Residual Water Saturation Research Articles

Estimating saturation exponent from NMR logging

A new interpretation of the relationship between the saturation exponent (n) and the water saturation (Sw) of a reservoir rock is presented. Based on the capillary theory and Purcell equation, the relationship between resistivity index (I) and the permeability (k), water-phase permeability (kw) has been obtained. By combining SDR model, such relationship can be transferred into a novel model of probing the saturation exponent under variable saturation conditions. Based on the theoretical derivation, NMR experimental measurements of core examples were implemented to testify the reliability brought by this development. Laboratory measurements of transverse relaxation were carried out on core samples from a formation in the Middle East. NMR experimental measurements were made with 50 samples fully water saturated. Measurements at various air/water saturation (i.e., at residual water saturation) were made on 16 samples among them obtained by different centrifuging speeds. The experimental results show that the calculated saturation exponent values and water saturations follow a power law relationship which is in accordance with researches have been published about that n is not a constant but a variable parameter dependent on water saturation, quantitatively. This study has inferred the quantitative relationship between n and Sw through NMR information firstly.

A Simulation Experimental Study on the Gas-Water Saturation Characteristics in the Process of Constant-Speed Gas Production Based on the Microscopic Model

This paper presents the important findings of research work that was undertaken on the residual water saturation of gas reservoirs that arises from the decrease in pore pressure during a constant-speed gas production process. To study the changes and distribution regularities of water-gas saturation, we used a micro-glass model to conduct a simulation study of the process of constant-speed gas production under pore pressures of 0.5 MPa, 1 MPa and 5 MPa. The results indicate that the total displacement power of the gas reservoir directly affects the development effect. The higher the pore pressures of the gas reservoir whose part of bound water may flow, the more difficult is the development of the reservoir due to the presence of more movable water, resulting in a poorer development effect. For a lower pore pressure of a gas reservoir, the bound water of the gas reservoir is generally immobile, that is, the gas production is single-phase gas seepage, resulting in an improved development effect. Implementing a reasonable development plan for a water-bearing gas reservoir with low permeability is clearly of great significance to ensure its effective development. Key words: Microscopic model; Constant speed; Gas production; Gas-water saturation; Variation characteristics; Simulation experiment

Residual liquids saturation development during two and three phase flow under gravity in square capillaries at different temperatures

An experimental study on heavy oil with air (two phase flow) and water and air (three phase flow) at different temperatures was carried out in square capillaries under gravity drainage conditions. Fluid retention characteristics (in the corners of capillaries) were determined and evaluated using the trapping number (NT). In air–heavy oil systems, when NT<2.7E−2, the residual oil saturation (Sor) was constant and equal at 55 and 85°C. The Sor was controlled by capillary forces regardless of viscous and gravity forces, including free fall gravity drainage (FFGD). For higher NT, the Sor was a function of competition between gravity, viscous and capillary forces. The Sor was always higher at 85°C compared to 55°C for the same gas injection rate and the difference increased as the NT augmented. FFGD experiments demonstrated that heavy oil retention depended on the Bond number and increased linearly as the Bond number increased.In the three phase systems (air–heavy oil–water) the oil retention did not diminish with the presence of water, which was also constant for the entire interval of NT at 55 and 85°C. High viscous forces originated from heavy oil were responsible for no change in the Sor. However, due to the water-wet nature of the capillary tubes, water was not completely swept. More Sor and residual water saturation were observed in air–water–heavy oil configuration, especially at 85°C, due to the unfavorable viscosity ratio oil/water and the negative spreading coefficient of water in oil in the presence of air. Finally, the change of wettability from water wet to oil wet did not modify the Sor but the water saturation decreased slightly for air–heavy oil–water systems.

Effects of operating mode and pressure on hydrate-based desalination and CO2 capture in porous media

The purpose of this study was to obtain the characteristics of CO2 hydrate formation and dissociation by using different experimental modes and pressures with glass beads. From the experiments, it was found that hydrate forms rapidly in each cycle, especially at high pressure. Hydrate blockage rarely appeared during hydrate formation and dissociation when applying gas flow (Case 2); this approach was significantly better than the other two experimental modes. The maximum hydrate saturations for the three experimental modes were 28%, 24% and 67.5%. The overall hydrate saturation of Case 3 was significantly better than those of the other two cases. When a heating process was applied to induce hydrate dissociation, the rapid backpressure decrease led to migration of the pore solution during depressurization. The minimal residual water after hydrate formation resulted in consistent residual water saturation after hydrate dissociation for Case 2. Considering hydrate saturation and operating pressure, 5.00MPa is a better choice for hydrate-based desalination and CO2 capture. If the initial residual solution can be completely converted to hydrate, this technology has potential for industrial applications.

Effect of Interfacial Tension on Water/Oil Relative Permeability on the Basis of History Matching to Coreflood Data

Summary The effect of interfacial tension (IFT) on the displacement of the nonwetting and wetting phases has been investigated by the use of simulations/history matching of flooding experiments. In surfactant flooding, a conventional assumption is to neglect the effect of capillary pressure (Pc) on measured two-phase properties. The methodology applied in this paper allows improved interpretation of experimental results by correcting for the influence of capillary end effects on the measured capillary desaturation curve (CDC) and on the estimated relative permeability (kr). Three fluid systems of different IFTs were prepared by use of a solvent system (CaCl2 brine/iso-octane/isopropanol) rather than a surfactant system with the assumption that both systems have similar flood behavior at reduced IFT. Three coreflood cycles, including multirate oil injection (drainage) followed by multirate water injection (imbibition), were carried out at each IFT in water-wet Berea cores. The kr functions corrected for capillary end effects were derived by numerically history matching the experimental production and pressure-drop (PD) history. A typical CDC is observed for the nonwetting phase oil, with a roughly constant plateau in residual oil saturation (ROS), Sor, below a critical capillary number (Ncc) and a declining slope above Ncc toward zero Sor. No influence of Pc was found for the nonwetting-phase CDC. The results from the displacement of the wetting phase formed an apparent CDC with a declining slope and no Ncc. Analyzing the wetting-phase results, we find that the wetting-phase CDC is not a true CDC. First, it is a plot of the average remaining water saturation (Sw) in the core which, in all the experiments, is higher than residual water saturation, Swr, obtained from Pc measurements. Second, we find that the remaining Sw is only partly a function of Nc. At low Nc, the water production (WP) is limited by capillary end effects. Rate-dependent WP observed with the high-IFT system is fully reproduced in simulations by use of constant kr and Pc. The remaining wetting-phase saturation at a low capillary number (Nc) is a result of the core-scale balance between viscous and capillary forces and would, for example, depend on the core length. At a higher Nc, the WP is found to be limited by the low kr tail, typical for wetting phases. However, we find that the kr functions become rate dependent at a higher Nc, and we assume that this rate dependency can be modeled as a function of Nc. The remaining wetting-phase saturation at a higher Nc would then be a function of Nc and the number of pore volumes (PVs) injected. The observed Nc dependency in the flow functions indicates a potential for the accelerated production of the wetting phase by use of surfactant. Assuming that the results obtained here for the wetting phase also apply to oil in a mixed-wet system, it is strongly recommended to evaluate the effect of both Pc and Ncc when designing a surfactant model for a mixed-wet field.

CO2/Water Displacement in Porous Medium Under Pressure and Temperature Conditions for Geological Storage

This paper presented CO2 injected into water saturated porous media for immiscible displacement using high-resolution MRI. The porous medium was formed from the packed bed of glass beads 0.2mm. CO2/water displacement processes were implemented by a spin echo sequence with MRI technique. CO2/water displacement process was investigated for different flow rates. Then CO2 and water distribution were distinguished from MRI images. Then residual water saturation were obtained at steady state. The effects of capillary number were investigated. The study provides useful data for transport process in CO2 storage.

Комплексні петроелектричні моделі вапняків девону та пісковиків кембрію Добротвірської площі Волино-Поділля

This paper deals with the technique and results of research into petroelectrical properties of complex terrigenous and carbonate reservoirs. Analyzed are electric data and their relation to capacity properties of Devonian limestones and Cambrian sandstones from Dobrotvirska area of Volyno-Podilia. The objective of the research was to build petroelectrical models of reservoir rocks based on the electrical parameters and their relation to capacity properties. Data on specific resistivity of reservoir rocks were used for specifying the range of its variation for different types and groups of rocks. These data were also essential for identifying the stratigraphic horizons, cross-sections and facies, as well as finding the relationship between specific resistivity and a range of factors such as mineral composition, pore structure, substance phase ratio, electric field intensity and frequency, and resistivity variations with epigenetic transformation and metamorphic changes in rocks. Laboratory data on electrical resistivity of rocks made it possible to interpret the results of employing electrometric well logging methods and electric exploration. Petrophysical laboratory data enabled us to determine the following properties: rock density (dry and saturated with synthetic brine), effective porosity (nitrogen and synthetic brine saturation methods), residual water saturation factor (by centrifugation), permeability (nitrogen stationary filtration method), interval time (P-wave velocity) and resistivity. There were obtained laboratory data on specific resistivity of rock samples (dry, partly and fully saturated with synthetic brine) in atmospheric and in simulated in-situ conditions. We estimated the petroelectrical parameters of Cambrian sandstones and Devonian limestones from Dobrotvirska area to find an empirical correlation between petroelectrical parameters, porosity and permeability of the studied rocks. The correlations are mainly approximated by power function and serve as the basis for geological interpretation of geophysical data. Electrometric methods have proved to be a powerful tool in both laboratory and field rock studies, being efficient enough to provide extensive information on rock properties.

Experimental Evaluation of SAGD/ISC Hybrid Recovery Method

Summary Most current in-situ recovery methods have limitations which restrict their application in many heavy-oil reservoirs. There is also a variety of undesirable environmental issues associated with existing thermal-recovery techniques. To overcome some of these problems, novel hybrid processes have been proposed that combine steam-assisted gravity drainage (SAGD) and in-situ-combustion (ISC) technologies. In the conventional ISC process, oil is displaced by an elevated-temperature combustion zone, but when the native oil mobility is low, this displacement becomes problematic because of the low oil mobility downstream of the combustion front. Heating the reservoir and reducing the distance between injector and producer can prevent such cold liquid blocking in the combustion process. This suggests that a well configuration that greatly decreases the distance between the injector and the producer (e.g., the SAGD well configuration) could be advantageous in ISC-based recovery methods. Moreover, running the SAGD operation in the initial period creates a vapour-filled depleted zone in the reservoir that would be sufficiently hot to start combustion on air injection. To investigate the feasibility of this idea, a hybrid experiment was conducted at a representative reservoir pressure. During the experiment, SAGD was operated in a physical model for a period and then combustion was started by switching from steam injection to air injection. A modified well arrangement was used to help the process operation, oil ignition, and combustion-front formation. Residual oil and water saturations in the model were analyzed. Also, core samples were extracted from the model to evaluate asphaltenes and coke formation. It was shown that it may be possible to recover nearly 70% of the original oil in place with a modified well arrangement.

Dynamic displacement and non-equilibrium dissolution of supercritical CO2 in low-permeability sandstone: An experimental study

An experimental setup was developed for conducting core-flood experiments of supercritical CO2 and water under pressures higher than 8.00MPa and a temperature of 40°C. Two representative low-permeability sandstone cores were obtained from the Shenhua Group CCS site in the Erdos Basin in China and the experimental study was in support of China's first field test. Unlike most laboratory experiments with two-phase CO2–water flow, dry CO2 was injected in the CO2-flood experiments, and deionized water (without dissolved CO2) was used in the water-flood experiments. In the CO2-flood experiments, dynamic displacement of water by injected CO2 was investigated using transient inlet and outlet pressures and transient flow rates of outflowing CO2 and water. The residual water saturation estimated at the end of the experiments (with an injection rate of 1.2mLmin−1) for both cores is 0.52. The higher residual water saturation can be attributed to the high CO2/water viscosity contrast and non-uniform displacement. The estimated relative CO2 permeability at residual water saturation varies from 0.13 to 0.23. During the water-flood experiments, non-equilibrium CO2 dissolution at the core scale was observed using the transient concentration of total dissolved CO2 in outflowing water. The non-equilibrium dissolution possibly results from non-uniform distribution of water and CO2 caused by sub-core heterogeneity. The endpoint CO2 saturation estimated varies from 0.17 to 0.10 for a low injection rate of 0.2mLmin−1. Additional experiments indicate that higher water injection rate (up to 2mLmin−1) drive more free-phase CO2 out of the cores, with less CO2 mass stored, because of CO2 density change with elevated pressure and weaker capillarity for low-permeability sandstone. Additional experiments with injected water of varying dissolved CO2 concentration (including CO2-saturated conditions) indicate that CO2 dissolution mobilizes additional free-phase CO2 out of the cores by enhanced displacement, and increases relative water permeability after CO2 displacement is complete, even though dissolution only accounts for 6–7% of the total CO2 mass initially in the cores before the experiments.

Applications of Non-linear Elastic Wavefield Inversion for 4D Seismic Data to Characterize the Injected Carbon Dioxide

Elastic parameters are fundamental in estimating rock properties, fluid saturation and pore pressure in carbon dioxide injection and 4D seismic survey efficiently provides spatial changes of elastic parameters as well as baseline parameters. Conversely elastic parameters are governed by microstructures of material and dynamic conditions of measurement and thus depend on the temporal and spatial scale. Logging data were useful in estimating elastic properties at 10-50kHz time scale, and under partially saturation condition they could be taken into seismic time scale at saturation rate estimated by “partially Patchy saturation model” currently proposed and evidenced in good matching with logging data analysis, which took residual water saturation into account and adapted for building elastic wave velocities in 3D monitor seismic cube.4D seismic survey data, acquired by Japex in 2003 and 2005 on the area of onshore RITE/METI carbon dioxide injection test site, were analysed incorporated with repeated time-lapse logging data matched in scale by the currently proposed method. In this study, 1) I newly built the most probable full-scale baseline and monitor elastic wave velocity model of the 4D seismic survey in the depth domain using time scale adjusted and calibrated 4D AI cube in the time domain and 2) examined the feasibility of non-linear elastic wavefield inversion of synthetic 4D seismic data. Results of non-linear elastic wavefield inversion successfully showed estimates of 4D elastic wave velocity changes at excellent quality and accuracy.

Experimental Drainage Dynamics Study of Supercritical CO2 and Water in Low-Permeability and Heterogeneous Rocks

Flooding experiments with deionized water and supercritical CO2 were conducted at 40°C and greater than 8MPa pressure on two cores, a low-permeability sandstone and a heterogeneous carbonate specimen, obtained from rocks outcropping in the Erdos Basin. Located in the northern China, the Erdos Basin has a prospective potential for large- scale CCS deployment. The drainage dynamics were investigated by using transient inlet and outlet pressures and transient flow rates of outflowing supercritical CO2 and water. We observed very different drainage dynamics and high residual water saturations that were interpreted as the combined results of: i) the low permeability of the solid specimens, ii) the large difference in viscosity between CO2 and water, iii) the non-uniform displacement of pore fluids caused by sub-core heterogeneity.

The impact of CO2 on the electrical properties of water bearing porous media – laboratory experiments with respect to carbon capture and storage

ABSTRACTWe conducted a detailed experimental investigation of the effect of CO2 injection on the electrical conductivity of water bearing porous media, needed for an improved geophysical monitoring of CO2 storage reservoirs. Therefore, we developed an experimental set‐up that allows to investigate electrical characteristics of the injection process as well as the impact of dissolved CO2 on pore water conductivity. We found that a gaseous, fluid and supercritical pure CO2 phase bears no relevant conductivity at pressures up to 13 MPa and temperatures up to 50° C. When CO2 dissolves in pore water, pressure‐dependent dissociation processes can double the pore water conductivity, that can be used in leakage detection. This is quantified by an adaptation of Archie’s law. The empirical adaptation and the experimental data are confirmed by combined geochemical‐geoelectrical modelling. Furthermore, water‐saturated sand samples were investigated while CO2 displaced the pore water at pressures up to 13 MPa and temperatures up to 40° C. A decrease in electrical conductivity by a factor of up to 33 was measured, corresponding to a residual water saturation of 14–19%. Qualitatively, a decrease was also demonstrated under supercritical conditions. As an integrative interpretation, a conceptual model of electrical rock properties during CO2 sequestration is presented.

Effects of Porous Medium Heterogeneity on Vadose Zone Desiccation: Intermediate‐Scale Laboratory Experiments and Simulations

Soil desiccation (drying), involving water evaporation induced by dry gas injection, is a potentially robust vadose zone remediation process to limit contaminant transport through the vadose zone. A series of four intermediate‐scale flow cell experiments was conducted in homogeneous and simple layered heterogeneous porous medium systems to investigate the effects of heterogeneity on desiccation of unsaturated porous media. The permeability ratios of porous medium layers ranged from about 5 to almost 2 orders of magnitude. The insulated flow cell was equipped with 20 humidity and temperature sensors while a dual‐energy γ system was used to determine water saturations at various times. The multiphase code STOMP was used to simulate the desiccation process. For the layered systems, results show that injected dry gas flowed predominantly in the higher permeability layer and delayed water removal from the lower permeability material. For the configurations tested, water vapor diffusion from the lower to the higher permeability zone was considerable over the duration of the experiments, resulting in much larger relative humidity values of the outgoing air than based on permeability ratios alone. Acceptable numerical matches with the experimental data were obtained when an extension of the saturation‐capillary pressure relation below the residual water saturation was used. The agreements between numerical and experimental results suggest that the correct physics is implemented in the simulator.

Permeability alteration induced by drying of brines in porous media

Permeability of reservoir rocks can be strongly altered by salt precipitation induced by drying. Indeed, gas injection in deep saline aquifers leads first to the brine displacement. The liquid saturation decreases near the injection point and reaches a residual water saturation. But at longer time, the water mass transfer to the gas phase by evaporation can become significant and the dissolved salt can precipitate in the porous structure. The solid salts fill the pores and the permeability decreases. Permeability alteration by salting out is a risk of injectivity decline in the context of CO2 geological storage in saline aquifers where high level of gas injection has to be maintained over decades. However, this problem has been poorly investigated. It implies physical processes that are strongly coupled: drying, water and gas flows in the porous structure and precipitation. This work is an experimental investigation aiming at measuring on natural rock samples the permeability alteration induced by convective drying where dry gas is injected through the sample. We show that alteration of permeability is strong and total blockage of the flow is even possible. We also show that the change in porosity due to the solid salt is heterogeneous along the rock samples. A local permeability-porosity relationship has been estimated from the measurements and we could deduce the permeability alteration function of time by modeling the drying dynamic. We show that it starts very early because capillary backflows are extremely efficient in this process to accumulate solid salt near the injection surfaces.

Development of an Instrumented Channel for Multiphase Flow in Unsaturated Soils

This paper presents the development of an instrumented channel for two-dimensional multiphase flow of automotive fuels in unsaturated soils. Flow experiments were performed using water or diesel in an eolian sand at residual water saturation, a particular case of multiphase flow. Aspects such as the visual monitoring of the infiltration experiments and the great reproducibility of the developed experimental protocol can be cited as highlights of this research. The two sets of tensiometers, hydrophilic and hydrophobic, used during the diesel experiment, responded differently. While the hydrophobic tensiometer, filled with diesel, measured the full range of diesel suctions, the hydrophilic tensiometers, filled with water, responded less effectively to the passage of the diesel wetting front. Flow experiments were modeled using Philip’s equation, considering the flow in unsaturated conditions above the wetting front. The time required for the diesel wetting front to reach the tensiometers was about 8.8 times higher than for water, considering the tensiometer readings, and, about 6.1 times higher than for water considering the visual observations. These values are comparable to the ratio of fluid mobilities [(w/w)/(diesel/diesel) = 5.5] of water and diesel.

Air-Water Interfacial Area and Capillary Pressure: Porous-Medium Texture Effects and an Empirical Function

The relationship between air-water interfacial area and capillary pressure under higher water-content conditions is investigated for four natural porous media. The results show that the magnitude of the air-water interfacial area increases with increasing capillary pressure, consistent with the decrease in water saturation. The maximum observed air-water interfacial areas are dependent upon the magnitude of residual water saturation, which itself is condition dependent. The more well-sorted porous medium exhibited a greater rate of change of air-water interfacial area with capillary pressure than the more poorly-sorted porous media. The observed relationship between air-water interfacial area and capillary pressure was quantified by coupling an empirical equation describing the air-water interfacial area vs. water saturation relationship with the van Genuchten equation relating water saturation and capillary pressure. This equation produced reasonable simulations of the measured data.

Enhanced gas-condensate production by wettability alteration to gas wetness

Many gas-condensate reservoirs experience a sharp drop in gas production due to condensation near the wellbore as pressure drops lower than the dew point. Wettability alteration approach has been demonstrated successful in laboratory. However few experiments have been conducted in real reservoir rock with a low permeability. The gas-condensate reservoirs impaired by condensation near the wellbore usually have low permeabilities. In this study, we conducted experiments in the rock sampled from the target gas field (Dongpu). Firstly a new and cheaper chemical was developed to change the rock wettability from preferential water- to gas-wetness effectively. This chemical was thermally stable at a temperature of 170 °C. Experimental results also showed that this chemical was effective at very high salinity. Secondly spontaneous water imbibition tests were run to show the effect of wettability alteration on recovery. Thirdly relative permeability data of gas and water were measured with and without wettability alteration to preferential gas-wetness. Experimental results demonstrated that the relative permeabilities of both the gas and the water phases were increased significantly after the wettability alteration to preferential gas-wetness. The residual water saturation was decreased and the gas production was enhanced greatly due to the wettability alteration.

Relative permeabilities of gas and water for different rank coals

Characteristics of gas–water two-phase flow through coal seams play crucial roles in water depletion and gas production associated with coalbed methane (CBM) recovery. One of the most important characteristic is the relative permeability of gas and water which is largely dependent on gas/water saturations in coal, varying with coal ranks. For better understanding of the seepage mechanism of the gas–water flow in coal, the relative permeabilities of gas and water in different rank coals selected from south Qinshui Basin have been investigated under various gas/water saturations through water replacement with methane using an unsteady-state method. The results have shown that the ratio of effective methane permeability and absolute permeability is obviously increasing with rank, implying that the gas slippage of high rank coal has more significant effect than the low rank coal. A series of relative permeability curves for selected coals have been obtained. All of these curves show that the selected coals are featured by smaller methane permeabilities and narrow spans of two-phase flow regions and lower relative permeability, and have low methane permeabilities under irreducible water condition as well. The experiments also revealed that the selected coals exhibit high residual water saturation with low relative permeabilities of gas and water. With increasing of the maximal vitrinite reflectance, the irreducible water saturation exhibits a U-shaped tendency whereas the methane permeability under the irreducible water condition generally increases. The irreducible water saturation slightly increases with increasing of vitrinite and weakly decreases as inertinite increases, while the methane permeability under irreducible water condition is negatively related with vitrinite and positively related to inertinite to some extent. The experimental data were further parameterized to correlate the relative permeabilities of methane and water to gas saturation, showing that a correlation of power function can fit the experiments well. As a result, a permeability model incorporated with coal rank and maceral compositions with gas saturation was developed to predict the relative permeabilities of gas (methane) and water in coals.

Water Infiltration in Layered Soils with Air Entrapment: Modified Green-Ampt Model and Experimental Validation

Air entrapment in soil is common in cases of farmland flood irrigation or intense rain. A simple, physically based model would be more useful than the complex two-phase (gaseous and liquid phase) flow model to describe water infiltration in layered soils with air entrapment. This study proposed a modified Green-Ampt model (MGAM) to simulate water infiltration in layered soils with consideration of entrapped air. A saturation coefficient Sa was introduced in MGAM to account for the resistance effect of air entrapment on infiltration. Sa had robust physical meaning, and was approximately equal to one minus the plus of the residual air and residual water saturation degree that could be determined from the soil water retention curve equation. In MGAM, the actual water content and hydraulic conductivity of the wetted zone were determined by multiplying Sa with the saturated values. Infiltration experiments in a 300-cm-long five-layered soil column and a 280-cm-deep eight-layered field soil profile were conducted to test the applicability of MGAM. For comparison, the infiltration process was also simulated by the traditional Green-Ampt model (TGAM), in which the wetted zone was assumed to be fully saturated, and the Bouwer Green-Ampt model (BGAM), in which the hydraulic conductivity of the wetted zone was half that of the saturated hydraulic conductivity. The estimated Sa values were very close to the measured saturation degree of soil layers at the termination of the experiment. The simulation results indicated that the TGAM overestimated the infiltration rate and cumulative infiltration, whereas the BGAM underestimated the infiltration rate and cumulative infiltration. Furthermore, the depths of the wetting fronts simulated by TGAM and BGAM were considerably smaller than those measured. The MGAM provided satisfactory simulation results and adequately described the infiltration process in both the laboratory soil column and the field soil profile.

The Method of Characteristics Applied to Oil Displacement by Foam

Summary Solutions obtained by the method of characteristics (MOC) provide key insights into complex foam enhanced-oil-recovery (EOR) displacements and the simulators that represent them. Most applications of the MOC to foam have excluded oil. We extend the MOC to foam flow with oil, where foam is weakened or destroyed by oil saturations above a critical oil saturation and/or weakened or destroyed at low water saturations, as seen in experiments and represented in foam simulators. Simulators account for the effects of oil and capillary pressure on foam using algorithms that bring foam strength to zero as a function of oil or water saturation, respectively. Different simulators use different algorithms to accomplish this. We examine SAG (surfactant-alternating-gas) and continuous foam-flood (coinjection of gas and surfactant solution) processes in one dimension, using both the MOC and numerical simulation. We find that the way simulators express the negative effect of oil or water saturation on foam can have a large effect on the calculated nature of the displacement. For instance, for gas injection in a SAG process, if foam collapses at the injection point because of infinite capillary pressure, foam has almost no effect on the displacement in the cases examined here. On the other hand, if foam maintains finite strength at the injection point in the gas-injection cycle of a SAG process, displacement leads to implied success in several cases. However, successful mobility control is always possible with continuous foam flood if the initial oil saturation in the reservoir is below the critical oil saturation above which foam collapses. The resulting displacements can be complex. One may observe, for instance, foam propagation predicted at residual water saturation, with zero flow of water. In other cases, the displacement jumps in a shock past the entire range of conditions in which foam forms. We examine the sensitivity of the displacement to initial oil and water saturations in the reservoir, the foam quality, the functional forms used to express foam sensitivity to oil and water saturations, and linear and nonlinear relative permeability models.