Phase diagrams

Petroleum reservoir fluids are complex mixtures containing many hydrocarbon components that range in size from light gases such as methane (C₁) and ethane (C₂) to very large hydrocarbon molecules containing 40 or more carbon atoms. Nonhydrocarbon components also may be present such as nitrogen, H₂S, or CO₂.

Water, of course, is present in essentially all reservoirs. At a given temperature and pressure, the components distribute between the solid, liquid, and vapor phases present in a reservoir. A phase is the portion of a system that is homogeneous, is bounded by a surface, and is physically seperable from other phases. Equilibrium phase diagrams offer convenient representations of the ranges of temperature, pressure, and composition within which various combinations of phases coexist. Phase behavior plays an important role in a variety of reservoir engineering applications, ranging from pressure maintenance to separator design to enhanced oil recovery (EOR) processes. This chapter reviews the fundamentals of phase diagrams used in such applications. Additional material on the role of phase equilibrium in petroleum/reservoir engineering can be found in Lake and Whitson and Brulé.

Phase diagrams for a single component

Fig. 1 summarizes the phase behavior of a single component. The saturation curves shown in Fig. 1 indicate the temperatures and pressures at which phase changes occur. At temperatures below the triple point, the component forms a vapor phase if the pressure is below that indicated by the sublimation curve and forms a solid phase at pressures above the curve. At pressures and temperatures lying on the sublimation curve, solid and vapor can coexist. At pressures and temperatures on the melting curve, solid and liquid are in equilibrium. At higher temperatures, liquid and vapor can coexist along the vaporization or vapor-pressure curve. If the pressure is greater than the vapor pressure, a liquid forms; if the pressure is lower than the vapor pressure, a vapor forms. The vapor-pressure curve terminates at the critical point. At temperatures above the critical temperature, T_c, a single phase forms over the entire range of pressures. For a single component, the critical temperature is the maximum temperature at which two phases can exist. Critical temperatures of hydrocarbons vary widely. Small hydrocarbon molecules have low critical temperatures, while large hydrocarbon molecules have much higher critical temperatures. Critical pressures generally decline as the molecular size increases. For instance, the critical temperature and pressure of C₁ are –117ºF and 668 psia; for decane, the values are 652ºF and 304 psia.

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  Fig. 1 – Phase behavior of a pure component.

For many reservoir engineering applications, liquid/vapor equilibrium is of greatest interest, although liquid/liquid equilibria are important in some EOR processes. Solid/liquid phase changes, such as asphaltene or paraffin precipitation (see Oil emulsions), occasionally occur in petroleum production operations.

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Fig. 2 shows typical volumetric behavior of a single component in the range of temperatures and pressures near the vapor-pressure curve in Fig. 1. If the substance under consideration is placed in a pressure cell at constant temperature, T₁, below T_c and at a low pressure (point A, for instance), it forms a vapor phase of high volume (low density). If the volume of the sample is decreased with the temperature held constant, the pressure rises. When the pressure reaches p_v(T₁) , the sample begins to condense. The pressure remains constant at the vapor pressure until the sample volume is reduced from the saturated vapor volume (V_V) to that of the saturated liquid (V_L). With further reductions in volume, the pressure rises again as the liquid phase is compressed. Small decreases in volume give rise to large pressure increases in the liquid phase because of the low compressibility of liquids. At a fixed temperature, T₂, above the critical temperature, no phase change is observed over the full range of volumes and pressures. Instead, the sample can be compressed from high volume (low density) and low pressure to low volume (high density) and high pressure with only one phase present.

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  Fig. 2 – Volumetric behavior of a pure component in the vapor/liquid region.

The phase rule

The number of components present in a system determines the maximum number of phases that can coexist at fixed temperature and pressure. The phase rule of Gibbs states that the number of independent variables that must be specified to determine the intensive state of the system is given by

....................(1)

where: F is the number of degrees of freedom n_c is the number of components n_p is the number of phases N_c is the number of constraints (e.g., chemical reactions)

For a single-component system, the maximum number of phases occurs when there are no constraints (N_c = 0) and no degrees of freedom (F = 0). Thus, the maximum number of possible phases is three. Therefore, if three phases coexist in equilibrium (possible only at the triple point), the pressure and temperature are fixed. If only two phases are present in a pure component system, then either the temperature or the pressure can be chosen. Once one is chosen, the other is determined. If the two phases are vapor and liquid, for example, choice of the temperature determines the vapor pressure at that temperature. These permitted pressure/temperature values lie on the vapor-pressure curve in Fig. 1.

In a binary system, two phases can exist over a range of temperatures and pressures. The number of degrees of freedom is calculated by

....................(2) therefore, both the temperature and pressure can be chosen, although there is no guarantee that two phases will occur at a specific choice of T and p.

For multicomponent systems, the phase rule provides little guidance because the number of phases is always far less than the maximum number that can occur. However, for typical applications, the temperature, pressure, and overall composition of a system are known in advance. This allows the number of phases in the system to be predicted by stability analysis, as described in the chapter on phase behavior in this volume.

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Noteworthy papers in OnePetro

Li, Y.K., Nghiem, L.X., Siu, A., 1985. "Phase Behaviour Computations For Reservoir Fluids: Effect Of Pseudo-Components On Phase Diagrams And Simulation Results", J. Can. Petrol. Tech., Vol. 24, No. 6, DOI: http://dx.doi.org/10.2118/85-06-02

Orr Jr., F.M. , Jensen, C.M., 1984. "Interpretation of Pressure-Composition Phase Diagrams for CO2/Crude-Oil Systems", SPE Journal, Vol. 24, No. 5, P. 485 - 497, DOI: http://dx.doi.org/10.2118/11125-PA

Quinones-Cisneros, S.E., Blackburn, M.B., Scriven L.E., and Davis, H.T. 1991. "Phase Behavior of CO2/Hydrocarbon Systems: Amendments to Previously Predicted Phase Diagrams", SPE Journal, Vol. 6, No. 1, P. 33 - 36, DOI: http://dx.doi.org/10.2118/18584-PA

External links

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See also

Binary phase diagrams

Quaternary phase diagrams

Ternary phase diagrams

Phase diagrams for EOR processes

Phase diagrams for reservoir fluid systems

PEH:Phase_Diagrams

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