Tie Line
A tie line in petroleum engineering and physical chemistry is a line segment drawn on a ternary phase diagram connecting the compositions of two distinct phases that are in thermodynamic equilibrium with each other at a specific temperature and pressure, where any overall mixture composition lying on the tie line will separate into two phases whose individual compositions are defined by the tie line's endpoints, and whose proportional volumes are determined by the lever rule (the composition closer to one endpoint has proportionally more of that phase's material); in surfactant flooding enhanced oil recovery, tie lines on the ternary diagram of oil, water, and surfactant are used to describe the microemulsion phase behavior at different surfactant concentrations and salinities, with the Winsor Type III region containing a set of tie lines connecting the microemulsion middle phase (which lies within the triangular three-phase region) to the excess oil phase and to the excess water phase, and the Winsor Type I and Type II regions each containing two-phase tie lines connecting the microemulsion phase to the excess oil or water; in reservoir fluid thermodynamics, the tie line concept appears in multicomponent phase diagrams for CO2-oil or gas injection EOR, where tie lines connect the equilibrium gas and liquid phase compositions in the two-phase region below the cricondenbar, with the critical tie line (whose length approaches zero at the critical point) providing the compositional pathway that determines whether a CO2 or enriched gas injection process achieves multiple contact miscibility with the reservoir oil.
Key Takeaways
- The lever rule applied to tie lines quantifies the volume fractions of each equilibrium phase from the overall mixture composition's position on the tie line: if the overall composition lies at a fractional distance x along the tie line from one endpoint (endpoint A, representing the composition of phase A) toward the other endpoint (endpoint B, representing the composition of phase B), then the volume fraction of phase A in the equilibrium mixture is (1 minus x) and the volume fraction of phase B is x; a mixture whose overall composition lies exactly at the midpoint of a tie line is exactly 50 percent phase A and 50 percent phase B by volume; a mixture whose overall composition lies very close to endpoint A consists mostly of phase A with a small amount of phase B; and a mixture whose overall composition lies at one of the endpoint compositions consists entirely of that phase, with no second phase present; the lever rule is applied in surfactant flooding phase behavior studies by mixing known amounts of oil, brine, and surfactant (defining the overall composition on the ternary diagram), observing the separated phase volumes after equilibration, and using the phase volumes to locate the endpoint compositions of the equilibrium phases on the ternary diagram, building up the tie line field by testing multiple overall compositions at the same temperature and salinity.
- Critical tie lines in multiple-contact miscibility analysis determine whether an injection gas or CO2 can achieve compositional miscibility with a reservoir oil through repeated equilibration and separation steps (multiple contact miscibility, MCM), without requiring the gas to match the oil's composition exactly at the injection point (first contact miscibility): the key tie line for vaporizing gas injection is the tie line passing through the overall injection gas composition, whose extension toward the two-phase boundary determines whether the enriched vapor composition at the boundary can reach the vapor-phase critical composition; the key tie line for condensing gas injection is the tie line passing through the overall oil composition, whose extension toward the boundary determines whether the enriched liquid composition can reach the liquid-phase critical composition; the crossover tie line (the tie line whose extensions in compositional space intersect the injection gas composition on one side and the reservoir oil composition on the other) determines the minimum enrichment level needed for condensing-vaporizing gas injection to achieve MCM; the tie line analysis is performed using the slimtube test (a long, thin tube packed with porous media in which the injection gas and reservoir oil are repeatedly contacted and the produced fluid compositions tracked) or by compositional simulation that traces the displacement front's compositional path through the two-phase region of the ternary or pseudoternary diagram.
- Surfactant flooding ternary diagram tie line analysis is the primary laboratory tool for designing surfactant flood formulations that achieve ultra-low interfacial tension (IFT) at optimal salinity conditions: a ternary diagram of oil, brine, and surfactant is constructed by mixing different overall compositions of the three components at a fixed temperature and observing the number and volumes of phases at equilibrium, then plotting the one-phase, two-phase, and three-phase regions and the tie lines within each two-phase region; the Winsor Type III three-phase region (where oil-rich, water-rich, and microemulsion middle phases coexist) is bounded by two two-phase regions (Type I below optimal salinity and Type II above), and the tie lines in each two-phase region converge toward the plait point (the critical point of the two-phase region where the equilibrium phases become identical); the IFT between equilibrium phases correlates with tie line length in the two-phase regions (shorter tie lines indicate compositions closer to the plait point and lower IFT), and the ultra-low IFT required for residual oil mobilization is achieved near the Winsor Type III region's boundaries where the tie lines connecting the three-phase region to the excess phases are shortest (approaching zero length at the invariant three-phase condition).
- Tie lines in two-component (binary) phase diagrams reduce to a single point (the compositions of the two equilibrium phases at a given temperature and pressure), but the tie line concept remains important in describing binary systems such as the CO2-reservoir brine phase diagram used in carbon capture and storage (CCS) calculations: in the binary CO2-water system, the two equilibrium phases at reservoir conditions are CO2-saturated water (brine containing dissolved CO2) and water-saturated CO2 (supercritical CO2 containing a small amount of dissolved water), with the tie line connecting these two equilibrium compositions at constant temperature and pressure; as reservoir pressure increases, the CO2 solubility in brine increases (the water-rich equilibrium composition moves toward higher CO2 content) and the water content in the CO2 phase decreases, with the tie line shortening as pressure increases toward the critical pressure of the binary mixture; the two-phase envelope bounded by the tie line endpoints defines the conditions under which CO2 injection into saline aquifers results in two-phase flow (CO2 and brine flowing simultaneously) versus single-phase dissolution (all CO2 dissolving into the brine), which determines the migration behavior and trapping efficiency of stored CO2 in geological carbon storage formations.
- Ternary diagram construction and tie line determination in the laboratory requires careful experimental technique because the equilibrium compositions of the two or three phases that define the tie lines must be measured accurately, not just the overall mixture composition: the standard technique is to prepare a series of overall compositions spanning the expected two-phase region, centrifuge or allow gravity to separate the phases completely, then analyze each separated phase by gas chromatography, refractive index measurement, or other composition-sensitive measurement to determine its endpoint composition on the ternary diagram; tie lines are constructed by connecting the analyzed compositions of the co-existing phases, and the consistency of the tie lines (all tie lines within the same two-phase region should be parallel or at least non-intersecting) provides a quality check on the analysis; scanning tie lines are sometimes constructed by changing the brine salinity at fixed overall oil-surfactant ratio to trace the transition from Winsor Type I (low salinity) through Type III (optimal salinity) to Type II (high salinity), with the optimal salinity for ultra-low IFT identified as the salinity where the Type III region is present and the tie lines connecting the three-phase region to the two excess phases are shortest.
Fast Facts
The ternary phase diagram and tie line concept were developed by physical chemists in the nineteenth century for describing multicomponent liquid equilibria, and were adapted for petroleum engineering applications beginning in the 1950s and 1960s when the oil industry began developing miscible flooding EOR processes that required understanding of the compositional pathway from injected gas or solvent to reservoir oil across the two-phase region of the hydrocarbon phase diagram. The surfactant flooding application of ternary diagrams and tie line analysis, developed in the 1970s and 1980s as part of the federally funded EOR research programs in the United States, established the phase behavior framework that remains the primary tool for surfactant and ASP flood formulation design today.
What Is a Tie Line?
A tie line on a phase diagram is a line segment connecting the compositions of two equilibrium phases that coexist at a specific temperature and pressure, used with the lever rule to determine the proportional volumes of each phase from any overall mixture composition within the two-phase region. In surfactant flooding, tie lines on the oil-water-surfactant ternary diagram map the Winsor type regions and the approach to ultra-low IFT at optimal salinity. In CO2 and gas injection EOR, the critical tie line analysis determines whether the injection process achieves multiple contact miscibility with the reservoir oil. Tie line length correlates with IFT between equilibrium phases, with shorter tie lines indicating compositions closer to the critical point and lower IFT.
Synonyms and Related Terminology
Tie line is also called a coexistence line, equilibrium line, or binodal tie line in thermodynamic phase behavior literature. Related terms include ternary diagram (the triangular composition diagram in which each vertex represents a pure component (oil, water, or surfactant) and any interior point represents a mixture of all three components, used in surfactant flooding and solvent EOR to map the phase regions (one-phase, two-phase, three-phase) and the tie lines connecting equilibrium phase compositions at constant temperature, pressure, and salinity), lever rule (the principle that the volume fraction of each equilibrium phase in a two-phase mixture is inversely proportional to the distance from the overall composition to that phase's endpoint on the tie line, allowing the phase volumes and compositions to be read directly from the ternary diagram without additional calculation), Winsor type (the classification of microemulsion phase behavior in the oil-water-surfactant system, with Type I (oil-in-water microemulsion coexisting with excess oil), Type II (water-in-oil microemulsion coexisting with excess water), and Type III (bicontinuous microemulsion coexisting with both excess oil and excess water) distinguished by the salinity and the positions of the tie lines connecting the two-phase and three-phase regions on the ternary diagram), multiple contact miscibility (MCM, the condition in gas or CO2 injection EOR in which the injected fluid is not first-contact miscible with the reservoir oil but achieves miscibility through repeated equilibration steps, with the feasibility of MCM determined by the critical tie line analysis of the ternary or pseudoternary phase diagram), and optimal salinity (the brine salinity at which a surfactant flooding system is in Winsor Type III phase behavior with equal oil and water solubilization ratios in the microemulsion phase, corresponding to the minimum interfacial tension between microemulsion and excess oil and water phases and the salinity at which the tie lines connecting the three-phase region to the excess phases are shortest on the ternary diagram).
Why Tie Line Analysis Is Central to EOR Phase Behavior Design
Whether a surfactant flood achieves ultra-low IFT and a gas injection achieves miscibility with the reservoir oil are not questions that can be answered without understanding where the equilibrium phase compositions lie on the ternary diagram and how the tie lines that connect them are oriented and dimensioned. The tie line is the graphical tool that connects laboratory phase behavior measurements to the field-scale EOR mechanism: a surfactant formulation whose ternary diagram shows short tie lines near a Winsor Type III region will achieve ultra-low IFT and mobilize residual oil; one with long tie lines far from any critical point will not. The investment in constructing accurate ternary diagrams with properly measured tie lines is the investment in knowing whether a proposed EOR program will work before committing the capital required to implement it.