Technical Notes Anal. Chem. 1995, 67, 212-219
Portable Thermal Pump for Supercritical Fluid Delivery Marc A. Adams, Emmanuel O.Otu,t Marat Kozliner,* Jacek Szubra,@and Januss Pawliszyn* Department of Chemistty, University of Waterloo, Waterloo, Ontario. N2L 3G 1 Canada
A new system to deliver supercritical fluid heats and cools a high-pressurevessel with check vahres at its inlet and outlet to direct flow. Two or more vessels can be heated in alternation to reduce pressure fluctuations. Heating and cooling mechanismsfor a portable pump are resistive heating combined with air cooling of a tube vessel or Peltier effect heat pumps. Two prototype pumps were built and tested, one using Joulean heating/convection cooling and the other using Peltier devices. Design and operation parameters for both types have been optimized theoretically. The Joulean heating design is simpler to build and control, but the Peltier design is more energy efficient and does not need extra features to liquefy C02. The Joulean heating prototype was tested to c o h the pump’s basic theory and feasibility. This pump design is simple and inexpensive and can produce continuous fluid delivery without refilling. The pump design is compact and energy efficient so it could be used in the field. Supercritical fluid (SF) is increasingly used in analytical chemistry for supercritical fluid extraction (SFE) and supercritical fluid chromatography (SFC), as evidenced by numerous journal reports. The most expensive component of an SF system is the pump that delivers fluid at high pressure. A new delivery approach discussed in this paper is simpler and less expensive than current standard delivery systems. Most commercial SF pumps are syringe, reciprocating, or pneumatic amplifer pumps. A syringe pump develops pressure quickly and steadily but uses a large volume of compressed fluid and needs to be refilled, perhaps in the middle of an experiment. SF-dedicated, reciprocating pumps and a pneumatic amplifier pump’ have recently been introduced commercially, but they have complicated mechanical systems. Other systems have been reported such as a liquid chromatography pump with refrigerated
component^.^^^ An SF pump based on thermal expansion of the fluid was previously reported by this laborat0ry,4%~,~ but is not portable because it uses a massive high-pressure vessel. A new thermal expansion pump design is based on the Carnot heat engine. The pump heats and cools a high-pressure vessel with check valves at each end to direct fluid flow. Two heat transfer mechanisms that are practical for a portable pump are to heat by electric current through a tube and cool with air convection and to heat and cool with Peltier effect heat pumps. Two prototype pumps were tested, one using Joulean heating and the other using Peltier devices, to evaluate components and to provide an experimental basis for theory. An experiment with the Joulean heating prototype demonstrates feasibility. The pump output pressure and flow rate, and the pump’s rate of energy usage can be estimated theoretically. The design parameters were optimized theoretically to minimize the power fot a given flow rate and pressure. The pump’s estimated output is sufficient for standard SFE and SFC applications. THEORY
Basic Principles. This new thermal pump system delivers supercritical fluid by heating and cooling a pump vessel with check valves connecting it to a tank and to a receiving vessel as outlined in Figure la. Opening the tank fills the pump and extraction vessel with fluid at tank pressure. When a single pump vessel is heated, the pressure of the fluid inside the pump increases so that the check valve to the tank closes, and when pressure is high enough, the check valve to the receiving vessel opens to add fluid and pressure. At a set time or temperature, the pump vessel is cooled and its internal pressure decreases so that the check valve to the receiving vessel closes, and when pressure is low enough, the check valve to the tank opens to refill the pump. At a set time or temperature, heating starts again. This sequence of heating and cooling repeats to build pressure in the extraction vessel stepwise until a maximum is reached and maintained. A pump with two vessels as shown in Figure l b can deliver fluid
735 Anderson Hill Rd., Purchase, NY 10577-1400. * Present address: Organic Residue Laboratory, NQAL, Nestle USA, 6625 Eiterman Rd., Dublin, OH 43017. 8 Science Electronic Shop, University of Waterloo, Waterloo, ON, Ontario N2L 3G1 Canada. (1) Pariente, G. L.; Pentoney, S. L., Jr.; Griffiths, P. R; Shafer, K H.Anal. Chem. 1987,59, 808-813.
Greibrokk, T.; Blilie, A. N.; Johansen, E. J.; Lundanes, E.Anal. Chem. 1984, 56,2681-2684. Greibrokk, T.; Doehl, J.; Farbrot, A; Iversen, B.J Chromatogr. 1986,371, 145. Pawliszyn, J. /. High Resolut. Chromatogr. 1990,13,199-201. US. Patent 5,237,824, Lawrence, M. J.; Colquoun, M.; Pawliszyn, J. Zntemational Symposium on Measurement of Toxic and Related Pollutants, US.EPA Report EPA/GOO/ 9-90/026 Raleigh, NC, 1990 pp 123-133.
212 Analytical Chemistry, Vol. 67, No. 7, January 7, 7995
0003-2700/95/0367-0212$9.00/0 0 1994 American Chemical Society
+ Resent address: Division of Natural Sciences, State University of New York,
a
Keq/K= 0.18(R)0.25
r
b
(3)
estimates the effective thermal conductivity in terms of the stationary fluid's thermal conductivity, K, and a term to account for convection, 0.18Ro.25, where R is the Rayleigh number of the fluid! The effective thermal diffusivity on the fluid will be ,veq= Keq/ec,where e is the density and c the heat capacity of the fluid. The temperature drop in the fluid from tube center to tube wall will be
Restrictor
Extraction Vessel
h(i.d.)2/16~e,
-
Valve Pressure transducer
Check valve
(4)
by the equation for transient heat transfer in a cylinder? Since the expression for the Rayleigh number R includes temperature drop and distance cubed as factors, eqs 4 and 3 give an expression for the maximum inner diameter for a given heating rate, h, and a given limit on the temperature drop. The metal tube walls, on the other hand, will have negligible temperature drop because of the relatively high thermal conductivity of metals.
Heating/Coolingtube
From C 0 2 supply-
Figure 1. Block diagrams of the basic thermal pump design.
continuously: one stage can deliver fluid at a constant rate while the other stage cools to refill and then reheats to reach output pressure, and when the first stage switches to cooling the second is ready to begin delivering fluid. Continuous or nearcontinuous delivery is necessary to avoid large pressure fluctuations, since at a flow rate of 0.01 g/s, 10 OOO psi, even a 5mL extractionvessel would drop by 10oO psi in 10 s. Miller and Davis used a similar design to deliver solvent for HPLC, but only at minute rates due to the small expansion coefficients of liquid^.^ The pump's output can be estimated from the fluid's equation of state. The increase in pressure from one pump injection, AI', satisfies the mass balance relation @(T-Jhk)
+ e (tevpev) vev = (tm,Pw+hp) vm + e ( t e v Q e v + W
PRINCIPLES OF THE JOULEAN HEATING/ CONVECTION COOLING DESIGN The power needed to drive a Joulean heating convection cooling pump is independent of tube length, tube diameter, and cycle time. The energy to heat a pump tube from T k to T,, by electric current will equal C(T,, - Tfi,J plus the heat lost to convection during heating, where Cis the heat capacity of tubing and fluid. C can be expressed as
= vmetal
&netal
+ vm ecfluid
(5)
where V represents volume and ec represents heat capacity multiplied by density. Enclosing the tube in a small-volume channel with flaps to prevent convection during heating reduces power to
where pf is the power to open and close one set of flaps. Substituting for C by eq 5 and for 1by eq 2 gives power =
vev
+ ilk
(1)
where e (T,p) represents fluid density as a function of temperature and pressure, Vvolume, k the mass flow rate out of the extraction vessel, and 1 the time between pump injections, and the subscripts min, max, tp, ev represent minimum, maximum, thermal pump, and extraction vessel, respectively. Equation 1 defines the sequence of extraction vessel pressures during pumping, P,, = PnVl AP,,Po = P&. At steady state
+
Note the extraction vessel volume does not affect steady state pressure. This characteristic means a large vessel could be connected on-line between pump and extraction vessel to reduce pressure fluctuations. The pump vessel inner diameter, i.d., and heating rate, h, are limited by the fluid's effective thermal conductivity, K , ,Le., the thermal conductivity accounting for the convection effect. The formula (7) Miller, T. E., Jr.; Davis, C. M. Anal. Chem. 1988, 60,1965-1968.
where] = Vmed/V, and Pis the output pressure. ]is independent of tubing diameter because the pressure rating for a hollow cylinder of a given material depends only on the ratio of its outer diameter to inner diameter.1° Thus, eq 7 shows power is independent of tube length or diameter, simplifjmg the design optimization, power is independent of cycle time, and optimum T h and T,, are independent of flow rate, simplifying the operation optimization. To ensure the pump is capable of delivering the output desired, the minimum tube volume for a given set of parameters depends on the cycle time, by eq 2. Cooling time or heating time can be calculated by (8) Mikheyev, M. Fundamentals of Heat Transfer; Mir Publishers: Moscow,
1968. (9) Carslaw, H. S.;Jeaeger, J. C. ConductionofHeat in Solids,2nd ed.; Clarendon Press: Oxford, UK, 1959. (10) Hydraulic Handbook, 7th ed.; Trade and Technical Press Ltd.: Morden, England, 1979.
Analytical Chemistry, Vol. 67, No. 1, January 1, 1995
213
a
b
Heat sink
C
Thermoelectric heat pump
Electrical leads Stainless steel tublng
Figure 2. Blowup diagram and some possible coil configurations for the Peltier device pump design.
where Q is the rate of heat transfer. The pump tubes could be cooled by free or forced air convection. Calculations show that a pump cooled by free convection, however, would need a relatively long tube and thus not be very portable. To calculate the tube length necessary with forced convection, suppose tubing is bent into a staggered bank in a channel with cross-sectional area A. The heat transfer coefficient for tubes in a staggered bank is independent of the distance between tubes and is given by
H = 0.3$(y)0’6
(9)
where d is the tube outer diameter and K, Y , and u are the conductivity, kinematic viscosity, and speed of air, respectively? Assuming air and tubing temperatures are roughly linear with respect to the channel axis the overall heat transfer should be close to H(Tmk- ?.air), where Fhkand T& are the average tube and air temperatures, respectively. The heat capacity of the air flow will be d @ c ) &so the air will rise in temperature by
which gives
4
1-1
PRINCIPLES OF THE PELTIER HEAT PUMP DESIGN The power needed to drive a Peltier device SF pump is independent of the capacities of the Peltier devices. Peltier effect heat pumps can both heat and cool a tube coil because reversing the electric current reverses the direction of heat pumping. Standard commercial Peltier chips consist of thermocouples connected in series electrically and parallel thermally arrayed between rectangular ceramic plates for electrical insulation. A tube coil could be sandwiched between Peltier chips as shown in Figure 2. The efficiency of a pump using Peltier chips can be calculated. All commercial chips have the same basic properties since the performance “of materials used in (thermoelectric) refrigerators at ordinary temperatures has remained virtually the same since 196o”.l1 Different chip models have different thermoelement cross-section-to-length ratios, G,and different numbers of thermocouples, N. The capacity of a Peltier chip is normally given as its GN value. The net quantity of heat pumped from the cold face of a chip is given by
QC= 2 N [ o c - Z2@/2G- K(Th - TJG] Solving algebraically for T&and using eq 8 gives the time to cool as
(14)
the heat released at the hot face is given by
and the electric current is given by
Z = G / Q [ Y /-~ U(Th - T J ] Cycle time must be at least twice the cooling time for continuous delivery, so by eq 2 the minimum tube length per stage is 214 Analytical Chemistry, Vol. 67, No. 1, January 1, 1995
(16)
where Th and Tcare the hot and cold face temperatures in degrees kelvin, a,8, and K are the Seebeck coefficient, electrical resistivity,
and thermal conductivity of the thermoelements,respectively, and v is the voltage per thermocouple.12 Temperature drops across tubing and chip plates will be small compared to across the fluid, so we can assume a uniform temperature for the coil and chip plates and a linear temperature gradient across thermoelements. Thus the thermal load per pump coil between two Peltier chips will be C = C, C, where Ct is the heat capacity of fluid, tube, and thermal contact filler, expressible as
+
ct
= vmetal@cmetal + vfluid@Cfluid + vfiUer@c611er
(17)
and C, is the heat capacity of one chip. Heat leakage from a properly insulated load should not be more than 10%.13 Therefore
and substituting for C and for cycle time using eq 2 gives the power as
Substituting for Q and I would be cumbersome to write out, but inspection shows the resulting expression for power is independent of G and of N. This result simpliiies the design optimization. To obtain a desired output, however, the pump must have suf6cient capacity. The minimum value of the total GN of all Peltier chips for a given set of parameters (Le., tank pressure, output pressure, flow rate, vc, Vh, and so forth) is determined by eq 2. Equation 8 can be used to calculate the cycle time. A simple analysis indicates the level of power for the Peltier chip pump design. If v, and Vh are assumed constant, eq 19 indicates vc and q, for minimum power for any given T A and Tm. Plotting minimumpower vs ( T h ,T& indicates the optimal ( T h , T d . This algorithm indicates the level of optimum power, but it accounts for only one cycle time, hence only one flow rate, and parameters are not constrained for steady, continuous fluid throughput. The efficiency of the Peltier device pump could be improved by optimizing the electric power curve instead of using constant v, and Oh. Specific voltages are necessary to reach high and low temperatures, but lower voltages are much more energy efficient when cooling a hot coil or heating a cold coil. A simple moditication would be to cut v, and vh in half when cooling a hot coil and when heating a cold coil. The branch of mathematics called optimal control theory must be applied to find the optimum power curve, but this analysis has not been attempted. EXPERIMENTAL SECTION Apparatus. Two prototypes were tested, one using Joulean
heating with convection cooling, the other using Peltier device heat pumps. For both models, annealed, in. 0.d. SS316 tubing and ‘/I6 in. 0.d. compatible fittings (Swagelok and Valco) connected gas tank, check valves, pump vessel tubes, pressure (11) Goldsmith, H.J. Electronic Refigeration; Ron Limited: London, 1986. (12) Melcor Electronic Products C o p . Melcor Engineering Catalog; Melcor: Trenton, NJ, 1993. (13) Products Catalogue;Thermoelectric Cooling America Corp.: Chicago, IL, 1992.
transducer, and extraction vessels. The tank was SFC/SFE grade carbon dioxide pressurized to 2000 psi with helium and with a full length dip tube (Air Products and Chemicals Inc., Allentown, PA). A vessel containing activated carbon and a metal filter with 2-pm pores was placed on-line between the tank and pump inlet as a precaution to protect check valves. Check valves were liquid chromatograph valves (Hewlett-Packard,Toronto, ON, Canada) with internal volumes of 22 or 23 pL. Pressure was measured with a flow-through, 25pL volume transducer accurate to within 100 psi (model SWOA-1oo00,Senso-Metrics, Inc., Simi Valley, CA). Extraction vessels were 8 . k m lengths of stainless steel tubing, l/&. o.d., 0.12-in. i.d. Fused silica capillary tubes (Polymicro Technologies, Phoenix, AZ) were used to allow flow from extraction vessels. The Joulean heating prototype was assembled from standard laboratory parts and accessories. A 3.8m length of annealed, ‘/I6 in. 0.d. SS316 tubing, 1.5-mL total internal volume, was held between laboratory stands. A thermocouple with a digital display circuit (Cole-Parmer) was clamped to the midpoint of the pump tube. A custom-made circuit, described below, was used to display the transducer signal. A Variac was connected to a 110 V/20 V transformer, slow-blow fuse, ammeter, and two leads to conduct up to 10 A through the pump tube. The Peltier device prototype was built with the coil codguration shown in Figure 2a. A sheet metal, “C”-shaped chassis surrounded the pump lengthwise. Two pieces of stainless steel tubing, ‘/gin. o.d., 0.085i. id., 1.7-mLinternal volume each, were bent into 4 cm 0.d. coils. Two thermocouples were made with 0.005 in. chrome1 and alumel wires, cold junctioned at the “C”shaped chassis, calibrated, then attached with thermal glue (152 K-A Bond, Wakefield Engineering Inc. Wakefield, MA) to the center of Peltier effect heat pumps (CP1.4127-10L, Melcor Electronic Products Corp., Trenton, NJ). The coils were sandwiched by heat pumps, one heat pump with a thermocouple for each coil. Aluminum plates, 2 x 2.5 x I/8 in., sandwiched the coil-pump sets. Both coil-module-plate sets were clamped 8.5 cm apart, center to center, between aluminum extrusions (heat sinks), 7-mm base with 2 x 25 mm fins 8 mm apart, bolted to each other and to the chassis. Thermal grease (Type 120, Wakefield Engineering) was applied between coils and modules, between modules and plates, and between plates and extrusions. The space between extrusions was insulated with spray-on polyurethane foam, and after setting, the foam was coated with silicone sealant, both obtained from a hardware store. A fan was bolted at one end of the chassis to ventilate the extrusions. The entire assembly was 40 x 30 x 12 cm and 1.5 kg. The Peltier pump was operated with an electronic controller, depicted schematically in Figure 3. The controller is operated by setting a pump cycle time between 24 and 86 s on a clock oscillator and by adjusting the electrical power to the heating modules. The controller directs power from a 12 VDC, 10-A supply by “H-bridges” composed of two Pchannel and two N-channel MOSFETS (IRF 9511 and IRF 511), one H-bridge for each Peltier chip pair. To change the direction of current a LOGIC-SHIFTER-DRIVER block converts transistor-to-transistor logic (lTL) levels to MOSFET transistor levels and turns off one pair of MOSFET transistors before turning on the second pair. The system’s maximum current, about 3 A, is provided for Peltier chips cooling a coil. Peltier chips are more efficient when heating than when cooling for a given current, so to keep pump Analytical Chemistty, Vol. 67, No. 1, January 1, 1995
215
Figure 3. Block diagram of the electronic controller for the Peltier device pump prototype. The section in the dotted square is a simplification of the actual design used in the experiments, because the extra electronics were later found to be unnecessary.
cycles symmetric heating power is dampened. A manual adjustment modulates from 98 to 0%the width of 8GHz pulses supplied to the Peltier modules that are heating a coil, by a circuit built around a TLC 556 chip (Texas Instruments). The voltage reference block provides buffered excitation voltage for the bridge configured transducer, and separate buffered voltage for setting a safe pressure limit. The signal from the pressure transducer is amplitied by an amplitier (AD 620, Analog Devices) and sent to an LED display and to a comparator. The comparator shuts off power to the modules if the transducer signal exceeds the safety limit or is disconnected. An OVERLOAD circuit section provides an adjustable current limit to protect the power supply and the power transistors. Thermocouple signals are processed and displayed by a circuit using LT1025 and ICL7650 chips. The thermocouples only monitor temperatures. Procedures. The dual-stage Peltier chip pump was tested in static mode with extraction vessels of different volumes, and with a sand-filled O.&mLvessel fitted with different restrictor sizes. For each test, its cycle time and heating power were adjusted to maximize pressure. Extraction vessels were always at room temperature. Temperatures were observed from the LED displays and pressures recorded with a chart recorder (Gould 110). All tests were repeated to ensure reproducibility. An experiment using the Joulean heating prototype demonstrates the feasibility of the pump design and validates the theory. The apparatus was used to step through the pump pressure sequence manually. No extraction vessel was used. A piece of tubing with one end silver-soldered was connected to the transducer outlet as a plug. Before the experiment, the pump was filled and then emptied three times to purge the system of contaminants. The tube was heated to above 50 "C and then while 216 Analytical Chemistry, Vol. 67,No. 1, January 1, 7995
it was cooling the tank was opened to fill the system with fluid. When the tube reached 30 "C, power was turned on until the tube temperature reached 60 "C, it was allowed to cool by free convection to 30 "C, then power was turned on again, and this cycle was repeated until pressure readings leveled off. This pump sequence test was repeated three times. RESULTS AND DISCUSSION The initial aim of this study was to test the pump design experimentally and to evaluate components for the pump. Thermoelectric modules performed consistently. Figure 4a shows part of a chart recording of thermocouple measurements of a Peltier chip oscillating between the set temperatures of 0 and 60 "C under constant electric power (controlled by an earlier version of the Peltier pump controller that supplies constant power and reverses current at set high and low temperatures). The cycle times deviated by only 2% over 30 min, without adjustment or automatic mechanism to control times. The Hewlett Packard valves have performed consistently for 1 year of use, and note in Figure 4b that backtlow and leakage are practically nil. Other check valves were tested and found inadequate because of large internal volume, contamination from prior use, or polymer seals being swelled by COz. Figure 4b shows a chart recording of extraction vessel pressure for the Peltier pump in static mode (no flow from the extraction vessel). Figure 4c is a chart recording of the pressure when flow is let out of the extraction vessel with a 21;um restrictor, showing the lower pressure and fluctuations caused by the flow. Figure 5 shows the extraction vessel pressures obtained by the Peltier pump for different T h . The results for the Peltier-devicepump agree qualitatively with theory in that reducing T h increased Pmax
b.
U.
C.
0
3
2
I
1
PUmO C"C*
Figure 6. Experimental and theoretical results for the pumping pressure sequence with the Joulean heating prototype. The dotted lines represent the maximum and minimum theoretical values for the possible values of the temperature and tank pressure, based on the accuracy of the measurements: Tmin = 30 "C,Tm, = 100 "C,KP= 1.5 mL, and Vev= 0.1 mL.
Figure 4. Chart recordings of (a) measurements of a themocouple in the Peltier pump protoype while using a controller that switched from heating to cooling at set temperatures, (b) pressure developed by the Peltier pump using the controller based on set cycle time, in static mode, Tmin = 0 "C,and Tm, = 70 "C, and (c) pressure developed by the Peltier pump using the controller based on set cycle time, in dynamic mode with a 0.6-mL extraction vessel connected to a 21-pm restrictor.
Table I. Steady State Pump Output Pressure (psi) for Different Parameter Valuesa
parameter, variation standard parameters
9600 psi
T d +20/-20 "C Tmax-20/+20 "C
5800/14400 7600/11500 8900/10200
-500/+500 psi 1x 2/92 k x 2/92 t2/x2 V,, -0.5/+0.5 mL T,, -20/+20 "C &k
v,
2000 loa,
-
/
IO 15 nme (min)
20
3600 psi 2800/4700 3100/4500 3460/3750 2100/5500 2100/5500 2150/5800
no change no change =
10
(
5
no change not applicable no change no change no change
flow rate k = 0.01 g/s (dynamic)
Standard parameter values: T d = 10 "C, Tmax= 90 "C, &,k 1700 psi, Vt,, = 1.5 mL, V, = 1.0 mL,1= 45 s, T, = 23 "C.
i
04 0
k = 0 g/s (static)
25
Figure 5. Experimental results with the Peltier pump prototype showing the effect of Tmin on the pressure developed in a 0.6-mL extraction vessel in the static mode: Tmax= 70 "C, Vtp = 1.O, and P b n k = 1700 psi.
proportionally and P, did not depend on V,. Tests repeated to check reproducibility obtained maximum pressures within 4%of each other. Because polyurethane foam had seeped between the tubing and Peltier chips, and because the Peltier chips covered only part of the pump tubes leaving dead volumes of 30% between check valves, the results in this study were 30-50% below theoretical estimates for an ideal pump. These problems would be easy to prevent in future prototypes. The results for the Joulean heating prototype agree perfectly with theory. Figure 6 shows the pressures recorded for each circulation of the pumping sequence experiment with the Joulean heating prototype. Figure 6 also shows the upper and lower theoretical estimates of the pumping sequence pressures for the given accuracy of the temperature and tank pressure measurements. Results agree within experimental error. To calculate the estimates, a subroutine was added to a program that gives e (T9) for C0214 using the Wagner equation of state15 to calculate the pump pressure sequence P, using eq 1. (14) Ely, J. F. CO2PAC (1.3): Equation of State FORTRANProgram; T h e m e physics Division 774.03, National Institute of Standards and Technology, Boulder, CO 80303. (15) Ely, James F., Ed. Supemitical Fluid Technology, CRC Press: Boca Raton, FL. 1991.
Table 1 shows the effect of parameters on the steady state output pressure of the basic pump design, as estimated theoretically. The computer program mentioned above was used to calculate the steady state pump pressures for C02 using eq 2. (COZis the only fluid considered is this study but the same logic and formulas could be used for other fluids.) The calculations assume an ideal pump, uniformly heated. An actual pump, however, will probably have dead volume in addition to a transition volume where the temperature changes from the dead volume temperature to pump temperature, because fittings and check valve housings cannot be heated easily. More refined calculations have shown dead volume under 5%will have only a minor effect on pump performance, as confumed by the pump pressure sequence experiment. To minimize dead volume, liquid chromatograph or SF chromatograph check valves can be used since they have low volume, typically 25 pL, and high pressure capacities. The flow rate of a pump delivering supercritical COZis limited by the pump vessel inner diameter and the pump volume. The thermal conductivity of supercritical C02 is between 25 and 75 mW/mK and its density times heat capacity is between 0.2 and 0.45 c ~ ~ / ~ L * At K .pressures ~ ~ J ~ above 2000 psi and temperatures between 0 and 300 "C, the Rayleigh number for COZwill usually be under 6.1 x 107-AT.6J(20) (for ATin degrees centrigrade and d in centimeters).17 To limit the fluid temperature drop to 1 "C at a heating or cooling rate of 2 "C/s, formulas 4,3, and 20 suggest we should have an inner diameter of ~0.085cm. Thus the smaller the tube diameter the higher the heating rate possible, for a given tube volume. This limit on tubing diameter does not compromise (16) Vesovic k B.; et al J. Phys. Chem. Ref Data 1990,19, 763. (17) Michels, A; Sengers, J. V. Physica 1962,28, 1238.
Analytical Chemistry, Vol. 67, No. 1, January 1, 1995
217
Table 2. Optimum Power and Settings for the Joulean Heatlng/Convection Cooling Pump under Different Conditions.
condition, variation standard conditions P -2000/+2000 psi Tmb -15/+15 "c P w +400/-400 psi J -0.9/+2.7
minimum power (not including $3 0 75 53/97 55/190 65/115 42/180
Settings Tmax
TeC) 30.5 30.5 15.5/45.5 30.5 30.5
k i n
(OC)
(cm)
293 220/368 235/523 263/388 293
200 186/212 170/290 190/240 110/500
Standard conditions: k = 0.01 g/s, P = 8000 psi, Tab = 30 "C, Pmk = 1500 psi, J = 1.6, and T- set arbitrarilyat 0.5 "C above ambient. To calculate the minimum tube length per stage in a fan-cooled pump the parameters were tube 0.d. = l/16 in., u = 300 cm/s, A = 100 cmz, and physical properties for dry air at 30 "C.
(u
pump efficiency, however, since the pressure rating for a hollow cylinder of a given material depends only on the ratio of the cylinder's outer diameter to inner diameter.1° A l/16 in. 0.d. tube of unannealed SS316 with a wall thickness of 0.012 in., J = 1.6, would be rated for 10 000 psi for temperatures up to 550 OC.18 Annealed SS316 has the same rating forJ = 4.3. A large-volume pump can deliver fluid at a high flow rate using a slow heating rate, so pump vessels could have larger diameter if desired. Table 2 lists the optimum power and settings for the Joulean heating/convection cooling design at different conditions. The values were calculated theoretically by using the computer program for the COZequation of state mentioned above. A pump using forced convection with spring-loaded flaps would be compact and attitude independent, and stages could be much longer than 2 m so the pump would be capable of higher flow rates if desired. A small, axial fan can blow air through a 10 x 10 cm channel at 300 cm/s drawing less than 40 W. Fans should be positioned to blow on the tubes because turbulence increases heat transfer by 60%,and tubes should be kept clean because fouling reduces heat transfer by 20%.8 Fittings and valve housings should be free to cool. Table 3 lists the optimum power and settings for the Peltier chip design for a selected group of parameters, as calculated by a computer program using the equations and algorithm given in the Theory section. The "standard" parameters were chosen by assuming a simple construction and were not chosen for optimum power. The calculations assumed oh and uc are constant and chip outside face temperature is 10 "C above ambient. The results indicate desirable Peltier device characteristics. The optimal T,, values show that Peltier chips should be capable of operating temperatures up to 200 "C. For the standard parameters used to calculate Table 3, the minimum GN is 70, which works out to a minimum GN of 18 for each of four Peltier devices in a two-stage pump. The GNd, value is directly proportional to flow rate, and to be capable of higher flow rates, larger coils could be sandwiched between four Peltier chips or more instead of two. Peltier chips should also be as thin as possible to reduce the thermal load, as explained below. For the parameters used to calculate Table 3, the heat capacity over pump volume term in eq 19 breaks down to 10%COz, 10% filler, 38% metal tubing, and 42% C,/V&. The term C,/V@ is proportional to the ratio of coil volume to face area and to the (18) Hoke Tubing Data Charts; Hoke Inc.: Cresskill, NJ, 1991.
218 Analytical Chemistry, Vol. 67, No. 7, January 1, 1995
length of thermoelements, assuming coil volume is proportional to the chip surface area and chip surface area is proportional to the number and cross section of thermoelements. The coil volume to area ratio could be maximized by soldering tubes into a triangular packing of several levels with loops, similar to the configuration of Figure 2c. Tight bends can reduce tube pressure rating so a coil prototype should undergo a burst test. Another option is to drill a metal block to produce a pump vessel. As mentioned in the Theory section, the efficiency of the Peltier device pump can also be improved by optimizing the electric power curve instead of using constant uc and uh. At the standard parameter values in Table 3, cutting uc and q, in half when cooling a hot coil and when heating a cold coil changed the calculated power to 105 from 125 W, although G N d increased to 95 from 70 cm. The Peltier chip pump design depends significantly on its construction. For filler, even the most thermally conductive filled epoxies would have a temperature drop reducing efficiency,lgbut tin-lead or silver solders have adequate thermal conductivities and have thermal masses similar to that of thermal epoxies. Large Peltier chips cannot be soldered, but polishing the coil flat, using thermal grease and applying pressure, will provide good thermal contact. Fan-cooled extrusions claim a thermal resistance of 0.07 OC/W for Peltier chips cooling20so they should keep chip outside face temperatures to within 10 "C of ambient. The pump assembly should be insulated throughout and sealed with a desiccant inside. The proposed Joulean heating and Peltier chip designs are comparable. For both designs power is directly proportional to flow rate, and power would be reduced using tubing made of stronger metal with thinner walls, i.e., smaller J, such as tubing made of SS 440C, which has twice the tensile strength of SS316. Either design could be controlled using an accurate pressure gauge and a feedback circuit, but control must also incorporate pump temperature to minimize power usage. The Joulean heating design would be easier to construct and control and could be used for fluids with high critical temperatures such as water. A Joulean heating pump would be able to achieve optimal performance for any given conditions and desired output, so long as the optimal parameters are within the pump's capability. The Peltier design is more efficient for COz and for fluids with lower critical temperatures such as Xe. The efficiency of the Peltier design is improved with larger volume coils, and if the power curve is optimized, efficiency would be improved with higher total capacity (total GN) of Peltier chips. Fluid tanks needed depend on which of the two designs. Tank pressure must be above vapor pressure in the pump vessel to fill it with high-density fluid. The Joulean heating design needs a tank superpressurized with helium, with a dip tube and held vertical, because the temperature in the pump will be slightly above ambient at the refill step. The Peltier chip design can operate with an ordinary tank, however, since the pump is cooled to below ambient so tank pressure will be above the vapour pressure in the pump vessel. Superpressurizing tanks with helium will reduce pump power, by eqs 7 and 19, but helium has been shown to dissolve in COz and affect its solvent properties. Modifier can be added to the supercritical fluid after the fluid leaves the pump, either by spiking the extraction vessel or by (19) Cullen, D. J.; Zawojski, M. S.; HolbrookA L. Plast. Eng. 1988,1,37-44. (20) Thermoelectric Product Catalog and Technical Reference Manual; Intemational ThermoelecMc Inc.: Chelmsford. MA, 1992.
Table 3. Optimum Power and Settings for the Peitler Device Pump under Different Condltionsa settings
condition, variation
minimum power (W)
standard conditions Tmb -15/+15 "c P -2000/+2000 psi P~ +400/-400 psi J -0.9/+2.7
125 113/133 85/165 117/135 75/275
T,,,i,, ("C)
6 0/10
12/2 10/3 6
T,, ("C)
vc
163 143/177 127/195 152/168 163
o
0.038 0.028/0.051 0.031/0.043 0.034/0.042 0.038
@lo
min total GN (cm)
0.112 0.111/0.108 0.082/0.137 0.102/0.116 0.112
70 77/61 76/70 75/70 42/154
Standard conditions: k = 0.01 g/s, P = 8000 si, Ptpnk 1500 psi, Tmb = 30 "C, Peltier chip outside face 10 "C above Tmb,pump vessels assumed coils, 1 tube thick, of l/* in. 0.d. 3316 tuting,J = T6,squared off with 5050 tin-lead solder. Coil face area 16 cmz, between 4 x 4 cm Peltier chips of thermal mass 2.78 cal/"C each (Melcor Model CP 1.4127-045L).
using a separate pump connected to the fluid line. The thermal pump would have poor performance pumping a fluid that already contained a modifier, however, because impurities reduce the pressure vs temperature gradient of pure fluids signiicantly. The portable thermal pump design is capable of delivering COz at pressures and flow rates used in SF applications. The maximum flow rate and pressure normally used in SFE currently are 2 mL/ min and 10 OOO psi. A twestage Joulean heating/air cooling pump with 10 m of tube per stage and one fan per stage could fit into a 30 x 30 x 20 cm case and would deliver 2 mL/min at 10 OOO psi drawing about 450 W. A Peltier chip pump using H O C coils with eight times the volume per chip as in Table 3 would deliver 2 mL/min at 10 000 psi drawing about 150 W. A deepcycle, carsize battery can provide 150 W for 4 h. Optimizing the power curve and engineering development should produce further improvement in energy efficiency. The thermal pump could also produce higher pressures if built with fittings and tubing rated for higher pressures. The pump's safety is assured by the commercial pressure ratings of tubes and fittings. The pump casing will protect against burst and heat hazards, and rupture disks could be connected
on-line between pump and extraction vessel without affecting pump performance. Safety features should also be incorporated into the electronics that control the pump. The pump design is simple and safe, so many laboratories would be capable of building a Joulean heating or the Peltier chip thermal pump for SF applications. ACKNOWLEWMENT Thanks to Dr. Frank Schweighardt for donating the C02 tank. Dr. Frank Goodman of the Applied Mathematics department helped with heat transfer modeling. This research was supported by Supelco Canada and the Natural Sciences and Engineering Research Council of Canada. The thermal pump technology is licensed exclusively to Supelco who is responsible for its commercial development.
Received for review May 18, 1994. Accepted August 22,
1994.B @Abstractpublished in Advance ACS Abstmcts, October 1, 1994.
Analytical Chemistry, Vol. 67, No. 1, January 1, 1995
219
