Phase diagrams of miscible processes

Before undertaking any type of compositional numerical simulation of a miscible flood, it is crucial to identify the phase behavior occurring in the reservoir. Phase diagrams are a typical method for representing phase behavior.

Ternary and pseudoternary phase diagrams

Ternary diagrams and pseudoternary diagrams have been used for decades to visualize conceptually the phase behavior of injection-fluid/crude-oil systems. This is done by representing multicomponent fluids or mixtures by three pseudocomponents and then plotting fluid compositions in the interior of an equilateral triangle with apexes that represent 100% of each pseudocomponent and where the side opposite an apex represents 0% of that pseudocomponent. Usually, the three pseudocomponents represent:

1. A fraction of low-molecular-weight materials
2. A fraction of intermediate-molecular-weight materials
3. A fraction of the higher-molecular-weight materials

For example, the low-molecular-weight fraction might include methane and nitrogen and perhaps CO₂ if CO₂ is the primary injection solvent. The intermediate-molecular-weight pseudocomponent might include the C₂ –C₆ hydrocarbons and perhaps CO₂ if the CO₂ is a constituent of an otherwise hydrocarbon injection solvent. The higher-molecular-weight pseudocomponent in this scheme would be the leftover C₇+ fraction. There is no particularly "right" way to divide a fluid into three pseudocomponents. Different injection processes may be better represented by one type of grouping vs. another, and different groupings may give somewhat different insights into phase-behavior mechanisms.

Pseudoternary diagrams apply rigorously only to true ternary systems, and a strictly ternary analogy may give a somewhat misleading view of the mass-transfer mechanisms that result in compositional enhancement. Even so, a pseudoternary diagram is still a useful way to represent some complex phase-behavior concepts that are not so easily visualized otherwise.

A ternary diagram represents phase behavior at a constant temperature and pressure. Fig. 1 is a traditional pseudoternary-diagram representation of phase behavior for the pseudo-components:

• C₁
• C_2–6
• C₇+

• 

  Fig. 1 – The vaporizing-gas-drive process (after Young and Martin).

The diagram in Fig. 1 has the following characteristics:

• There is a bubblepoint curve representing oil mixtures at their bubblepoint and a dewpoint curve representing solvent mixtures at their dewpoint. These curves come together at a critical composition.
• The dashed lines, called tie lines, connect liquid and solvent compositions that are in equilibrium.
• All mixtures inside the region bounded by the bubblepoint and dewpoint curves consist of two phases.
• The tie line that passes through a given mixture composition gives the equilibrium solvent and liquid compositions for this mixture where it intersects the dewpoint and bubblepoint curves.
• The tie line that just passes through the critical composition is called the critical tie line.
• All mixtures outside the region bounded by the dewpoint and bubblepoint curves are single phase.

Vaporizing solvent drive process

Fig. 1 shows how compositions change in situ when a lean injection solvent displaces an oil represented by point A, whose composition lies just to the right of the limiting tie line.

The injection solvent identified on the C₁–C_2–6 side of the triangle has a high methane content. When this solvent mixes with the reservoir fluid, an overall composition such as M1 may result. M1 is in the two-phase region of the diagram and consists of dewpoint solvent G1 and bubblepoint liquid L1.

As more solvent is injected, solvent G1, formed in the first contact, is pushed ahead, where it contacts fresh reservoir fluid. Upon mixing, solvent G1 and the reservoir fluid form another overall mixture, M2, which consists of dewpoint solvent G2 and bubblepoint liquid L2.

Solvent G2 then flows ahead and contacts fresh reservoir fluid, forming an overall mixture M3, which consists of dewpoint solvent G3 and bubblepoint liquid L3.

In this way, solvent at the displacing front is progressively enriched to the critical composition P, which is first-contact miscible with the reservoir fluid.

In the vaporizing solvent drive process, compositional enhancement occurs by the injection solvent vaporizing intermediate-molecular-weight hydrocarbons from the oil and enriching the composition at the solvent front. For pseudoternary phase behavior, as long as the reservoir fluid composition lies to the right of the limiting tie line through the critical point, multiple contact miscibility can be achieved. If oil composition should lie to the left of the critical tie line, solvent enrichment can occur only to the composition of dewpoint solvent lying on the tie line that can be extended to pass through the oil composition. For example, if reservoir oil B were being displaced by the injection solvent, enrichment of the solvent front could occur only up to dewpoint solvent G2. Although multiple contact miscibility is not achieved, efficient immiscible vaporization may still occur (depending on the compositions actually achieved) and should be evaluated for effectiveness.

The mechanism for compositional enhancement described above can be effective for other solvents besides lean hydrocarbon solvent. N₂ and flue gas solvent can give compositionally enhanced displacements by this mechanism, although with different MMPs. CO₂ also achieves compositionally enhanced displacement by a similar mechanism, although for lower temperatures the mechanism may be one of liquid/liquid extraction rather than vaporization.

The conceptual argument given above indicates that compositions in the solvent/oil transition zone lie along the dewpoint curve until the critical composition is reached so that no transition-zone compositions lie inside the two-phase region. Because of mixing caused by diffusion and reservoir flow mechanisms, this is not the case in practice. Transition-zone compositions cut into the two-phase region, causing some solvent-flood residual oil to be left behind the solvent front.

Condensing solvent drive process

Fig. 2 shows another mechanism whereby compositional enhancement can occur in a solvent flood. The oil is a bubblepoint liquid lying on the bubblepoint curve. For this phase behavior, an injection solvent that has composition A on the C₁–C_2–6 side of the triangle is completely miscible with the oil because the line connecting oil with composition A passes through only the single-phase region. However, according to the traditional ternary diagram view of phase behavior, solvents that have compositions between A and B can develop multicontact miscibility in the following manner.

• 

  Fig. 2 – The condensing-gas-drive process (after Young and Martin).

Solvent B lies just to the right of the critical tie line. When this solvent mixes with the original oil, an overall composition such as M1 may result, which is in the two-phase region. M1 consists of dewpoint solvent G1 and bubblepoint liquid L1, which are in equilibrium.

Injection of fresh injection solvent B pushes the equilibrium solvent G1 ahead and contacts residual oil around the injector that now has composition L1. B mixes with L1 and forms a new overall composition in the two-phase region, M2, which splits into a new equilibrium solvent G2 and equilibrium liquid L2. Continued injection of solvent B pushes the new solvent G2 out of the way, and B mixes with liquid L2 to form a new overall mixture M3. Thus, solvent B successively contacts oil around the injector and enriches the oil along the bubblepoint curve by condensation of the intermediate-molecular-weight hydrocarbons that were used to enrich C₁–C_2–6 mixtures to composition B. This enrichment of the oil proceeds until the enriched oil reaches the critical composition P at the critical point. Composition P is then first-contact miscible with solvent B. According to this concept, there is a transition zone of contiguously miscible liquid compositions from the original oil composition to the critical composition.

This method of solvent flooding historically was called the condensing-solvent-drive process because condensation of the intermediate-molecular-weight hydrocarbons into the oil was thought to be the mechanism responsible for the development of multicontact miscibility. In this process, miscibility is generated and propagated through the porous medium at the rear of the transition zone.

According to the pseudoternary diagram of Fig. 2, if the composition of injection solvent were to the left of the critical tie line, the displacement would be immiscible because the oil could never be enriched to the critical composition. For example, if solvent C were injected, the oil could be enriched only to composition L1 on the tie line that passes through C when the tie line is extended. Further contact of L1 with C only gives new overall mixtures that are on the tie line, so equilibrium solvent G1 on the tie line ends up displacing oil L1, and G1 and L1 are immiscible. The criterion for condensing-solvent-drive multiple-contact miscibility is that the injection-solvent composition must lie to the right of the critical tie line on the ternary diagram.

For most oils, however, the mechanism described previously for an enriched-solvent displacement is too simplified. Compositional enhancement occurs by a mixed mechanism that has both vaporizing and condensing features, as described below.

Condensing/vaporizing process

Fig. 3 shows a pseudoternary diagram for a condensing/vaporizing displacement in which the equilibrium vapor and liquid compositions were calculated for a simulated slimtube displacement with a compositional simulator. The two-phase region has an hourglass shape. There is what looks like a condensing lobe in which vapor and liquid are trying to come together at a critical composition similar to condensing-solvent drive. However, before this happens, vapor and liquid compositions begin to diverge at the trailing part of the displacement.

• 

  Fig. 3 – The condensing/vaporizing process (after Rogers and Grigg).

Zick and Stalkup first explained this behavior. Zick deduced that in addition to condensation of intermediate-molecular-weight hydrocarbons from the injection solvent, vaporization of mid-range hydrocarbons from the oil also played an important role. Zick explained this mechanism in the following way:

The easiest way to understand the condensing/vaporizing mechanism is to consider an oil/solvent system composed of essentially four groups of components.

1. Lean components, such as methane, nitrogen, and carbon dioxide, which usually have equilibrium K-values greater than one
2. Light intermediate components, such as ethane, propane, and butane, which are the enriching components present in the injection solvent
3. Middle intermediates, which are present in the oil but not significantly present in the injection solvent. These are components that can be vaporized from the oil. The lightest component in this group typically ranges from butane to decane, depending on the injection solvent composition. The heaviest component in this group cannot be defined precisely, but it might be around C₃₀
4. Everything else, i.e., those heavy components in the oil which are very difficult to vaporize

When the enriched solvent comes into contact with the oil, the light intermediates condense from the solvent into the oil, making the oil lighter. The equilibrium solvent is more mobile than the oil, so it moves ahead and is replaced by fresh injection solvent, from which more light intermediates condense, making the oil even lighter. If this kept occurring until the oil was light enough to be miscible with the injection solvent, it would constitute the condensing-solvent-drive mechanism. However, this is unlikely to occur within a real reservoir oil. As the light intermediates are condensing from the injection solvent into the oil, the middle intermediates are being stripped from the oil into the solvent. Because the injection solvent contains none of these middle intermediates, they cannot be replenished in the oil. After a few contacts between the oil and the injection solvent, the oil becomes essentially saturated in the light intermediates, but it continues to lower the middle intermediates, which are stripped out and carried ahead by the mobile solvent phase. The light intermediates of the injection solvent cannot substitute for the middle intermediates the oil is losing. So after the first few contacts make the oil lighter by net condensation of intermediates, subsequent contacts make the oil heavier by net vaporization of intermediates. Once this begins to occur, the oil no longer has a chance of becoming miscible with the solvent. Ultimately, all the middle intermediates are removed, and the residual oil will be very heavy, containing only the heaviest, nonvolatile fraction and the components present in the injection solvent.

If the mechanism stopped there, a considerable amount of oil would remain unrecovered. However, there are further steps to the mechanism. Consider the oil in place slightly downstream from the injection point. The first solvent it will see will not be the injection solvent, but the equilibrium solvent. This relatively lean solvent essentially will be injection solvent that has lost most of its light intermediates and picked up a very small amount of middle intermediates. There will be very little mass transfer between this solvent and the fresh oil. The solvent that follows, however, will be richer. Eventually, the solvent that comes through will be solvent that has passed over oil that was saturated in the light intermediates. Therefore, this solvent will have approximately the same amount of light intermediates as the injection solvent. However, it will also contain a small amount of middle intermediates that it stripped from the oil over which it passed. Thus, it actually will be a little richer than the original injection solvent. The oil that sees this solvent will receive slightly more condensable intermediates than did the oil just upstream. Before the vaporization process takes over and again makes it heavier, this oil will become slightly lighter than the upstream oil had become.

This process continues farther downstream. The farther downstream, the richer the solvent that eventually comes through because it will have passed over an increasing amount of residual oil, allowing it to pick up increasing amounts of middle intermediates. This is beginning to sound like the vaporizing-solvent-drive mechanism, in which a lean injection solvent passes over an oil rich in intermediates, vaporizing the intermediates and becoming richer and richer until it becomes rich enough to be miscible with the original oil. There is a significant difference, however. The solvent in the condensing/vaporizing mechanism does not become rich enough to be miscible with the original oil. The original oil does not have to be rich in intermediates, nor does it even have to be undersaturated, both of which are necessary conditions for developing a vaporizing-solvent-drive mechanism. Instead, the solvent develops only enough richness by the vaporization part of the mechanism so that it nearly generates a condensing-solvent-drive mechanism with the original oil. The intermediates that were originally present in the solvent, plus those that were stripped from the oil, condense when the solvent encounters fresh oil downstream. This condensation proceeds in a manner very much like the condensing-solvent-drive mechanism. A sharp transition zone develops and propagates, and multicontact miscibility is almost achieved before the condensation process reverts to the vaporization process. The vaporization results in a trail of residual oil being left behind the moving transition zone, although the saturation level of the residual oil supplies subsequent solvent with the middle intermediates necessary to continue the propagation of the transition zone. The intermediates are vaporized from the residual oil, carried upstream into and beyond the transition zone, condensed there, and again become part of the residual oil after the transition zone has passed.

The condensing region is at the leading edge of the enriched-solvent displacement. The vaporizing region, with a small saturation of residual oil, is at the trailing end. In between is the sharp, two-phase transition zone, the two phases of which are almost—but not quite—miscible. The propagation of the sharp transition zone results in a very efficient, "apparently miscible" displacement, even though miscibility is not actually developed (except possibly, and only speculatively, as the displacement front travels to infinite distances, relative to dispersion length scales, downstream of the injection point). The sharpness of the transition zone deteriorates rapidly as either the pressure or the enrichment of the injection solvent falls below some critical value, resulting in the reduced displacement efficiencies typical of immiscible displacements.

Several authors have examined the condensing/vaporizing process in detail by solving the hyperbolic equations that describe the interaction of phase behavior with flow. . The most notable are referenced below, which led to the direct proof that the condensing/vaporizing process exists. Their analytical solutions show that the composition paths in a 1-D displacement trace an upstream pseudo-ternary surface where an intermediate component in the gas (CO2 if injected) is condensed into the equilibrium oil, while at the trailing edge the path traverses a pseudo-ternary surface where an intermediate component in the oil is then vaporized by the gas. The displacements are chromatographic-like where the most volatile components are produced first.

Mixing by diffusion and flow mechanisms affects how close the mixed mechanism gets to multicontact miscibility. The greater the mixing, the farther vapor and liquid compositions remain apart in the neck of the hourglass, which results in larger solvent-flood residual oil.

Effect on capillary number

In all the processes just described, equilibrium solvent and oil properties become more similar as compositions become more similar and approach the critical composition. This causes the interfacial tension between the solvent and oil to decrease as the solvent and oil compositions become more alike. This in turn causes the capillary number for oil displacing solvent to increase.

The capillary number is defined as

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

where k = permeability, Δp_g = pressure gradient through the displacing phase, and σ = interfacial tension.

Below a threshold value of capillary number, solvent-flood residual oil and solvent/oil relative permeability remain unchanged. Above the threshold, residual oil begins to decrease with increasing capillary number, and the solvent and oil relative permeability curves begin to straighten, ultimately becoming straight lines at very high values of the capillary number. These changes may have contradictory effects on a displacement. For a given equilibrium oil and solvent composition near the critical composition, solvent-flood residual oil saturation may be a bit lower than it would because of phase-behavior effects alone. However, solvent mobility may be higher because of the more favorable solvent relative permeability, which may result in somewhat poor sweep. The overall effect needs to be evaluated with a simulator that accounts for changing capillary number.

Nomenclature

Nca	=	capillary number, dimensionless
Δpg	=	pressure gradient through the displacing phase, psi
σ	=	interfacial tension, dynes/cm
k	=	permeability, md

Noteworthy papers in OnePetro

Johns, R. T., Dindoruk, B., & Orr, F. M. (1993, July 1). Analytical Theory of Combined Condensing/Vaporizing Gas Drives. Society of Petroleum Engineers. doi:10.2118/24112-PA

Monroe, W. W., Silva, M. K., Larson, L. L., & Orr, F. M. (1990, August 1). Composition Paths in Four-Component Systems: Effect of Dissolved Methane on 1D CO2 Flood Performance. Society of Petroleum Engineers. doi:10.2118/16712-PA

Orr, F. M., & Taber, J. J. (1987, January 1). Phase Diagrams (1987 PEH Chapter 23). Society of Petroleum Engineers.

Orr, F. M., & Jensen, C. M. (1984, October 1). Interpretation of Pressure-Composition Phase Diagrams for CO2/Crude-Oil Systems. Society of Petroleum Engineers. doi:10.2118/11125-PA

Orr, F. M., Yu, A. D., & Lien, C. L. (1981, August 1). Phase Behavior of CO2 and Crude Oil in Low-Temperature Reservoirs. Society of Petroleum Engineers. doi:10.2118/8813-PA

External links

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See also

Miscible flooding

Equations of state for miscible processes

Compositional simulation of miscible processes

Phase diagrams for EOR processes

PEH:Miscible_Processes