Energy & Fuels 1991, 5, 924-932
924
Wax Precipitation from North Sea Crude Oils. Thermodynamic Modeling
4.
Karen Schou Pedersen* and Per Skovborg CALSEP A/S, Lyngby Hovedgade 29, DK-2800 Lyngby, Denmark
Hans Petter Renningsen Production Laboratories, STATOIL a.s., Forus, N-4001 Stavanger, Norway Received
April 29,
1991. Revised
Manuscript Received September
9, 1991
Wax precipitation measurements on 16 North Sea oil mixtures have been used to improve the model of Won for prediction of liquid-wax phase equilibria. It is shown that the amount of wax precipitated as a function of temperature at atmospheric pressure can be predicted with reasonable accuracy using regular solution theory for the liquid and solid phases. The solid-phase solubility parameters must be somewhat increased as compared with the solubility parameters of normal paraffins and the assumed amount of heat liberated during the liquid-wax transition has to be reduced considerably as compared to the melting enthalpies of pure normal paraffins. Finally, the difference between the liquid- and wax-phase heat capacities must be taken into consideration, a term which has been neglected in most previous wax precipitation model developments. A major part of the enthalpy change observed during the wax precipitation process seems to originate from phase transitions taking place in the already
formed
wax.
The Thermodynamic Basis of Liquid-Wax
Introduction
Equilibria
The crude oils produced in the North Sea are often being processed or transported at conditions where the heavy hydrocarbons contained in the oil may precipitate as a solid waxy material. This precipitation is undesirable because it may cause deposition and eventually plug the process equipment and/or pipelines. In the design and operation of oil production facilities, it is therefore essential to be able to predict the conditions where wax precipitation may take place and the amounts in which wax may form. Two different models have been proposed for the prediction of wax precipitation from naturally occurring oil mixtures. Won1 used regular solution theory to describe the nonidealities in the oil (liquid) and wax (solid) phases. Hansen et al.4 applied polymer solution theory for the oil phase while the wax phase was assumed to be an ideal mixture. As reported by Hansen et al., the cloud points obtained using the model of Won are somewhat higher than those measured. Hansen et al. used measured cloud points to determine the interaction parameters in their model, and the calculated and measured cloud points were therefore in reasonable agreement. At the time when the two mentioned models were published, experimental data were lacking for the amount of wax precipitated from petroleum fluids as a function of temperature. The calculated results for the amount of wax precipitated as a function of temperature could therefore not be compared with experimental data. This type of experimental data is now available.5
At thermodynamic equilibrium between a liquid (oil) phase and a solid (wax) phase, the fugacity of component i, fi, in the oil phase must be equal to the fugacity, /f, of component i in the
phase:
fi=ff The liquid-phase fugacity of component i as follows
fr
2"3
=
7pxp/?L exp
(1) can be
expressed
(2)
yf is the activity coefficient of component i in the liquid phase, xj1 the mole fraction of component i in the liquid phase, /¡ the standard-state fugacity of component i in the liquid phase, V\ the molar liquid volume of component i, P the pressure, R the gas constant, and T the temperature. Similarly the solid (wax)-phase fugacity of component i may be written as
where
f?
=
y?x?fis exp
(3)
yf is the activity coefficient of component i in the phase, xf the mole fraction of component i in the wax phase, f°s the standard-state fugacity of component i in the solid (wax) phase, and Vf the molar solid (wax) volume of component i. By combining eqs 1,2, and 3 the criterion of equal fugacities can be expressed as where wax
(1) Won, K. W. “Continuous Thermodynamics for Solid-Liquid Equilibria: Wax Formation from Heavy Hydrocarbon Mixtures”. Paper presented at the AIChE Spring Metting, Houston, TX, March 25,1985. (2) Won, K. W. “Thermodynamics for Solid Solution-Liquid-Vapor Equilibria: Wax Phase Formation from Heavy Hydrocarbon Mixtures”. Paper presented at the 4th International Conference on Fluid Properties and Phase Equilibria for Chemical Process Design, Helsingor, Denmark, May 11-16, 1986. (3) Won, K. W. Fluid Phase Equilib. 1989, 53, 377. (4) Hansen, J. H.; Fredenslund, Aa.; Pedersen, K. S.; Renningsen, H. P. AIChE J. 1989, 34, 12.
0887-0624/91/2505-0924$02.50/0
wax
(5) Pedersen, W. B.; Hansen, A. B.; Larsen, E.; Nielsen, A. B.; Ronningsen, . P. Wax Precipitation from North Sea Crude Oils. 2. Solid Phase Content as Function of Temperature Determined by Pulsed NMR. Energy Fuels, this issue. ©
1991 American Chemical Society
Wax Precipitation from North Sea Crude Oils
Energy & Fuels, Vol. 5, No.
By assuming that the liquid- and solid-phase molar volumes are independent of pressure this expression can be simplified to
6, 1991
925
derived for the ratio between the mole fractions of component i in the wax phase and in the liquid phase:
RTJt kC'(c»-£®d;r+ Experimental observations6 have shown that the solidification of a paraffinic hydrocarbon is associated with a decrease in the volume by approximately 10%. Wax precipitated from a crude oil is probably less crystalline than an n-paraffin wax and the contraction associated with the liquid-wax transition must therefore be expected not to exceed 10%. At low to moderate pressures, volume differences of this order of magnitude will have little influence on the liquid-wax equilibrium because the exponential term will be close to unity. For this reason the volume difference between the substances in the liquid and solid states have been neglected in previous model work in which case the equilibrium relation can be simplified to
i'r'Ci-Cf \ mJt dT)(m 1
—
In the models of Won1’2 and Hansen et al.4 it is assumed that the liquid- and solid-phase heat capacities are equal. With this assumption eq 11 reduces to
The models of Won and Hansen et al. differ in the way the liquid- and solid-phase activity coefficients are determined. Won uses regular solution theory which means that the activity coefficients are determined from the solubility parameters ,· of the individual components VH3L
In
RT
The standard-state fugacities at temperature T and pressure P of component i in the liquid and wax phases, respectively, can be interrelated as follows AGad
RT In (f°s/rL)
=
A). To calculate AG^j the following general thermodynamic relation is used: AG
=
AH
-
TAS
(8)
For a pure component in liquid form, the liquid-solid transition will usually take place at the normal melting temperature, ', and the heat liberated will be equal to the heat of fusion, AH' (the molar enthalpy of the substance will change by -AH'). For many pure substances including normal paraffins which are some of the main constituents of the wax formed from an oil mixture, the heats (or enthalpy) of fusion at the normal melting point are known from measurements. When the normal paraffins or the other wax forming components are dissolved in an oil phase, the liquid-solid transition will, however, not necessarily take place at the normal melting temperature. As shown in Appendix A, the enthalpy change associated with a liquid-solid phase transition at a temperature T lower than ', can be calculated as =
AHad
-AH' +
Cf) dT
-
(9)
where Cp is the liquid-phase heat capacity and C® the solid-phase heat capacity. In a similar manner, the following expression may be derived for the entropy change associated with the liquid-wax transition: ASad
=
AH'
'
p^CL-C®
JT
^
dT
(10)
(6) Templin, P. R.
Ind. Eng. Chem. 1956, 48,
i =
154.
V®(6®
yf
®
=
-
®)2
(13)
RT
(14)
