exchangers in the arrangement ( / = I, (/ = 2, (
conventional system) heat pump system) size compressor)
Use equations t9 and 20
I
CaLcuLate costs
]
~'Crc.,, ]rZlrc.,, ~Aur, /
CaLcuLate economic factors (PBP) and ZIMARG,N from equations 24 and 26
//
CALLEOOT
I
Output subroutine
I
I /
I ( stop ) Fig. 6. Main flowchart for the computer programme for assessing economics of heat pump assisted distillation systems.
(v) Select a suitable working fluid for the heat pump assisted distillation system. (vi) Perform a heat balance on this system and establish possible imbalance in heat load. (vii) Depending on the answers to step (vi), decide on the optional use of the excess heat, or the means of supplementing recycled heat. (viii) Assign a value to the one variable in the model to be investigated, having fixed all others. (ix) Estimate the sizes of all main equipment items in the system. (x) Cost these equipment items and estimate the annual cost of utilities. (xi) Estimate the payback period (PBP) for the additional capital investment on the heat pump assisted distillation system, over that for the conventional system. (xii) Assign a new value to the vairable being investigated and return to step (viii). Observe the effect on the payback period. A computer programme of the model has been written in Fortran 77 and consists of a main programme and three sub-programmes. The flowchart for the main programme is presented in Fig. 6. The economic evaluations are carried out by the main programme and the design calculations are performed by the sub-programmes EDIST and DESIGN. The third-sub-
200
T.O.
OMIDEYI el t//.
p r o g r a m m e E O U T is a n o u t p u t s u b r o u t i n e . In all, a b o u t seventy i n p u t variables are r e q u i r e d bv the p r o g r a m m e . T h e influence o f a n y o f these seventy v a r i a b l e s on the p a y b a c k p e r i o d can be investigated by v a r y i n g o n l y o n e at a time. T h e p a y b a c k p e r i o d will o b v i o u s l y be m o r e sensitive to s o m e v a r i a b l e s t h a n others. A careful e x a m i n a t i o n o f the seventy s h o u l d highlight t h o s e which are m o r e likely to be o f i m p o r t a n c e . A s m e n t i o n e d a b o v e , the choice o f the differential t e m p e r a t u r e driving forces in the m a i n h e a t e x c h a n g e r s will be m o s t i m p o r t a n t . A s in c o n v e n t i o n a l distillation, the o p e r a t i n g reflux ratio, the feed s t r e n g t h a n d c o l u m n c a p a c i t y m u s t be c o n s i d e r e d . F r o m an o p e r a t i o n a l viewpoint, the r u n n i n g time o f the e q u i p m e n t will certainly influence the p a y b a c k period. T h e unit costs o f utilities will v a r y f r o m o n e c o u n t r y to a n o t h e r a n d m u s t t h e r e f o r e be c o n s i d e r e d appropriately. Acknowledgement Authors wish to thank Professor F. A. Holland and Dr. S. Devotta for their valuable contribution towards the preparation of this paper.
REFERENCES 1. J. T. Mix, J. S. Dwec,k, R. C. Weinberg and R. C. Armstrong, Energy conservation in distillation. Chem. Engng Prog. 74, 49-55 (1978). 2. B. Linnhoff, H. Dunford and R. Smith, Heat integration of distillation columns into overall processes. Chem. Engng Sci. (in press). 3. H. R. Null, Heat pumps in distillation, Chem. Engng Prog. 72, 58-64 (1976). 4. B. D. Tyreus and W. L. Luyben, Two towers cheaper than one?, Hydrocarbon Processing 54, 93-96 ~1975). 5. F. A. Holland, F. A. Watson and S. Dcvotta, Thermodynamic Design Data for Heat Pump Sy~tems, Pergamon Press. Oxford (1982). 6. A. (3. Gutierrez, S. A. K. EI-Meniawy, F. A. Watson and F. A. Holland, Operating characteristics of a water-water heat pump system using RI2, Indian Chem. Engr 21, 16-26 (1979). 7. S. Devotta and P. J. Diggory, D~isa and theoretical aspects of heat pump systems, Applied Energy 11, 125-150 (1982). 8. A. W o i n ~ y and S. gmigeh~-dli,Relationships for calculation ofoptimal reflux in rectifying towers. Revta Chimie 32, 541-547 (1981). 9. P. Welsby and S. I~votta, Private communication. Department of Chemical and Gas Engincenng, University of Salford. 10. A. Guthric, Data and techniques for preliminary capital cost estimating, Chem. Engng. 76, 114-121 (1969). 11. R. S. Hall, J. Matlcy and K. J. MeNaughton, Current costs of process equipment, Chem~ Engng. 89, 80-116 (1982).