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Evaluation of hyperfiltration systems for sweet cheese whey. 2. Design studies and cost estimation
Journal of Food Engineering
4 (1985)
53-69
Evaluation of Hyperfiltration Systems for Sweet Cheese Whey. 2. Design Studies and Cost Estimation M.J.
van der Waal*
Wafilin BV, PO Box 5,777O AA Hardenberg,
The Netherlands
and J. Hiddink Netherlands
Institute
for Dairy Research, PO Box 20,67 10 BA Ede, The Netherlands ABSTRACT
Part 1 of this paper showed the technical feasibility of using hyperfiltra-
tion with tubular membranes for whey concentration in a recirculation system or a single-pass system; here an economic evaluation is carried out in which, after an optimization procedure, both systems are compared. Both systems result in approximately the same permeate cost for the cases investigated, but the single-pass system was limited in volume reduction because of pressuredrop. As the two systems are economically comparable, the ultimate choice between them will be based on general advantages and disadvantages, and on considerations specific to the application. Investment cost for a hyperfiltration installation for whey concentration appears to be proportional to (feed-ratelo’ ‘. Permeate cost is proportional to (feed-rate)-0’32, based on 80% availability, 20 h production time per day and 4 h cleaning time per day. Electrical energy required ranged from 3.4 to 6.3 kWh mm3permeate.
LIST OF SYMBOLS A A b
eff
ci
Constant used in general cost eqn (8) Constant used in eqn (7) for pump efficiency Exponent used in general cost eqn (8) Concentration of flow i (70 w/v)
* Present address: Twente University of Technology,
Enschede, The Netherlands.
53 of Food Engineering 0260-8774/85/$03.30 - 0 Elsevier Applied Science Publishers Ltd, England, 1985. Printed in Great Britain.
Journal
54
M. J. van der Waal, J. Hiddink
C
Constant in eqn (10) for estimation of permeate cost Internal diameter of membrane tube (m) Fanning friction factor I: F,, F2 Non-analytical functions, to be determined numerically, used in eqns (3f) and (4~) Constant in eqn (9) for estimation of investment cost I 1 Length of a (part of) membrane tube (m) P Pressure (Pa) AP Pressure drop (Pa) Volume flow-rate (m3 s-l or m3 11-r) Q r Exponent used in eqn (7) for pump efficiency Reynolds number Re T Temperature (“C) Linear velocity parallel to membranes inside membrane tube U (m s-l) Specific density (kg me3) P
1. INTRODUCTION In Part 1 (Hiddink and van der Waal, 1984) experiments are described in which sweet cheese whey was concentrated using hyperfiltration systems equipped with tubular membranes. For these experiments a one stage recirculation system and a single-pass (once-through) system, both provided by Wafilin BV, were used. A mathematical model, fitted to the experimental results, enabled local permeate fluxes at different operating conditions, such as pressure, flow-velocity and concentration to be predicted. In Part 2 an economic evaluation is carri.ed out, using the mathematical model, in which the two system types are optimized for minimum permeate cost.
2. METHOD OF CALCULATION OF PERMEATE PRODUCTION FOR THE RECIRCULATION AND SINGLE-PASS SYSTEMS When the local velocity inside the tubular membrane, and the local pressure and concentration are known, the permeate flux at that place
Evaluation
of hyperfiltration
systems for sweet cheese
whey ~ 2
55
be
4f. fpu2.;
AP=
(1)
in which: 4f = 0.3 16Re-0’25
(2)
for a smooth wall. In the recirculation system, part of the concentrate is fed back to the feed side of the membrane tube (Fig. 1). For such a system in steady state the following mass-balances can be written (subscripts correspond to numbers in Figs 1 and 2):
91 = Qe+Qs
(34
Q, +Qs
WI
Q2 =
Qs = Q4 + Qs Q&
= Q,c,
(3c) (since Q&‘, = 0)
(3d) (3e)
Q2C2 = Q,C, + QsG Qs = NC,,
Q3, T, P2, membrane
type)
(3f)
L
6
Fig. 1. A recirculation stage. In a recirculation system one or more stages are operated in series. Before the first stage, the feed is pressurized by a high pressure Pump.
56
M. J. van der Waal, J. Hiddink
For a given set of process variables, all concentrations, flows and pressures can be calculated by iteration, in which C3 is used as a parameter for the iteration. If more than one recirculation stage is included, the calculation is similar for each stage. For the single-pass system (no recirculation flow, Fig. 2), the mass balances are written as:
CW
Q, = Q4+ Qs Q4C4 = Q&i
(since Q6C6 = 0)
Q6 = F2(C,, Q,, T, f’,, membrane type)
(4b) (4c)
Here also, for a given set of process variables, all concentrations, flows and pressures can be calculated, in this case without iteration as no recirculation takes place.
3. BASIS AND METHOD OF ESTIMATION
OF INVESTMENT
COST
After an installation is designed, the investment and operating costs can be estimated for this particular installation. In the dairy industry all equipment should be hygienic. The modules containing the membranes and interconnecting bends are assumed to be made of PVC, other parts of stainless steel (AISI 304). The installation under consideration is an automatic one, involving flow and pressurecontrol, as well as a logic controller for start-up, shut-down, cleaning operations, etc. An essential part of the installation is the provision for cleaning, not only of the membranes, but also the plant.
Fig. 2. A single-pass section. In a single-pass system one or more sections are installed in series. Each section contains an adequate number of parallel modules, in order to meet flow requirements. Before the first section the feed is pressurized by a high pressure pump.
Evaluation of hyperfiltration
systems for sweet cheese whey ~ 2
51
Cost estimates for all items could be derived from the literature (e.g. Guthrie, 1970; WEBCI prijzenboekje, 1980). For this study, however, actual quotations from suppliers were used and for commercial reasons cannot be disclosed. As discrete quotations cannot be used in this optimization procedure, these quotations are fitted to a continuous function of the type: Cost is proportional
to (size or capacity)b
The proportionality constant and the exponent b were adjusted each subject. For this study the following components were costed:
(5) for
1. Modules. Modules containing seven membrane tubes of 14.4 mm internal diameter are used. The modules are installed in pairs, so that all flows can be fed and collected on the same side of the installation. In the recirculation system all tubes in a module are used in parallel. In the single-pass system all tubes are connected in series with help of special endcaps. 2. Membranes. Membranes of type WFR 950 are assumed. 3. Interconnecting PVC bends.
4. Stainless steel piping and frames. 5. Pumps and motors. It is assumed that plunger pumps are used for the high pressure feed. Within the feed rate range considered, 5-50 m3 h-‘, only three pump sizes are taken into account, with capacities of 5, 10 and 17 m3 h-‘. By installing more pumps in parallel if necessary, the required feed rate can be handled. In the case of parallel pumps, only one pump is assumed to be connected to a speed-controller. All recirculation pumps - identical for each stage - are assumed to be of the centrifugal type, as is the cleaning pump, to be mentioned below. In all cases, pump motors are included. 6. Pretreatment equipment. Since for a given feed flow rate the investment in pretreatment equipment is constant, for comparison and optimization purposes it is not included in the calculations. 7. Instrumentation. Included are the necessary measuring devices for pH, temperature, flow and pressures. 8. Controllers and all other electrical items. These appeared to be sensitive to the distance between the reverse-osmosis installation and the control panel, which was accordingly fixed arbitrarily at 10m.
58
M. J. van der Waai. J. Hiddink
9. Valves. 10. Cleaning equipment. This includes chemicals, dosing chemicals, spray 1 1. Engineering, assembling, overhead, for designing, assembling, start-up,
tanks for rinsing water, cleaning head unit and cleaning pump. etc. This includes all manpower etc.
All the above cost items determine the total investment mated installation. The price includes installation cost buildings, facilities, taxes and transportation are excluded.
4. METHOD OF ESTIMATION
for an autobut cost of
OF COST OF WATER REMOVAL
The cost of removal of 1 m3 permeate is determined by the cost of depreciation and interest, energy, chemicals, labour, maintenance and insurance. Cost of labour for supervision is not included in this study. 4.1.
Depreciation
and interest
A linear depreciation is assumed and an interest rate of 10% year-‘. In this study the depreciation time for the membranes was taken as 2 years, for the PVC parts 5 years and for the remainder of the installation 10 years. A production time of 20 h day-’ is assumed, reserving 4 h day-’ for rinsing, cleaning and sanitizing. 282 production days year-’ are assumed, the balance being holidays, weekend, maintenance, etc. 4.2 Energy An electricity price of Dfl 0.15 (kWh)-’ is assumed and a steam price of Dfl 30 ton-‘. The electrical energy consumption of the centrifugal pumps is calculated from: kW = flow-rate The efficiency
X
of centrifugal efficiency
differential
pressure G-efficiency
pumps is approximated = Aeff X (flow-rate)
in which for flow-rates <20 m3 h-l, Aeff = 0.438, rates of 20-200 m3 h-‘, Aeff = 0.396, r = 0.125.
(6)
by: (7) r = 0.091; for flow-
Evaluation of hyperfiltration
systems for sweet cheese whey -- 2
59
For the feedpump a constant efficiency of 80% was assumed, for the electric motors 90% and for the speedcontroller 85%; so for the controlled pump an overall efficiency of 61.2% was derived. 4.3 Chemicais, maintenance and insurance 4.3.1
Chemicals
Acid for pH-adjustment of the whey was included for operation at 30°C. When operating at a lower temperature of, e.g., 18OCor 10°C, no acid dosing is assumed in the calculations; however, in practice, this may sometimes be necessary, depending on the whey composition and degree of concentration. Cleaning chemicals are assumed to be used once a day for sanitizing and flux restoration. Included is enzymic cleaning and disinfection with active chlorine. Water cost for cleaning is not taken into account. 4.3.2. Maintenance 4% of the initial investment is allowed for maintenance 4.3.3.
cost per year.
Insurance
The insurance cost is taken to be 0.25% of the initial investment.
5. OPTIMIZATION PROCEDURE For any given set of design conditions it is possible to estimate the cost of permeate. The aim of this study was to determine the design conditions at which the permeate cost is a minimum, within constraints such as maximum pressure, minimum velocity or minimum permeate production. In this study, all stages in a recirculation system have the same module arrangement. The constraints are a maximum pressure of 4.5 MPa, and maximum and minimum flow-rates of 5 and 1 m s-l, respectively, in the tubular membranes which are of 14.4 mm internal diameter. With certain design conditions it is possible that some constraint would be breached. In that event an imaginary cost is added to the calculated one, the extra
M. J. van der Waal, J. Hiddink
60
cost being greater the greater the departure outside the constraint. This forces the optimization procedure to adjust the conditions so that all constraints are obeyed. In this study a hierarchical optimization procedure is used. First, the number of stages is fixed as a whole number. For this number of stages, the variables - flow velocity, feed pressure, number of modules in parallel and number in series -~~are simultaneously varied with the help of the modified simplex procedure known as the Nelder-Mead procedure (Nelder and Mead, 1965). Here the number of modules is temporarily considered as being non-integral. This procedure is carried out for various numbers of stages or sections. For the most promising number of stages or sections the number of modules is then taken as being an integer and, starting from the optimum of the previous step, the optimum module arrangement is determined. Finally for the best module arrangement, the optimum pressure and flow velocity are determined more precisely, leading to the final result. An illustration of the intermediate results of this procedure is given in Table 1.
6. RESULTS
OF DESIGN STUDIES AND OF COST CALCULATIONS
Calculations were carried out for installations with feed capacities of 5, 10, 25 and 50 m3 h-l concentrating to volume reductions of 33, 50, 66, 75 and SO%, at temperatures of 10, 18 and 30°C. The layout of the automatic installation was the simplest possible: - no booster pump to increase the pressure at high concentrations the single-pass system; -- identical stages in the recirculation system; ._. all stages or sections being cleaned at the same time.
in
6.1 Design studies In the design studies the cost of water removal was minimized by optimizing module arrangement, applied pressure and flow velocity. In Table 2 results are given at a volume reduction of 50% for both systems,
Evaluation of hyperfiltration systems for sweet cheese whey - 2
61
TABLE 1 Example of Intermediate Results in the Optimization Procedure (Recirculation System: Feed-rate = 10 m3 h-‘, Process Temperature = 30°C, Volume Reduction = 50%) Step one: non-integral number of modules; search for optimum number of stages. Number of stages
(ml
Number of tubes in parallel in a stage
176.64 128.76 112.20
32.13 20.30 14.98
Tube length per stage
1 2 3
Permeate cost (Dfl m-3)
7.475 7,255 7.26 1
Step nvo: whole number of modules; search for optimum module arrangement in
the stages. Number of stages
Tube length per stage (m)
2 2 2 2 2
132 144 120 132 132
Number of tubes in parallel in a stage
Permeate cost (Dfl me3)
21 21 21 28 14
7.362 7.53 1 7.369 8.175 13.100”
a Insufficient permeate production within the constraints. Step three: continued optimization with optimum module arrangement. Number of stages
Tube length per stage (ml
2
and at 75% volume pressure-drop it was a booster pump for a tendency towards permeate fluxes, so
132
Number of tubes in parallel in a stage
21
Permeate cost (Dfl mW3)
7.277
reduction for a recirculation system. Because of not possible to design a single-pass system without a volume reduction of 75%. This table indicates low flow-velocities. This results in relatively low a larger membrane area is required than with high
M. J. van der Waal, J. Hiddink
62
Comparison
TABLE 2 of a Recirculation System and a Single-pass System, Optimized a Feed-rate of 10 m3 h-’ and a Process Temperature of 30°C Recirculation sysrem
Recirculation sys tern Estimated contributions to permeate Volume reduction (%) Number of stages/sections Tube length/number of tubes parallel
cost: 50 7
75 5
however,
the resulting
50
3
96111
4.3 1.0 19.9
4.3 1.3 16.4
lS’/lZ x7/9 8416 3.7 1.3 19.1
4.4
4.3
4.0
0.64
0.59
1.79 __
1.96 3.06 0.84 1.03 0.06 I.57
Cost estimate (DfI rnM3permeate, January 1981 prices): Energy 066 Depreciation 1.90 membranes and modules other parts 2.87 Steam and chemicals 0.82 Maintenance 0.98 Insurance 0.06 Total permeate cost 7.28 -_
velocities;
Single-pass system
137/71
Average pressure (MPa) Average flow velocity (m s-l) Average permeate flux (litre mm2h-‘) Energy consumption (kWh mm3 permeate)
increase
balanced by decreased energy cost. In all calculations it was assumed membranes occurs during long-term
that
7.78 __
0.86 0.86 0.05 6.98
in depreciation no progressive
for
cost is counterfouling
of the
operation at the optimized flow velocity. If this condition is not realized, a higher velocity may be necessary to increase the mass-transfer at the membrane wall. The corresponding design change would result in a higher cost for energy, but lower capital investment.
Evaluation of hyperfiltration
6.2.
63
Energy consumption
Energy ~ -
systems for sweet cheese whey - 2
consumed
by this process is used for:
pressurizing the feed stream; circulation of the pressurized flow in the recirculation system; operation of the cleaning pump; heating the enzymic cleaning solution to a temperature of about 30°C.
As the cost of the steam required appears to be only about 2%’ of the total energy cost, only the cost of electrical energy for the pumps will be considered here. The relative contribution of energy cost to the permeate cost is surprisingly low: in all calculations the contribution did not exceed 12.5%, for both the single-pass and the recirculation system (see Table 2). In a series of calculations for single-pass systems, the electrical energy consumed ranged from 3.7 to 4.3 kWh rnw3 permeate at 50% volume reduction for all temperatures and capacities considered. At 33% volume reduction this figure is higher, as more feed must be pumped to produce 1 m3 permeate. In a series of calculations for recirculation systems, the electrical energy consumed ranged from 3.4 to 6.3 kWh me3 permeate at volume reductions ranging from 33 to 80%. Taking only 66% volume reduction into account, the energy ranged from 3.4 to 5.0 kWh me3 permeate. From these figures it can be concluded that there is little difference in energy consumption between the single-pass and the recirculation systems.
6.3 Influence
of temperature
From Fig. 3 it can be seen that - as expected - the permeate cost increases with decreasing temperature. This is caused by the lower membrane permeability and smaller diffusion coefficients for the dissolved solids, requiring an increased membrane area. Not included here are heat-exchangers to heat the whey to the desired temperature, or the necessary thermal energy.
64
M. J. van der Waal, J. Hiddink
0
A”
1
1
I
10
20
3a temperature
(OC)
Fig. 3. Cost of water removal as a function of the process temperature for a recirculation system (0) (66% volume reduction) and a single-pass system (H) (50% volume reduction). (Whey feed-rate = 10 m3 h-l.)
6.4
Influence of degree of volume reduction
For a given whey feed-rate, a part of the installation, such as the feed pump, part of the piping and instrumentation, is independent of volume reduction, as is the energy required to pressurize the feed flow; so the permeate cost decreases with increasing volume reduction at low volume reductions (see Fig. 4). At high volume reduction, however, because of increasing osmotic pressure and pressure-drop, a more-than-proportional membrane area must be added for the required permeate production. In addition more energy will be consumed to circulate the pressurized flow and the cleaning solution. This causes the unit permeate cost to increase with increasing volume reduction. At 30°C and a whey feed-rate of 10 m3 h-’ these influences produce a minimum estimated cost at about 50% volume reduction for the single-pass system and about 66% volume reduction for the recirculation system (see Fig. 4). Because of pressure-drop it was not possible to design a single-pass system for a volume reduction of 66%, within the maximum pressure and minimum flow-rate limits.
Evaluation of hyperfiltration
systems for sweet cheese whey -- 2
65
10
2-
I 30
0 0
I I 50 80 10 volume reduction I%
Fig. 4. Estimated permeate cost price as a function of volume reduction for a recirculation system(m) and a single-pass system (0). (Whey feed-rate = 10 m3 h-‘, process temperature = 3022.)
Inclusion of an extra booster pump would reduce the basic advantage of a single-pass system of being simple and straightforward compared to the recirculation system. As the flexibility of operation of a recirculation system far exceeds that of a single-pass system, and the investment as well as the permeate cost are not greatly different, it was not considered useful to include a booster pump in the single-pass system; so calculations for that type of installation were not made. It should be noted here that the results take into account the hyperfiltration installation as an isolated unit. When whey is transported by vehicle or pipeline after concentration, or if the concentrated whey is to be further concentrated by evaporation, the figures for the overall optimum may change. 6.5 Influence of feed capacity It is widely found that for complete ment cost varies with capacity as:
installations
Cost = A. Capacityb
or components,
invest(8)
For many installations or components the value of b is around 0.6, ranging from 0.35 to O-9 (Gallagher, 1970; Holland et al., 1979). The values of A and b can vary with capacity.
M. J. van der Waal, J. Hiddink
66
The same form of cost equation was used for estimating costs of different parts of the hyperfiltration installation, as given above. For the installations considered as a whole, the same relation holds, as can be concluded from Figs 5 and 6. Very often it is assumed that for membrane installations b = 1; however, from Figs 5 and 6 it can be seen that in this design study investment and water removal costs can be estimated roughly from: Investment Permeate
= I. (feed rate)“’
(9)
cost = c’. (feed rate)-0’32
(10)
In an earlier publication (van der Waal et al., 1980), concerning reverse-osmosis installations to be used for greenhouse irrigation, it was concluded that the investment as a function of capacity could be estimated from b = 0.76. The corresponding unit permeate cost could be estimated from b = -0.18. In this case the design was based on
6-
z
2
z
1.5 i E E 0.8 g 1
0.6 ‘=
2 -
1
Fig. 5.
-
1 2
I 4
I 6
I I 8 10
I 20
I I 40 60 feed ( m3ihl
0.2
100
Effect of capacity on investment cost and cost of permeate for a recirculation system. (Process temperature = 30°C, volume reduction = 66%)
Evaluation
of hyperfiltration
systems for sweet cheese
whey - 2
61
6
2 1.5
z
z z
z
1
“u E E” 5
0.8
.;
0.6 0.4
0.2
1
I
I
1
I
2
4
6
8 10
I
I
I
1
20
40
60
feed
Fig. 6.
100
(m3,i,)
Effect of capacity on investment cost and cost of permeate for a singlepass system. (Process temperature = 30°C, volume reduction = 50%. j
other requirements and circumstances. No limiting flux (caused by gel formation) and a lower osmotic pressure of the feed water (about 70 kPa compared to about 500 kPa for whey) were assumed for the greenhouse installations. Further, the permeate quality was required to be better than some fixed minimum, but the feed flow-rate was not fixed. Both studies show that the required investment is less than proportional to the capacity, and that the permeate cost decreases with increasing capacity as can be seen from the values of the exponent b. The same conclusion can be made from analysis of the paper of Larson and Leitner (1979) who made a study of desalination units of permeate capacities 150 m3 h-r and larger, resulting in exponents of 0.8 for investment and -0.1 1 for permeate cost, as well as from the paper of Dejmek and Engwall (1980), who found an exponent b of 0.72 for investment in ultrafiltration units in the dairy industry.
68
M. J. van der Waal, J. Hiddink
7. COMPARISON OF SINGLE-PASS SYSTEMS AND RECIRCULATION SYSTEMS Some general differences
between
the two systems are given below:
(i) single-pass system: only one pump is operating during permeate production, resulting in a simple installation, especially for smaller volume reductions; ~ because of the high pressure-drop, the membranes at the concentrated end are not as effectively used as those at the feed end; ~~ variations in feed flow-rate or concentration ratio can have a significant effect on the pressure-drop and internal flow-rate. An almost constant feed condition is a necessity; - reduced membrane permeability caused by fouling or scaling results in an increased pressure-drop, so either excessive power must be supplied or the membranes at the concentrated end become ineffective. In the latter case the required volume reduction cannot be maintained. (ii) recirculation system: at least two pumps are required during normal operation, often more, so that the installation is more complex. -- with the proper recirculation, the membranes at the concentrated end are used as effectively as those at the feed end, because all stages operate at the same pressure, even when it is necessary to operate at different flow velocities from the design conditions. variations in feed flow-rate and concentration ratio can be tolerated without affecting process conditions substantially. ~ reduction of membrane permeability caused by fouling or scaling does not result in a severely increased pressure-drop compared to the system pressure, i.e. all membranes, even at the concentrate end, will remain effective. Comparing the cost of permeate removal in both installations, it must be concluded that both installation types result in almost the same figures, as seen in Table 2, in which three examples are given, with a partial breakdown of their costs,
Evaluation of hyperfiltration
systems for sweet cheese whey - 2
The decision on which installation be based not only on cost comparison as flexibility of operation.
69
should be installed will therefore but on other considerations such
ACKNOWLEDGEMENTS This study was made possible by a grant for a research project from the Ministry of Economic Affairs of The Netherlands, and was carried out with the cooperation of Wafilin BV of Hardenberg, NIZO in Ede and the Twente University of Technology at Enschede, all in The Netherlands. Discussions with H. J. Fontein of the Twente University of Technology on the optimization procedure were very useful.
REFERENCES Dejmek, P. and Engwall, H. (1980). System options and costs in dairy ultrafiltration. Desalination, 35, 397-400. Gallagher, J. T. (1970). Rapid estimation of plant costs. In: Modern Cost-Engineering Techniques, ed. H. Popper, McGraw-Hill, New York, pp. 3-10. Guthrie, K. M. (1970). Capital cost estimating. In: Modern Cost-Engineering Techniques, ed. H. Popper, McGraw-Hill, New York, pp. 80-106. Hiddink, J. and van der Waal, M. J. (1984). Evaluation of hyperfiltration systems for sweet cheese whey. 1. Experimental results with a single-pass and a recirculation system. Journal of Food Engineering, 3,225-39. Holland, F. A., Watson, F. A. and Wilkinson, J. K. (1979). How to estimate capital costs. In: Modern Cost Engineering: Methods and Data, McGraw-Hill, New York. Larson, T. J. and Leitner, G. (1979). Desalting seawater and brackish water: a cost update. Desalination, 30, 525-39. Nelder, J. A. and Mead, R. (1965). A Simplex method for function minimization. Computer J., 7,308-13.
van der Waal, M. J., Logeman, F. P. and Fontein, H. J. (1980). Evaluation of tubular membrane systems. Proc. 7th Int. Symp. on Fresh Water from the Sea, Amsterdam, 23-26 September. WEBCI prijzenboekje. (1980). Ed. Dutch Association of Cost Engineers. Stichting Nederlandse apparaten voor de Procesindustrie, December.
4 (1985)
53-69
Evaluation of Hyperfiltration Systems for Sweet Cheese Whey. 2. Design Studies and Cost Estimation M.J.
van der Waal*
Wafilin BV, PO Box 5,777O AA Hardenberg,
The Netherlands
and J. Hiddink Netherlands
Institute
for Dairy Research, PO Box 20,67 10 BA Ede, The Netherlands ABSTRACT
Part 1 of this paper showed the technical feasibility of using hyperfiltra-
tion with tubular membranes for whey concentration in a recirculation system or a single-pass system; here an economic evaluation is carried out in which, after an optimization procedure, both systems are compared. Both systems result in approximately the same permeate cost for the cases investigated, but the single-pass system was limited in volume reduction because of pressuredrop. As the two systems are economically comparable, the ultimate choice between them will be based on general advantages and disadvantages, and on considerations specific to the application. Investment cost for a hyperfiltration installation for whey concentration appears to be proportional to (feed-ratelo’ ‘. Permeate cost is proportional to (feed-rate)-0’32, based on 80% availability, 20 h production time per day and 4 h cleaning time per day. Electrical energy required ranged from 3.4 to 6.3 kWh mm3permeate.
LIST OF SYMBOLS A A b
eff
ci
Constant used in general cost eqn (8) Constant used in eqn (7) for pump efficiency Exponent used in general cost eqn (8) Concentration of flow i (70 w/v)
* Present address: Twente University of Technology,
Enschede, The Netherlands.
53 of Food Engineering 0260-8774/85/$03.30 - 0 Elsevier Applied Science Publishers Ltd, England, 1985. Printed in Great Britain.
Journal
54
M. J. van der Waal, J. Hiddink
C
Constant in eqn (10) for estimation of permeate cost Internal diameter of membrane tube (m) Fanning friction factor I: F,, F2 Non-analytical functions, to be determined numerically, used in eqns (3f) and (4~) Constant in eqn (9) for estimation of investment cost I 1 Length of a (part of) membrane tube (m) P Pressure (Pa) AP Pressure drop (Pa) Volume flow-rate (m3 s-l or m3 11-r) Q r Exponent used in eqn (7) for pump efficiency Reynolds number Re T Temperature (“C) Linear velocity parallel to membranes inside membrane tube U (m s-l) Specific density (kg me3) P
1. INTRODUCTION In Part 1 (Hiddink and van der Waal, 1984) experiments are described in which sweet cheese whey was concentrated using hyperfiltration systems equipped with tubular membranes. For these experiments a one stage recirculation system and a single-pass (once-through) system, both provided by Wafilin BV, were used. A mathematical model, fitted to the experimental results, enabled local permeate fluxes at different operating conditions, such as pressure, flow-velocity and concentration to be predicted. In Part 2 an economic evaluation is carri.ed out, using the mathematical model, in which the two system types are optimized for minimum permeate cost.
2. METHOD OF CALCULATION OF PERMEATE PRODUCTION FOR THE RECIRCULATION AND SINGLE-PASS SYSTEMS When the local velocity inside the tubular membrane, and the local pressure and concentration are known, the permeate flux at that place
Evaluation
of hyperfiltration
systems for sweet cheese
whey ~ 2
55
be
4f. fpu2.;
AP=
(1)
in which: 4f = 0.3 16Re-0’25
(2)
for a smooth wall. In the recirculation system, part of the concentrate is fed back to the feed side of the membrane tube (Fig. 1). For such a system in steady state the following mass-balances can be written (subscripts correspond to numbers in Figs 1 and 2):
91 = Qe+Qs
(34
Q, +Qs
WI
Q2 =
Qs = Q4 + Qs Q&
= Q,c,
(3c) (since Q&‘, = 0)
(3d) (3e)
Q2C2 = Q,C, + QsG Qs = NC,,
Q3, T, P2, membrane
type)
(3f)
L
6
Fig. 1. A recirculation stage. In a recirculation system one or more stages are operated in series. Before the first stage, the feed is pressurized by a high pressure Pump.
56
M. J. van der Waal, J. Hiddink
For a given set of process variables, all concentrations, flows and pressures can be calculated by iteration, in which C3 is used as a parameter for the iteration. If more than one recirculation stage is included, the calculation is similar for each stage. For the single-pass system (no recirculation flow, Fig. 2), the mass balances are written as:
CW
Q, = Q4+ Qs Q4C4 = Q&i
(since Q6C6 = 0)
Q6 = F2(C,, Q,, T, f’,, membrane type)
(4b) (4c)
Here also, for a given set of process variables, all concentrations, flows and pressures can be calculated, in this case without iteration as no recirculation takes place.
3. BASIS AND METHOD OF ESTIMATION
OF INVESTMENT
COST
After an installation is designed, the investment and operating costs can be estimated for this particular installation. In the dairy industry all equipment should be hygienic. The modules containing the membranes and interconnecting bends are assumed to be made of PVC, other parts of stainless steel (AISI 304). The installation under consideration is an automatic one, involving flow and pressurecontrol, as well as a logic controller for start-up, shut-down, cleaning operations, etc. An essential part of the installation is the provision for cleaning, not only of the membranes, but also the plant.
Fig. 2. A single-pass section. In a single-pass system one or more sections are installed in series. Each section contains an adequate number of parallel modules, in order to meet flow requirements. Before the first section the feed is pressurized by a high pressure pump.
Evaluation of hyperfiltration
systems for sweet cheese whey ~ 2
51
Cost estimates for all items could be derived from the literature (e.g. Guthrie, 1970; WEBCI prijzenboekje, 1980). For this study, however, actual quotations from suppliers were used and for commercial reasons cannot be disclosed. As discrete quotations cannot be used in this optimization procedure, these quotations are fitted to a continuous function of the type: Cost is proportional
to (size or capacity)b
The proportionality constant and the exponent b were adjusted each subject. For this study the following components were costed:
(5) for
1. Modules. Modules containing seven membrane tubes of 14.4 mm internal diameter are used. The modules are installed in pairs, so that all flows can be fed and collected on the same side of the installation. In the recirculation system all tubes in a module are used in parallel. In the single-pass system all tubes are connected in series with help of special endcaps. 2. Membranes. Membranes of type WFR 950 are assumed. 3. Interconnecting PVC bends.
4. Stainless steel piping and frames. 5. Pumps and motors. It is assumed that plunger pumps are used for the high pressure feed. Within the feed rate range considered, 5-50 m3 h-‘, only three pump sizes are taken into account, with capacities of 5, 10 and 17 m3 h-‘. By installing more pumps in parallel if necessary, the required feed rate can be handled. In the case of parallel pumps, only one pump is assumed to be connected to a speed-controller. All recirculation pumps - identical for each stage - are assumed to be of the centrifugal type, as is the cleaning pump, to be mentioned below. In all cases, pump motors are included. 6. Pretreatment equipment. Since for a given feed flow rate the investment in pretreatment equipment is constant, for comparison and optimization purposes it is not included in the calculations. 7. Instrumentation. Included are the necessary measuring devices for pH, temperature, flow and pressures. 8. Controllers and all other electrical items. These appeared to be sensitive to the distance between the reverse-osmosis installation and the control panel, which was accordingly fixed arbitrarily at 10m.
58
M. J. van der Waai. J. Hiddink
9. Valves. 10. Cleaning equipment. This includes chemicals, dosing chemicals, spray 1 1. Engineering, assembling, overhead, for designing, assembling, start-up,
tanks for rinsing water, cleaning head unit and cleaning pump. etc. This includes all manpower etc.
All the above cost items determine the total investment mated installation. The price includes installation cost buildings, facilities, taxes and transportation are excluded.
4. METHOD OF ESTIMATION
for an autobut cost of
OF COST OF WATER REMOVAL
The cost of removal of 1 m3 permeate is determined by the cost of depreciation and interest, energy, chemicals, labour, maintenance and insurance. Cost of labour for supervision is not included in this study. 4.1.
Depreciation
and interest
A linear depreciation is assumed and an interest rate of 10% year-‘. In this study the depreciation time for the membranes was taken as 2 years, for the PVC parts 5 years and for the remainder of the installation 10 years. A production time of 20 h day-’ is assumed, reserving 4 h day-’ for rinsing, cleaning and sanitizing. 282 production days year-’ are assumed, the balance being holidays, weekend, maintenance, etc. 4.2 Energy An electricity price of Dfl 0.15 (kWh)-’ is assumed and a steam price of Dfl 30 ton-‘. The electrical energy consumption of the centrifugal pumps is calculated from: kW = flow-rate The efficiency
X
of centrifugal efficiency
differential
pressure G-efficiency
pumps is approximated = Aeff X (flow-rate)
in which for flow-rates <20 m3 h-l, Aeff = 0.438, rates of 20-200 m3 h-‘, Aeff = 0.396, r = 0.125.
(6)
by: (7) r = 0.091; for flow-
Evaluation of hyperfiltration
systems for sweet cheese whey -- 2
59
For the feedpump a constant efficiency of 80% was assumed, for the electric motors 90% and for the speedcontroller 85%; so for the controlled pump an overall efficiency of 61.2% was derived. 4.3 Chemicais, maintenance and insurance 4.3.1
Chemicals
Acid for pH-adjustment of the whey was included for operation at 30°C. When operating at a lower temperature of, e.g., 18OCor 10°C, no acid dosing is assumed in the calculations; however, in practice, this may sometimes be necessary, depending on the whey composition and degree of concentration. Cleaning chemicals are assumed to be used once a day for sanitizing and flux restoration. Included is enzymic cleaning and disinfection with active chlorine. Water cost for cleaning is not taken into account. 4.3.2. Maintenance 4% of the initial investment is allowed for maintenance 4.3.3.
cost per year.
Insurance
The insurance cost is taken to be 0.25% of the initial investment.
5. OPTIMIZATION PROCEDURE For any given set of design conditions it is possible to estimate the cost of permeate. The aim of this study was to determine the design conditions at which the permeate cost is a minimum, within constraints such as maximum pressure, minimum velocity or minimum permeate production. In this study, all stages in a recirculation system have the same module arrangement. The constraints are a maximum pressure of 4.5 MPa, and maximum and minimum flow-rates of 5 and 1 m s-l, respectively, in the tubular membranes which are of 14.4 mm internal diameter. With certain design conditions it is possible that some constraint would be breached. In that event an imaginary cost is added to the calculated one, the extra
M. J. van der Waal, J. Hiddink
60
cost being greater the greater the departure outside the constraint. This forces the optimization procedure to adjust the conditions so that all constraints are obeyed. In this study a hierarchical optimization procedure is used. First, the number of stages is fixed as a whole number. For this number of stages, the variables - flow velocity, feed pressure, number of modules in parallel and number in series -~~are simultaneously varied with the help of the modified simplex procedure known as the Nelder-Mead procedure (Nelder and Mead, 1965). Here the number of modules is temporarily considered as being non-integral. This procedure is carried out for various numbers of stages or sections. For the most promising number of stages or sections the number of modules is then taken as being an integer and, starting from the optimum of the previous step, the optimum module arrangement is determined. Finally for the best module arrangement, the optimum pressure and flow velocity are determined more precisely, leading to the final result. An illustration of the intermediate results of this procedure is given in Table 1.
6. RESULTS
OF DESIGN STUDIES AND OF COST CALCULATIONS
Calculations were carried out for installations with feed capacities of 5, 10, 25 and 50 m3 h-l concentrating to volume reductions of 33, 50, 66, 75 and SO%, at temperatures of 10, 18 and 30°C. The layout of the automatic installation was the simplest possible: - no booster pump to increase the pressure at high concentrations the single-pass system; -- identical stages in the recirculation system; ._. all stages or sections being cleaned at the same time.
in
6.1 Design studies In the design studies the cost of water removal was minimized by optimizing module arrangement, applied pressure and flow velocity. In Table 2 results are given at a volume reduction of 50% for both systems,
Evaluation of hyperfiltration systems for sweet cheese whey - 2
61
TABLE 1 Example of Intermediate Results in the Optimization Procedure (Recirculation System: Feed-rate = 10 m3 h-‘, Process Temperature = 30°C, Volume Reduction = 50%) Step one: non-integral number of modules; search for optimum number of stages. Number of stages
(ml
Number of tubes in parallel in a stage
176.64 128.76 112.20
32.13 20.30 14.98
Tube length per stage
1 2 3
Permeate cost (Dfl m-3)
7.475 7,255 7.26 1
Step nvo: whole number of modules; search for optimum module arrangement in
the stages. Number of stages
Tube length per stage (m)
2 2 2 2 2
132 144 120 132 132
Number of tubes in parallel in a stage
Permeate cost (Dfl me3)
21 21 21 28 14
7.362 7.53 1 7.369 8.175 13.100”
a Insufficient permeate production within the constraints. Step three: continued optimization with optimum module arrangement. Number of stages
Tube length per stage (ml
2
and at 75% volume pressure-drop it was a booster pump for a tendency towards permeate fluxes, so
132
Number of tubes in parallel in a stage
21
Permeate cost (Dfl mW3)
7.277
reduction for a recirculation system. Because of not possible to design a single-pass system without a volume reduction of 75%. This table indicates low flow-velocities. This results in relatively low a larger membrane area is required than with high
M. J. van der Waal, J. Hiddink
62
Comparison
TABLE 2 of a Recirculation System and a Single-pass System, Optimized a Feed-rate of 10 m3 h-’ and a Process Temperature of 30°C Recirculation sysrem
Recirculation sys tern Estimated contributions to permeate Volume reduction (%) Number of stages/sections Tube length/number of tubes parallel
cost: 50 7
75 5
however,
the resulting
50
3
96111
4.3 1.0 19.9
4.3 1.3 16.4
lS’/lZ x7/9 8416 3.7 1.3 19.1
4.4
4.3
4.0
0.64
0.59
1.79 __
1.96 3.06 0.84 1.03 0.06 I.57
Cost estimate (DfI rnM3permeate, January 1981 prices): Energy 066 Depreciation 1.90 membranes and modules other parts 2.87 Steam and chemicals 0.82 Maintenance 0.98 Insurance 0.06 Total permeate cost 7.28 -_
velocities;
Single-pass system
137/71
Average pressure (MPa) Average flow velocity (m s-l) Average permeate flux (litre mm2h-‘) Energy consumption (kWh mm3 permeate)
increase
balanced by decreased energy cost. In all calculations it was assumed membranes occurs during long-term
that
7.78 __
0.86 0.86 0.05 6.98
in depreciation no progressive
for
cost is counterfouling
of the
operation at the optimized flow velocity. If this condition is not realized, a higher velocity may be necessary to increase the mass-transfer at the membrane wall. The corresponding design change would result in a higher cost for energy, but lower capital investment.
Evaluation of hyperfiltration
6.2.
63
Energy consumption
Energy ~ -
systems for sweet cheese whey - 2
consumed
by this process is used for:
pressurizing the feed stream; circulation of the pressurized flow in the recirculation system; operation of the cleaning pump; heating the enzymic cleaning solution to a temperature of about 30°C.
As the cost of the steam required appears to be only about 2%’ of the total energy cost, only the cost of electrical energy for the pumps will be considered here. The relative contribution of energy cost to the permeate cost is surprisingly low: in all calculations the contribution did not exceed 12.5%, for both the single-pass and the recirculation system (see Table 2). In a series of calculations for single-pass systems, the electrical energy consumed ranged from 3.7 to 4.3 kWh rnw3 permeate at 50% volume reduction for all temperatures and capacities considered. At 33% volume reduction this figure is higher, as more feed must be pumped to produce 1 m3 permeate. In a series of calculations for recirculation systems, the electrical energy consumed ranged from 3.4 to 6.3 kWh me3 permeate at volume reductions ranging from 33 to 80%. Taking only 66% volume reduction into account, the energy ranged from 3.4 to 5.0 kWh me3 permeate. From these figures it can be concluded that there is little difference in energy consumption between the single-pass and the recirculation systems.
6.3 Influence
of temperature
From Fig. 3 it can be seen that - as expected - the permeate cost increases with decreasing temperature. This is caused by the lower membrane permeability and smaller diffusion coefficients for the dissolved solids, requiring an increased membrane area. Not included here are heat-exchangers to heat the whey to the desired temperature, or the necessary thermal energy.
64
M. J. van der Waal, J. Hiddink
0
A”
1
1
I
10
20
3a temperature
(OC)
Fig. 3. Cost of water removal as a function of the process temperature for a recirculation system (0) (66% volume reduction) and a single-pass system (H) (50% volume reduction). (Whey feed-rate = 10 m3 h-l.)
6.4
Influence of degree of volume reduction
For a given whey feed-rate, a part of the installation, such as the feed pump, part of the piping and instrumentation, is independent of volume reduction, as is the energy required to pressurize the feed flow; so the permeate cost decreases with increasing volume reduction at low volume reductions (see Fig. 4). At high volume reduction, however, because of increasing osmotic pressure and pressure-drop, a more-than-proportional membrane area must be added for the required permeate production. In addition more energy will be consumed to circulate the pressurized flow and the cleaning solution. This causes the unit permeate cost to increase with increasing volume reduction. At 30°C and a whey feed-rate of 10 m3 h-’ these influences produce a minimum estimated cost at about 50% volume reduction for the single-pass system and about 66% volume reduction for the recirculation system (see Fig. 4). Because of pressure-drop it was not possible to design a single-pass system for a volume reduction of 66%, within the maximum pressure and minimum flow-rate limits.
Evaluation of hyperfiltration
systems for sweet cheese whey -- 2
65
10
2-
I 30
0 0
I I 50 80 10 volume reduction I%
Fig. 4. Estimated permeate cost price as a function of volume reduction for a recirculation system(m) and a single-pass system (0). (Whey feed-rate = 10 m3 h-‘, process temperature = 3022.)
Inclusion of an extra booster pump would reduce the basic advantage of a single-pass system of being simple and straightforward compared to the recirculation system. As the flexibility of operation of a recirculation system far exceeds that of a single-pass system, and the investment as well as the permeate cost are not greatly different, it was not considered useful to include a booster pump in the single-pass system; so calculations for that type of installation were not made. It should be noted here that the results take into account the hyperfiltration installation as an isolated unit. When whey is transported by vehicle or pipeline after concentration, or if the concentrated whey is to be further concentrated by evaporation, the figures for the overall optimum may change. 6.5 Influence of feed capacity It is widely found that for complete ment cost varies with capacity as:
installations
Cost = A. Capacityb
or components,
invest(8)
For many installations or components the value of b is around 0.6, ranging from 0.35 to O-9 (Gallagher, 1970; Holland et al., 1979). The values of A and b can vary with capacity.
M. J. van der Waal, J. Hiddink
66
The same form of cost equation was used for estimating costs of different parts of the hyperfiltration installation, as given above. For the installations considered as a whole, the same relation holds, as can be concluded from Figs 5 and 6. Very often it is assumed that for membrane installations b = 1; however, from Figs 5 and 6 it can be seen that in this design study investment and water removal costs can be estimated roughly from: Investment Permeate
= I. (feed rate)“’
(9)
cost = c’. (feed rate)-0’32
(10)
In an earlier publication (van der Waal et al., 1980), concerning reverse-osmosis installations to be used for greenhouse irrigation, it was concluded that the investment as a function of capacity could be estimated from b = 0.76. The corresponding unit permeate cost could be estimated from b = -0.18. In this case the design was based on
6-
z
2
z
1.5 i E E 0.8 g 1
0.6 ‘=
2 -
1
Fig. 5.
-
1 2
I 4
I 6
I I 8 10
I 20
I I 40 60 feed ( m3ihl
0.2
100
Effect of capacity on investment cost and cost of permeate for a recirculation system. (Process temperature = 30°C, volume reduction = 66%)
Evaluation
of hyperfiltration
systems for sweet cheese
whey - 2
61
6
2 1.5
z
z z
z
1
“u E E” 5
0.8
.;
0.6 0.4
0.2
1
I
I
1
I
2
4
6
8 10
I
I
I
1
20
40
60
feed
Fig. 6.
100
(m3,i,)
Effect of capacity on investment cost and cost of permeate for a singlepass system. (Process temperature = 30°C, volume reduction = 50%. j
other requirements and circumstances. No limiting flux (caused by gel formation) and a lower osmotic pressure of the feed water (about 70 kPa compared to about 500 kPa for whey) were assumed for the greenhouse installations. Further, the permeate quality was required to be better than some fixed minimum, but the feed flow-rate was not fixed. Both studies show that the required investment is less than proportional to the capacity, and that the permeate cost decreases with increasing capacity as can be seen from the values of the exponent b. The same conclusion can be made from analysis of the paper of Larson and Leitner (1979) who made a study of desalination units of permeate capacities 150 m3 h-r and larger, resulting in exponents of 0.8 for investment and -0.1 1 for permeate cost, as well as from the paper of Dejmek and Engwall (1980), who found an exponent b of 0.72 for investment in ultrafiltration units in the dairy industry.
68
M. J. van der Waal, J. Hiddink
7. COMPARISON OF SINGLE-PASS SYSTEMS AND RECIRCULATION SYSTEMS Some general differences
between
the two systems are given below:
(i) single-pass system: only one pump is operating during permeate production, resulting in a simple installation, especially for smaller volume reductions; ~ because of the high pressure-drop, the membranes at the concentrated end are not as effectively used as those at the feed end; ~~ variations in feed flow-rate or concentration ratio can have a significant effect on the pressure-drop and internal flow-rate. An almost constant feed condition is a necessity; - reduced membrane permeability caused by fouling or scaling results in an increased pressure-drop, so either excessive power must be supplied or the membranes at the concentrated end become ineffective. In the latter case the required volume reduction cannot be maintained. (ii) recirculation system: at least two pumps are required during normal operation, often more, so that the installation is more complex. -- with the proper recirculation, the membranes at the concentrated end are used as effectively as those at the feed end, because all stages operate at the same pressure, even when it is necessary to operate at different flow velocities from the design conditions. variations in feed flow-rate and concentration ratio can be tolerated without affecting process conditions substantially. ~ reduction of membrane permeability caused by fouling or scaling does not result in a severely increased pressure-drop compared to the system pressure, i.e. all membranes, even at the concentrate end, will remain effective. Comparing the cost of permeate removal in both installations, it must be concluded that both installation types result in almost the same figures, as seen in Table 2, in which three examples are given, with a partial breakdown of their costs,
Evaluation of hyperfiltration
systems for sweet cheese whey - 2
The decision on which installation be based not only on cost comparison as flexibility of operation.
69
should be installed will therefore but on other considerations such
ACKNOWLEDGEMENTS This study was made possible by a grant for a research project from the Ministry of Economic Affairs of The Netherlands, and was carried out with the cooperation of Wafilin BV of Hardenberg, NIZO in Ede and the Twente University of Technology at Enschede, all in The Netherlands. Discussions with H. J. Fontein of the Twente University of Technology on the optimization procedure were very useful.
REFERENCES Dejmek, P. and Engwall, H. (1980). System options and costs in dairy ultrafiltration. Desalination, 35, 397-400. Gallagher, J. T. (1970). Rapid estimation of plant costs. In: Modern Cost-Engineering Techniques, ed. H. Popper, McGraw-Hill, New York, pp. 3-10. Guthrie, K. M. (1970). Capital cost estimating. In: Modern Cost-Engineering Techniques, ed. H. Popper, McGraw-Hill, New York, pp. 80-106. Hiddink, J. and van der Waal, M. J. (1984). Evaluation of hyperfiltration systems for sweet cheese whey. 1. Experimental results with a single-pass and a recirculation system. Journal of Food Engineering, 3,225-39. Holland, F. A., Watson, F. A. and Wilkinson, J. K. (1979). How to estimate capital costs. In: Modern Cost Engineering: Methods and Data, McGraw-Hill, New York. Larson, T. J. and Leitner, G. (1979). Desalting seawater and brackish water: a cost update. Desalination, 30, 525-39. Nelder, J. A. and Mead, R. (1965). A Simplex method for function minimization. Computer J., 7,308-13.
van der Waal, M. J., Logeman, F. P. and Fontein, H. J. (1980). Evaluation of tubular membrane systems. Proc. 7th Int. Symp. on Fresh Water from the Sea, Amsterdam, 23-26 September. WEBCI prijzenboekje. (1980). Ed. Dutch Association of Cost Engineers. Stichting Nederlandse apparaten voor de Procesindustrie, December.