AN INVESTIGATION OF TEMPERATURE CORRECTION FACTORS OF LIGHT HYDROCARBON FUELS

Transcription

1 AN INVESTIGATION OF TEMPERATURE CORRECTION FACTORS OF LIGHT HYDROCARBON FUELS A Report for National Measurement System Department for Innovation, Universities and Skills Kingsgate House Victoria Street London SW1E 6SW Project No: FFRE31 September 2008 Report No: XXXX/XXX Page 1 of XX MONTH YEAR Project No: XXXXXX

2 The work described in this report was carried out by TUV NEL Ltd under contract to the Department for Innovation, Universities & Skills ( the Department ) as part of the National Measurement System s Engineering & Flow Programme. The Department has a free licence to copy, circulate and use the contents of this report within any United Kingdom Government Department, and to issue or copy the contents of the report to a supplier or potential supplier to the United Kingdom Government for a contract for the services of the Crown. For all other use, the prior written consent of TUV NEL Ltd shall be obtained before reproducing all or any part of this report. Applications for permission to publish should be made to: Contracts Manager TUV NEL Ltd Scottish Enterprise Technology Park East Kilbride G75 0QF jduff@tuvnel.com Tel: +44 (0) TUV NEL Ltd 2008

3 TUV NEL Ltd EAST KILBRIDE GLASGOW G75 0QF UK Tel: +44 (0) Fax: +44 (0) AN INVESTIGATION OF TEMPERATURE CORRECTION FACTORS OF LIGHT HYDROCARBON FUELS A Report for National Measurement System Department for Innovation, Universities and Skills Kingsgate House Victoria Street London SW1E 6SW Prepared by: Date: September 2008 Dr. Andy Johns Approved by: Date: September 2008 Dr. Linda Rowan for M Valente Managing Director Project No: FFRE31 Page 1 of 14 September 2008

4 EXECUTIVE SUMMARY Custody transfer transactions of liquid fuels such as Liquid Petroleum Gas (LPG) have traditionally been based on the volume occupied by the liquid at standard conditions (15 o C and the bubble-point equilibrium pressure). However light hydrocarbons are stored and transferred at conditions quite different from standard conditions. This means that a measurement of liquid volume at operating temperature and pressure must be converted to the volume at standard conditions. The equation used to perform the conversion involves the use of a correction factor C TL for the effect of temperature on volume. The currently recognized standard for determination of C TL is the GPA Technical Publication TP-25. It is based on data from careful experimental measurements. Over the last years, computational models for the calculation of thermodynamic properties of pure substances and their mixtures have improved in accuracy. Software packages that predict the liquid density directly as a function of both temperature and pressure are commercially available. This approach provides a potential alternative to the GPA TP-25 document. The main objective of work described in this Report is to compare the predictions of these new thermodynamic models (in commercially available quality software) with the GPA TP-25 standard methodology. The software packages under consideration use EOS (equation of state) based models that predict the density of a fluid at specified temperature and pressure and molar composition. Two reputable software packages were selected for the comparisons: PPDS produced by TUV NEL Ltd. REFPROP produced by USA National Institute for Science and Technology. These packages were chosen because they are commercially available and have been implemented by leading experts in the field of thermophysical properties who have access to high quality experimental data at national standards laboratories. Three representative fluids were selected to assess the applicability of the software packages, namely (1) pure propane, (2) pure butane and (3), a mixture of propane and butane containing 0.8 mole-fraction of propane. The results of the comparisons showed excellent agreement between the predictions of the volume correction factor C TL from PPDS and REFPROP for pure butane and propane. Over a representative temperature range the differences between the software packages and the TP-25 standard are within to the RMS error of the standard. It can therefore be concluded that the software packages can be used as an alternative to the TP-25 standard. Project No: FFRE31 Page 2 of 14 September 2008

5 CONTENTS Page NOTATION INTRODUCTION OBJECTIVES SOFTWARE PACKAGE SELECTION REFPROP PPDS GPA TP RESULTS Validation of the TP-25 VBA Code Module Comparison with PPDS and REFPROP Codes Experimental Data Uncertainty CONCLUSION... 9 REFERENCES... 9 ACKNOWLEDGMENTS... 9 APPENDIX Project No: FFRE31 Page 3 of 14 September 2008

6 NOTATION C PL Volume correction factor for pressure - C TL Volume correction factor for temperature - P Pressure N.m -3 T Temperature K V Specific volume m 3.kg -1 ρ Density kg.m -3 Project No: FFRE31 Page 4 of 14 September 2008

7 1 INTRODUCTION The increasing use of light hydrocarbons as new sources of fuel, e.g. LNG (Liquid Natural Gas) and LPG (Liquid Petroleum Gas) has highlighted the problem of correcting the flowing liquid volumes for these substances to equivalent volumes at standard conditions so that a custody transfer transaction can take place. The basic equation for performing the conversion is: ρ = (1) eq CTL C PL ρ60 In equation (1) the correction from a standard density at 60 o F at the bubble-point equilibrium pressure ρ, to the actual density, ρ, at line conditions is effected by eq 60 applying two separate correction factors: one for temperature, C TL, and the other for pressure, C PL. The American GPA (Gas Processors Association) commissioned a joint research project on this subject that was undertaken by the USA National School of Mines in Colorado and the National Institute of Standards and Technology (NIST) who published their findings [1,2] in The objective of that work was to improve the accuracy of the correction factors used in equation 1 above by making careful experimental measurements on a series of light hydrocarbons and some of their mixtures. At that time the recognised standard for obtaining the volume correction factor for temperature effects, C TL, was the ASTM/IP Petroleum Measurement Table D-1250 [3]. Table 24 of that publication covers fluids with a relative density less than The corresponding adopted standard for the calculation of C PL was the API Manual of Petroleum Measurement Standards, Chapter [4]. After the publication of the research reports [3,4], the GPA went on to publish Technical Publication TP-25 [5] in 1998 which was jointly endorsed by ASTM (the American Standards for Testing and Materials), API (American Petroleum Institute) and the GPA itself. TP-25 was produced under the API standardization procedures and is designated as an API standard. Over the last years, computational models for the calculation of thermodynamic properties of pure substances and their mixtures have improved in accuracy. The prevalence of powerful personal computers have made it easy to obtain software packages from reputable sources that will calculate the density directly as a function of both temperature and pressure. 2 OBJECTIVES The main objective of the work described here is to ascertain how the new models for calculating thermodynamic properties (obtainable from commercially available quality software) are capable of meeting the GPA TP-25 standard for volume correction of these light hydrocarbons. The software packages under consideration are all EOS (equation of state) based models which calculate the density of a fluid at specified temperature and pressure and molar composition, rather than calculate the correction factors C TL and C PL directly. 3 SOFTWARE PACKAGE SELECTION Two reputable software packages were selected for the comparisons: Project No: FFRE31 Page 5 of 14 September 2008

8 REFPROP produced by USA National Institute for Science and Technology. PPDS produced by TUV NEL Ltd. These packages were chosen because they are commercially available and have been implemented by leading experts in the field of thermophysical properties who have access to high quality experimental data at national standards laboratories. 3.1 REFPROP The mixture models used in REFPROP vary by type of mixture (i.e., refrigerant or hydrocarbon mixtures). Constituents typically found in natural gas can be modeled by the latest GERG model [6]. This is an extended corresponding states model which uses the principle that all substances can be mapped onto a universal equation of state by applying some reducing parameters that are specific for each fluid. i.e. { P P, V / V, T T } = 0 f / / (2) In equation (2) P c, V c, and T c are the critical constants for a given fluid. 3.2 PPDS c c The PPDS software has a range of common thermodynamic models which can be used. The one that was deemed most suitable uses the extended corresponding states method of Lee and Kesler [7] to calculate the density and cubical expansion coefficient for a mixture. This was an early implementation of the corresponding states technique which bases the properties of a given mixture on an interpolation between the equations for two hypothetical fluids (called the simple fluid and reference fluid). 3.3 GPA TP-25 An EXCEL workbook implementation of the GPA TP-25 standard was coded as a VBA (Visual Basic for Applications) module. This provided a framework from within which both REFPROP and PPDS calculations were compared. 4 RESULTS 4.1 Validation of the TP-25 VBA code module The VBA code was validated against the 18 sample calculations set out in the GPA standard and the results are shown in Table 1 in the Appendix. The shaded columns in the table are the 2 inputs; temperature in Fahrenheit and relative density, and the third column is the output correction factor, CTL_EX from the TP-25 standard. To the right of the shaded column are the corresponding results for the coded correction function in the EXCEL workbook. The inputs to this function are temperature in Celsius and saturated liquid density at that that temperature. The output from the function for the correction factor is given in the column labelled CTL_OUT. The difference between the standard values and the calculated values (multiplied by 10 5 ) are shown in the rightmost shaded column of the table. Examples 12 through to 16 are deliberate error condition calculations. For all examples that are valid (i.e. Ex 1 11 and Ex 17 18), the differences are negligible. Any differences arise from the mandated use of rounded input values in the standard, where the input temperature is rounded to 0.1 o F and the relative density to c Project No: FFRE31 Page 6 of 14 September 2008

9 The VBA code, which uses double precision arithmetic throughout, does not implement any rounding of the input parameters. 4.2 Comparison with PPDS and REFPROP Codes To compare the results of calculating C TL from the two software packages, 3 fluids were selected, namely (1) Pure Propane, (2) Pure Butane and (3), a mixture of Propane and Butane containing 0.8 mole-fraction of propane. Both PPDS and REFPROP return values for the liquid density at specified temperatures and pressures and also values of the Volume Expansion coefficient, alpha, α, which is defined by: 1 ρ T α = (3) ρ p Both programs were run over a range of temperatures from 0 to 40 Celsius to obtain saturated liquid densities and Volume Expansion Coefficients. C TL was obtained from the ratio of the calculated density to the density at standard conditions. The results of the comparisons are shown in Tables 2-5 in the Appendix. Figure 1 below shows the values of the Volume Expansion Coefficient calculated for the 3 selected fluids using the 2 software packages. The open symbols are data from the PPDS software, whilst the crosses are the corresponding data from the REFPROP package. It is clear from Figure 1 that the values from the two sources are in very close agreement. Coefficient of Cubical Expansion for the Saturated Liquid Expansion coefficient [ o C -1 ] PPDS Propane PPDS Butane REFPROP - Propane REFPROP - Butane PPDS[0.8]Propane + [0.2]Butane REFPROP [0.8]Propane + [0.2]Buane Temperature [ o C] Figure 1 Comparison of Volume Expansion Coefficients Figure 2 below shows a comparison of the C TL values predicted by PPDS and REFPROP with those from the TP-25 standard. It shows a plot of the differences, expressed as percentages, between C TL calculated from the TP-25 standard and the value from the relevant software package. Project No: FFRE31 Page 7 of 14 September 2008

10 Implementation of the TP-25 standard for C TL requires the relative density at either the working condition or standard conditions. For each software package the corresponding TP-25 C TL values were obtained using the saturated liquid density predicted by the package at the standard conditions. In the case of pure propane and butane, the calculated values of α and the saturated liquid density from PPDS and REFPROP are in very close agreement. Thus, for clarity, only the REFPROP values are plotted for the pure components in Figure 2. Propane Butane REFPROP{[0.8]Propane + [0.2]Butane} PPDS{[0.8]Propane+[0.2]Butane} (CTL,TP-25 - CTL,calc)/CTL,TP-25 % Temperature ( o C) Figure 2 Differences Between TP-25 and PPDS/REFPROP Values 4.3 Experimental Data Uncertainty The available experimental data on liquid density for a number of light hydrocarbons and some of their mixtures has been surveyed by Holcomb et al. and reported in GPA Research Report RR-147 [1]. According to the authors, the available published experimental data for pure propane agree to within ±5 kg.m -3 over a liquid range from 310 K to 370 K. The corresponding experimental liquid densities for pure butane agree to within ±1 kg.m -3 in the temperature interval from 300 K to 410 K. The isochoric PVT liquid density measurements of Holcomb et al. [1] for their propane and butane mixture agree with other published data to within ±10 kg.m -3 over a liquid range from 240 K to 420 K. From an analysis of their experimental apparatus and measurement procedure, Holcomb estimated the expanded uncertainty in the NIST density measurements (95% confidence interval) to be ± 0.05%. The standard for the computation of C TL is based on a corresponding states model that used the NIST high-accuracy experimental data for light hydrocarbons in its derivation. Ely [2] in his published report outlines the development of the model and concludes that the RMS (root mean square) percentage error in C TL values is better than ± 0.2%. Figure 2 shows that, over the temperature range from 0 to 40 o C, both PPDS and REFPROP can be used to calculate C TL for propane and butane to within ±0.02% of the TP-25 standard. This is well within the RMS error in the TP-25 standard quoted above. Project No: FFRE31 Page 8 of 14 September 2008

11 Although the agreement in Figure 2 for the mixture is poorer than for the pure components, the difference is still within the margin of ± 0.2%. 5 CONCLUSION This exercise has shown excellent agreement between the predictions of the volume correction factor C TL from PPDS and REFPROP for pure butane and propane. Over a representative temperature range the differences between the software packages and the TP-25 standard are within to the RMS error of the standard. It can therefore be concluded that the software packages can be used as an alternative to the TP-25 standard. REFERENCES [1] Holcomb, C.D.; Magee, J.W.; Haynes, W.M. Density Measurements on Natural Gas Liquids. Research Report RR-147, Gas Processors Association, (1996). [2] Ely, J.F. Volume Correction Factors for Natural Gas Liquids Phase II. Research Report RR-148. Gas Processors Association, (1996) [3] ASTM-IP Petroleum Measurement Tables. ASTM, Washington D.C., (1952), pp [4] Manual of Petroleum Measurement Standards. American Petroleum Institute, Washington D.C., Chapter Compressibility Factors for Hydrocarbons: Relative Density (60 o F/60 o F) and -50 o F to 140 o F Metering temperature. [5] Temperature Correction for the Volume of Light Hydrocarbons Tables 24E and 23E. Technical Publication TP-25. Gas Processors Association, September (1998). [6] Kunz, O., Klimeck, R., Wagner, W., Jaeschke, M. The GERG-2004 Wide-Range Reference Equation of State for Natural Gases and Other Mixtures. GERG Technical Monograph. Fortschr.-Ber. VDI, VDI-Verlag, Düsseldorf, (2006) [7] Lee, B.I. and Kesler, M.G. A generalised thermodynamic correlation based on three-parameter corresponding states. AIChE. J.,1975, vol. 21(3), pp ACKNOWLEDGMENTS This report was compiled as part of a flow metrology project entitled Measurement requirements for Liquefied Natural Gas, Liquefied Petroleum Gas, Compressed Natural Gas, and Hydrogen, under the National Measurement System s (NMS) Engineering and Flow Programme ( The NMS is part of the United Kingdom Government s Department for Innovation, Universities and Skills (DIUS) Project No: FFRE31 Page 9 of 14 September 2008

12 APPENDIX TABLE 1 TESTING VBA CODE MODULE FOR THE GPA TP-25 STANDARD Wat_den_ kg.m -3 Wat_den_ kg.m -3 GPA TP-25 Standard examples VBA Ctl Calculation function (this sheet) Ex_# Tf_in Rd_in Ctl_ex Tc_in Den_in Ctl_out 10 5.Ctl_Diff [-] [-] [-] [-] [-] Project No: FFRE31 Page 10 of 14 September 2008

13 TABLE 2 PROPANE COMPARISON REFPROP: Propane Saturated Liquid Phase Temp. alpha Density CTL_std CTL (REFPROP) CTL-Diff ( C) (1/K) (kg/m³) % Project No: FFRE31 Page 11 of 14 September 2008

14 TABLE 3 BUTANE COMPARISON REFPROP: Butane Saturated Liquid Phase Temp. alpha Density CTL_std CTL (REFPROP) CTL-Diff ( C) (1/K) kg/m 3 % E Project No: FFRE31 Page 12 of 14 September 2008

15 TABLE 4 REFPROP MIXTURE COMPARISON REFPROP: [0.8]Propane + [0.2]Butane Mixture Temp. alpha Density CTL_std CTL (REFPROP) CTL-Diff ( C) (1/K) kg/m 3 % Project No: FFRE31 Page 13 of 14 September 2008

16 TABLE 5 PPDS MIXTURE COMPARISON PPDS: [0.8]Propane + [0.2]Butane Mixture Temp. alpha Density CTL_std CTL (PPDS) CTL-Diff ( o C) (1/K) kg/m 3 % Project No: FFRE31 Page 14 of 14 September 2008