Designing for Super- Critical Fluid Service Working with Supercritical Fluids Poses Challenges When Designing Heat Exchangers

ELECTRONICALLY REPRINTED FROM NOVEMBER 2019 Heat Exchangers: Designing for Super- critical Fluid Service Working with supercritical fluids poses challenges when designing heat exchangers. Some practical tips and precautions are presented here

Graham James R. Lines ndustrial applications involving fluids at high Graham Corp. pressure — pressure above the critical pres- sure of a particular fluid — are increasing in Inumber. This is due to the beneficial proper- ties of supercritical fluids (SCFs) or simply due to very high pressures required for certain ap- IN BRIEF plications. Examples include supercritical CO2 THERMAL DUTY acting as a solvent in an extraction process, supercritical water for waste treatment via an TEMPERATURE VERSUS THERMAL DUTY oxidation process (Figure 1), supercritical nitro- gen for an enhanced-oil-recovery process or FLUID PROPERTY supercritical methane in compressed natural- VARIATION gas service. Table 1 provides a list of the critical HEAT-TRANSFER points for a number of different fluids [1]. The COEFFICIENT phase diagram for CO2, the most commonly used SCF, is shown in Figure 2. SUMMARY Proper design of heat transfer equipment requires greater care and a deeper under- standing of supercritical fluid properties, and in particular, how those properties may vary as temperature changes. This article FIGURE 1. This heat exchanger is used for supercritical water provides design considerations for heat ex- oxidation service. Both hot and cold fluids operate above criti- changers in supercritical service in order to cal pressure achieve reliable process performance. the thermal duty of the heat-exchanger, Q. Under normal conditions, this is most com- Thermal duty monly expressed as Equation (1). When presented with supercritical design requirements, an initial step is to determine (1)

TABLE 1. CRITICAL POINTS FOR VARIOUS FLUIDS [1] Where: · Substance Temperature Pressure m = mass flowrate °F K psia bara Cp = average specific heat capacity ∆T = temperature change Carbon dioxide 87.9 304.2 1,071.8 73.9 It is common for an end user that is re- Carbon monoxide –220.3 133 507.6 35.0 questing a design to provide fluid properties, Hydrogen –399.7 33.3 188.5 13.0 such as the average heat capacity, at the Methane –115.7 191.1 673.0 46.4 average temperature. In supercritical service, Nitrogen –232.5 126.2 491.7 33.9 this can lead to an incorrect determination of thermal duty. Instead, the best practice is to Oxygen –181.0 154.8 736.8 50.8 calculate thermal duty considering change in Water 705.5 647.3 3,203.8 220.9 enthalpy, ∆h, as shown in Equation (2). Heating 1,450 psia CO2 Heating fluid is water at 250°F 10,000 Solid 300.00

1,000 250.00 Liquid Supercritical fluid 100 200.00 Critical point 150.00 10 Pressure, bars Pressure, Triple point Gas 100.00 1 200 250 300 350 400 50.00 Temperature, K Water temperature, °F FIGURE 2. The phase diagram for carbon dioxide illustrates the location of the critical point - CO2 temperature, °F

(50.00) - 500,000 1,000,00 1,500,000 (2) Thermal duty, Btu/h

FIGURE 3. This temperature versus thermal duty graph shows the non-linearity of CO2 curve when heat- Specific heat can greatly vary with ing CO at a pressure of 1,450 psia temperature when operating in the 2 supercritical region. For this reason, tion (2). For such a case, a heat Pseudocritical pressure and tem- the change in enthalpy is the most exchanger would be undersized by perature is a point where the spe- appropriate term for determining approximately 20% if the thermal cific-heat capacity reaches a maxi- the thermal duty. This is best illus- duty using average specific heat mum value. There is great variation trated via an example. Consider a was applied. in specific heat capacity when, at a supercritical CO2-extraction ap- given pressure (isobar), the temper- plication where CO2 at 1,450 psia Temperature versus thermal ature approaches, reaches and sur- (1,000 kPa) and a mass flowrate of duty passes the pseudocritical tempera- 11,023 lb/h (5,000 kg/h) must be Best practice is to graph tempera- ture. Let’s return to Figure 3, which heated from –10°F to 150°F (–23.3 ture change and heat release to un- shows a supercritical-CO2-heating to 65.6°C). The specific heat capac- derstand the shape of the curve. Su- application with water as the heat- ity of CO2 at the average tempera- percritical fluids can have surprisingly ing fluid. The temperature versus ture is 0.637 Btu/lb°F (0.637 kcal/ shaped curves caused by property thermal-duty curve follows with CO2 kg°C). The enthalpy at the inlet and variation as temperature changes. heated from –10°F to 150°F, and outlet temperatures are 63.3 Btu/ In many services, supercritical flu- water cooled from 240°F to 140°F. lb (35.2 kcal/kg) and 189.4 Btu/lb ids will have nonlinear temperature Notice that for CO2, the shape (105.2 kcal/kg), respectively. versus thermal-duty curves, such as of the curve is nonlinear. Common Using enthalpy change, [Equa- seen in Figure 3 [2]. This is especially thinking is that the shape of the heat- tion (2)] the thermal duty is 11,023 relevant when operating conditions ing curve is linear, which is true for × (189.4–63.3) = 1,390,000 Btu/h are between the critical pressure most sensible-heating applications. (350,000 kcal/h). and pseudocritical pressure. First we The nonlinear shape in supercriti- One can see that by using Equa- should define these terms. cal fluid service is due to the large tion (1) with an average specific-heat Critical pressure is the pressure variation in enthalpy and, therefore, capacity and temperature change, above which a fluid is amorphous; specific heat capacity as the CO2 is the thermal duty is 1,123,500 Btu/h that is, where there is not a distinc- heated. In this instance, the super- (283,150 kcal/h) or 81% of the true tion between liquid and gas phases, critical CO2-heating curve bends into required duty determined by Equa- regardless of the temperature. the water curve, thereby, reducing

2,500 psia carbon monoxide heating Supercritical water interchanger Ethylene glycol 220°F to 100°F Supercritical water 4,000 psia 900°F to 500°F Carbon monoxide 160°F to –320°F Supercritical water 4,000 psia 674°F to 350°F 300 Water Carbon monoxide 200 1,000 900 Hot-side temperature, °F Cold-side temperature, °F 100 800 700 0 14.5% difference WMTD versus LMTD 600 -100 WMTD = 212°F 500 LMTD = 185°F 400 = 190°F -200 WMTD 300 LMTD = 185°F -300 200 100 -400 0 0 500,000 1,000,000 1,500,000 2,000,000 0 500,000 1,000,000 1,500,000 2,000,000 2,500,000 3,000,000 3,500,000 4,000,000 4,500,000 Thermal duty, Btu/h Thermal duty, Btu/h FIGURE 4. Shown here are two examples of non-linear behavior of temperature versus thermal duty, and the resulting values calculated for WMTD and LMTD 725 psia carbon dioxide 1,450 psia carbon dioxide 3,000 psia carbon dioxide Water 240°F to 140°F Water 240°F to 140°F Water 240°F to 140°F Carbon dioxide 150°F to –10°F Carbon dioxide 150°F to –10°F Carbon dioxide 140°F to –10°F 300 300 300 250 250 250 200 200 200 150 150 150 T, °F T, °F T, °F 100 100 100 50 50 50 0 WMTD = 130.3°F 0 = 103.7°F 0 WMTD = 113.5°F -50 -50 WMTD -50 0% 20% 40% 60% 80% 100% 0% 20% 40% 60% 80% 100% 0% 20% 40% 60% 80% 100% Percent of thermal duty Percent of thermal duty Percent of thermal duty

Water temperature, °F CO2 temperature, °F

FIGURE 5. Shown here are the heating curves for CO2 at three different pressures the effective mean-temperature difference. the required surface area differs by 40% (see Table 2). Conventional methods for countercurrent flow would Two additional examples comparing WMTD and determine the log mean-temperature difference (LMTD) LMTD are shown in Figure 4, which reinforces the using terminal temperature difference with a classic cal- risk associated with using the linear LMTD calcula- culation as given by Equation (3) tion and how the WMTD calculation yields a different number. The key take-away here is to plot the duty versus temperature and perform a segmented WMTD (3) calculation to get it correct. It is also interesting to compare the shape of the CO2 Due to the shape of the CO2 curve, a classic LMTD heating curve for the very same temperature change calculation will overstate the effective mean-temperature from –10 to 150°F for three different isobars, as shown difference (MTD). In this example, it overstates MTD by in Figure 5. A pressure of 725 psia is below the critical 13%, as the next calculation shows. pressure. As the CO2 is heated, there is sensible heating Best practice is to apply a segmental approach, break- of liquid CO2 up to the boiling temperature of 57.7°F. This ing the temperature curve into segments of smaller tem- is followed by isothermal boiling until all of the CO2 is va- perature changes and applying LMTD calculation for porized, and then gas sensible superheating to 150°F. In each step. This yields a duty-weighted, mean-tempera- contrast, at a pressure of 3,000 psia, which is well above ture difference (WMTD), shown in Equation (4). the critical pressure, the heating curve is close to linear and comparable to a sensible heating. For the 1,450- psia case, which is near to critical pressure, the shape of (4) the heating curve is nonlinear and atypical.

Using 10 segments, one for each 16 degree rise in Fluid property variation CO2 temperature, Equation (4) yields WMTD = 103.7°F. There can be wide variation in fluid properties, such as For reliable performance and accurate heat-exchanger density, specific heat capacity, viscosity and thermal con- sizing, always consider using the WMTD calculation ductivity, between the inlet and the outlet temperature. when the temperature profile is nonlinear. Again, when operating between the critical pressure and Consider together thermal duty and LMTD and how the pseudocritical pressure, the specific heat may vary dramatically different the heat-exchanger selection will greatly with temperature. Good practice is to graph the be. When average specific heat is used, coupled with fluid properties as a function of temperature to under- a classic LMTD, and that is compared to an enthalpy stand how extreme the variation might be. At a pressure based thermal duty with a segmental WMTD, that con- well above the critical pressure and beyond the pseudo- cern for great care is apparent. Assuming the overall critical pressure, such a wide variation is reduced. Refer- heat-transfer coefficient (U) is the same in either case, ring again to the 1,450 psia supercritical CO2 example 1,450 psi CO2 fluid property variation with temperature (Figure 5), the graph shown in Figure 6 300% Thermal depicts how fluid properties vary from Specific heat Density Viscosity conductivity 250% an inlet temperature of –10°F to an 70°F = average temperature outlet temperature of 150°F. Specific between inlet and outlet 200% heat capacity stands out. Noteworthy is the pseudocritical point, which is 150% 1,450 psia and approximately 110°F. Specific heat reaches a maximum at 100%

Percent variation Percent the pseudocritical point and is lower

50% on either side of this point. The graph provides comparison for how prop- 0% erties vary up or down from proper- -20 0 20 40 60 80 100 120 140 160 Temperature, °F ties determined at average tempera- FIGURE 6. Near the pseudocritical pressure, physical properties vary considerably as a function of tem- ture of 70°F (the average of –10°F perature, especially the specific heat and 150°F). Variation of Re, Pr and HTC with temperature Heat transfer coefficient 1,450 psig CO2 –10°F to 150°F 400% Supercritical fluids are often on the Re (left-hand scale) Pr (right-hand scale) HTC (right-hand scale) 200% tubeside of a heat exchanger due to 350% 175% the high operating pressure, which 300% 150% is mechanically easier to contend 70°F average temperature with on the tubeside. Fluid prop- 250% 125% erties directly influence the heat- 200% 100% Variation, % Variation, transfer coefficient. When applying 150% 75% a classic Nusselt equation for in- 100% 50% tube flow at turbulent conditions, one can identify how a local heat- 50% 25% transfer coefficient is impacted by 0% 0% -20 0 20 40 60 80 100 120 140 160 fluid properties, by the relationship Temperature, °F between the Nusselt number, Nu, FIGURE 7. The variation of Re, Pr and HTC as a function of temperature is shown here for CO2 at 1,450°C Reynold number, Re, and Prandtl number, Pr: density, specific heat and viscosity. Further to a segmental approach (5) used to determine WMTD, it is rec- (7) ommended that HTC is considered Expression (5) reduces to Expres- segmentally as well to capture HTC sion (6), which shows the relation variation along the temperature (8) between the tubeside heat-transfer change. The graph shown in Figure coefficient, HTC, and the physical 7 illustrates that, for 1,450 psig CO2, Where: properties of viscosity, η, thermal the calculated HTC variance is 87% Twall,ID = Tubewall temperature at conductivity, κ and specific heat, CP: at the inlet, 157% near the pseudo- the inside surface of the tube critical point and 90% at the outlet Twall,OD = Tubewall temperature at compared to the HTC determined at the outside surface of the tube (6) the average temperature of 70°F. This TTS = Tubeside bulk temperature From the graph shown in Figure 6, observation supports using a seg- TSS = Shellside bulk temperature the specific heat variation greatly af- mental approach (or discretization of U = Overall heat transfer coefficient fects HTC, as does the viscosity and temperature change) to capture cor- HTC = Supercritical fluid heat-transfer the thermal conductivity. rectly the local LMTD and HTC. coefficient Research with supercritical fluids As noted previously, the bulk or av- HSS = Shellside heat transfer has found there can be significant erage fluid properties can vary signifi- coefficient radial property variation within a tube cantly from the fluid properties at the Let’s return to the CO2 heating ap- between average bulk temperature tube wall. Such variation will also in- plication at 1,450 psig. By applying a properties and those at the tube-wall fluence HTC. The following equations segmental analysis with 10°F incre- temperature. There are factors one are used for determining tubewall ments, we can compare the bulk or might apply to reflect the impact of temperature on the inside (supercriti- average temperature to the temper- bulk and tube-wall fluid properties for cal fluid side) and outside surface. ature of the tubewall inside diameter. There can be order-of-magnitude differences between bulk and tube- Bulk and tubewall property variation wall properties when working with CO2 bulk temperature Tubewall I.D. temperature Water bulk temperature 300 supercritical fluids. The graph shown in Figure 8 plots the tubewall tem- 250 perature along the heat curve and illustrates how the fluid properties 200 vary greatly between the bulk and

150 those at wall temperature. 130° Some literature suggests using

Temperature, °F Temperature, 100 film-temperature properties. Film Property 50°F 130°F temperature is commonly consid- 50 ered to be the average of segment Density, lb/ft3 57.5 20.6 50° Specific heat capacity, Btu/lb-°F 0.559 0.975 bulk and tubewall temperatures. 0 Viscosity, cP 0.097 0.026 Other literature applies correction Thermal conductivity, Btu/(h-ft-°F) 0.063 0.0254 -50 factors for variation in specific heat 0 10 20 30 40 50 60 70 80 90 100 and density. The author suggests Percent of thermal duty applying physical properties that FIGURE 8: This graph shows the variation of properties in the bulk and at the tubewall as a function of directionally drive the calculated temperature HTC lower to provide a degree of Supercritical water Supercritical carbon dioxide 12.0 4.5 10.0 4.0 3.5 3,300 psia 8.0 3.0 1,250 psia 3,500 psia 2.5 1,450 psia 6.0 3,700 psia 1,650 psia 3,900 psia 2.0 1,850 psia 4,100 psia 4.0 1.5 2,050 psia 4,300 psia 4,500 psia 1.0 2,500psia Specific heat, Btu/lb-°F Specific heat, Specific heat, Btu/lb-°F Specific heat, 2.0 5,000 psia 0.5 3,000 psia 0.0 0.0 600 625 650 675 700 725 750 775 800 825 850 875 60 80 100 120 140 160 180 Temperature, °F Regions where specific heat varies Temperature, °F greatly with changes in both pressure and temperature resulting in nonlinear temperature versus thermal duty curves Supercritical nitrogen Supercritical methane 2.5 4.5 4.0 2.0 3.5 500 psia 3.0 700 psia 1.5 600 psia 2.5 800 psia 800 psia 2.0 900 psia 1.0 900 psia 1,000 psia 1.5 1,000 psia 1,100 psia 0.5 1,500 psia 1.0 1,200psia Specific heat, Btu/lb-°F Specific heat, 2,000 psia Btu/lb-°F Specific heat, 0.5 2,500 psia 0.0 0.0 -320 -300 -280 -260 -240 -220 -200 -180 -160 -140 -120 -100 -200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 20 Temperature, °F Temperature, °F FIGURE 9. These graphs show the variation of specific heat with temperature at several isobars for four different fluids. The shift of the pseudocritical tempera- ture can be observed

TABLE 2. COMPARISON OF LINEAR VERSUS SEGMENTED CALCULATION duty to understand shape of the Parameter Best practice Risky practice curve • When warranted, perform a seg- Thermal duty ( ), Btu/h 1,123,500 ( -based) Q 1,390,000 (∆h-based) Cp mental analysis to capture cor- MTD, °F 103.7 (segmented) 117.5 (linear) rectly WMTD and within each Q/MTD 13,404 9,566 segment to determine surface Area, ft2 (if U = 100) 134 96 area necessary based on segment thermal duty, segment LMTD and segment HTC safety. Film temperature serves as temperature is 90°F. Recall a previ- • Evaluate bulk and wall property a good surrogate for determining ous definition for pseudocritical tem- variation to determine if further what properties to apply. The author perature and pseudocritical pressure HTC refinement is necessary n further suggests comparing bulk that describes where specific heat Edited by Gerald Ondrey and film properties and using that is a maximum. This is shown as the property that yields a lower calcu- apex for each isobar in the graphs References lated HTC. If, however, the design shown in Figure 9. 1. Van Wylen, Gordon J. and Sonntag, Richard E., “Fun- damentals of Classical Thermodynamics,” Wiley, Hobo- provides adequate safety factors, ken, N.J., 1993. such as, for example, a 60% cleanli- Summary 2. All fluid-property modeling used to gener- ness factor or a 50% excess area, Supercritical fluid heat transfer war- ate the graphs was done using NIST REF- PROP webbook, https://webbook.nist.gov/ then using film temperature for fluid rants more careful consideration chemistry/name-ser. properties is adequate. than normally needed for more tra- Each supercritical fluid is unique, ditional heat-exchanger designs. Author and the temperature-pressure region This is due to fluid property varia- James R. Lines is president and where a nonlinear thermal-duty curve tions when operating above the CEO of Graham Corp. (20 Florence Ave., Batavia, N.Y. 14020; Phone: is most likely will depend on a given critical point and for a given iso- 585-343-2216; Fax: 585-343- fluids’ properties. The closer the bar when the operating tempera- 1097; Email: jlines@graham-mfg. operating pressure is to the critical ture is near to, or passes through com), a position he has held since 2008. Prior to that, Lines served as pressure, the more variation in spe- the pseudocritical temperature. At president and COO and as a director cific heat as temperature changes a pressure well above the critical of the company. He has been working at the company in various capacities is to be expected. Carbon dioxide point there is less concern as prop- since 1984, holding positions of vice president and general has a critical pressure of 1,072 psia. erty variation is not as significant. manager, vice president of Engineering, and vice president of Figure 9 illustrates how specific heat Key design considerations include Sales and Marketing. Prior to joining the management team, he served as an application engineer and sales engineer as varies as temperature varies for dif- the following: well as a product supervisor. Lines holds a B.S. in aerospace ferent isobars. Note that the specific • Determine the thermal duty of a engineering from the State University of New York at Buffalo. heat of 1,100 psia CO , which is just supercritical fluid using enthalpy The author’s company has designed and successfully sup- 2 plied its Heliflow heat exchangers in supercritical service for slightly greater than the critical pres- change carbon monoxide, carbon dioxide, nitrogen, hydrogen, oxy- sure, is 29.72 Btu/lb°F when the • Graph temperature versus thermal gen, methane, water and various other fluids.

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