Impact of the Buoyancy–Viscous Force Balance on Two-Phase Flow in Layered Porous Media

Abstract

Motivated by geological carbon storage and hydrocarbon recovery, the effect of buoyancy and viscous forces on the displacement of one fluid by a second immiscible fluid, along parallel and dipping layers of contrasting permeability, is characterized using five independent dimensionless numbers and a dimensionless storage or recovery efficiency. Application of simple dimensionless models shows that increased longitudinal buoyancy effects increase storage efficiency by reducing the distance between the leading edges of the injected phase in each layer and decreasing the residual displaced phase saturation behind the leading edge of the displacing phase. Increased transverse buoyancy crossflow increases storage efficiency if it competes with permeability layering effects, but reduces storage efficiency otherwise. When both longitudinal and transverse buoyancy effects are varied simultaneously, a purely geometrical dip angle group defines whether changes in storage efficiency are dominated by changes in the longitudinal or transverse buoyancy effects. In the limit of buoyancy-segregated flow, we report an equivalent, unidimensional flow model which allows rapid prediction of storage efficiency. The model presented accounts for both dip and layering, thereby generalizing earlier work which accounted for each of these but not both together. We suggest that the predicted storage efficiency can be used to compare and rank geostatistical realizations, and complements earlier heterogeneity measures which are applicable in the viscous limit.

Buoyancy segregation suppresses viscous fingering in horizontal displacements in a porous layer

“…The less viscous input fluid intrudes into the ambient fluid sufficiently far that the destabilising increase in the magnitude of the pressure gradient associated with the viscosity contrast is smoothed over the extent of the interface. Buoyancy segregation corresponds to a monotonic interface, and the input fluid may be forced into the low-permeability region (see also Debbabi et al 2018). We note that there may be significant intermingling of the fluids in the transient evolution to the buoyancy-segregated flow (e.g.…”

“…Buoyancy segregation corresponds to a monotonic interface, and the input fluid may be forced into the low-permeability region (see also Debbabi et al. 2018). We note that there may be significant intermingling of the fluids in the transient evolution to the buoyancy-segregated flow (e.g.…”

Capillary trapping in a vertically heterogeneous porous layer

“…Such behaviour has been observed in layers which partition into two sublayers of differing permeability in the case of an injection-driven flow and an inclined buoyancy-driven flow (Huppert, Neufeld & Strandkvist 2013; Debbabi et al. 2018). This instability does not occur in cases with no shock or with a shock at the bottom of the layer, which is associated with the high mobility of the ambient fluid.…”

“…However, if the layer inclination, θ , is sufficient, this may not occur and the interface may advance upslope most rapidly in the middle of the layer leading to a possible cross-layer Rayleigh-Taylor type instability and the invalidation of our model. Such behaviour has been observed in layers which partition into two sublayers of differing permeability in the case of an injection-driven flow and an inclined buoyancy-driven flow (Huppert, Neufeld & Strandkvist 2013;Debbabi et al 2018). This instability does not occur in cases with no shock or with a shock at the bottom of the layer, which is associated with the high mobility of the ambient fluid.…”

Rapid Flow Diagnostics for Prototyping of Reservoir Concepts and Models for Subsurface Co2 Storage

“…Therefore τ and the derived properties provide near real-time, but approximate, feedback on how geological uncertainties could impact CO 2 storage and the migration of CO 2 in the reservoir while CO 2 is being injected. For further details on the numerical calculation of FD and the derivation and application of additional dynamic metrics, such as the Lorenz coefficient, we refer readers to Aarnes et al (2007) To assess where in the reservoir CO 2 migration is controlled by viscous forces, we quantify the relative dominance between the gravity and viscous forces through the (transverse) gravity number (Debbabi et al, 2018)…”