Immiscible

Key Takeaways

• Immiscible displacement in waterflood operations is governed by the Buckley-Leverett equation (derived in 1942 from Darcy's law applied to two-phase immiscible flow), which describes the saturation profile of the advancing water front as a function of the fractional flow of water (f_w = water flux / total flux) and the position along the flow path: the fractional flow curve (f_w versus water saturation S_w) is derived from the relative permeability functions of the rock (the curves that describe how the effective permeability to each phase varies with saturation) and the viscosity ratio of water to oil; in a homogeneous 1D system with favorable viscosity ratio (water more viscous than oil, rare for light crude), the displacement is piston-like and recovery is high; in the more common unfavorable viscosity ratio (water viscosity 1 cp, light oil viscosity 1 to 5 cp), the fractional flow curve shows an S-shaped character with a significant viscous fingering tendency that reduces displacement efficiency; the Welge graphical construction (a tangent from residual oil saturation to the f_w curve) provides the shock saturation at the displacement front and the average saturation behind the front at breakthrough, from which the recovery factor at breakthrough can be calculated without solving the full PDE; after breakthrough, the producing well produces increasing water cut as the average saturation behind the front continues to increase toward the maximum water injection saturation determined by the residual oil saturation to waterflood (Sorw).
• Interfacial tension (IFT) between the immiscible oil and water phases determines the capillary pressure at each pore throat and governs the distribution of fluids in the pore space: capillary pressure Pc = 2*sigma*cos(theta)/r (where sigma is the IFT in mN/m, theta is the contact angle, and r is the pore throat radius) creates pressure differences across curved oil-water interfaces that trap residual oil in small pores after waterflood (the microscopic displacement inefficiency, quantified by the residual oil saturation); typical crude oil-water IFT values range from 15 to 30 mN/m, with lighter, lower-viscosity crude oils generally having higher IFT (less polar crude is more immiscible with water) and heavier, higher-API gravity crudes with more polar components having lower IFT; surfactant injection (chemical EOR) reduces the IFT between oil and water by several orders of magnitude (from 15 mN/m to 10^-3 mN/m or lower), reducing the capillary number (ratio of viscous to capillary forces) sufficiently to mobilize residual oil that is trapped by capillary forces after conventional waterflood; the relationship between capillary number and residual oil saturation is described by the capillary desaturation curve (CDC), which shows that Sorw decreases steeply as the capillary number increases above approximately 10^-5 (the threshold below which waterflood residual oil is not mobilized); ultra-low IFT surfactant flooding can reduce Sorw from 20 to 30 percent (after waterflood) to 2 to 5 percent (after surfactant flood), potentially recovering an additional 10 to 25 percent of original oil in place.
• Gas-oil immiscible displacement differs fundamentally from water-oil displacement because of the large density difference and compressibility of the gas phase: in a gas injection flood below the minimum miscibility pressure (immiscible gas injection), the low viscosity of gas (approximately 0.01 to 0.05 cp versus 0.5 to 10 cp for reservoir oil) creates a severe viscous instability (mobility ratio M = k_rg/mu_g / k_ro/mu_o, where k_r are relative permeabilities at displacement conditions; M much greater than 1 indicates fingering tendency) that causes gas to finger through the oil in preferential channels rather than displacing oil in a piston-like front; gravity segregation (gas rising to the top of the reservoir due to buoyancy) further reduces sweep efficiency unless the reservoir is thin, steeply dipping, or the injection rate is low enough to maintain a stable gravity-dominated displacement; the combination of viscous fingering and gravity override in immiscible gas flooding typically results in poor volumetric sweep (50 to 70 percent of the reservoir contacted) and moderate displacement efficiency (leaving 20 to 40 percent of the oil in contacted zones as residual), giving overall recovery factors of 30 to 50 percent OOIP for immiscible gas floods versus 40 to 60 percent for miscible gas floods and 35 to 55 percent for conventional waterfloods in the same reservoirs.
• Minimum miscibility pressure (MMP) is the threshold pressure above which an immiscible fluid pair (typically CO2 and crude oil, or enriched hydrocarbon gas and crude oil) transitions to miscible displacement, fundamentally changing the displacement mechanism from capillary-controlled two-phase flow to a single-phase displacement with no residual phase: the MMP for CO2-crude oil systems depends on the crude oil composition (lighter, higher-API crudes have lower MMP than heavier crudes because the C5-C20 intermediate components that participate in multiple-contact miscibility development are more abundant and mobile in light crudes), the reservoir temperature (higher temperature increases MMP by reducing the condensate drop-out from CO2 during multiple contacts), and the CO2 purity (presence of CH4 increases MMP while H2S and N2 decrease MMP in different proportions); MMP is measured in the laboratory by slim-tube displacement experiments (measuring the recovery factor from a packed tube as a function of injection pressure, with the MMP defined as the pressure at which recovery reaches approximately 90 percent or the slope of the recovery curve changes) or by the rising bubble apparatus (observing the miscibility of a CO2 bubble rising through the crude oil at controlled pressure); reservoir operations at pressures above the MMP achieve near-piston-like displacement with residual oil saturation approaching zero (miscible), while operations at pressures below the MMP use immiscible CO2 flooding with residual oil saturation controlled by IFT and relative permeability rather than by MMP.
• Produced water treatment and reinjection in offshore facilities is directly controlled by the immiscibility of oil and water: produced water (the water that comes to the surface with the produced oil and gas, including connate formation water displaced from the reservoir and injected seawater that has broken through to producing wells) must be treated to remove dispersed oil droplets before reinjection or overboard discharge, because the natural immiscibility of oil and water only drives separation of free oil (droplets above approximately 100 microns diameter that settle by gravity in seconds to minutes) rather than dispersed or emulsified oil (droplets below 20 to 50 microns diameter that remain suspended by surface charge repulsion and Brownian motion); the treatment train for produced water on a typical offshore platform combines a primary vessel (free-water knockout or production separator that removes free gas and large oil droplets by gravity in 2 to 5 minutes residence time), a secondary vessel (hydrocyclone or flotation unit that removes dispersed oil droplets by centrifugal force or by attachment to rising air bubbles), and polishing equipment (compact flotation units, sand filters, or electrostatic coalescers) that reduces dispersed oil to below the discharge limit (30 ppm in the North Sea per OSPAR, 42 ppm monthly average in the US Gulf of Mexico per EPA); the immiscibility of oil and water enables these physical separation processes, but also creates the emulsion stability that makes separation of very fine droplets difficult and that requires chemical demulsifiers to break tight crude oil-water emulsions formed during high-velocity flow through chokes, valves, and pipe fittings.