NBS NAT L INST. OF STAND & TECH R.LC. Reference PySU- ca^oRs AlllDM SE^T7S IMBSIR 79-1612 ISOBUTANE: PROVISIONAL THERMODYNAMIC FUNCTIONS FROM 114 TO 700 K AT PRESSURES TO 700 BAR Robert D. Goodwin Thermophysical Properties Division National Engineering Laboratory National Bureau of Standards Boulder, Colorado 80303 Prepared for: Gas Research Institute 10 West 35th Street Chicago, Illinois 60616 July 1979 QC- 100 .056 79-1612 1 7 1979 NBSIR 79-1612 ’ « \ ISOBUTANE: PROVISIONAL THERMODYNAMIC FUNCTIONS FROM 114 TO 700 K AT PRESSURES TO 700 BAR Robert D. Goodwin Thermophysical Properties Division National Engineering Laboratory National Bureau of Standards Boulder, Colorado 80303 July 1979 Prepared for: Gas Research Institute IOl West 35th Street Chicago, Illinois 60616 U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary Sidney Harman, Under Secretary Jordan J. Baruch, Assistant Secretary for Science and Technology NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director CONTENTS Page 1. INTRODUCTION 1 2. PHYSICAL PROPERTIES . 1 2.1 Fixed-Point Values 2 2.2 Melting Line and Vapor Pressures 2 2.3 The Orthobaric Densities 4 2.4 The Virial Equation 5 2.5 The Equation of State 6 2.6 The Ideal Gas Functions 8 2.7 Thermal oop Computations 8 2.8 The Heats of Vaporization 9 2.9 Saturated Liquid Specific Heats 9 3. COMPUTATIONAL METHODS 10 3.1 The Homogeneous Domain 10 3.2 The Saturated Liquid 11 3.3 The Compressed Liquid 12 4. TESTS AND COMMENTS 12 5. TABLES OF PHYSICAL AND THERMODYNAMIC PROPERTIES 14 5.1 Calculated P-p-T Isochores and Isotherms 14 5.2 The Joule-Thomson Inversion Locus ' 14 5.3 Thermophysical Properties of the Saturated Liquid 14 5.4 Thermophysical Properties Along Selected Isobars 15 6. ACKNOWLEDGMENTS 15 7. REFERENCES 16 APPENDIX A. Symbols and Units 20 APPENDIX B. Fixed-Point Values for Isobutane 21 APPENDIX C. Computer Programs 163 iii LIST OF FIGURES Page Figure 1. The densi ty-temperature diagram of isobutane 22 Figure 2. The P-T locus of P-p-T data for isobutane 23 Figure 3. Comparison of enthalpies at T = 250 F 24 Figure 4. Comparison of enthalpies for saturated liquid 25 Figure 5. Calculated enthalpy at P = 50 bar 26 LIST OF TABLES Table 1. Vapor pressures of isobutane 27 Table 2. Densities of saturated liquid 29 Table 3. Densities of saturated vapor 33 Table 4, Second virial coefficients 35 Table 5. Coefficients of the equation of state 36 Table 6, Calculated P(p) critical isotherm . 37 Table 7. Summary of P-p-T data 39 Table 8. Comparisons with P-p-T data 40 Table 9. Comparisons with data for ideal gas functions 49 Table 10. Interpolated ideal gas functions 50 Table 11. Specific heats for saturated liquid at T < T^ 51 Table 12. Estimated coexistence data at T < Tj^ 52 Table 13. The heats of vaporization 53 Table 14. Comparisons with data for Cp(p,T) 56 Table 15. Comparisons of functions at T = 250 F 58 Table 16 Comparisons of functions at T = 440 K 59 Table 17. Comparisons with Starling, et al . on isotherms 60 Table 18. Calculated P(T) isochores 66 Table 19. Calculated P(p) isotherms 82 Table 20. The Joule-Thomson inversion locus 101 Table 21. Thermophysical properties of saturated liquid 102 Table 22. Thermophysical properties along isobars 105 IV ISOBUTANE: PROVISIONAL THERMODYNAMIC FUNCTIONS FROM 114 to 700 K AT PRESSURES TO 700 BAR Robert D. Goodwin Thermophysical properties of isobutane are tabulated at in- tegral temperatures along isobars over the entire range of fluid states. Results for the compressed liquid, from the triple- to the boiling-point, have been estimated by use of the highly con- strained, nonanalytic equation of state, because experimental P-p-T data are lacking in this region. Key words: Densities; enthalpies; entropies; equation of state; internal energies; isobars; isobutane; isochores; isotherms; Joule-Thomson inversion; latent heats of vaporization; melting line; orthobaric densities; specific heats; speeds of sound; vapor pressures. V 1. INTRODUCTION Isobutane not only is a component of liquefied natural gas (LNG), but also may become an important heat-exchange fluid for geothermal cycles [37]. The present report is fifth in a series on the pure component of LNG, namely methane, ethane, propane, n-butane, and isobutane. Earlier compendia on isobutane have been presented by Das, et al . [12], and by Starling, et al . [37]. Functions for ideal gas states recently were computed from spectroscopic data by Chen, et al . [6]. A survey of available data quite recently has been prepared by Kestin, et al . [25], and thermodynamic properties have been tabulated by Mil ora and Combs [28a]. Our objective in this report is to provide additional background and provisional derived properties on isobutane. At present, serious deficiencies exist in accurate experimental P-p-T data for the single phase, and for the coexistence boundary: vapor-pressures; orthobaric densities; and heats of vaporization. Whereas no P-p-T compressibility data exist for compressed liquid isobutane at temperatures roughly below 300 K, there are accurate data for the saturated liquid densities. By use of these data in the present, highly constrained equation of state, we have estimated thermophysical properties for the compressed liquid at low temperatures. Also presented here are formulations of the vapor pressures, the orthobaric densities, the virial equation, the equation of state, the ideal gas thermofunctions, the heats of vaporization, specific heats for the saturated liquid, thermophysical properties on the liquid-vapor coexistence boundary from the triple- to the critical-point, and thermophysical properties at integral temperatures along isobars from 0 .1 through 700 bar. To validate present work, some comparisons are made with results of Sage and Lacey [34], of Das, et al . [12], and of Starling, et al . [37]. 2. PHYSICAL PROPERTIES Symbols and units appear in Appendix A. The density-temperatures diagram of isobutane is presented by fig. 1. The upper, left corner gives the freezing liquid line. 2.1 Fixed-Point Values These values are listed in Appendix B. (a) The Triple Point . The temperature is adopted from Das, et al . [12]. The pressure is obtained from our vapor-pressure eq. (2). The liquid density is assigned for consistency with data in eq. (3). The vapor density is obtained from our saturated-vapor densities eq. (4). (b) The Boiling Point . The temperature is from our vapor-pressure eq. (2) at a pressure of 1 atm = 1.01325 bar. Liquid and vapor densities are from eqs. (3) and (4). (c) The Critical Point . The temperature of 408.0 K is adopted in present work on the basis of fitting orthobaric densities, P-p-T data, and examining behavior of the calculated critical isotherm. Beattie, et al . [2] derived the experimental value 134.98 + 0.05°C (Int.). The present critical density of 3.86 mol/L is adopted on the same basis as Tq, above. Beattie, et al . found 3.80 + 2 percent mol/L. The critical pressure from our vapor-pressure eq. (2) i 36 .549 bar, as compared with 36.477 + 0.05 bar found by Beattie, et al . 2.2 Melting Line and Vapor Pressures (a) The Melting Line . Measurements were described by Reeves, Scott, and Babb [32]. We are grateful for a private communication from Professor Stanley E Babb, Jr., October 2, 1978, giving these, lower-pressure data for isobutane. P,bar 140 .6 ”1140 160.3 3047 164.7 3720 = By graphical approximations (for T-^ 113.55 K) , we have estimated the constants Pq = 430 bar, and e = 6.08 for the Simon equation. = - P P, - P„ [(T/T^f 1], ( 1 ) These constants differ greatly from those for other substances, e.g.. 2 P^, bar e Methane 1909 1 .85 Ethane 2560 2.179 Propane 7180 1 .283 n-butane 3634 2.210 Isobutane 430 6.08 (b) The Vapor Pressures . Data used for adjusting eq. (2) appear in table 1. Values at ID = 40 have been derived via thermal loops, as described in [17], by use of the saturated liquid specific heat data of Aston [1] from the triple- to the boiling-point; the heat of vaporization at the normal boiling point [1]; the ideal gas thermofunctions formulated here in section 2.6; the virial equation formulated here in section 2.4; and, for the minor contribution of V*dP to AH on the saturated liquid path, we also used preliminary vapor-pressure and saturated liquid densities equations. Equation (2) is similar to previous forms [17,18,19]. The arguments for eq. (2) are x(T) E T/T^, u(T) E (1 - 1/x), = - £n(P) a + b*u + c*x + d*x^ + e*x^ + f*x*(l x)^ , (2) where P is in bar, e = 1.95, and - a = 13.8083 5297 d = 112.7583 3458 b = 9 .3726 9200 e = - 52.4214 0768 c = -70.5466 3008 f = 47 .8112 2198 Exponent c was selected for a best "fit" of P-p-T data under the constraint that, at the critical point, the slope of the critical isochore, from the equation of state, be equal to the slope of the vapor-pressure equation, 3P/3T = dP^/dT. The fit of present vapor-pressure data is totally insensitive to values 3 1.1 j< e <. 1.95, but the critical-point slope is dependent on the value of e. The present slope at the critical point is dPo/dT = 0.6341 bar/K. The last column of table 1 gives the experimental difference, - - ^n(P/P^)/£n(P^/P^) - (1 T^/T)/(l T^/T^) , which would be zero for the elementary vapor-pressure equation, £n(P) = a - b/T, when a and b are eliminated by constraint to the end-points.