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PEH:Phase Diagrams
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Fig. 8.1 summarizes the phase behavior of a single component. The saturation curves shown in Fig. 8.1 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, Tc, 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.
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 the chapter on crude oil emulsions in this volume), occasionally occur in petroleum production operations.
Fig. 8.2 shows typical volumetric behavior of a single component in the range of temperatures and pressures near the vapor-pressure curve in Fig. 8.1. If the substance under consideration is placed in a pressure cell at constant temperature, T1, below Tc 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 pv(T1) , the sample begins to condense. The pressure remains constant (see Sec. 8.3) at the vapor pressure until the sample volume is reduced from the saturated vapor volume (VV) to that of the saturated liquid (VL). 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.
Fig. 8.3 is a pressure-composition (p-x-y) phase diagram that shows typical vapor/liquid phase behavior for a binary system at a fixed temperature below the critical temperature of both components. At pressures below the vapor pressure of Component 2, pv2, any mixture of the two components forms a single vapor phase. At pressures between pv1 and pv2, two phases can coexist for some compositions. For instance, at pressure pb, two phases will occur if the mole fraction of Component 1 lies between xB and xE. If the mixture composition is xB, it will be all liquid; if the mixture composition is xE, it will be all vapor. At constant temperature and pressure, the line connecting a liquid phase and a vapor phase in equilibrium is known as a tie line. In binary phase diagrams such as Fig. 8.3, the tie lines are always horizontal because the two phases are in equilibrium at a fixed pressure. For 1 mole of mixture of overall composition, z, between xB and xE, the number of moles of liquid phase is
....................(8.3)
Eq. 8.3 is an inverse lever rule because it is equivalent to a statement concerning the distances along a tie line from the overall composition to the liquid and vapor compositions. Thus, the amount of liquid is proportional to the distance from the overall composition to the vapor composition, divided by the length of the tie line.
Phase diagrams such as Fig. 8.3 can be determined experimentally by placing a mixture of fixed overall composition in a high-pressure cell and measuring the pressures at which phases appear and disappear. For example, a mixture of composition xB would show the behavior indicated qualitatively in Fig. 8.4. At a pressure less than pd (Fig. 8.3), the mixture is a vapor. If the mixture is compressed by injecting mercury into the cell, the first liquid, which has composition xA, appears at the dewpoint pressure, pd. As the pressure is increased further, the volume of liquid grows as more and more of the vapor phase condenses. The last vapor of composition xE disappears at the bubblepoint pressure, pb.
If the system temperature is above the critical temperature of one of the components, the phase diagram is similar to that shown in Fig. 8.5. At the higher temperature, the two-phase region no longer extends to the pure Component 1 side of the diagram. Instead, there is a critical point, C, at which liquid and vapor phases are identical. The critical point occurs at the maximum pressure of the two-phase region. The volumetric behavior of mixtures containing less Component 1 than the critical mixture, xc, is like that shown in Fig. 8.4. Fig. 8.6 shows the volumetric behavior of mixtures containing more Component 1. Compression of the mixture of composition x2 (in Fig. 8.5) leads to the appearance of liquid phase of composition x1 when pressure pd1 is reached. The volume of liquid first grows and then declines with increasing pressure. The liquid phase disappears again when pressure pd2 is reached. Such behavior is called "retrograde vaporization" or "retrograde condensation" if the pressure is decreasing.
If the system temperature is exactly equal to the critical temperature of Component 1, the critical point on the binary pressure-composition phase diagram is positioned at a Component 1 mole fraction of 1.0. Fig. 8.7 shows the behavior of the two-phase regions as the temperature rises. As the temperature increases, the critical point moves to lower concentrations of Component 1. As the critical temperature of Component 2 is approached, the two-phase region shrinks, disappearing altogether when the critical temperature is reached.
Fig. 8.8 shows a typical locus of critical temperatures and pressures for a pair of hydrocarbons. The critical locus shown in Fig. 8.8 is the projection of the critical curve in Fig. 8.7 onto the p-T plane. Thus, each point on the critical locus represents a critical mixture of different composition, although composition information is not shown on this diagram. For temperatures between the critical temperature of Component 1 and Component 2, the critical pressure of the mixtures can be much higher than the critical pressure of either component. Thus, two phases can coexist at pressures much greater than the critical pressure of either component. If the difference in molecular weight of the two components is large, the critical locus may reach very high pressures. Fig. 8.9 gives critical loci for some hydrocarbon pairs.[3]
The binary phase diagrams reviewed here are those most commonly encountered. However, more complex phase diagrams involving liquid/liquid and liquid/liquid/vapor equilibriums do occur in hydrocarbon systems at very low temperatures (well outside the range of conditions encountered in reservoirs or surface separators) and in CO2/crude oil systems at temperatures below approximately 50°C. See Stalkup[4] and Orr and Jensen[5] for reviews of such phase behavior.
Phase behavior of mixtures containing three components is represented conveniently on a triangular diagram such as those shown in Fig. 8.10. Such diagrams are based on the property of equilateral triangles that the sum of the perpendicular distances from any point to each side of the diagram is a constant equal to the length of any of the sides. Thus, the composition of a point in the interior of the triangle can be calculated as
....................(8.4)
where
....................(8.5)
Several other useful properties of triangular diagrams are a consequence of this fact. For mixtures along any line parallel to a side of the diagram, the fraction of the component of the corner opposite to that side is constant (Fig. 8.10b). In addition, mixtures lying on any line connecting a corner with the opposite side contain a constant ratio of the components at the ends of the side (Fig. 8.10c). Finally, mixtures of any two compositions, such as A and B in Fig. 8.10d, lie on a straight line connecting the two points on the ternary diagram. Compositions represented on a ternary diagram can be expressed in volume, mass, or mole fractions. For vapor/liquid equilibrium diagrams, mole fractions are most commonly used.
Fig. 8.11 shows the typical features of a ternary phase diagram for a system that forms a liquid and a vapor at fixed temperature and pressure. Mixtures with overall compositions that lie inside the binodal curve will split into liquid and vapor. Tie lines connect compositions of liquid and vapor phases in equilibrium. Any mixture with an overall composition along a tie line gives the same liquid and vapor compositions. Only the amounts of liquid and vapor change as the overall composition changes from the liquid side of the binodal curve to the vapor side. If the mole fractions of Component i in the liquid, vapor, and overall mixture are xi, yi, and zi, the fraction of the total moles in the mixture in the liquid phase is given by
....................(8.6)
Eq. 8.6 is another lever rule similar to that described for binary diagrams. The liquid and vapor portions of the binodal curve meet at the plait point, a critical point at which the liquid and vapor phases are identical. Thus, the plait-point mixture has a critical temperature and pressure equal to the conditions for which the diagram is plotted. Depending on the pressure, temperature, and components, a plait point may or may not be present.
Any one ternary diagram is given for fixed temperature and pressure. As either the temperature or pressure is varied, the location of the binodal curve and slopes of the tie lines may change. Fig. 8.12 shows the effect of increasing pressure on ternary phase diagrams for mixtures of C1, butane (C4), and decane (C10) at 160°F.[6][7] The sides of the ternary diagram represent a binary system; therefore, the ternary diagram includes whatever binary tie lines exist at the temperature and pressure of the diagram. Fig. 8.13 shows the corresponding binary phase diagrams for the C1–C4 and C1–C10 pairs. The C4–C10 pair is not shown because it forms two phases only below the vapor pressure of C4, approximately 120 psia at 160°F (see Fig. 8.9).
As Fig. 8.12 shows, at 1,000 psia the two-phase region is a band that stretches from the C1–C10 side of the diagram to the tie line on the C1–C4 side. If the pressure is increased above 1,000 psia, the liquid composition line shifts to higher methane concentrations; methane is more soluble in both C4 and C10 at the higher pressure (see Fig. 8.13). The two-phase region detaches from the C1–C4 side of the diagram at the critical pressure of the C1–C4 pair (approximately 1,800 psia). As the pressure increases above that critical pressure, the plait point moves into the interior of the diagram (Fig. 8.12, lower diagrams). With further increases in pressure, the two-phase region continues to shrink. It would disappear completely from the diagram if the pressure reached the critical pressure of the C1–C10 system at 160°F (nearly 5,200 psia).
According to the phase rule, three phases may coexist at a fixed temperature and pressure for some ternary systems. Fig. 8.14 shows the general structure of such systems. The three-phase region (3Φ) on a ternary diagram is represented as a triangle in Fig. 8.14. Any overall composition lying within the three-phase region splits into the same three phases (I, II and III). Only the amounts of each phase change as the overall composition varies within the three-phase region. Given 1 mole of an overall mixture in the three-phase region, the geometrical relations
....................(8.7)
with
....................(8.8)
determine the fraction of each phase. The edges of the three-phase region are tie lines for the associated two-phase (2Φ) regions; thus, there is a two-phase region adjacent to each of the sides of the three-phase triangle. Three-phase regions can exist in several phase diagrams applied in the design of EOR processes. Examples are discussed in Secs. 8.7 and 8.8.
Phase diagrams for systems with four components can be represented conveniently on a tetrahedral diagram like that shown in Fig. 8.15a, which shows a quaternary phase diagram calculated with the Peng-Robinson[8] equation of state for mixtures of methane (C1), C3, C6, and hexadecane (C16) at 200°F and 2,000 psia. These phase diagrams have a property similar to that of ternary diagrams: the sum of the lengths of perpendicular lines drawn from a composition point in the interior of the diagram to the four faces of the diagram is a constant length. Hence, the fractions of four components can be represented by an extension of Eq. 8.4 to four components.
The faces of the quaternary diagram are ternary phase diagrams. Fig. 8.15b shows the ternary diagram for the ternary methane (C1)/hexane (C6)/hexadecane (C16) system, which is the bottom face of the quaternary diagram. The two-phase region is a band across the diagram, and there is no critical point on that face. Fig. 8.15c shows the C1/C3/C16 system, which is the left face of the quaternary diagram. That ternary system does have a critical point. While the ternary diagram for C1/C3/C6 is not shown separately, it is qualitatively similar to the diagram for the C1/C3/C16 system in Fig. 8.15c.
The two-phase region in the interior of the quaternary diagram is a 3D region of composition space bounded by the ternary two-phase regions on the faces. Within that region, every mixture composition forms two phases, and each composition point lies on a tie line that connects equilibrium vapor and liquid compositions. A vertical slice through the two-phase region is shown in Fig. 8.15a, along with a few tie lines that lie in the interior of the diagram. The mole fraction of liquid phase is still calculated with Eq. 8.6, which applies to systems with any number of components.
The boundary of the two-phase region in the interior of the quaternary diagram is divided into two parts: a surface that includes all the vapor-phase compositions and a corresponding surface of liquid-phase compositions. The dividing line between the liquid and vapor surfaces is a critical locus (the dotted line in Fig. 8.15c) that connects the critical point in the C1/C3/C16 face (Fig. 8.15a) with the critical point in the C1/C3/C6 face. The critical locus is a set of compositions at which the liquid and vapor phases have identical compositions and properties. The compositions and limiting tie lines on the critical locus play important roles in the description of EOR processes (see Sec. 8.8).
Real reservoir fluids contain many more than two, three, or four components; therefore, phase-composition data can no longer be represented with two, three or four coordinates. Instead, phase diagrams that give more limited information are used. Fig. 8.16 shows a pressure-temperature phase diagram for a multicomponent mixture; it gives the region of temperatures and pressures at which the mixture forms two phases. The analog of Fig. 8.16 for a binary system can be obtained by taking a slice at constant mole fraction of Component 1 through the diagram in Fig. 8.7. Also given are contours of liquid-volume fractions, which indicate the fraction of total sample volume occupied by the liquid phase; however, Fig. 8.16 does not give any compositional information. In general, the compositions of coexisting liquid and vapor will be different at each temperature and pressure.
At temperatures below the critical temperature (point C), a sample of the mixture described in Fig. 8.16 splits into two phases at the bubblepoint pressure (Fig. 8.4) when the pressure is reduced from a high level. At temperatures above the critical temperature, dewpoints are observed (Fig. 8.6). In this multicomponent system, the critical temperature is no longer the maximum temperature at which two phases can exist. The critical point is the temperature and pressure at which the phase compositions and all phase properties are identical.
The bubblepoint, dewpoint, and single-phase regions shown in Fig. 8.16 are sometimes used to classify reservoirs. At temperatures greater than the cricondentherm, which is the maximum temperature for the formation of two phases, only one phase occurs at any pressure. For instance, if the hydrocarbon mixture in Fig. 8.16 were to occur in a reservoir at temperature TA and pressure pA (point A), a decline in pressure at approximately constant temperature caused by removal of fluid from the reservoir would not cause the formation of a second phase.
While the fluid in the reservoir remains a single phase, the produced gas splits into two phases as it cools and expands to surface temperature and pressure at point A′. Thus, some condensate would be collected at the surface even though only one phase is present in the formation. The amount of condensate collected depends on the operating conditions of the separator. The lower the temperature at a given pressure, the larger the volume of condensate collected (Fig. 8.16).
Dewpoint reservoirs are those for which the reservoir temperature lies between the critical temperature and the cricondentherm for the reservoir fluid. Production of fluid from a reservoir starting at point B in Fig. 8.16 causes liquid to appear in the reservoir when the dewpoint pressure is reached. As the pressure declines further, the saturation of liquid increases because of retrograde condensation. Because the saturation of liquid is low, only the vapor phase flows to producing wells. Thus, the overall composition of the fluid remaining in the reservoir changes continuously.
The phase diagram shown in Fig. 8.16 is for the original composition only. The preferential removal of light hydrocarbon components in the vapor phase generates new hydrocarbon mixtures, which have a greater fraction of the heavier hydrocarbons. Differential liberation experiments, in which a sample of the reservoir fluid initially at high pressure is expanded through a sequence of pressures, can be used to investigate the magnitude of the effect of pressure reduction on the vapor composition. At each pressure, a portion of the vapor is removed and analyzed. These experiments simulate what happens when condensate is left behind in the reservoir as the pressure declines. See Pedersen, Fredenslund, and Thomassen[9] for more details on pressure/volume/temperature experiments.
As the reservoir fluid becomes heavier, the boundary of the two-phase region in a diagram like Fig. 8.16 shifts to higher temperatures. Thus, the composition change also acts to drive the system toward higher liquid condensation. Such reservoirs are candidates for pressure maintenance by lean gas injection to limit the retrograde loss of condensate or for gas cycling to vaporize and recover some of the liquid hydrocarbons.
Bubblepoint reservoirs are those in which the temperature is less than the critical temperature of the reservoir fluid (point D in Fig. 8.16). These reservoirs are sometimes called undersaturated because the fraction of light components present in the oil is too low for a gas phase to form at that temperature and pressure. Isothermal pressure reduction causes the appearance of a vapor phase at the bubblepoint pressure. Because the compressibility of the liquid phase is much lower than that of a vapor, the pressure in the reservoir declines rapidly during production in the single-phase region. The appearance of the much more compressible vapor phase reduces the rate of pressure decline. The volume of vapor present in the reservoir grows rapidly with reduction of reservoir pressure below the bubblepoint.
Because the vapor viscosity is much lower than the liquid viscosity and the gas relative permeability goes up markedly with increasing gas saturation, the vapor phase flows more easily. Hence, the produced gas/oil ratio climbs rapidly. Again, pressure maintenance by waterdrive, water injection, or gas injection can improve oil recovery substantially over the 10 to 20% recovery typical of pressure depletion in these solution-gas-drive reservoirs. As in dewpoint reservoirs, the composition of the reservoir fluid changes continuously once the two-phase region is reached.
There is, of course, no reason why initial reservoir temperatures and pressures cannot lie within the two-phase region. Oil reservoirs with gas caps and gas reservoirs with some liquids present are common. There also can be considerable variation in the initial composition of the reservoir fluid. The discussion of single-phase, dewpoint, and bubblepoint reservoirs is based on a phase diagram for one fluid composition. Even for one fluid, all the types of behavior occur over a range of temperatures. In actual reservoir settings, the composition of the reservoir fluid correlates with depth and temperature. Deeper reservoirs usually contain lighter oils.[10]
Fig. 8.17 shows the relationships between oil gravity and depth for two basins. The higher temperatures of deeper reservoirs alter the original hydrocarbon mixtures to produce lighter hydrocarbons over geologic time.[10] Low oil gravity, low temperature, and relatively small amounts of dissolved gas all combine to produce bubblepoint reservoirs. High oil gravity, high temperatures, and a high concentration of light components produce dewpoint or condensate systems.
Fig. 8.18[11] shows phase diagrams typical of those used to describe the behavior of surfactant systems. In these ternary diagrams, the components shown are no longer true thermodynamic components because they are mixtures. A crude oil contains hundreds of components, and the brine and surfactant pseudocomponents also may be complex mixtures. The simplified representation, however, has obvious advantages for describing phase behavior, and it is reasonably accurate as long as each pseudocomponent has approximately the same composition in each phase. In Fig. 8.18a, for instance, the "oil" pseudocomponent can appear in an oil-rich phase or in a phase containing mostly surfactant and brine. If the oil solubilized into the surfactant/brine phase is nearly the same mixture of hydrocarbons as the original "oil," then the representation in terms of pseudocomponents is reasonable. The compositions shown in Fig. 8.18 are in volume fractions. An inverse lever rule similar to Eqs. 8.3 and 8.6 gives the relationship between the volumes of the two phases for a given overall composition, as Fig. 8.18 illustrates.
Fig. 8.18a is a phase diagram for the liquid/liquid equilibrium behavior typical of mixtures of brines of low salinity with oil. If there is no surfactant present, the oil and brine are immiscible; mixture compositions on the base of the diagram split into essentially "pure" brine in equilibrium with "pure" oil. The addition of surfactant causes some oil to be solubilized into a microemulsion rich in brine. That phase is in equilibrium with a phase containing nearly pure oil. Thus, in the low-salinity brine, the surfactant partitions into the brine phase, solubilizing some oil. The plait point in Fig. 8.18a lies close to the oil corner of the diagram. Because only two phases occur and the tie lines all have negative slope, such phase is often called Type II(-).
Phase diagrams for high-salinity brines are often similar to Fig. 8.18b. In the high-salinity systems, the surfactant partitions into the oil phase and solubilizes water into an oil-external microemulsion. In this case, the plait point is close to the brine apex on the ternary diagram. For intermediate salinities, the phase behavior can be more complex, as Fig. 8.18c shows. A triangular three-phase region occurs (see Fig. 8.14) for which the phases are a brine-rich phase, an oil-rich phase, and a microemulsion phase. There is a two-phase region adjacent to each of the sides of the three-phase triangle. In Fig. 8.18c, the two-phase region at low surfactant concentrations is too small to show on the diagram. It must be present, however, because oil and brine form only two phases in the absence of surfactant.
Fig. 8.19 is an example of a p-x diagram for mixtures of CO2 (containing a small amount of C1 contamination) with crude oil from the Rangely field.[12] The behavior of binary mixtures of CO2 with a particular oil is reported for a fixed temperature; therefore, the oil is represented as a single pseudocomponent. The bubblepoint and dewpoint pressures, the regions of pressure and composition for which two or more phases exist, and information about the volume fractions of the phases are indicated. However, the diagrams provide no information about the compositions of the phases in equilibrium.
Fig. 8.20 illustrates the reason for the absence of composition data and gives data reported by Metcalfe and Yarborough[13] for a ternary system of CO2, C4, and C10. Binary-phase data for the CO2–C4[14] and CO2–C10[15] systems also are included. Fig. 8.20 shows a triangular solid within which all possible compositions (mole fractions) of CO2–C4–C10 mixtures for pressures between 400 and 2,000 psia are contained. The two-phase region is bounded by a surface that connects the binary-phase envelope for the CO2–C10 binary pair to that on the CO2–C4 side of the diagram. That surface is divided into two parts-liquid compositions and vapor compositions.
Tie lines connect the compositions of liquid and vapor phases in equilibrium at a fixed pressure. Thus, the ternary phase diagram for CO2–C4–C10 mixtures at any pressure is just a constant pressure (horizontal) slice through the triangular prism. Several such slices at different pressures are shown in Fig. 8.20. At pressures below the critical pressure of CO2–C4 mixtures (1,184 psia), both CO2–C10 and CO2–C4 mixtures form two phases for some range of CO2 concentrations. At 400 and 800 psia, the two-phase region is a band across the diagram. Above the critical pressure of CO2–C4 mixtures, CO2 is miscible with C4 and ternary slices at higher pressures show a continuous binodal curve on which the locus of liquid compositions meets that of vapor compositions at a plait point. The locus of plait points connects the critical points of the two binary pairs.
To see the effect of representing the phase behavior of a ternary system on a pseudobinary diagram, consider a p-x diagram for "oil" composed of 70 mol% C10 and 30 mol% C4. At any fixed pressure, the mixtures of CO2 and oil, which would be investigated in an experiment to determine a p-x diagram, lie on a straight line (the dilution line), which connects the original oil composition with the CO2 apex. Thus, a p-x diagram for this system is a vertical slice through the triangular prism shown in Fig. 8.20. The saturation pressures on a p-x diagram are those at which the dilution plane intersects the surface that bounds the two-phase region. Bubblepoint pressures occur where the dilution plane intersects the liquid composition side of the two-phase surface, while dewpoint pressures occur at the intersection with vapor compositions. Comparison of the phase envelope on the resulting p-x diagram with binary phase diagrams yields the following observations.
Figs. 8.19 and 8.21 illustrate the complexity of phase behavior observed for CO2/crude oil systems. Fig. 8.19 gives the behavior of mixtures of CO2 (with approximately 5% C1 as a contaminant) with Rangely crude oil at 160°F. The oil has a bubblepoint pressure of approximately 350 psia. Mixtures containing up to approximately 80 mol% CO2 (+ C1) show bubblepoints, while those containing more CO2 show dewpoints. At the relatively high temperature of the Rangely field, only two phases, a liquid and a vapor, form. At lower temperatures, more complex phase behavior can occur.
Fig. 8.21 shows the behavior of mixtures of an oil containing no dissolved gas from the Wasson field[4] with CO2. At 90°F and 105°F, the mixtures form a liquid and a vapor at low pressures and two liquid phases at high pressures and high CO2 concentrations. They form three phases, two liquids and a vapor, for a small range of pressures at high CO2 concentrations. The liquid/liquid and liquid/liquid/vapor behavior disappears if the temperature is high enough. At 120°F (Fig. 8.21c), the three-phase region disappears. For the systems studied to date, 120°F appears to be a reasonable estimate of the maximum temperature for liquid/liquid/vapor separations. See Stalkup[4] and Orr and Jensen[5] for detailed discussions of such phase behavior. Well-characterized ternary systems that display similar behavior are described by Larsen et al.,[16] who report ternary diagrams like Fig. 8.14 for CO2/hydrocarbon systems.
For ternary systems, two mechanisms can lead to the development of a multicontact miscible displacement: vaporizing drives and condensing drives. Fig. 8.22a demonstrates the features of a vaporizing drive for the displacement of a C6–C16 mixture (O1) by pure C1. The displacement composition path traverses the two-phase region along two key tie lines in compositional space: the tie line that extends through the injected gas composition (the injection tie line) and the tie line that extends through the initial oil composition (the initial tie line).[17][18] As the pressure is increased, the two-phase region shrinks and, at some point, one of the key tie lines become a critical tie line (a tie line that is tangent to the two-phase region at a critical point).
Fig. 8.22b demonstrates the features of a condensing gas drive for a C1–C3 mixture displacing oil consisting of C1 and C16. In this case, the injection tie line is closer to the critical point, and as the pressure is increased, it is the first to become a critical tie line. For both cases, the pressure at which one of the key tie lines become a critical tie line is known as the minimum miscibility pressure (MMP).[18] Thus, in three-component systems, a displacement can be multicontact miscible only if one of the two key tie lines is a critical tie line. If it is the initial oil tie line that is critical, the displacement is a vaporizing drive, and if the injection gas tie line is the critical tie line, the displacement is a condensing drive.
For four-component systems, the displacement path has been shown to include a third key tie line referred to as the crossover tie line.[19] Fig. 8.22c shows the crossover tie line. Just as in the ternary displacements, miscibility develops when any one of the key tie lines reduces to a critical point. If the pressure in Fig. 8.22c is increased, the crossover tie line will become a critical tie line before either the initial or injection tie lines. Hence, the existence of the crossover tie line introduces a third mechanism for the development of multicontact miscibility. This mechanism is known as the combined condensing/vaporizing drive.[20][21] Fig. 8.22c shows that the displacement composition path for a four-component system in which a mixture of C1 and C3 displaces an oil containing C1, C6, and C16 includes a vaporizing segment connected to a condensing segment by the crossover tie line.
With each additional component added to the displacement process, another crossover tie line is added to the displacement composition path. The MMP for such multicomponent gas-injection processes can be determined by locating the key tie lines and calculating the length of these tie lines as the pressure is increased. The MMP is the pressure at which one of the key tie lines has zero length. Fig 8.23[22] reports the result of such a calculation for a 15-component fluid description. In this system, the injection gas contains 11 components and is rich in C1 but includes N2, CO2, and hydrocarbons up to C7. The eighth crossover tie lie becomes a critical tie line at the MMP of 5,350 psia. Displacements that display the combined condensing/vaporizing mechanism are common in oilfield fluid systems.
Publication Information
Petroleum Engineering Handbook
Larry W. Lake, Editor-in-Chief
Volume I – General Engineering
John R. Fanchi, Editor
Copyright 2007, Society of Petroleum Engineers
Chapter 8 – Phase Diagrams
ISBN 978-1-55563-108-6
Get permission for reuse
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 such as nitrogen, H2S, or CO2 also may be present. 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 separable 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[1] and Whitson and Brulé.[2]
Phase Diagrams for a Single Component
Fig. 8.1 summarizes the phase behavior of a single component. The saturation curves shown in Fig. 8.1 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, Tc, 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.
Fig. 8.1 – 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 the chapter on crude oil emulsions in this volume), occasionally occur in petroleum production operations.
Fig. 8.2 shows typical volumetric behavior of a single component in the range of temperatures and pressures near the vapor-pressure curve in Fig. 8.1. If the substance under consideration is placed in a pressure cell at constant temperature, T1, below Tc 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 pv(T1) , the sample begins to condense. The pressure remains constant (see Sec. 8.3) at the vapor pressure until the sample volume is reduced from the saturated vapor volume (VV) to that of the saturated liquid (VL). 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.
Fig. 8.2 – 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
....................(8.1)
where F is the number of degrees of freedom, nc is the number of components, np is the number of phases, and Nc 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 (Nc = 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. 8.1.
In a binary system, two phases can exist over a range of temperatures and pressures. The number of degrees of freedom is calculated by
....................(8.2)
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. Secs. 8.4 through 8.8 introduce the types of phase diagrams that can be used to portray the thermodynamic phenomena that play important roles in oil and gas production.
Binary Phase Diagrams
Fig. 8.3 is a pressure-composition (p-x-y) phase diagram that shows typical vapor/liquid phase behavior for a binary system at a fixed temperature below the critical temperature of both components. At pressures below the vapor pressure of Component 2, pv2, any mixture of the two components forms a single vapor phase. At pressures between pv1 and pv2, two phases can coexist for some compositions. For instance, at pressure pb, two phases will occur if the mole fraction of Component 1 lies between xB and xE. If the mixture composition is xB, it will be all liquid; if the mixture composition is xE, it will be all vapor. At constant temperature and pressure, the line connecting a liquid phase and a vapor phase in equilibrium is known as a tie line. In binary phase diagrams such as Fig. 8.3, the tie lines are always horizontal because the two phases are in equilibrium at a fixed pressure. For 1 mole of mixture of overall composition, z, between xB and xE, the number of moles of liquid phase is
....................(8.3)Eq. 8.3 is an inverse lever rule because it is equivalent to a statement concerning the distances along a tie line from the overall composition to the liquid and vapor compositions. Thus, the amount of liquid is proportional to the distance from the overall composition to the vapor composition, divided by the length of the tie line.
Fig. 8.3 – Pressure-composition diagram for a binary mixture at a temperature below the critical temperature of both components.
Phase diagrams such as Fig. 8.3 can be determined experimentally by placing a mixture of fixed overall composition in a high-pressure cell and measuring the pressures at which phases appear and disappear. For example, a mixture of composition xB would show the behavior indicated qualitatively in Fig. 8.4. At a pressure less than pd (Fig. 8.3), the mixture is a vapor. If the mixture is compressed by injecting mercury into the cell, the first liquid, which has composition xA, appears at the dewpoint pressure, pd. As the pressure is increased further, the volume of liquid grows as more and more of the vapor phase condenses. The last vapor of composition xE disappears at the bubblepoint pressure, pb.
Fig. 8.4 – Volumetric behavior of a binary mixture at constant temperature that shows a bubblepoint pressure.
If the system temperature is above the critical temperature of one of the components, the phase diagram is similar to that shown in Fig. 8.5. At the higher temperature, the two-phase region no longer extends to the pure Component 1 side of the diagram. Instead, there is a critical point, C, at which liquid and vapor phases are identical. The critical point occurs at the maximum pressure of the two-phase region. The volumetric behavior of mixtures containing less Component 1 than the critical mixture, xc, is like that shown in Fig. 8.4. Fig. 8.6 shows the volumetric behavior of mixtures containing more Component 1. Compression of the mixture of composition x2 (in Fig. 8.5) leads to the appearance of liquid phase of composition x1 when pressure pd1 is reached. The volume of liquid first grows and then declines with increasing pressure. The liquid phase disappears again when pressure pd2 is reached. Such behavior is called "retrograde vaporization" or "retrograde condensation" if the pressure is decreasing.
Fig. 8.5 – Pressure-composition phase diagram for a binary mixture at a temperature above the critical temperature of Component 1.
Fig. 8.6 – Volumetric behavior of a binary mixture at constant temperature showing retrograde condensation.
If the system temperature is exactly equal to the critical temperature of Component 1, the critical point on the binary pressure-composition phase diagram is positioned at a Component 1 mole fraction of 1.0. Fig. 8.7 shows the behavior of the two-phase regions as the temperature rises. As the temperature increases, the critical point moves to lower concentrations of Component 1. As the critical temperature of Component 2 is approached, the two-phase region shrinks, disappearing altogether when the critical temperature is reached.
Fig. 8.7 – Regions of temperature, pressure, and composition for which two phases occur in a binary liquid/vapor system.
Fig. 8.8 shows a typical locus of critical temperatures and pressures for a pair of hydrocarbons. The critical locus shown in Fig. 8.8 is the projection of the critical curve in Fig. 8.7 onto the p-T plane. Thus, each point on the critical locus represents a critical mixture of different composition, although composition information is not shown on this diagram. For temperatures between the critical temperature of Component 1 and Component 2, the critical pressure of the mixtures can be much higher than the critical pressure of either component. Thus, two phases can coexist at pressures much greater than the critical pressure of either component. If the difference in molecular weight of the two components is large, the critical locus may reach very high pressures. Fig. 8.9 gives critical loci for some hydrocarbon pairs.[3]
Fig. 8.8 – Pressure-temperature diagram: a projection of the vapor-pressure pv1 and pv2) curves and locus of critical points for binary mixtures. Points C1 and C2 are the critical points of the pure components.
Fig. 8.9 – Vapor-pressure curves for light hydrocarbons and critical loci for selected hydrocarbon pairs.
The binary phase diagrams reviewed here are those most commonly encountered. However, more complex phase diagrams involving liquid/liquid and liquid/liquid/vapor equilibriums do occur in hydrocarbon systems at very low temperatures (well outside the range of conditions encountered in reservoirs or surface separators) and in CO2/crude oil systems at temperatures below approximately 50°C. See Stalkup[4] and Orr and Jensen[5] for reviews of such phase behavior.
Ternary Phase Diagrams
Phase behavior of mixtures containing three components is represented conveniently on a triangular diagram such as those shown in Fig. 8.10. Such diagrams are based on the property of equilateral triangles that the sum of the perpendicular distances from any point to each side of the diagram is a constant equal to the length of any of the sides. Thus, the composition of a point in the interior of the triangle can be calculated as
....................(8.4)where
....................(8.5)Several other useful properties of triangular diagrams are a consequence of this fact. For mixtures along any line parallel to a side of the diagram, the fraction of the component of the corner opposite to that side is constant (Fig. 8.10b). In addition, mixtures lying on any line connecting a corner with the opposite side contain a constant ratio of the components at the ends of the side (Fig. 8.10c). Finally, mixtures of any two compositions, such as A and B in Fig. 8.10d, lie on a straight line connecting the two points on the ternary diagram. Compositions represented on a ternary diagram can be expressed in volume, mass, or mole fractions. For vapor/liquid equilibrium diagrams, mole fractions are most commonly used.
Fig. 8.10 – Properties of ternary diagrams.
Fig. 8.11 shows the typical features of a ternary phase diagram for a system that forms a liquid and a vapor at fixed temperature and pressure. Mixtures with overall compositions that lie inside the binodal curve will split into liquid and vapor. Tie lines connect compositions of liquid and vapor phases in equilibrium. Any mixture with an overall composition along a tie line gives the same liquid and vapor compositions. Only the amounts of liquid and vapor change as the overall composition changes from the liquid side of the binodal curve to the vapor side. If the mole fractions of Component i in the liquid, vapor, and overall mixture are xi, yi, and zi, the fraction of the total moles in the mixture in the liquid phase is given by
....................(8.6)Eq. 8.6 is another lever rule similar to that described for binary diagrams. The liquid and vapor portions of the binodal curve meet at the plait point, a critical point at which the liquid and vapor phases are identical. Thus, the plait-point mixture has a critical temperature and pressure equal to the conditions for which the diagram is plotted. Depending on the pressure, temperature, and components, a plait point may or may not be present.
Fig. 8.11 – Ternary phase diagram at a constant temperature and pressure for a system that forms a liquid and a vapor.
Any one ternary diagram is given for fixed temperature and pressure. As either the temperature or pressure is varied, the location of the binodal curve and slopes of the tie lines may change. Fig. 8.12 shows the effect of increasing pressure on ternary phase diagrams for mixtures of C1, butane (C4), and decane (C10) at 160°F.[6][7] The sides of the ternary diagram represent a binary system; therefore, the ternary diagram includes whatever binary tie lines exist at the temperature and pressure of the diagram. Fig. 8.13 shows the corresponding binary phase diagrams for the C1–C4 and C1–C10 pairs. The C4–C10 pair is not shown because it forms two phases only below the vapor pressure of C4, approximately 120 psia at 160°F (see Fig. 8.9).
Fig. 8.12 – Ternary phase diagram for the methane/butane/decane system at 160° F.
Fig. 8.13 – Pressure-composition phase diagram for methane/butane and methane/decane binary systems at 160°F.
As Fig. 8.12 shows, at 1,000 psia the two-phase region is a band that stretches from the C1–C10 side of the diagram to the tie line on the C1–C4 side. If the pressure is increased above 1,000 psia, the liquid composition line shifts to higher methane concentrations; methane is more soluble in both C4 and C10 at the higher pressure (see Fig. 8.13). The two-phase region detaches from the C1–C4 side of the diagram at the critical pressure of the C1–C4 pair (approximately 1,800 psia). As the pressure increases above that critical pressure, the plait point moves into the interior of the diagram (Fig. 8.12, lower diagrams). With further increases in pressure, the two-phase region continues to shrink. It would disappear completely from the diagram if the pressure reached the critical pressure of the C1–C10 system at 160°F (nearly 5,200 psia).
According to the phase rule, three phases may coexist at a fixed temperature and pressure for some ternary systems. Fig. 8.14 shows the general structure of such systems. The three-phase region (3Φ) on a ternary diagram is represented as a triangle in Fig. 8.14. Any overall composition lying within the three-phase region splits into the same three phases (I, II and III). Only the amounts of each phase change as the overall composition varies within the three-phase region. Given 1 mole of an overall mixture in the three-phase region, the geometrical relations
....................(8.7)with
....................(8.8)determine the fraction of each phase. The edges of the three-phase region are tie lines for the associated two-phase (2Φ) regions; thus, there is a two-phase region adjacent to each of the sides of the three-phase triangle. Three-phase regions can exist in several phase diagrams applied in the design of EOR processes. Examples are discussed in Secs. 8.7 and 8.8.
Fig. 8.14 – Generic ternary phase diagram with three-phase region.
Quaternary Phase Diagrams
Phase diagrams for systems with four components can be represented conveniently on a tetrahedral diagram like that shown in Fig. 8.15a, which shows a quaternary phase diagram calculated with the Peng-Robinson[8] equation of state for mixtures of methane (C1), C3, C6, and hexadecane (C16) at 200°F and 2,000 psia. These phase diagrams have a property similar to that of ternary diagrams: the sum of the lengths of perpendicular lines drawn from a composition point in the interior of the diagram to the four faces of the diagram is a constant length. Hence, the fractions of four components can be represented by an extension of Eq. 8.4 to four components.
The faces of the quaternary diagram are ternary phase diagrams. Fig. 8.15b shows the ternary diagram for the ternary methane (C1)/hexane (C6)/hexadecane (C16) system, which is the bottom face of the quaternary diagram. The two-phase region is a band across the diagram, and there is no critical point on that face. Fig. 8.15c shows the C1/C3/C16 system, which is the left face of the quaternary diagram. That ternary system does have a critical point. While the ternary diagram for C1/C3/C6 is not shown separately, it is qualitatively similar to the diagram for the C1/C3/C16 system in Fig. 8.15c.
Fig. 8.15 – Properties of the quaternary phase diagram.
The two-phase region in the interior of the quaternary diagram is a 3D region of composition space bounded by the ternary two-phase regions on the faces. Within that region, every mixture composition forms two phases, and each composition point lies on a tie line that connects equilibrium vapor and liquid compositions. A vertical slice through the two-phase region is shown in Fig. 8.15a, along with a few tie lines that lie in the interior of the diagram. The mole fraction of liquid phase is still calculated with Eq. 8.6, which applies to systems with any number of components.
The boundary of the two-phase region in the interior of the quaternary diagram is divided into two parts: a surface that includes all the vapor-phase compositions and a corresponding surface of liquid-phase compositions. The dividing line between the liquid and vapor surfaces is a critical locus (the dotted line in Fig. 8.15c) that connects the critical point in the C1/C3/C16 face (Fig. 8.15a) with the critical point in the C1/C3/C6 face. The critical locus is a set of compositions at which the liquid and vapor phases have identical compositions and properties. The compositions and limiting tie lines on the critical locus play important roles in the description of EOR processes (see Sec. 8.8).
Reservoir Fluid Systems
Real reservoir fluids contain many more than two, three, or four components; therefore, phase-composition data can no longer be represented with two, three or four coordinates. Instead, phase diagrams that give more limited information are used. Fig. 8.16 shows a pressure-temperature phase diagram for a multicomponent mixture; it gives the region of temperatures and pressures at which the mixture forms two phases. The analog of Fig. 8.16 for a binary system can be obtained by taking a slice at constant mole fraction of Component 1 through the diagram in Fig. 8.7. Also given are contours of liquid-volume fractions, which indicate the fraction of total sample volume occupied by the liquid phase; however, Fig. 8.16 does not give any compositional information. In general, the compositions of coexisting liquid and vapor will be different at each temperature and pressure.
Fig. 8.16 – Pressure-temperature phase diagram (phase envelope) for a mixture of fixed composition.
At temperatures below the critical temperature (point C), a sample of the mixture described in Fig. 8.16 splits into two phases at the bubblepoint pressure (Fig. 8.4) when the pressure is reduced from a high level. At temperatures above the critical temperature, dewpoints are observed (Fig. 8.6). In this multicomponent system, the critical temperature is no longer the maximum temperature at which two phases can exist. The critical point is the temperature and pressure at which the phase compositions and all phase properties are identical.
The bubblepoint, dewpoint, and single-phase regions shown in Fig. 8.16 are sometimes used to classify reservoirs. At temperatures greater than the cricondentherm, which is the maximum temperature for the formation of two phases, only one phase occurs at any pressure. For instance, if the hydrocarbon mixture in Fig. 8.16 were to occur in a reservoir at temperature TA and pressure pA (point A), a decline in pressure at approximately constant temperature caused by removal of fluid from the reservoir would not cause the formation of a second phase.
While the fluid in the reservoir remains a single phase, the produced gas splits into two phases as it cools and expands to surface temperature and pressure at point A′. Thus, some condensate would be collected at the surface even though only one phase is present in the formation. The amount of condensate collected depends on the operating conditions of the separator. The lower the temperature at a given pressure, the larger the volume of condensate collected (Fig. 8.16).
Dewpoint reservoirs are those for which the reservoir temperature lies between the critical temperature and the cricondentherm for the reservoir fluid. Production of fluid from a reservoir starting at point B in Fig. 8.16 causes liquid to appear in the reservoir when the dewpoint pressure is reached. As the pressure declines further, the saturation of liquid increases because of retrograde condensation. Because the saturation of liquid is low, only the vapor phase flows to producing wells. Thus, the overall composition of the fluid remaining in the reservoir changes continuously.
The phase diagram shown in Fig. 8.16 is for the original composition only. The preferential removal of light hydrocarbon components in the vapor phase generates new hydrocarbon mixtures, which have a greater fraction of the heavier hydrocarbons. Differential liberation experiments, in which a sample of the reservoir fluid initially at high pressure is expanded through a sequence of pressures, can be used to investigate the magnitude of the effect of pressure reduction on the vapor composition. At each pressure, a portion of the vapor is removed and analyzed. These experiments simulate what happens when condensate is left behind in the reservoir as the pressure declines. See Pedersen, Fredenslund, and Thomassen[9] for more details on pressure/volume/temperature experiments.
As the reservoir fluid becomes heavier, the boundary of the two-phase region in a diagram like Fig. 8.16 shifts to higher temperatures. Thus, the composition change also acts to drive the system toward higher liquid condensation. Such reservoirs are candidates for pressure maintenance by lean gas injection to limit the retrograde loss of condensate or for gas cycling to vaporize and recover some of the liquid hydrocarbons.
Bubblepoint reservoirs are those in which the temperature is less than the critical temperature of the reservoir fluid (point D in Fig. 8.16). These reservoirs are sometimes called undersaturated because the fraction of light components present in the oil is too low for a gas phase to form at that temperature and pressure. Isothermal pressure reduction causes the appearance of a vapor phase at the bubblepoint pressure. Because the compressibility of the liquid phase is much lower than that of a vapor, the pressure in the reservoir declines rapidly during production in the single-phase region. The appearance of the much more compressible vapor phase reduces the rate of pressure decline. The volume of vapor present in the reservoir grows rapidly with reduction of reservoir pressure below the bubblepoint.
Because the vapor viscosity is much lower than the liquid viscosity and the gas relative permeability goes up markedly with increasing gas saturation, the vapor phase flows more easily. Hence, the produced gas/oil ratio climbs rapidly. Again, pressure maintenance by waterdrive, water injection, or gas injection can improve oil recovery substantially over the 10 to 20% recovery typical of pressure depletion in these solution-gas-drive reservoirs. As in dewpoint reservoirs, the composition of the reservoir fluid changes continuously once the two-phase region is reached.
There is, of course, no reason why initial reservoir temperatures and pressures cannot lie within the two-phase region. Oil reservoirs with gas caps and gas reservoirs with some liquids present are common. There also can be considerable variation in the initial composition of the reservoir fluid. The discussion of single-phase, dewpoint, and bubblepoint reservoirs is based on a phase diagram for one fluid composition. Even for one fluid, all the types of behavior occur over a range of temperatures. In actual reservoir settings, the composition of the reservoir fluid correlates with depth and temperature. Deeper reservoirs usually contain lighter oils.[10]
Fig. 8.17 shows the relationships between oil gravity and depth for two basins. The higher temperatures of deeper reservoirs alter the original hydrocarbon mixtures to produce lighter hydrocarbons over geologic time.[10] Low oil gravity, low temperature, and relatively small amounts of dissolved gas all combine to produce bubblepoint reservoirs. High oil gravity, high temperatures, and a high concentration of light components produce dewpoint or condensate systems.
Fig. 8.17 – Increase in °API gravity with depth: (a) Ordovician Ellenberger reservoirs in Delaware Val Verde basin and (b) Pennsylvanian Tensleep reservoirs in Wyoming.
Phase Diagrams for EOR Processes
Phase behavior plays an important role in a variety of EOR processes. Such processes are designed to overcome, in one way or another, the capillary forces that act to trap oil during waterflooding. Interpretation of phase diagrams is particularly important in the design of surfactant/polymer processes and gas-injection processes.
Surfactant/Polymer Floods
In surfactant/polymer displacement processes, the effects of capillary forces are reduced by injection of surfactant solutions that contain molecules with oil- and water-soluble portions. Such molecules migrate to the oil/water interface and reduce the interfacial tension, thereby reducing the magnitude of the capillary forces that resist movement of trapped oil.Fig. 8.18[11] shows phase diagrams typical of those used to describe the behavior of surfactant systems. In these ternary diagrams, the components shown are no longer true thermodynamic components because they are mixtures. A crude oil contains hundreds of components, and the brine and surfactant pseudocomponents also may be complex mixtures. The simplified representation, however, has obvious advantages for describing phase behavior, and it is reasonably accurate as long as each pseudocomponent has approximately the same composition in each phase. In Fig. 8.18a, for instance, the "oil" pseudocomponent can appear in an oil-rich phase or in a phase containing mostly surfactant and brine. If the oil solubilized into the surfactant/brine phase is nearly the same mixture of hydrocarbons as the original "oil," then the representation in terms of pseudocomponents is reasonable. The compositions shown in Fig. 8.18 are in volume fractions. An inverse lever rule similar to Eqs. 8.3 and 8.6 gives the relationship between the volumes of the two phases for a given overall composition, as Fig. 8.18 illustrates.
![Fig. 8.18 – Ternary representation of phase diagrams.[11]](/w/images/thumb/4/48/Vol1_Page_388_Image_0001.png/103px-Vol1_Page_388_Image_0001.png)
Fig. 8.18 – Ternary representation of phase diagrams.[11]
![Fig. 8.18 – Ternary representation of phase diagrams.[11]](/File:Vol1_Page_388_Image_0001.png)
Fig. 8.18a is a phase diagram for the liquid/liquid equilibrium behavior typical of mixtures of brines of low salinity with oil. If there is no surfactant present, the oil and brine are immiscible; mixture compositions on the base of the diagram split into essentially "pure" brine in equilibrium with "pure" oil. The addition of surfactant causes some oil to be solubilized into a microemulsion rich in brine. That phase is in equilibrium with a phase containing nearly pure oil. Thus, in the low-salinity brine, the surfactant partitions into the brine phase, solubilizing some oil. The plait point in Fig. 8.18a lies close to the oil corner of the diagram. Because only two phases occur and the tie lines all have negative slope, such phase is often called Type II(-).
Phase diagrams for high-salinity brines are often similar to Fig. 8.18b. In the high-salinity systems, the surfactant partitions into the oil phase and solubilizes water into an oil-external microemulsion. In this case, the plait point is close to the brine apex on the ternary diagram. For intermediate salinities, the phase behavior can be more complex, as Fig. 8.18c shows. A triangular three-phase region occurs (see Fig. 8.14) for which the phases are a brine-rich phase, an oil-rich phase, and a microemulsion phase. There is a two-phase region adjacent to each of the sides of the three-phase triangle. In Fig. 8.18c, the two-phase region at low surfactant concentrations is too small to show on the diagram. It must be present, however, because oil and brine form only two phases in the absence of surfactant.
Gas-Injection Processes
Miscible displacement processes are designed to eliminate interfaces between the oil and the displacing phase, thereby removing the effects of capillary forces between the injected fluid and the oil. Unfortunately, fluids that are strictly miscible with oil are too expensive for general use. Instead, fluids such as C1, C1 enriched with intermediate hydrocarbons, CO2, or nitrogen are injected, and the required miscible-displacing fluid is generated by mixing the injected fluid with oil in the reservoir. Phase behavior of gas/oil systems is often summarized in pressure-composition (p-x) diagrams.Fig. 8.19 is an example of a p-x diagram for mixtures of CO2 (containing a small amount of C1 contamination) with crude oil from the Rangely field.[12] The behavior of binary mixtures of CO2 with a particular oil is reported for a fixed temperature; therefore, the oil is represented as a single pseudocomponent. The bubblepoint and dewpoint pressures, the regions of pressure and composition for which two or more phases exist, and information about the volume fractions of the phases are indicated. However, the diagrams provide no information about the compositions of the phases in equilibrium.
Fig. 8.19 – Pressure-composition diagram. Gas 1 system for Rangely oil: 95% CO2 and 5% CH4 gas system at 160°F.
Fig. 8.20 illustrates the reason for the absence of composition data and gives data reported by Metcalfe and Yarborough[13] for a ternary system of CO2, C4, and C10. Binary-phase data for the CO2–C4[14] and CO2–C10[15] systems also are included. Fig. 8.20 shows a triangular solid within which all possible compositions (mole fractions) of CO2–C4–C10 mixtures for pressures between 400 and 2,000 psia are contained. The two-phase region is bounded by a surface that connects the binary-phase envelope for the CO2–C10 binary pair to that on the CO2–C4 side of the diagram. That surface is divided into two parts-liquid compositions and vapor compositions.
Fig. 8.20 – Phase behavior of CO2-C4-C10 mixtures at 160°F.
Tie lines connect the compositions of liquid and vapor phases in equilibrium at a fixed pressure. Thus, the ternary phase diagram for CO2–C4–C10 mixtures at any pressure is just a constant pressure (horizontal) slice through the triangular prism. Several such slices at different pressures are shown in Fig. 8.20. At pressures below the critical pressure of CO2–C4 mixtures (1,184 psia), both CO2–C10 and CO2–C4 mixtures form two phases for some range of CO2 concentrations. At 400 and 800 psia, the two-phase region is a band across the diagram. Above the critical pressure of CO2–C4 mixtures, CO2 is miscible with C4 and ternary slices at higher pressures show a continuous binodal curve on which the locus of liquid compositions meets that of vapor compositions at a plait point. The locus of plait points connects the critical points of the two binary pairs.
To see the effect of representing the phase behavior of a ternary system on a pseudobinary diagram, consider a p-x diagram for "oil" composed of 70 mol% C10 and 30 mol% C4. At any fixed pressure, the mixtures of CO2 and oil, which would be investigated in an experiment to determine a p-x diagram, lie on a straight line (the dilution line), which connects the original oil composition with the CO2 apex. Thus, a p-x diagram for this system is a vertical slice through the triangular prism shown in Fig. 8.20. The saturation pressures on a p-x diagram are those at which the dilution plane intersects the surface that bounds the two-phase region. Bubblepoint pressures occur where the dilution plane intersects the liquid composition side of the two-phase surface, while dewpoint pressures occur at the intersection with vapor compositions. Comparison of the phase envelope on the resulting p-x diagram with binary phase diagrams yields the following observations.
- Tie lines do not, in general, lie in the dilution plane; they pierce that plane. This means that the composition of vapor in equilibrium with a bubblepoint mixture on the p-x diagram is not the same as that of the dewpoint mixture at the same pressure.
- The critical point on the p-x diagram occurs where the locus of critical points pierces the dilution plane. It is not, in general, at the maximum saturation pressure on the p-x diagram. The maximum pressure occurs where the binodal curve in a horizontal slice is tangent to the dilution plane. The critical point on the p-x diagram can lie on either side of the maximum pressure, depending on the position of locus of plait points on the two-phase surface.
Figs. 8.19 and 8.21 illustrate the complexity of phase behavior observed for CO2/crude oil systems. Fig. 8.19 gives the behavior of mixtures of CO2 (with approximately 5% C1 as a contaminant) with Rangely crude oil at 160°F. The oil has a bubblepoint pressure of approximately 350 psia. Mixtures containing up to approximately 80 mol% CO2 (+ C1) show bubblepoints, while those containing more CO2 show dewpoints. At the relatively high temperature of the Rangely field, only two phases, a liquid and a vapor, form. At lower temperatures, more complex phase behavior can occur.
Fig. 8.21 shows the behavior of mixtures of an oil containing no dissolved gas from the Wasson field[4] with CO2. At 90°F and 105°F, the mixtures form a liquid and a vapor at low pressures and two liquid phases at high pressures and high CO2 concentrations. They form three phases, two liquids and a vapor, for a small range of pressures at high CO2 concentrations. The liquid/liquid and liquid/liquid/vapor behavior disappears if the temperature is high enough. At 120°F (Fig. 8.21c), the three-phase region disappears. For the systems studied to date, 120°F appears to be a reasonable estimate of the maximum temperature for liquid/liquid/vapor separations. See Stalkup[4] and Orr and Jensen[5] for detailed discussions of such phase behavior. Well-characterized ternary systems that display similar behavior are described by Larsen et al.,[16] who report ternary diagrams like Fig. 8.14 for CO2/hydrocarbon systems.
Fig. 8. - p-x diagrams for mixtures of CO2 with Wasson oil, where L1 is liquid phase (oil rich), L2 is liquid phase 2 (CO2-rich phase), and V is the vapor phase. Dashed lines indicate constant volume fraction of L1 phase.
Multicontact Miscibility in Gas-Injection Processes
Phase diagrams of the types described here are often used to represent miscible gas-injection processes. The simplest form of miscibility is first contact miscibility. It occurs when a given gas is injected into oil at a temperature and pressure at which any mixture of the oil and gas result in a single-phase fluid. For an oil/gas pair to be first contact miscible, the dilution line, which connects the oil composition and the gas composition, cannot intersect the two-phase region. The lowest pressure at which first contact miscibility can occur is the pressure at which the dilution line is tangent to the two-phase boundary; therefore, this pressure is referred to as the first contact miscibility pressure. However, multicontact miscibility can develop at pressures lower, often substantially lower, than the first contact miscibility pressure.For ternary systems, two mechanisms can lead to the development of a multicontact miscible displacement: vaporizing drives and condensing drives. Fig. 8.22a demonstrates the features of a vaporizing drive for the displacement of a C6–C16 mixture (O1) by pure C1. The displacement composition path traverses the two-phase region along two key tie lines in compositional space: the tie line that extends through the injected gas composition (the injection tie line) and the tie line that extends through the initial oil composition (the initial tie line).[17][18] As the pressure is increased, the two-phase region shrinks and, at some point, one of the key tie lines become a critical tie line (a tie line that is tangent to the two-phase region at a critical point).
Fig. 8.22 – Condensing and vaporizing segments in gas-injection processes.
Fig. 8.22b demonstrates the features of a condensing gas drive for a C1–C3 mixture displacing oil consisting of C1 and C16. In this case, the injection tie line is closer to the critical point, and as the pressure is increased, it is the first to become a critical tie line. For both cases, the pressure at which one of the key tie lines become a critical tie line is known as the minimum miscibility pressure (MMP).[18] Thus, in three-component systems, a displacement can be multicontact miscible only if one of the two key tie lines is a critical tie line. If it is the initial oil tie line that is critical, the displacement is a vaporizing drive, and if the injection gas tie line is the critical tie line, the displacement is a condensing drive.
For four-component systems, the displacement path has been shown to include a third key tie line referred to as the crossover tie line.[19] Fig. 8.22c shows the crossover tie line. Just as in the ternary displacements, miscibility develops when any one of the key tie lines reduces to a critical point. If the pressure in Fig. 8.22c is increased, the crossover tie line will become a critical tie line before either the initial or injection tie lines. Hence, the existence of the crossover tie line introduces a third mechanism for the development of multicontact miscibility. This mechanism is known as the combined condensing/vaporizing drive.[20][21] Fig. 8.22c shows that the displacement composition path for a four-component system in which a mixture of C1 and C3 displaces an oil containing C1, C6, and C16 includes a vaporizing segment connected to a condensing segment by the crossover tie line.
With each additional component added to the displacement process, another crossover tie line is added to the displacement composition path. The MMP for such multicomponent gas-injection processes can be determined by locating the key tie lines and calculating the length of these tie lines as the pressure is increased. The MMP is the pressure at which one of the key tie lines has zero length. Fig 8.23[22] reports the result of such a calculation for a 15-component fluid description. In this system, the injection gas contains 11 components and is rich in C1 but includes N2, CO2, and hydrocarbons up to C7. The eighth crossover tie lie becomes a critical tie line at the MMP of 5,350 psia. Displacements that display the combined condensing/vaporizing mechanism are common in oilfield fluid systems.
Fig. 8.23 – Tie-line length vs. pressure for a multicomponent gas-injection process.
Nomenclature
| a | = | length of line a in Fig. 8.14 |
| b | = | length of line b in Fig. 8.14 |
| c | = | length of line c in Fig. 8.14 |
| C | = | critical point |
| d | = | length of line d in Fig. 8.14 |
| e | = | length of line e in Fig. 8.14 |
| f | = | length of line f in Fig. 8.14 |
| F | = | number of degrees of freedom |
| i | = | component i |
| L | = | liquid phase |
| Lk | = | perpendicular distance from a given point to side in an equilateral triangle (k=1, 2, 3) |
| LT | = | side length in equilateral triangle |
| nc | = | number of components |
| np | = | number of phases |
| Nc | = | number of constraints |
| p | = | pressure, m/Lt2, psi |
| pA | = | pressure at point A, m/Lt2, psi |
| pb | = | bubblepoint pressure, m/Lt2, psi |
| pc | = | critical pressure, m/Lt2, psi |
| pd | = | dewpoint pressure of mixture xB, m/Lt2, psi |
| pd1 | = | lower dewpoint pressure mixture x2, m/Lt2, psi |
| pd2 | = | upper dewpoint pressure mixture x2, m/Lt2, psi |
| pt | = | total pressure, m/Lt2, psi |
| pv | = | vapor pressure, m/Lt2, psi |
| pv1 | = | saturation pressure of pure component 1, m/Lt2, psi |
| pv2 | = | saturation pressure of pure component 2, m/Lt2, psi |
| T | = | temperature, T, K |
| T1 | = | constant temperature below Tc, T, K |
| T2 | = | constant temperature above Tc, T, K |
| TA | = | temperature at point A, T, K |
| Tc | = | critical temperature, T, K |
| V | = | vapor |
| Vc | = | critical volume, L3, ft3 |
| VL | = | saturated liquid volume, L3, ft3 |
| VV | = | saturated vapor volume, L3, ft3 |
| x1 | = | mole fraction of component 1 |
| x2 | = | mole fraction of component 2 |
| x3 | = | mole fraction of component 3 |
| xA | = | saturated liquid composition at pd |
| xB | = | saturated vapor composition at pd |
| xC | = | critical mixture |
| xE | = | vapor phase composition in equilibrium with xB from overall mixture z |
| xi | = | mole fraction of component i in the liquid phase |
| yi | = | mole fraction of component i in the vapor phase |
| z | = | overall composition in mole fractions |
| zi | = | mole fraction of component i in the overall composition |
| βI | = | mole fraction of phase I |
| βII | = | mole fraction of phase II |
| βIII | = | mole fraction of phase III |
| βi | = | mole fraction of phase i |
| βj | = | mole fraction of phase j |
| 2Φ | = | two-phase region |
| 3Φ | = | three-phase region |
References
- ↑ Lake, L.W. 1989. Enhanced Oil Recovery. Englewood Cliffs, New Jersey: Prentice Hall.
- ↑ Whitson, C.H. and Brulé, M.R. 2000. Phase Behavior, No. 20, Chap. 3. Richardson, Texas: Henry L. Doherty Monograph Series, Society of Petroleum Engineers.
- ↑ GPSA. 1972. GPSA Engineering Data Book, 9th edition. Tulsa, Oklahoma: Gas Processors Suppliers Association.
- ↑ 4.0 4.1 4.2 Stalkup Jr., F.I. 1983. Miscible Displacement, Vol. 8. Richardson, Texas: Henry L. Doherty Monograph Series, SPE.
- ↑ 5.0 5.1 Orr, F.M. Jr. and Jensen, C.M. 1984. Interpretation of Pressure-Composition Phase Diagrams for CO2/Crude Oil Systems. SPE J. 24 (5): 485–497. SPE-11125-PA. http://dx.doi.org/10.2118/11125-PA
- ↑ Reamer, H.H., Fiskin, J.M., and Sage, B.H. 1949. Phase Equilibria in Hydrocarbon Systems. Ind. Eng. Chem. 41 (12): 2871-2875. http://dx.doi.org/10.1021/ie50480a052
- ↑ Sage, B.H. and Lacey, W.N. 1950. Thermodynamic Properties of the Lighter Paraffin Hydrocarbons and Nitrogen: Monograph on API Research Project 37. New York: American Petroleum Institute.
- ↑ Peng, D.-Y. and Robinson, D.B. 1976. A New Two-Constant Equation of State. Industrial & Engineering Chemistry Fundamentals 15 (1): 59–64. http://dx.doi.org/10.1021/i160057a011
- ↑ Pedersen, K.S., Fredenslund, A.A., and Thomassen, P. 1989. Properties of Oils and Natural Gases, Contributions in Petroleum Geology and Engineering. Houston, Texas: Gulf Publishing Company.
- ↑ 10.0 10.1 Hunt, J.M. 1979. Petroleum Geochemistry and Geology. San Francisco, California: W.H. Freeman and Co.
- ↑ 11.0 11.1 Nelson, R.C. and Pope, G.A. 1978. Phase Relationships in Chemical Flooding. SPE J. 18 (5): 325–338. SPE-6773-PA. http://dx.doi.org/10.2118/6773-PA
- ↑ Graue, D.J. and Zana, E.T. 1981. Study of a Possible CO2 Flood in the Rangely Field, Colorado. J Pet Technol (July 1981): 1312.
- ↑ Metcalfe, R.S. and Yarborough, L. 1979. The Effect of Phase Equilibria on the CO2 Displacement Mechanism. SPE J. 19 (4): 242–252. SPE-7061-PA. http://dx.doi.org/10.2118/7061-PA
- ↑ Reamer, H.H., Fiskin, J.M., and Sage, B.H. 1949. Phase Equilibria in Hydrocarbon Systems. Ind. Eng. Chem. 41 (12): 2871-2875. http://dx.doi.org/10.1021/ie50480a052
- ↑ Reamer, H.H. and Sage, B.H. 1963. Phase Equilibria in Hydrocarbon Systems. Volumetric and Phase Behavior of the n-Decane-CO2 System. J. Chem. Eng. Data 8 (4): 508-513. http://dx.doi.org/10.1021/je60019a010
- ↑ Larson, L.L., Silva, M.K., Taylor, M.A. et al. 1989. Temperature Dependence of L1/L2/V Behavior in CO2/Hydrocarbon Systems. SPE Res Eng 4 (1): 105-114. SPE-15399-PA. http://dx.doi.org/10.2118/15399-PA
- ↑ Dumore, J.M., Hagoort, J., and Risseeuw, A.S. 1984. An Analytical Model for One-Dimensional, Three-Component Condensing and Vaporizing Gas Drives. Society of Petroleum Engineers Journal 24 (2): 169-179. SPE-10069-PA. http://dx.doi.org/10.2118/10069-PA
- ↑ 18.0 18.1 Johns, R.T. and Orr Jr., F.M. 1996. Miscible Gas Displacement of Multicomponent Oils. SPE J. 1 (1): 39–50. SPE-30798-PA. http://dx.doi.org/10.2118/30798-PA Cite error: Invalid
<ref>tag; name "r18" defined multiple times with different content - ↑ Monroe, W.W., Silva, M.K., Larson, L.L. et al. 1990. Composition Paths in Four-Component Systems: Effect of Dissolved Methane on 1D CO2 Flood Performance. SPE Res Eng 5 (3): 423–432. SPE-16712-PA. http://dx.doi.org/10.2118/16712-PA
- ↑ Zick, A.A. 1986. A Combined Condensing/Vaporizing Mechanism in the Displacement of Oil by Enriched Gases. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 5–8 October. SPE 15493. http://dx.doi.org/10.2118/15493-MS
- ↑ Johns, R.T., Dindoruk, B., and Orr Jr., F.M. 1993. Analytical Theory of Combined Condensing/Vaporizing Gas Drives. SPE Advanced Technology Series 1 (2): 7–16. SPE-24112-PA. http://dx.doi.org/10.2118/24112-PA
- ↑ Jessen, K., Michelsen, M., and Stenby, E.H. 1998. Global approach for calculating minimum miscibility pressure. Fluid Phase Equilib. 153 (2): 251–263. http://dx.doi.org/10.1016/S0378-3812(98)00414-2
SI Metric Conversion Factors
| °API | 141.5/(131.5+°API) | = | g/cm3 | ||
| ft | × | 3.048* | E – 01 | = | m |
| °F | (°F − 32)/1.8 | = | °C | ||
| psi | × | 6.894 757 | E + 00 | = | kPa |
*