Designing for Super- Critical Fluid Service Working with Supercritical Fluids Poses Challenges When Designing Heat Exchangers
Total Page:16
File Type:pdf, Size:1020Kb
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).