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V- T of COMPRESSED LIQUIDS at HIGH PRESSURES

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V- T of COMPRESSED LIQUIDS at HIGH PRESSURES INVESTIGATION of the CORRELATIONS P- V- T of COMPRESSED LIQUIDS at HIGH PRESSURES A Thesis Submitted to the College of Engineering of Al-Nahrain University in Partial Fulfillment of the Requirements for the Degree of Master of Science in Chemical Engineering by NOOR SABEH MAJIED AL-QAZAZ (B.Sc. in Chemical Engineering 2002) Rbee el- awal 1426 April 2005 ABSTRACT Prediction of the accurate values of molar volume of compressed liquids is very important in process design calculation and other industrial applications. Experimental measurements of molar volume V for compressed fluids are very expensive , so in order to obtain accurate V values, attention has been turned to calculate it from equation of state Alto and Kiskinen[1] equation for pure non polar component, using correlations to Tait equation for polar component, and modification of Rackett equation are used for mixtures. In this study five types of equations of state were used to calculate molar volume V for pure non polar compressed liquid, they are Alto and Kiskinen, Tait, Peng- Robinson, Soave- Redlich- Kowng, Lee- Kesler. These equations were tested against 241 experimental data points of pure non polar compressed liquids and it was found that Aalto and Kiskinen equation is the best compared with the other equations. The results of Alto and Kiskinen gives the average absolute percent deviation of 11 pure components was 0.6276. For pure polar compound using four equations of state, Soave- Redlich- Kowng, Peng- Robinson, Alto and Kiskinen, Tait. These equations were tested against 63 experimental data points of polar compressed liquids and it was found that Tait equation is the best compared with the other equations. A new correlation for Tait equation was made to improve its accuracy and this was done by replacing the two terms in Tait equation (pressure and vapor pressure) with reduced pressure Pr and reduced saturated pressure Prs as follows: β + Pr V =Vs 1− c ln β + Prs I Prediction using this equation agreed with the experimental data where the average absolute percent deviation for 3 polar compounds with 63 experimental data points was 2.1529. For mixtures two equations were used to calculate molar volumes of compressed mixtures, Teja equation and Tait equation with HBT mixing rules, the extend of Tait equation to be applicable for mixtures, with Hankinson- Brobst- Thomson (HBT) mixing rules and modified Rackett equation is applied for mixtures to evaluate the pseudo saturated liquid mixtures which can be written as: 2/ 7 RTcm []1+()1−Trm Vsm = Z cm Pcm This equation agreed with the experimental data where the average percent deviation of 291 points for 7 mixtures was 4.9386, thus this new proposed equation has improved the accuracy considerably and may be considered very satisfactory. II List of Content PAGE ABSTACT I LIST of CONTENT III NOMENCLATURE VI CHAPTEER ONE 1 INTRODUCTION CHAPTER TWO LITRITURE SERVEY 2.1 Equation of State 3 2.2 Law of Corresponding States 3 2.3 The Third Parameter 4 2.3.1 Critical Compressibility Factor 4 2.3.2 Acentric Factor 4 2.4 Polar Compounds 5 2.5 Vapor Pressure 5 2.5.1 Wagner Equation 6 2.6 Critical Properties 6 2.7 Reduced Properties 7 2.8 Compressed Liquid 7 2.9 Alternative Analytical Method 9 2.9.1 Yen and Woods Method 9 2.9.2 A Generalized Correlation for the 10 compressibilities for Normal Liquids 2.10 2.10.1 van der Waals Equation 13 2.10.2 Redlich- Kwong Equation 14 2.10.3 Wilson Equation 15 2.10.4 Soave Equation 16 2.10.5 Peng- Robinson Equation 17 2.11 Lee- Kesler Correlations 17 2.12 Tait Equation for Compressed Liquids 18 2.13 Compressed Liquid Densities based on 20 III Hankinson- Thomson saturated liquid density 2.13.1 Hankinson- Brobst- Thomson Model 20 2.13.2 Alto et al. equation 20 2.13.3 Alto and Kiskinen equation 21 2.13.4 Hankinson- Thomson Model for Saturated density 23 2.14 Mixing Rules 25 2.14.1 The Hankinson-Brobst-Thomson (HBT) 25 2.14.2 An improved Correlation for densities of 25 Compressed liquid and liquid mixtures 2.14.3 Densities of liquid at their Bubble Point 28 2.15 Higher Parameter and Alterative CSP Approaches 29 CHAPTER THREE INVESTIGATION AND DISCUSSION 3.1 Introduction to the Investigation 31 3.2 Pure Component 33 3.2.1 Experimental Data 33 3.2.2 Equations of states 34 3.2.3 Comparison between Tait and Aalto equation 37 3.3 Summary of the Investigation 45 3.4 Sample of calculation of volume of compressed 46 liquid for pure component 3.5 Improvement of Tait equation for polar component 50 of pure liquids in this work 3.6 Sample of calculation for Polar Compounds 54 3.7 Application to mixtures 57 3.7.1 Teja Equation 57 3.7.2 Investigation to the mixtures 57 3.8 Development Method for Mixture in this work 59 3.9 Sample of calculation for Mixture of liquid 62 3.10 Discussion 66 IV CHAPTER FOUR 4.1 Conclusion 75 4.2 Recommendation 77 REFERENCES 78 Appendix A (A-1) Appendix B (B-1) Appendix C (C-1) V NOMENCLATURE A B Constants used in the cubic equation of states AK Aalto and Kiskinen equation BWR Benedict- Webb- Rubin c Constant used in Tait equation LK Lee- Kesler HBT Hankinson- Brobst- Thomson method HT Hankinson- Thomson equation m Constant used in to equations (2-44, 2-46, 2- 51) P Pressure atm Pc Critical Pressure atm Pr Reduced Pressure Prs Reduced Saturated Pressure Ps Saturated Pressure atm PR Peng- Robinson equation R Universal gas Constant atm.cm3/mol.K SRK Soave- Redlich- Kwong equation T Temperature K Tc Critical Temperature K Tr Reduced Temperature -------- V Molar volume cm3/mol 3 Vc Critical Volume cm /mol Vr Reduced volume -------- 3 Vs Saturated volume cm /mol Vrs Reduced saturated volume ------- (0) 3 VR , Functions of Tr for HBT correlations,eq.(2- cm /mol (d) VR 73, 2-74) V* Characteristic volume used in AK equation x Mole fraction Z Compressibility Factor Zc Critical Compressibility Factor ZRA Rackett Compressibility Factor VI GREEK α Constant used in the cubic equation of state Riedel s third Parameter eq. (2-37) βs The isothermal Compressibility of saturated liquid used in Chueh and Prausnitz eq.(2-18) ρ Molar density mol/cm3 3 ρc Critical Molar density mol/cm 3 ρs Saturated density mol/cm ρrs Reduced saturated density ----------- Φ Fugacity coefficient ω Acentric Factor Superscript R1 Simple fluid (eq.2-101) R2 Reference fluid (eq. 2-101) Subscript i Component i ij Component ij m Mixture s Saturated VII CHAPTER ONE INTRODUCTION Molar volume is one of the most important thermodynamic properties of a compound. In almost all design calculations, there is a need for the values of molar volume. For saturated liquid or vapor and for gas phase, volume V, is important in high- pressure processing and particularly in the design and operation of high- pressure pumps for all liquids in the chemical process industries. The volume- handing and power characteristics of such pumps are strongly influenced by a liquid’s isothermal bulk compressibility, k. All liquids will compress significantly at high pressure [1]. Densities are needed in many engineering problems such as process calculations, simulations, equipment and pipe design, and liquid metering calculations. A good density correlation should be accurate and reliable over the whole liquid region from the freezing point to the critical point. In most practical cases, the fluids of interest are mixtures [2]. This work was made to study the equations which were used for calculating the molar volume of compressed liquids, and shows which equation gives good results than the other equations. The principal aim of this work is to study the existing equations for calculating the molar volume, and to modify or improve the best equation in order to come out with an equation, or equations, that may predict the molar volume for pure compressed liquid or for mixture of compressed liquids with high accuracy. 1 This study includes a modification of Tait equation to be accurately applicable to pure polar compressed liquid and introduces new mixing rules for saturated liquid density which is applied to calculate the molar volume of mixtures. 2 CHAPTER TWO LITERATURE SURVEY 2.1 Equation of State [3, 4, 5] An equation of state is an equation that relates pressure, temperature, and specific volume. Many different equations of state have been developed over the years. Some have been purely empirical and others have been based on kinetic theory and/or thermodynamic considerations. However all are empirical in the sense that the constants must be determined from experimental observations, and the equations are valid only for interpolation in the region where experimental data have been obtained. While the equation of state primarily describe gas- phase properties, many modern equations are also useful for prediction of liquid-phase properties of the substance. A thorough understanding of these methods is necessary to understanding of classical thermodynamics. The simplest equation of state is that for an ideal gas. 2.2 Law of Corresponding States [3, 6] van der Waals in1897 introduced the theorem of corresponding states, which states that different compounds at identical conditions of reduced temperature and reduced pressure will exhibit identical reduced volumes. It was expanded to say that they will have the same compressibility factor (Z). Ζ = f (Τr ,Ρr ) (2-1) However, this approach is only strictly applicable for spherical, nonpolar molecules. For more complex molecules additional parameter(s) are necessary .three parameters approaches have been demonstrated to be successful in correlating properties for non-spherical, nonpolar 3 Three alternate parameter have been proposed: critical compressibility Factor (Lydersen, Hougen, and Greenkorn) [7], alpha (Riedel)[8], and acentric factor (Pitzer)[6].
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