Phase diagrams for EOR processes

Phase behavior plays an important role in a variety of enhanced oil recovery (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. 1 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. 1a, 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. 1 are in volume fractions. An inverse lever rule similar to Eqs. 1 and 8.6 gives the relationship between the volumes of the two phases for a given overall composition, as Fig. 1 illustrates.

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

Eq. 1 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.

....................(2)

Eq. 2 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. 1 – Ternary representation of phase diagrams.

Fig. 1a 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. 1a 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. 1b. 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. 1c shows. A triangular three-phase region occurs (see Fig. 8.14) for which the phases are:

• A brine-rich phase
• An oil-rich phase
• A microemulsion phase

There is a two-phase region adjacent to each of the sides of the three-phase triangle. In Fig. 1c, 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. 2 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. 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. 2 – Pressure-composition diagram. Gas 1 system for Rangely oil: 95% CO₂ and 5% CH₄ gas system at 160°F.

Fig. 3 illustrates the reason for the absence of composition data and gives data reported by Metcalfe and Yarborough for a ternary system of CO₂, C₄, and C₁₀. Binary-phase data for the CO₂–C₄ and CO₂–C₁₀ systems also are included. Fig. 3 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. 3 – 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. 3. 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. 3. 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.

It is apparent from Fig. 3 that the composition of the original oil has a strong influence on the shape of the saturation-pressure curve and on the location of the critical point on the p-x diagram. If the oil had been richer in C₄, the critical pressure and maximum pressure both would have been lower. Thus, it should be anticipated that the appearance of p-x diagrams for CO₂/crude oil systems should depend on the composition of the oil.

Figs. 2 and 4 illustrate the complexity of phase behavior observed for CO₂/crude oil systems. Fig. 2 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. 4. - 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.

Fig. 4 shows the behavior of mixtures of an oil containing no dissolved gas from the Wasson field 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. 4c), 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 and Orr and Jensen for detailed discussions of such phase behavior. Well-characterized ternary systems that display similar behavior are described by Larsen et al., who report ternary diagrams like Fig. 5 for CO₂/hydrocarbon systems.

• 

  Fig. 5 – Generic ternary phase diagram with three-phase region.

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. 5a 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:

• Tie line that extends through the injected gas composition (the injection tie line)
• Tie line that extends through the initial oil composition (the initial tie line).

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. 5 – Condensing and vaporizing segments in gas-injection processes.

Fig. 5b 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). 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. Fig. 5c 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. 5c 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. Fig. 5c 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 6 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. 6 – Tie-line length vs. pressure for a multicomponent gas-injection process.

Noteworthy papers in OnePetro

Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read

External links

Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro

See also

Phase diagrams

Phase diagrams for reservoir fluid systems

Quaternary phase diagrams

Ternary phase diagrams

Binary phase diagrams

PEH:Phase_Diagrams