Foam injection is a promising enhanced-oil-recovery (EOR) technology that significantly improves the sweep efficiency of gas injection. Simulation of foam/oil displacement in reservoirs is an expensive process for conventional simulation because of the strongly nonlinear physics, such as multiphase flow and transport with oil/foam interactions. In this work, an operator-based linearization (OBL) approach, combined with the representation of foam by an implicit-texture (IT) model with two flow regimes, is extended for the simulation of the foam EOR process. The OBL approach improves the efficiency of the highly nonlinear foam-simulation problem by transforming the discretized nonlinear conservation equations into a quasilinear form using state-dependent operators. The state-dependent operators are approximated by discrete representation on a uniform mesh in parameter space. The numerical-simulation results are validated by using three-phase fractional-flow theory for foam/oil flow. Starting with an initial guess depending on the fitting of steady-state experimental data with oil, the OBL foam model is regressed to experimental observations using a gradient-optimization technique. A series of numerical validation studies is performed to investigate the accuracy of the proposed approach. The numerical model shows good agreement with analytical solutions at different conditions and with different foam parameters. With finer grids, the resolution of the simulation is better, but at the cost of more expensive computations. The foam-quality scan is accurately fitted to steady-state experimental data, except in the low-quality regime. In this regime, the used IT foam model cannot capture the upward-tilting pressure gradient (or apparent viscosity) contours. 1D and 3D simulation results clearly demonstrate two stages of foam propagation from inlet to outlet, as seen in the computed-tomography (CT) coreflood experiments: weak foam displaces most of the oil, followed by a propagation of stronger foam at lower oil saturation. OBL is a direct method to reduce nonlinearity in complex physical problems, which can significantly improve computational performance. Taking its accuracy and efficiency into account, the data-driven OBL-based approach could serve as a platform for efficient numerical upscaling to field-scale applications.

@en

Foam flow in porous media without oil shows two regimes depending on foam quality (gas fractional flow). Complexity and limited data on foam/oil interactions in porous media greatly restrict understanding of foam in contact with oil. Distinguishing which regimes are affected by oil is key to modeling the effect of oil on foam. We report steady-state corefloods to investigate the effect of oil on foam through its effect on the two flow regimes. We fit the parameters of a widely used local-equilibrium (LE) foam model to data for concurrent foam/oil flow. This research provides a practical approach and initial data for simulating foam enhanced oil recovery (EOR) in the presence of oil. To ensure steady state, oil is coinjected with foam at a fixed ratio of oil (U _o ) to water (U _w ) superficial velocities in a Bentheimer Sandstone core. Model oils used here consist of a composition of hexadecane, which is benign to foam stability, and oleic acid (OA), which can destroy foam. Varying the concentration of OA in the model oil allows one to examine the effect of oil composition on steady-state foam flow. Experimental results show that oil affects both high- and low-quality regimes, with the high-quality regime being more sensitive to oil. In particular, oil increases the limiting water saturation (S _w ) in the high-quality regime and also reduces gas-mobility reduction in the low-quality regime. Unevenly spaced !p contours in the high-quality regime suggest either strongly shear-thinning behavior or an increasingly destabilizing effect of oil. In some cases, the pressure gradient (!p) in the low-quality regime decreases with increasing U _w at fixed gas superficial velocity (U _g ), either with or without oil. This might reflect either an effect of oil, if oil is present, or easier flow of bubbles under wetter conditions. Increasing the OA concentration extends the high-quality regime to lower foam qualities, indicating more difficulty in stabilizing foam. Thus, oil composition plays as significant a role as oil saturation (S _o ). A model fit assuming a fixed S _w and including shear thinning in the low-quality regime does not represent the two regimes when the oil effect is strong enough. In such cases, fitting S _w to each !p contour and excluding shear thinning in the low-quality regime yield a better match to these data. The dependency of S _w on S _o is not yet clear because of the absence of oil-saturation data in this study. Furthermore, none of the current foam-simulation models captures the upward-tilting !p contours in the low-quality regime.

@en

The effectiveness of foam for mobility control in the presence of oil is key to foam enhanced oil recovery (EOR). A fundamental property of foam EOR is the existence of two steady-state flow regimes: the high-quality regime and the low-quality regime. Experimental studies have sought to understand the effect of oil on foam through its effect on these two regimes. Here, we explore the effect of oil on the two flow regimes for one widely used foam model. The STARS (CMG 2015) foam model includes two algorithms for the effect of oil on foam: In the “wet-foam” model, oil changes the mobility of full-strength foam in the low-quality regime, and in the “dry-out” model, oil alters the limiting water saturation around which foam collapses. We examine their effects as represented in each model on the two flow regimes using a Corey relative permeability function for oil. Specifically, we plot the pressure-gradient contours that define the two flow regimes as a function of superficial velocities of water, gas, and oil, and show how oil shifts behavior in the regimes. The wet-foam model shifts behavior in the low-quality regime with no direct effect on the high-quality regime. The dry-out model shifts behavior in the high-quality regime but not the low-quality regime. At fixed superficial velocities, both models predict multiple steady states at some injection conditions. We perform a stability analysis of these states using a simple 1D simulator with and without incorporating capillary diffusion. The steady state attained after injection depends on the initial state. In some cases, it appears that the steady state at the intermediate pressure gradient is inherently unstable, as represented in the model. In some cases, the introduction of capillary diffusion is required to attain a uniform steady state in the medium. The existence of multiple steady states, with the intermediate one being unstable, is reminiscent of catastrophe theory and of studies of foam generation without oil. @en

We present a CT coreflood study of foam flow with two representative oils: hexadecane C₁₆ (benign to foam) and a mixture of 80 wt% C₁₆ and 20 wt% oleic acid (OA) (very harmful to foam). The purpose is to understand the transient dynamics of foam, both generated in-situ and pre-generated, as a function of oil saturation and type. Foam dynamics with oil (generation and propagation) are quantified through sectional pressure-drop measurements. Dual-energy CT imaging monitors phase saturation distributions during the corefloods. With C₁₆, injection with and without pre-generation of foam exhibits similar transient behavior: strong foam moves quickly from upstream to downstream and creates an oil bank. In contrast, with 20 wt % OA, pre-generation of foam gives very different results from co-injection, suggesting that harmful oils affect foam generation and propagation differently. Without pre-generation, initial strong-foam generation is very difficult even at residual oil saturation about 0.1; the generation finally starts from the outlet (a likely result of the capillary-end effect). This strong-foam state propagates backwards against flow and very slowly. The cause of backward propagation is unclear yet. However, pre-generated foam shows two stages of propagation, both from the inlet to outlet. First, weak foam displaces most of the oil, followed by a propagation of stronger foam at lower oil saturation. Implicit-texture foam models for enhanced oil recovery cannot distinguish the different results between the two types of foam injection with very harmful oils. This is because these models do not distinguish between pre-generation and co-injection of gas and surfactant solution.

@en

We present a CT coreflood study of foam, both pre-generated and generated in-situ, displacing oil, as a function of oil type and saturation. Foam generation and propagation are reflected through sectional pressure measurements. Dual-energy CT imaging monitors in-time phase saturations. With an oil less harmful to foam (hexadecane), injection with and without pre-generation of foam exhibits similarities: propagation of a foam bank through a core and later refinement of foam texture. In contrast, with an oil destabilizing to foam (with 20 wt% oleic acid in the hexadecane), pre-generation of foam behaves very differently from co-injection, suggesting very-different effects on foam generation and propagation. Without pre-generation, strong-foam generation is very difficult even at residual oil saturation (about 0.1); generation finally starts from the outlet (likely a result of the capillary-end effect). This strong-foam state propagates upstream very slowly. Pre-generated foam shows two stages of propagation, both from the inlet to outlet. First, weak foam displaces most of the oil, followed by a propagation of stronger foam at lower oil saturation. This dependence on injection method with harmful oil is not represented in currently applied foam models, which need further improvements for reliable prediction of foam for enhanced oil recovery.@en

Understanding the interplay of foam and non-aqueous phases in porous media is key to improving the design of foam for enhanced oil recovery and remediation of aquifers and soils. A widely used implicit-texture foam model predicts phenomena analogous to cusp catastrophe theory: the surface describing foam apparent viscosity as a function of fractional flows folds backwards on itself. Thus there are multiple steady states fitting the same injection condition J defined by the injected fractional flows. Numerical simulations suggest the stable injection state among multiple possible states but do not explain the reason.
We address the issue of multiple steady states from the perspective of wave propagation, using three-phase fractional-flow theory. The wave-curve method is applied to solve the two conservation equations for composition paths and wave speeds in 1D foam-oil flow. There is a composition path from each possible injection state J to the initial state I satisfying the conservation equations. The stable displacement is the one with wave speeds (characteristic velocities) all positive along the path from J to I. In all cases presented, two of the paths feature negative wave velocity at J; such a solution does not correspond to the physical injection conditions. A stable displacement is achieved by either the upper, strong-foam state or lower, collapsed-foam state, but never the intermediate, unstable state. Which state makes the displacement depends on the initial state of a reservoir. The dependence of the choice of the displacing state on initial state is captured by a boundary curve.@en

Foam has unique microstructure in pore networks and reduces gas mobility significantly, which improves considerably the sweep efficiency of gas injection. Foam injection is thus regarded as a promising enhanced oil recovery (EOR) technology. One key to success of foam EOR is foam stability in presence of oil. This thesis seeks to understand fundamentally both steady-state and transient foam flow with oil in porous media through theoretical analysis and coreflood measurements. A quantitative modeling study is conducted to illustrate how the two algorithms ("wet-foam" model and "dry-out" model) represent the effect of oil on foam. Experimental observations evidently show that the two foam regimes without oil also apply to foam with oil, i.e. high- and low-quality regimes depending on foam quality. Oil affects both regimes with a stronger effect on the high-quality regime. Model fitting to data shows that currently applied implicit-texture (IT) foam models are suitable to represent foam flow with oil; both wet-foam model and dry-out model are needed to describe the effect of the oil on the two foam regimes. Three-phase fractional-flow theory together with the wave curve method (WCM) is applied to understand foam displacements with oil. Theoretical solutions suggest foam displacement cannot bank up an oil bank with oil saturation greater than an upper limit for stable foam. A critical phenomenon, i.e. that some injection conditions correspond to more than one possible foam states as predicted by the IT model, has been analyzed with fractional-flow theory and the WCM. We show how to determine the unique displacing state; the choice of the displacing state depends on initial state. Fundamentally, a boundary curve in ternary saturation space is defined that captures the nature of the dependence of the displacement on initial state. In addition, a new capillary number definition for micromodels is derived from a force balance on a ganglion trapped by capillarity. The definition in particular accounts for the impact of pore geometry and its validity is verified using two-phase flow data in micromodels. Based on current findings, some open questions concerning foam-oil interactions in porous media are defined and summarized at the end of this thesis.@en

A new capillary number (N _ca ) definition is proposed for 2-D etched micromodels. We derive the new definition from a force balance on a nonwetting ganglion trapped by capillarity. It incorporates the impact of pore microstructure on mobilization. The geometrical factors introduced can be estimated directly from image analysis of the pore network etched in the micromodel, without conducting flow experiments. The improved fit of the new N _ca to published data supports its validity. The new definition yields a consistent trend in the capillary-desaturation curve. The conventional N _ca definitions proposed for porous rock give a large scatter in the capillary-desaturation curve for data in micromodels. This is due to the different type of flow in micromodels, as 2-D networks, relative to 3-D geological porous media. In particular, permeability is dominated by channel depth in micromodels with shallow depth of etching, and generally, there is no simultaneous multiphase flow under capillary-dominated conditions. Applying the conventional definitions to results in micromodels may lead to misleading conclusions for fluid transport in geological formations.

@en

Foam flow in porous media without oil shows two regimes, depending on foam quality (gas fractional flow). Complexity and limited data on foam-oil interactions in porous media greatly restrict understanding of foam in contact with oil. Distinguishing which regimes are affected by oil is key to modelling the effect of oil on foam. We report steady-state corefloods to investigate the effect of oil on foam through its effect on the two flow regimes. We fit parameters of the widely used STARS foam model to data for foam-oil concurrent flow. This research provides a practical approach and initial data for simulating foam EOR in the presence of oil. To ensure steady state, oil is co-injected with foam at a fixed ratio of oil (Uo) to water (Uw) superficial velocities in a Bentheimer sandstone core. Model oils used here consist of two components: hexadecane, which is benign to foam stability, and oleic acid, which can destroy foam. Varying the concentration of oleic acid in the model oil allows one to examine the effect of oil composition on steady-state foam flow. Experimental results show that oil impacts both high- and low-quality regimes, with the high-quality regime more vulnerable to oil. In particular, oil increases the limiting water saturation (Sw^∗) in the high-quality regime and also lessens gas mobility reduction in the low-quality regime. The high-quality regime is strongly shear-thinning in the presence of oil. Pressure gradient (p) in the low-quality regime, in some cases, decreases with increasing Uw at fixed gas superficial velocity (Ug), either with or without oil. This may reflect either an effect of oil, if oil is present, or easier flow of bubbles under wetter conditions. Increasing oleic acid concentration extends the high-quality regime to lower foam qualities, indicating more difficulty in stabilizing foam. Thus oil composition plays as significant a role as oil saturation. A model fit assuming a fixed Sw∗ and including shear-thinning in the low-quality regime doesn't represent each regime when the oil effect is strong enough. In such cases, fitting Sw∗ to each p contour and excluding shear-thinning in the low-quality regime yields a better match to data. The dependency of Sw∗ on oil saturation is not yet clear owing to absence of oil-saturation data in this study. Furthermore, none of the current foam simulation models can capture the upward-tilting p contours in the low-quality regime.

@en

Determining the most influential reservoir parameters on the GAGD process is an essential step to understanding the EOR process efficiency. In this paper, we introduce Bayesian Model Averaging (BMA) as a stochastic linear modelling approach to select the most influential parameters affecting the Gas Assisted Gravity Drainage (GAGD) Process performance in a multilayer heterogeneous sandstone oil reservoir. Lithofacies and petrophysical property model was reconstructed considering multiple-point geostatistics for 3D property distribution. CO2 is injected through vertical injectors at the top two layers. The 2nd three layers were left as a transition to allow a vertical depth interval for gas gravity drainage. Horizontal producers were set up through the sixth, seventh, and eighth layers where the oil saturation has the highest levels. The last four layers were left with no injection/production activity. The studies reservoir factors are horizontal permeability, anisotropy ratio (Kv/Kh), and porosity. Latin Hypercube Design created many simulation jobs and the elimination was conducted by the BMA stochastic approach, which adopts posterior probability to choose the best model among a set of candidate models. Moreover, the accurate determining of influential factors through BMA has led to better understanding of the effect of heterogeneity and anisotropy on the GAGD process. @en

The effectiveness of foam for mobility control in the presence of oil is key to foam EOR. A fundamental property of foam EOR is the existence of two steady-state flow regimes: the high-quality regime and the low-quality regime. Experimental studies have sought to understand the effect of oil on foam through its effect on these two regimes. Here we explore the existence of multiple steady states for one widely used foam model. The widely used STARS foam model includes two algorithms for the effect of oil on foam: in the "wet-foam" model, oil changes the mobility of full-strength foam in the low-quality regime; in the "dry-out" model, oil alters the limiting water saturation at which foam collapses. We examine their effect on the two flow regimes, using Corey relative permeabilities for oil. Specifically, we plot the pressure-gradient contours that define the two flow regimes as a function of superficial velocities of water, gas and oil and show how oil shifts behavior in the regimes. There are two ways to study the effect of oil on steady-state foam: 1) at fixed oil saturation. This is the way a simulator represents the effect, but it is difficult if not impossible to fix this condition in a laboratory coreflood. 2) at fixed superficial velocities. In both kinds of plots, the wet-foam model shifts behavior in the low-quality regime with no direct effect on the high-quality regime. The dry-out model shifts behavior in the high-quality regime but not the low-quality regime. At fixed superficial velocities, both models predict multiple steady states at some injection conditions. We investigate these states using a simple 1D simulator with and without incorporating capillary diffusion. The steady-state attained after injection depends on the initial state. In some cases, it appears that the steady state at intermediate pressure gradient is inherently unstable as represented in the model. In some cases introduction of capillary diffusion is required to attain a uniform steady-state in the medium. The existence of multiple steady states, with the middle one unstable, is reminiscent of catastrophe theory and of studies of foam generation without oil. @en