Heriot-Watt University Research Gateway A New Thermodynamic Model for Paraffin Precipitation in Highly Asymmetric Systems at High Pressure Conditions Citation for published version: Ameri Mahabadian, M, Chapoy, A & Tohidi Kalorazi, B 2016, 'A New Thermodynamic Model for Paraffin Precipitation in Highly Asymmetric Systems at High Pressure Conditions', Industrial and Engineering Chemistry Research, vol. 55, no. 38, pp. 10208–10217. https://doi.org/10.1021/acs.iecr.6b02804 Digital Object Identifier (DOI): 10.1021/acs.iecr.6b02804 Link: Link to publication record in Heriot-Watt Research Portal Document Version: Peer reviewed version Published In: Industrial and Engineering Chemistry Research General rights Copyright for the publications made accessible via Heriot-Watt Research Portal is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. 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Page 1 of 38 Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 A New Thermodynamic Model for Paraffin 8 9 10 11 Precipitation in Highly Asymmetric Systems at 12 13 14 15 High Pressure Conditions 16 17 18 19 1 1, 2* 1 20 Mohammadreza Ameri Mahabadian , Antonin Chapoy , Bahman Tohidi 21 22 1 23 Hydrates, Flow Assurance & Phase Equilibria Research Group, Institute of Petroleum 24 25 Engineering, Heriot-Watt University, Edinburgh, Scotland, UK 26 27 28 2Mines Paristech, CTP – Centre Thermodynamique des procédés, 35 rue St Honoré 77305 29 30 Fontainebleau, France 31 32 33 34 KEYWORDS 35 36 37 Solid-fluid equilibrium, Paraffin wax, High pressure, Asymmetric systems, Clausius- 38 39 Clapeyron equation, Thermophysical properties 40 41 42 ABSTRACT 43 44 The predictions of the crystallization temperature and the amount of precipitates of paraffin 45 46 47 waxes at high pressure conditions may be inaccurate using existing thermodynamic models. 48 49 This is mainly due to the lack of experimental data on the molar volume of solid paraffins at 50 51 high pressures. This inaccuracy is even more pronounced for mixtures of high asymmetry. 52 53 The present work provides a new accurate modelling approach for solid-fluid equilibrium 54 55 56 (SFE) at high pressure conditions, more specifically, for highly asymmetric systems. In 57 58 1 59 60 ACS Paragon Plus Environment Industrial & Engineering Chemistry Research Page 2 of 38 1 2 3 contrast to the conventional methods for high pressure SFE modelling which define Poynting 4 5 molar volume correction term, to calculate the paraffin solid phase non-ideality at high 6 7 pressures, the new method exploits the values of thermophysical properties of importance in 8 9 10 SFE modelling (temperatures and enthalpies of fusion and solid-solid transition) evaluated at 11 12 the high pressure condition using a new insight to the well-known Clausius-Clapeyron 13 14 equation. These modified parameters are then used for evaluation of the fugacity in the solid 15 16 phase at higher pressure using the fugacity of pure liquid at the same pressure and applying 17 18 19 the well-established formulation of the Gibbs energy change during melting. Therefore, the 20 21 devised approach does not require a Poynting correction term. The devised approach coupled 22 23 with the well-tested UNIQAC activity coefficient model is used to describe the non-ideality 24 25 of the solid phase. For the fluid phases, the fugacities are obtained with the SRK EoS with 26 27 binary interaction parameters calculated with a group contribution scheme. The model is 28 29 30 applied to highly asymmetric systems with SFE experimental data over a wide range of 31 32 pressures. It is first used to predict crystallization temperature in binary systems at high 33 34 pressures and then verified by applying it on multicomponent mixtures resembling 35 36 intermediate oil and natural gas condensates. 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 2 59 60 ACS Paragon Plus Environment Page 3 of 38 Industrial & Engineering Chemistry Research 1 2 3 1. Introduction 4 5 6 Formation of paraffinic solids is well documented to be able to impose considerable 7 8 operational costs due to decreasing flow efficiency and, in the worst case, pipeline blockage. 9 10 Due to high expenses of the remediation approaches for wax deposition problem (such as 11 12 13 chemical dissolution and pigging), prevention is always the best option which in turn calls for 14 15 accurate risk assessment of the wax formation problem, i.e. identifying the 16 17 temperature/pressure conditions under which the waxes form. Although not as important as 18 19 temperature, the pressure can have a significant effect on the wax phase boundary (see for 20 21 1 2 22 example the work of Pan et al. ). In fact, as outlined by Pauly et al. , in mixtures with 23 24 significant light end proportions, the pressure change can considerably affect the chance of 25 26 wax formation through retrograde condensation, depressurization and Joule-Thomson effect. 27 28 Several thermodynamic models have been proposed in the literature for estimating wax 29 30 31 precipitation onset and the amount of wax formed inside the wax phase boundary. The 32 33 performance of existing models are (as will be shown later) good at low pressure conditions 34 35 as long as accurate thermodynamic models for the description of fluid and solid phases as 36 37 well as a precise correlation for calculating thermophysical properties of alkanes are utilised. 38 39 Paraffinic SFE calculations at high pressures using existing methodologies may show high 40 41 42 deviations compared to experimental data, more visibly in systems of high asymmetry with 43 44 high proportions of the light end which are the main subject of this study. The main motive 45 46 for studying such systems is their resemblance of volatile oils and gas condensates which 47 48 might form wax 1,3 . With similar intention, a handful of experimental studies in the literature, 49 50 51 mainly on binaries, have been focused on SFE in highly asymmetric systems. The purpose of 52 53 the current study is the development of a new thermodynamic model for the extension of one 54 55 of the accurate existing schemes for SFE modelling to high pressures. The next section 56 57 provides the background on the modelling wax precipitation at high pressures and the 58 3 59 60 ACS Paragon Plus Environment Industrial & Engineering Chemistry Research Page 4 of 38 1 2 3 complete formulation of the developed model. It also presents a modification of an existing 4 5 method. An extensive comparison of the devised methodology with the existing models is 6 7 then provided in the Results and Discussions Section. 8 9 10 11 2. Methodology 12 13 14 2.1. Background 15 16 The equilibrium calculations in the paraffin wax forming systems require evaluation of the 17 18 fugacity of precipitating components in the solid phase(s) which, consequently, calls for the 19 20 21 evaluation of fugacity of pure components in the solid state. The fugacity of pure paraffins in 22 23 the solid state, , are well-established to be related to the pure components’ liquid 24 ∗ 25 ͚$ fugacity, , by 4: 26 ∗ 27 ͚$ 28 29 f tr 30 ∗ f tr (1) 31 ͚$ Δ͂$ ͎ Δ͂$ ͎ 32 ∗ = ͙ͬͤ ʬ ʦ1 − ʧ + ʦ1 − ʧʭ ͚$ ͎͌ ͎$ ͎͌ ͎$ 33 34 35 It is assumed here that the Gibbs free energy change due to thermal contributions during 36 37 phase changes (heat capacity effect) are negligible, as confirmed through sensitivity 38 39 analysis 5.