Page 387 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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9. APPLICATIONS: PHASE EQUILIBRIUM CALCULATIONS 367
Vapor Phase
V moles
y i
Petroleum Fluid
F moles
Composition z i Liquid Solution all phases
T F , P F L moles at T and P
x i L
Solid Solution
S moles
x i S
Non-equilibrium state Equilibrium state
FIG. 9.1—Typical vapor–liquid–solid equilibrium for solid precipitation.
calculations related to petroleum and natural gas production. calculations are the most widely used VLE calculations by
VLE calculations are needed in design and operation of sepa- both chemical and reservoir engineers in the petroleum pro-
ration units such as multistage surface separators at the sur- cessing and production.
face facilities of production fields, distillation, and gas absorp-
tion columns in petroleum and natural gas processing as well
as phase determination of reservoir fluids. LLE calculations 9.2 VAPOR–LIQUID EQUILIBRIUM
are useful in determination of amount of water dissolved in CALCULATIONS
oil or amount of oil dissolved in water under reservoir con-
ditions. SLE calculations can be used to determine amount VLE calculations are perhaps the most important types
and the conditions at which a solid (wax or asphaltene) may of phase behavior calculations in the petroleum industry.
be formed from a petroleum fluid. Cloud-point temperature They involve calculations related to equilibrium between two
(CPT) can be accurately calculated through SLE calculations. phases of liquid and vapor in a multicomponent system. Con-
VSE calculation is used to calculate hydrate formation and sider a fluid mixture with mole fraction of each component
the conditions at which it can be prevented. shown by z i is available in a sealed vessel at T and P. Under
Schematic of a system at vapor–liquid–solid equilibrium these conditions assume the fluid can exist as both vapor and
(VLSE) is shown in Fig. 9.1. The system at its initial con- liquid in equilibrium. Furthermore, assume there are total of
ditions of T F and P F is in a nonequilibrium state. When it F mol of fluid in the vessel at initial temperature and pres-
reaches to equilibrium state, the conditions change to T and sure of T F and P F as shown in Fig. 9.1. The conditions of the
P and new phases may be formed. The initial composition of vessel change to temperature T and pressure P at which both
the fluid mixture is z i ; however, at the final equilibrium con- vapor and liquid can coexist in equilibrium. Assume V mol of
ditions, compositions of vapor, liquid, and solid in terms of vapor with composition y i and L(= F − V) mol of liquid with
S
L
mole fractions are specified as y i , x , and x , respectively. The composition x i are produced as a result of phase separation
i i
amount of feed, vapor, liquid, and solid in terms of number of due to equilibrium conditions. No solid exists at the equilib-
moles is specified by F, V, L, and S, respectively. Under VLE rium state and S = 0 and for this reason composition of liquid
conditions, no solid is formed (S = 0) and at VSE state no phase is simply shown by x i . The amount of vapor may be ex-
liquid exists at the final equilibrium state (L = 0). The system pressed by the ratio of V/F or V F for each mole of the mixture.
S
L
variables are F, z i , T, P, V, y i , L, x , S, and x , where in a typi- The parameters involved in this equilibrium problem are T,
i
i
cal equilibrium calculation, F, z i , T, and P are known, and V, P, z i , x i , y i , and V F (for the case of F = 1). The VLE calcu-
L, S, y i , x , and x are to be calculated. In some calculations lations involve calculation of three of these parameters from
S
L
i
i
such as bubble point calculations, T or P may be unknown three other known parameters.
and must be calculated from given information on P or T and Generally there are five types of VLE calculations: (i) Flash,
the amount of V, L,or S. Calculations are formulated through (ii) bubble-P, (iii) bubble-T, (iv) dew-P, and (v) dew-T. (i) In
both equilibrium relations and material balance for all com- flash calculations, usually z i , T, and P are known while x i , y i ,
ponents in the system. Two-phase equilibrium such as VLE and V are the unknown parameters. Obviously calculations
or SLE calculations are somewhat simpler than three-phase can be performed so that P or T can be found for a known
equilibrium such as VLSE calculations. value of V. Flash separation is also referred as flash distilla-
In this chapter various types VLE and SLE calculations tion. (ii) In the bubble-P calculations, pressure of a liquid of
are formulated and applied to various petroleum fluids. Prin- known composition is reduced at constant T until the first
ciples of phase equilibria were discussed in Section 6.8 vapor molecules are formed. The corresponding pressure is
through Eqs. (6.171)–(6.174). VLE calculations are formu- called bubble point pressure (P b ) at temperature T and estima-
lated through equilibrium ratios (K i ) and Eq. (6.201), while tion of this pressure is known as bubble-P calculations. For
SLE calculations can be formulated through Eq. (6.208). In analysis of VLE properties, consider the system in Fig. 9.1
addition there are five types of VLE calculations that are dis- without solid phase (S = 0). Also assume the feed is a liquid
cussed in the next section. Flash and bubble point pressure with composition (x i = z i )at T = T F and P F . Now at constant

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