The Origin of Non-thermal Fluctuations in Multiphase Flow in Porous Media

Core flooding experiments to determine multiphase flow in properties of rock such as relative permeability can show significant fluctuations in terms of pressure, saturation, and electrical conductivity. That is typically not considered in the Darcy scale interpretation but treated as noise. However, in recent years, flow regimes that exhibit spatio-temporal variations in pore scale occupancy related to fluid phase pressure changes have been identified. They are associated with topological changes in the fluid configurations caused by pore-scale instabilities such as snap-off. The common understanding of Darcy-scale flow regimes is that pore-scale phenomena and their signature should have averaged out at the scale of representative elementary volumes (REV) and above. In this work, it is demonstrated that pressure fluctuations observed in centimeter-scale experiments commonly considered Darcy-scale at fractional flow conditions, where wetting and non-wetting phases are co-injected into porous rock at small (<10−6) capillary numbers are ultimately caused by pore-scale processes, but there is also a Darcy-scale fractional flow theory aspect. We compare fluctuations in fractional flow experiments conducted on samples of few centimeters size with respective experiments and in-situ micro-CT imaging at pore-scale resolution using synchrotron-based X-ray computed micro-tomography. On that basis we can establish a systematic causality from pore to Darcy scale. At the pore scale, dynamic imaging allows to directly observe the associated breakup and coalescence processes of non-wetting phase clusters, which follow “trajectories” in a “phase diagram” defined by fractional flow and capillary number and can be used to categorize flow regimes. Connected pathway flow would be represented by a fixed point, whereas processes such as ganglion dynamics follow trajectories but are still overall capillary-dominated. That suggests that the origin of the pressure fluctuations observed in centimeter-sized fractional flow experiments are capillary effects. The energy scale of the pressure fluctuations corresponds to 105-106 times the thermal energy scale. This means the fluctuations are non-thermal. At the centimeter scale, there are non-monotonic and even oscillatory solutions permissible by the fractional flow theory, which allow the fluctuations to be visible and—depending on exact conditions—significant at centimeter scale, within the viscous limit of classical (Darcy scale) fractional flow theory. That also means that the phenomenon involves both capillary aspects from the pore or cluster scale and viscous aspects of fractional flow and occurs right at the transition, where the physical description concept changes from pore to Darcy scale.

Fast Evaluation Model of Surfactant Flooding Based on Modification Fractional Flow Theory

At present, the numerical simulation of surfactant flooding is implemented by commercial software, which requires a lot of input data, resulting in slow calculation speed and heavy workload. So it was not suitable for surfactant flooding revovery evaluation in a large number of oilfields. This paper presents a fast evaluation model of surfactant flooding based on modification fractional flow theory. Viral expansion, interfacial tension calculation formula, and the relative permeability correction model are introduced to simulate the surfactant displacement mechanism. The simulation model is applied in a low permeability reservoir, and the simulation results are compared with the eclipse software results. Their results are similar, which show that this model presents certain reliability.

Application of Fractional Flow Theory for Analytical Modeling of Surfactant Flooding, Polymer Flooding, and Surfactant/Polymer Flooding for Chemical Enhanced Oil Recovery

Fractional flow theory still serves as a powerful tool for validation of numerical reservoir models, understanding of the mechanisms, and interpretation of transport behavior in porous media during the Chemical-Enhanced Oil Recovery (CEOR) process. With the enrichment of CEOR mechanisms, it is important to revisit the application of fractional flow theory to CEOR at this stage. For surfactant flooding, the effects of surfactant adsorption, surfactant partition, initial oil saturation, interfacial tension, and injection slug size have been systematically investigated. In terms of polymer flooding, the effects of polymer viscosity, initial oil saturation, polymer viscoelasticity, slug size, polymer inaccessible pore volume (IPV), and polymer retention are also reviewed extensively. Finally, the fractional flow theory is applied to surfactant/polymer flooding to evaluate its effectiveness in CEOR. This paper provides insight into the CEOR mechanism and serves as an up-to-date reference for analytical modeling of the surfactant flooding, polymer flooding, and surfactant/polymer flooding CEOR process.

Fractional-Flow Theory for Non-Newtonian Surfactant-Alternating-Gas Foam Processes

Foam can improve sweep efficiency in gas-injection-enhanced oil recovery. Surfactant-alternating-gas (SAG) is a favored method of foam injection. Laboratory data indicate that foam can be non-Newtonian at low water fractional flow fw, and therefore during gas injection in a SAG process. We investigate the implications of this finding for mobility control and injectivity, by extending fractional-flow theory to gas injection in a non-Newtonian SAG process in radial flow. We make most of the standard assumptions of fractional-flow theory (incompressible phases, one-dimensional displacement through a homogeneous reservoir, instantaneous attainment of local equilibrium), excluding Newtonian mobilities. For this initial study, we ignore the effect of changing or non-uniform oil saturation on foam. Non-Newtonian behavior at low fw implies that the limiting water saturation for foam stability varies as superficial velocity decreases with radial distance from the well. We discretize the domain radially and perform Buckley–Leverett analysis on each narrow increment in radius. Solution characteristics move outward with fixed fw. We base the foam model parameters and non-Newtonian behavior on laboratory data in the absence of oil. We compare results to mobility and injectivity determined by conventional simulation, where grid resolution is usually limited. For shear-thinning foam, mobility control improves as the foam front propagates from the well, but injectivity declines somewhat with time. This change in mobility ratio is not that at steady state at fixed water fractional flow in the laboratory, however, because the shock front in a non-Newtonian SAG process does not propagate at fixed fractional flow (though individual characteristics do). Moreover, the shock front is not governed by the conventional condition of tangency to the fractional-flow curve, though it continually approaches this condition. Injectivity benefits from the increased mobility of shear-thinning foam near the well. The foam front, which maintains a constant dimensionless velocity for Newtonian foam, decelerates somewhat with time for shear-thinning foam. For shear-thickening foam, mobility control deteriorates as the foam front advances, though injectivity improves somewhat with time. Overall, however, injectivity suffers from reduced foam mobility at high superficial velocity near the well. The foam front accelerates somewhat with time. Conventional simulators cannot adequately represent these effects, or estimate injectivity accurately, in the absence of extraordinarily fine grid resolution near the injection well.

Analytical Solutions for Spontaneous Imbibition: Fractional-Flow Theory and Experimental Analysis

Summary We present analytical solutions for capillary-controlled displacement in one dimension by use of fractional-flow theory. We show how to construct solutions with a spreadsheet that can be used for the analysis of experiments as well as matrix-block-scale recovery in field settings. The solutions can be understood as the capillary analog to the classical Buckley-Leverett solution (Buckley and Leverett 1942) for viscous-dominated flow, and are valid for cocurrent and countercurrent spontaneous imbibition (SI), as well as for arbitrary capillary pressure and relative permeability curves. They can be used to study the influence of wettability, predicting saturation profiles and production rates characteristic for water-wet and mixed-wet conditions. We compare our results with in-situ measurements of saturation profiles for SI in a water-wet medium. We show that the characteristic shape of the saturation profile is consistent with the expected form of the relative permeabilities. We discuss how measurements of imbibition profiles, in combination with other measurements, could be used to determine relative permeability and capillary pressure.

Applying Fractional-Flow Theory Under the Loss of Miscibility

Summary This paper examines the limits of the Walsh and Lake (WL) method for predicting the displacement performance of solvent flood when miscibility is not achieved. Despite extensive research on the applications of fractional-flow theory, the prediction of flow performance under the loss of miscibility has not been investigated thoroughly. We introduce the idea of an analogous first-contact miscible (FCM) flood to study miscibly degraded simultaneous water and gas (SWAG) displacements using the WL method. Furthermore, numerical simulation is used to validate the WL solution on one oil/solvent pair. In the simulations, the loss of miscibility (degradation) is attributed to either flow-associated dispersion or insufficient pressure to develop the miscibility. 1D SWAG injection simulations suggest that results of the WL method and the simulations are consistent when dispersion is limited. For the 2D displacements, the predicted optimal water-alternating-gas (WAG) ratio is accurate when the permeable medium is fairly homogeneous with a limited crossflow or is heterogeneous with a large lateral correlation length (the same size or greater than the interwell spacing). The results suggest that the accuracy of the WL method improves as crossflow is reduced. In addition, linear growth of the mixing zone with time is observed in cases for which the predicted optimal WAG ratio is consistent with the simulation results. Hence, we conclude that the WL solution is accurate when the mixing zone grows linearly with time.