The flow properties of naturally fractured reservoirs are dominated by flow through the fractures. In a previous study we showed that even a well-connected fracture network behaves like a much sparser network when the aperture distribution is broad enough: i.e., most fractures can be eliminated while leaving a sub-network with virtually the same permeability as the original fracture network. In this study, we focus on the influence of eliminating unimportant fractures which carry little flow on the inferred characteristic matrix-block size. We model a two-dimensional fractured reservoir in which the fractures are well-connected. The fractures obey a power-law length distribution, as observed in natural fracture networks. For the aperture distribution, because information from the subsurface is limited, we test a number of cases: log-normal distributions (from narrow to broad), and power-law distributions (from narrow to broad). The matrix blocks in fractured reservoirs are of varying sizes and shapes; we adopt the characteristic radius and the characteristic length to represent the characteristic matrix-block size. We show how the characteristic matrix-block sizes increase from the original fracture network to the dominant sub-network. This suggests that the matrix-block size, or shape factor, used in dual-porosity/dual-permeability waterflood or enhanced oil recovery (EOR) simulations or in homogenization should be based not on the entire fracture population but on the sub-network that carries almost all of the injected fluid (water or EOR agent).@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

Surfactant-alternating-gas (SAG) is a favored method of foam injection, which has been proved as an efficient way for enhancing oil recovery. However, foam flow is extremely complicated, and there are still unsolved problems for foam application. One is liquid injectivity. Our previous studies suggest that the injectivity in a SAG process is determined by propagation of several banks near the injection well that are not represented by current foam models. Uniform bank properties were assumed. However, in a companion paper, our experimental results show that the dimensionless propagation velocity and the total mobility of banks during the liquid-injection period depends on superficial velocity. Shearing-thinning behavior is observed. In radial flow, the superficial velocity varies with distance from the well. In this study, we scale-up the experimental results using a radial bank-propagation model. The comparison of liquid injectivity estimated from conventional foam simulators (Peaceman equation) and the bank-propagation model show that the conventional foam models cannot represent the effect of the superficial-velocity-dependent fluid properties during liquid injection in a SAG process. The shear-thinning behavior can lead to much better liquid injectivity than expected, which should be accounted for in a field application of a SAG foam process.@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

We present a comparative study of foam coreflood experiments with various surfactant concentrations. Plots of apparent viscosity vs. injected gas fraction were obtained for surfactant concentrations at the critical micelle concentration and above. Bulk foam stability was measured for all concentrations and compared with the coreflood results. There were different responses to surfactant concentration in bulk and in corefloods. The coreflood results were matched with an implicit-texture foam model, and the dependency of the model parameters on the surfactant concentration is discussed. Fitting the data requires relating the surfactant concentration to the dry-out function or the limiting capillary pressure. @en

Fracture network connectivity and aperture (or conductivity) distribution are two crucial features controlling flow behavior of naturally fractured reservoirs. The effect of connectivity on flow properties is well documented. In this paper, however, we focus here on the influence of fracture aperture distribution. We model a two-dimensional fractured reservoir in which the matrix is impermeable and the fractures are well connected. The fractures obey a power-law length distribution, as observed in natural fracture networks. For the aperture distribution, since the information from subsurface fracture networks is limited, we test a number of cases: log-normal distributions (from narrow to broad), power-law distributions (from narrow to broad), and one case where the aperture is proportional to the fracture length. We find that even a well-connected fracture network can behave like a much sparser network when the aperture distribution is broad enough (α ≤ 2 for power-law aperture distributions and σ ≥ 0.4 for log-normal aperture distributions). Specifically, most fractures can be eliminated leaving the remaining dominant sub-network with 90% of the permeability of the original fracture network. We determine how broad the aperture distribution must be to approach this behavior and the dependence of the dominant sub-network on the parameters of the aperture distribution. We also explore whether one can identify the dominant sub-network without doing flow calculations.@en

tAqueous foams play an important role in many industrial processes, from ore separation by froth flotationto enhanced oil recovery (EOR). In the latter case, the foam is used as a means of increasing the sweepefficiency through the oil bearing rock – the complex, structure dependent, flow behavior of the foammeans that it has improved penetration of lower permeability regions than would be obtained with aNewtonian fluid. An understanding of how foam behaves when flowing through a rock is therefore of greatimportance when selecting suitable surfactants for EOR processes. Previous tests have suggested thatthere is no reliable correlation between bulk foam behavior and foam behavior in a rock core, especially inthe presence of oil. We present a comparative study of bulk stability tests and core floods with foam, bothwith and without oil. Core-flood tests were conducted in rock cores with a diameter of 1 cm, significantlysmaller than typical cores. Apparent viscosity/injected gas fraction response curves were obtained, bothwith and without oil in the system.The current work finds that, in the absence of oil, there is a positive correlation between bulk foamstability and core-flood performance. Bulk foam experiments can therefore be a useful screening tool togive a good indication of the surfactant performance in the core flood. However, in the presence of oil,although there was a general trend of increasing maximum apparent viscosity with increasing bulk foamstability, no strong correlation was found between bulk foam stability and the performance in the corefor the experiments performed.@en

An enhanced-oil-recovery (EOR) pilot test has multiple goals, among them to demonstrate oil recovery, verify the properties of the EOR agent in-situ, and provide the information needed for scale-up to an economic process. Given the complexity of EOR processes and the inherent uncertainty in the reservoir description, it is a challenge to discern the properties of the EOR agent in-situ in the midst of geological uncertainty. We propose a general workflow and present a case study to illustrate this challenge: a polymer EOR process in a 2D layer-cake reservoir. The polymer is designed to have a viscosity of 60 cp in-situ. There is uncertainty in the reservoir description, represented here by a range of values of Dykstra Parsons coefficient and different spatial arrangements of layers. We allow that the polymer process might fail in-situ and viscosity could be 20% of that intended. We test whether the signals of this difference at injection and production wells would be statistically significant in the midst of the geological uncertainty. Specifically, we compare the deviation caused by loss of polymer viscosity to the scatter caused by the geological uncertainty using the statistical 95% confidence interval. Among the signals considered, the ‘rate of rise in injection pressure with polymer injection’ and ‘maximum injection pressure in the injector’ give the most reliable indications of whether a polymer viscosity was maintained in-situ. If unintended and uncontrolled fracturing of the injection well is considered likely during polymer injection, however, injection pressure may be an unreliable indicator of in-situ polymer viscosity. In that case a diagnostic fracture-injection/falloff test could produce the needed indication of polymer viscosity in-situ. ‘Polymer breakthrough time’ and ‘cumulative oil production at the end of process’ give indications of polymer in-situ loss in some of the cases. With a more severe viscosity loss, e.g. 90% or worse, these signals give a statistically significant indication of loss of polymer viscosity in all of the cases.@en

Surfactant-alternating-gas (SAG) is a preferred method of foam injection, which is a promising means of enhanced oil recovery. Liquid injectivity in a SAG process is commonly problematic. Our previous studies suggest that the liquid injectivity can be better than expected due to the existence of a collapsed-foam region formed during the gas-injection period ahead of the liquid-injection period. A single superficial velocity was used in those studies to examine the flow behavior during gas- and liquid-injection periods, separately. However, in radial flow from an injection well, superficial velocity decreases with distance from the injection well. Understanding the effect of superficial velocity on gas and liquid injectivities is important, but remains unexplored. In this study, we first examine gas injection at different superficial velocities following foam injection. We then study the effect of liquid superficial velocity on the liquid injectivity following a similar volume of gas injection. Our results show that during a prolonged period of gas injection following foam, the propagation velocity and the total mobility of the collapsed-foam bank are not significantly affected by the gas superficial velocity. During liquid injection after a period of gas injection, the dimensionless propagation velocities and the total mobilities of the forced-imbibition bank and the gas-dissolution bank follow a power-law dependence on the liquid superficial velocity. Liquid fingering through the weakened-foam region shows strongly shear-thinning behavior. It is also observed from X-ray computer-tomography experiments that the liquid fingers are wider if the liquid superficial velocity is greater. The impact of the shear-thinning behavior on the estimation of liquid injectivity in a field application is the subject of a companion paper.@en

Foam is utilized in enhanced oil recovery and CO2 sequestration. Surfactant-alternating-gas (SAG) is a preferred approach for placing foam into reservoirs, due to it enhances gas injection and minimizes corrosion in facilities. Our previous studies with similar permeability cores show that during SAG injection, several banks occupy the area near the well where fluid exhibits distinct behaviour. However, underground reservoirs are heterogeneous, often layered. It is crucial to understand the effect of permeability on fluid behaviour and injectivity in a SAG process. In this work, coreflood experiments are conducted in cores with permeabilities ranging from 16 to 2300 mD. We observe the same sequence of banks in cores with different permeabilities. However, the speed at which banks propagate and their overall mobility can vary depending on permeability. At higher permeabilities, the gas-dissolution bank and the forced-imbibition bank progress more rapidly during liquid injection. The total mobilities of both banks decrease with permeability. By utilizing a bank-propagation model, we scale up our experimental findings and compare them to results obtained using the Peaceman equation. Our findings reveal that the liquid injectivity in a SAG foam process is misestimated by conventional simulators based on the Peaceman equation. The lower the formation permeability, the greater the error.@en

Foam is utilized in enhanced oil recovery and CO2 sequestration. Surfactant-alternating-gas (SAG) is a preferred approach for placing foam into reservoirs, due to it enhances gas injection and minimizes corrosion in facilities. Our previous studies with similar permeability cores show that during SAG injection, several banks occupy the area near the well where fluid exhibits distinct behaviour. However, underground reservoirs are heterogeneous, often layered. It is crucial to understand the effect of permeability on fluid behaviour and injectivity in a SAG process. In this work, coreflood experiments are conducted in cores with permeabilities ranging from 16 to 2300 mD. We observe the same sequence of banks in cores with different permeabilities. However, the speed at which banks propagate and their overall mobility can vary depending on permeability. At higher permeabilities, the gas-dissolution bank and the forced-imbibition bank progress more rapidly during liquid injection. The total mobilities of both banks decrease with permeability. By utilizing a bank-propagation model, we scale up our experimental findings and compare them to results obtained using the Peaceman equation. Our findings reveal that the liquid injectivity in a SAG foam process is misestimated by conventional simulators based on the Peaceman equation. The lower the formation permeability, the greater the error.@en

Foam is utilized in enhanced oil recovery and CO2 sequestration. Surfactant-alternating-gas (SAG) is a preferred approach for placing foam into reservoirs, due to it enhances gas injection and minimizes corrosion in facilities. Our previous studies with similar permeability cores show that during SAG injection, several banks occupy the area near the well where fluid exhibits distinct behaviour. However, underground reservoirs are heterogeneous, often layered. It is crucial to understand the effect of permeability on fluid behaviour and injectivity in a SAG process. In this work, coreflood experiments are conducted in cores with permeabilities ranging from 16 to 2300 mD. We observe the same sequence of banks in cores with different permeabilities. However, the speed at which banks propagate and their overall mobility can vary depending on permeability. At higher permeabilities, the gas-dissolution bank and the forced-imbibition bank progress more rapidly during liquid injection. The total mobilities of both banks decrease with permeability. By utilizing a bank-propagation model, we scale up our experimental findings and compare them to results obtained using the Peaceman equation. Our findings reveal that the liquid injectivity in a SAG foam process is misestimated by conventional simulators based on the Peaceman equation. The lower the formation permeability, the greater the error.@en

We present a set of steady-state foam-flood experimental data for four sandstones with different permeabilities, ranging between 6 and 1900 mD, and with similar porosity. We derive permeability-dependent foam parameters with two modelling approaches, those of Boeije and Rossen (2015a) and a non-linear least-square minimization approach (Eftekhari et al., 2015). The two approaches can yield significantly different foam parameters. Thus, we critically assess their ability in deriving reliable foam parameter estimates. In particular, the way the two approaches treat shear-thinning foam behaviour and foam coalescence is discussed. The foam parameter set acquired from the latter approach is further used as input in foam diversion calculations: this serves to evaluate mobility predictions in non-communicating reservoir layers. This study aims to provide a framework to integrate experimental work, modelling and simple qualitative diversion calculations to provide a background for the upscaling of foam studies, with particular focus on heterogeneous systems.@en

We present a set of steady-state foam-flood experimental data for four sandstones with different permeabilities, ranging between 6 and 1900 mD, and with similar porosity. We derive permeability-dependent foam parameters with two modelling approaches, those of Boeije and Rossen (2015a) and a non-linear least-square minimization approach (Eftekhari et al., 2015). The two approaches can yield significantly different foam parameters. Thus, we critically assess their ability in deriving reliable foam parameter estimates. In particular, the way the two approaches treat shear-thinning foam behaviour and foam coalescence is discussed. The foam parameter set acquired from the latter approach is further used as input in foam diversion calculations: this serves to evaluate mobility predictions in non-communicating reservoir layers. This study aims to provide a framework to integrate experimental work, modelling and simple qualitative diversion calculations to provide a background for the upscaling of foam studies, with particular focus on heterogeneous systems.@en

We present a set of steady-state foam-flood experimental data for four sandstones with different permeabilities, ranging between 6 and 1900 mD, and with similar porosity. We derive permeability-dependent foam parameters with two modelling approaches, those of Boeije and Rossen (2015a) and a non-linear least-square minimization approach (Eftekhari et al., 2015). The two approaches can yield significantly different foam parameters. Thus, we critically assess their ability in deriving reliable foam parameter estimates. In particular, the way the two approaches treat shear-thinning foam behaviour and foam coalescence is discussed. The foam parameter set acquired from the latter approach is further used as input in foam diversion calculations: this serves to evaluate mobility predictions in non-communicating reservoir layers. This study aims to provide a framework to integrate experimental work, modelling and simple qualitative diversion calculations to provide a background for the upscaling of foam studies, with particular focus on heterogeneous systems.@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 c Foam can divert flow from higher- to lower-permeability layers and thereby improve vertical conformance in gas-injection enhanced oil recovery. Recently, Kapetas et al. (2015) measured foam properties in cores from four sandstone formations ranging in permeability from 6 to 1900 md, and presented parameter values for foam model fit to those data. Permeability affects both the mobility reduction of wet foam in the "low-quality" foam regime and the limiting capillary pressure at which foam collapses. Kapetas et al. showed how foam would divert injection between layers of these formations if all layers were full of foam injected at a given quality (gas fractional flow). Here we examine the effects of injection method on diversion in a dynamic foam process using fractional-flow modeling and the model parameters derived by Kapetas et al. Like them, we consider a hypothetical reservoir containing non-communicating layers with the properties of the four formations in their study. The effectiveness of diversion varies greatly with injection method. In a SAG (surfactant-alternatinggas) process, diversion of the first slug of gas depends on foam behavior at very high foam quality. Mobility in the foam bank during gas injection depends on the nature of a shock front that bypasses most foam qualities usually studied in the laboratory. The foam with the lowest mobility at fixed foam quality does not necessarily give the lowest mobility in a SAG process. In particular, diversion in SAG depends on how and whether foam collapses at low water saturation; this property varies greatly among the foams reported by Kapetas et al. Moreover, diversion depends on the size of the surfactant slug received by each layer before gas injection. This of course favors diversion away from high-permeability layers that receive a large surfactant slug, but there is an optimum surfactant slug size: too little surfactant and diversion from high-permeability layers is not effective; too much and mobility is reduced in lowpermeability layers, too. For a SAG process, it is very important to determine if foam collapses completely at irreducible water saturation. In addition, we show the diversion expected in a foam-injection process as a function of foam quality. The faster propagation of surfactant and foam in the higher-permeability layers aids in diversion, as expected. This depends on foam quality and non-Newtonian foam mobility and varies with time of injection. Injectivity is extremely poor with foam injection, but is not necessarily worse than waterflood in some effective SAG foam processes atastrophe theory and of studies of foam generation without oil. @en