Process optimization for clean manufacturing: Supercritical fluid extraction for B-carotene production

Computers chem. Engng Vol.20, Suppl.,pp. S1383-S1388, 1996

Pergamon

S0098-1354(96)00237-2

Copyright© 1996ElsevierScienceLid Printed in GreatBritain.All rightsreserved 0098-1354/96 $15.00+0.00

PROCESS OPTIMIZATION FOR CLEAN MANUFACTURING: SUPERCRITICAL FLUID EXTRACTION FOR B-CAROTENE PRODUCTION G. KALAMPOUKAS AND G.A. DERVAKOS Department of Chemical Engineering. UMIST, PO Box 88, Manchester M60 IQD, UK

The relatively high cost of Supercritical Fluid Extraction (SFE) processes has been a major obstacle in the widespread use of the technology. In this work, it is demonstrated that this cost can be reduced significantly by applying the mathematical programming approach and formulating the problem of designing these processes as a Mixed Integer Nonlinear Programming (MINLP) model. Application of the model to the isolation of 13-carotene from algal cells has shown that SFE can easily outperform traditional organic-solvent-based extraction processes. Finally, a new heuristic is proposed to assist in the design of SFE processes which involve poorly soluble natural products.

INTRODUCTION During the last two decades, there has been significant activity to commercialize Supereritical Fluid Extraction (SFE) processes (McHugh and Krukonis. 1986). It has been suggested that SFE can complete or even substitute traditional industrial separation processes. Supercritical Fluids (SFs) exhibit physical properties and process characteristics that make them ideal solvents, such as good solvent power and improved mass transfer capabilities. Moreover, the solvent power of a SF can be altered by changing the pressure and/or the temperature. One of the most promising SFE applications is the extraction of natural substances for which treatment with nontoxic, environmentally friendly solvents at low temperatures is essential in order to meet strict health, environmental or food-processing standards. The SFE extraction of [~-carotene from algal cells is a case in point (Mendes et al., 1995). The key cost driver in SFE processes appear to be the capital cost and, more specifically, the number of installed equipment units and their size (King et al., 1990). More often than not, large scale commercial operations require more than one extraction/separation vessel connected in parallel; this is due to specific process requirements and to manufacturing size limitations for high pressure vessels. In this work, the problem of selecting the optimum number of process units and their size, as well as the optimum set of operating conditions (pressure, temperature and flowrates) has been formulated as a Mixed Integer Non Linear Programming (MINLP) model. Optimization of the model will yield a process structure with minimum annualized cost.

MODEL DEVELOPMENT The general flowsheet of the SFE process under consideration is shown in Fig 1. The process operates continuously, extracting solids ( I]-carotene in this case) from a liquid mixture. In the extraction vessel the feed mixture (13-carotene and water) contacts the solvent and an equilibrium can be achieved by controlling the solvent flowrate. The raffinate is collected at the bottom of the vessel where it is discharged, while the extract f o w s to the separator. Before the separation vessel the solvent power of the SF is reduced by lowering the pressure. S1383

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Therefore the supercritical mixture is flashed across a pressure reduction valve. There are four different phases entering the separator vessel: supercritical C02, gaseous COa, water and solid 13-carotene. The extract falls to the bottom of the vessel from where it is collected. Depending on the state of the solvent at ambient temperatures, either a pump or a compressor can be used for raising the pressure. When the solvent is in the gas state, it is possible to liquify the solvent and then pump it (Fig 1, dashed-line circuit). In this model, a compressor has been used for high pressure generation (Fig 1, continuous line). In the downstream heat exchanger the supercritical fluid is heated up to the required temperature for the solvent to reach the appropriate conditions when entering the extraction vessel. Flowing upwards in the vessel, in counterflow with the pumped feed from the top, additional extract is dissolved continuously and the closed loop cycle continues. A key function of the compressor is to control the solvent flowrate and, thus, its size depends on the recycle stream flowrate. The role of the letdown valve is to control the pressure of the system. Inevitably, a small amount of solvent loss occurs, but this is made-up by stream 7.

Feed

(~D

~

(D

L co 2

2.,.; U

Ilcatt ¢xchlmgcr 2

i

Heat exchanger 1

Compremior

~., Pump

Figure

t

~

~

.

.

.

.

.

Condenser

1:

SFE process flowsheet.

A first application of mathematical programming to the design of SFE processes has been reported by Cygnarowicz and Seider (1990) who have investigated a strategy for locating the optimal designs in the extraction of 13-carotene with supercritical CO z. In this work, the problem has been formulated as an MINLP model. Indeed, the number of models and applications formulated as mixed integer problems has been rapidly increased over the last years. It is only in recent years that new algorithms and software have became available commercially for MINLP (Grossmann and Kravanja, 1995). The model for optimization of the SFE process for 13-carotene isolation was developed on the commercial software package GAMS. The DICOPT++ solver, which is based on the Augrnented-Penalty/Outer-Approximation/Equality-Relaxation algorithm, was used to solve the MINLP problem. The model formulation is presented below: Variables Binary: Real:

N,,I, , N...,.p,, P,~,.. T,..,,,, P.,'e.; T~.~,#,. F,, ~ D~,,. D..p,~.

Objective function

o.~,r

. ~ ' = . C . ~ , ~v

= Cop,,

* Cq~,

.C~

4" C,,~

k~4t/

4"

M

M 4" C ~ , h.~a~

• C,.~,

(1)

* cmpvl

4" C,.~

• C~,,

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In this model, the minimization of the annualized cost of the SFE process has been selected as the objective function; this is the sum of the annual operating cost and the capital cost of the equipment, divided by the expected period (M in years) of retum on investment. It should be noted that the supereritical fluid extraction step is, by far, the most important element of the total manufacturing cost of the final product. Therefore, the above objective function should result in optima comparable with those obtained by maximizing the net present value of the venture. Maximization of the net present value, which is perhaps the most appropriate criterion for this type of problems, incorporates raw material and product costs. The latter is, however, difficult to forecast in this case, as it depends largely upon market perceptions regarding the links between 13-carotene and its cancer prevention properties and the differences between the synthetic and the natural forms of the product. Minimization of the armualized cost of the SFE process is, therefore, a reasonable compromise and has been chosen as the objective function. Finally, capital and operating costs have been correlated with the model variables listed above. For example, the capkal cost of the extractor and the separator has been linked with vessel diameter D k (k= extr, separ) and vessel pressure Pk, using standard cost correlations.

Constraints Extractor mass balance

F,,j+ r,.j- &j- F,.j

j = ~-carotene , CO 2, HuO

(2)

Separator mass" balance

&j- Fs.j- F,,o 0

j

.

~-carotene

(3)

, C O 2, H 2 0

CO e replenishment

Fsj+ FTjo

(4)

j = CO 2

Recovery constraint F r j ~ 0.99 • F~j

,

j

=

p-carotene

(5)

Quali(y constraint

F,,p.c,,m,~ .MIVp_¢,~¢,~ u 0 . 9 0 - ( ~ F,, 1 .MIVj )

,

j

J

=

[~-carotene , CO

2,

H20

(6)

where MW represents molecular weight.

Non-negativity constraints on the flowrates F~,j> 0

(7)

i = 1,2 ...... 7 j

= [~-carotene

, C O 2,

H20

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European Symposium on Computer Aided Process Engineering---6. Part B

Solubili(y of t-carotene in COe CO 1

Sp_~o,ou,. =f ( T , P )

(8) e.g.

S (323 K, P~o) = 2.8576 • 10 -7,e e~,.0.00~014,

Solubility of COe in HeO

Solubility of H20 in COg S~ °~ =f ( r , P )

(10)

x'a'p_~ = f(D a,, A ,V) ~ 2 hours

(11)

Residence time constraint

where D ~ is the extractor diameter, A is the aspect ratio of the extractor and V is the maximum possible molar flowrate through the extractor as determined by the flooding velocity.

lnput material constraints Kmol

Fi.p.,,,ou, ' : 0.002 [ - - - - - ~ ]

Fl.u2o = 0.2 [ - - - ~ - ]

(12) Kmol

o 0 0 I---T-]

F,.,I o o 0.o

RESULTS AND DISCUSSION The effect of plant capacity on the number of extractors/separators needed to produce natural 13-carotene which meets the quality constraints described above is shown in Table 1. Due to the constraints imposed on the maximum size of individual vessels, a larger number of vessels appears to be needed to meet a higher market demand. As expected, increasing the plant capacity results in a concurrent increase in the amount of COa which is recycled back to the extractor in order to dissolve 13-carotene (Fig 2). In addition, the unit cost for isolating I~carotene is reduced with increasing plant capacity, albeit at a much lower rate above a plant capacity capable of meeting 75% of the world demand (Fig 3); this is due to the need for an additional separator vessel above a plant capacity of 75%. However, while the overall unit cost for purifying 13-carotene was shown to decrease with increasing plant capacity, the relative contribution of the various elements of the capital cost - which is the dominant component in SFE processes - appears to be fairly constant, with the cost of the extractors clearly dominating the economics of the process (Fig 4). An interesting result is that the optimizer appears to always converge at the highest allowable levels of pressure and temperature in the extractor vessel(s). This can be explained by the fact that the solubility of 13-carotene in CO2 is clearly a strong function of these quantities. Admittedly, it is questionable whether the upper limits for pressure (1000 bar) and temperature (355 K) used in this work can be realistically achieved. While operating the process at a temperature of 355 K may be feasible, due to the residence time of the heat-labile 13-carotene being limited to only 2 hours, operating the extractor at 1000 bar may not be always practicable. Reducing this pressure to a lower value has confirmed the dramatic effect that pressure exerts on the economies of the process; decreasing the maximum allowable pressure in the extractor vessel to 775 bar resulted in a 10-fold increase in

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the recycle of CO2 which, in turn, necessitated the use of 19 extractors and 4 separator vessels (instead of 2 extractors and 1 separator in the base case) resulting in an increase of the annualizod unit purification cost by 7fold. On the other hand, the optimum pressure in the separator vessel(s) appears to be a strong function of the desired quality of the final product. Relaxing the content of the final product in -13carotene from 94% to 90% results in a drop of the optimum separator pressure from 450 bar to a little over 150 bar. This is a particularly important result in view of the fact that the [3-carotene currently in the market is significantlymore diluted, sometimes by 95%. The amount of 13-carotene that is recovered from the feed depends on the solvent recycle (Fig 6). Furthermore, as it has a/ready been demons~ated, the amount of the recycle solvent has a direct effect on the overall annualized cost. In this ease, the sensitivity of the capital cost in relation to the cost of the compressor is fairly high, since the operating cost is very low and two extractors are required for recovery values from 70% to 100%. If the recovery constraint is relaxed to less than 70%, the solvent recycle flowrate can be handled by one extractor. In summary, MINLP appears to be extremely valuable in the preliminary design of SFE processes. An interesting heuristic emerging from this work is that one should favour extremes of pressure and temperature in the extractor vessel.

NOTATION A C~pi, Cope,

Di

F,,, M MW

iv, P, s~ r, V

aspect ratio capital cost, [$] operating cost, [S/year] diameter (m) flowrate of component (j) in stream (i), [Kmol/hl time horizon for investment [years] molecular weight number of vessels pressure in vessel i, [bar] solubility of (i) in (j) temperature in vessel i, [K] maximum molar flowrate [Kmol/h]

Greek symbols T e.,ar

Subscripts extr sep

residence time in the extractor [h] objective function

extractor separator

REFERENCES Cygnarowicz, M.L. and Seider, W.D. Design and Control of a Process to Extract p-Carotene with Supercritical Carbon Dioxide, Biotechnol. Prog., 6, 82-91, (1990). Grossmann, I.E. and Kravanja, Z. Mixed-Integer Nonlinear Programming Techniques for Process Systems Engineering, Computers chem. Engng., 19, S189-$204, (1995). King, M.B., Catchpole, OJ. and Bott, T.R. Energy and Economic Assessment of Near-Critical Extraction Processes, IChemE Symposium Series No 119, 165-186 (1990) McHugh, M. and Krukonis, V. Supercritical Fluid Extraction, Butterworth, Boston, USA (1986) Mendes, ILL., Coelho, J.P., Femandes, H.L., Marrucho, IJ., Ca~al, J.M.S, Novais, J.M. and Palavra, A.F. Applications of Supercritical COz Extraction to Microalgae and Plants, J.Chem.Tech.Biotechnol., 62, 53-59 (1995) Viswanathan, J. and I.E. Grossmarm, A Combined Penalff Function and Outer-Approximation Method for MINLP Optimization, Computers chem. Engng., 14, 769-782, (1990).

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European Symposium on Computer Aided Process Engineering--6. Part B

Plant capacity as % of the world wide market for natural 13carotene

Number of Extractors

leO~

Number of Separators

160~140. ~120 ~

25

2

1

50

4

1

75

6

1

~10o~

$

,

I

211

100

8

2

125

10

2

,

40

I

'

60 Plant capacity,

I

'

]

:

~

,

:

80 100 120 %of thev,qoddmarket

140

Figure 2: Effect of plant capacity on the amount of COz required in the recycle stream.

Table 1: Number of extractors / separators needed to meet different fractions of the world demand for 13-carotene.

Cost Componenls (25%of thewoddmarket)

Capital

9

21.5

\

8-

/ 2o D

cooler(0.33%)'1 heatexchanger(0.2O%)-II compressor2 (3.64%)-~ | comprec~sorI ( 8 . 8 j ~ . ~

2o.s

separators (19.93%) - -

~5 8

i1,5 i ;

~3

~

(67.05%)

extractors

<2 ,

,

25

50 Plant capacity,

,

,

" ~ " ~

75 100 125 %of theworldmarket

18.5

Figure 3: Effect of plant capacity on the overall annualized cost (e) and the unit cost (I) for isolating 3-carotene.

Figure 4: Breakdown of the capital cost components.

35

2.25

~2 .~.oA~,,~.~

:2.20 ~'

"t

2.15

P

~.~

2.10 w 2.06 ~

2.oo .El '~ ,

•

150 '; 90

,

1.90

• 91

92

93

.

6

~

<

1.2 ~ 15

94

B-carotenein theproduct[wt %]

Figure 5: Sensitivity analysis - effect of the quality constraint on separator pressure (e) and the associated amualized cost (a).

t

=

5O

I

6O

i

I

i

I

J

I

70 8O 9O [%]of B-carotenemcovore¢l

,

100

Figure 6: Sensitivity malysis - effect of the recovery constraint on C02 recycled (e) md the annualized cost (l).