Modelling foam improved oil recovery: towards a formulation of pressure-driven growth with flow reversal

Grassia

2022

Proc. R. Soc. A.

Self Cite

A two-dimensional foam system comprised of three bubbles is studied via simulations with the viscous froth model. Bubbles are arranged in a so-called staircase configuration and move along a channel due to imposed driving back pressure. This flowing three-bubble system has been studied previously on the basis that it interpolates between a simpler staircase structure (a simple lens, which breaks up via so-called topological transformations if driven at high pressure) and an infinite staircase (which sustains arbitrarily large driving pressure without breaking). Depending on bubble size relative to channel size, different solution branches for the three-bubble system were found: certain branches terminate (as for the simple lens) in topological transformations and others reach (as for an infinite staircase) a geometrically invariant migrating state. The methodology used previously was, however, a purely steady state one, and hence did not interrogate stability of the various branches, nor the role of imposing different driving pressures upon topological transformation type. To address this, unsteady state three-bubble simulations are realized here. Stable solution branches without topological transformation exist for comparatively low driving pressures. For sufficiently high imposed back pressures, however, topological transformations occur, albeit with imposed pressure now influencing the transformation type.

Section: (Iv) Eliminating Topological Transformation At High P Bmentioning

confidence: 99%

“…Due to foam's low mobility, by controlling how it moves, the flow of other fluids within the medium can be controlled also. How foam moves and rearranges inside a channel along which it is being transported is then a matter of great interest since the microscale dynamics impact the global process behaviour [10].…”

Section: Introductionmentioning

confidence: 99%

Viscous froth model applied to the dynamic simulation of bubbles flowing in a channel: three-bubble case

Grassia

2022

Proc. R. Soc. A.

Self Cite

“…Modelling how foam propagates inside the reservoir is of great interest, since we cannot see what is happening underground. Fortunately, there have been numerous studies of the mechanisms by which foam is generated within and propagates within porous media [5,10,[19][20][21][22][23][24][25][26], so insights into the elements that are required within a model are available. In porous media, foam films can severely restrict the motion of gas; the gas mobility falls due to the presence of foam films blocking the flow paths of gas [22].…”

Section: (A) Foam In Porous Mediamentioning

confidence: 99%

Breakdown of similarity solutions: a perturbation approach for front propagation during foam-improved oil recovery

Grassia

2021

Proc. R. Soc. A.

Self Cite

The pressure-driven growth model has been employed to study a propagating foam front in the foam-improved oil recovery process. A first-order solution of the model proves the existence of a concave corner on the front, which initially migrates downwards at a well defined speed that differs from the speed of front material points. At later times, however, it remains unclear how the concave corner moves and interacts with points on the front either side of it, specifically whether material points are extracted from the corner or consumed by it. To address these questions, a second-order solution is proposed, perturbing the aforementioned first-order solution. However, the perturbation is challenging to develop, owing to the nature of the first-order solution, which is a similarity solution that exhibits strong spatio-temporal non-uniformities. The second-order solution indicates that the corner’s vertical velocity component decreases as the front migrates and that points initially extracted from the front are subsequently consumed by it. Overall, the perturbation approach developed herein demonstrates how early-time similarity solutions exhibiting strong spatio-temporal non-uniformities break down as time proceeds.

Foam Propagation with Flow Reversal

Grassia²

2023

Transp Porous Med

With a view towards modelling the foam improved oil recovery process, fractional flow theory is used to study the dynamics of a foam as it propagates in a porous medium that is initially filled with liquid. In particular, a case is studied whereby, at a certain time, the net pressure driving the foam is decreased below the hydrostatic pressure at depth, leading to a local change in the flow direction. This is known as flow reversal. In both forward and reverse flow, the boundary between foamed gas and liquid is found as a discontinuous jump in liquid saturation. Over a certain thickness in the neighbourhood of this discontinuity, foam is finely textured, and the mobility of foamed gas drops by orders of magnitude relative to either pure gas or pure liquid. In reverse flow, however, the foam mobility itself and also the thickness over which low mobilities apply might differ from the forward flow case. Fractional flow theory reveals that the thickness of the low mobility region, and hence the resistance to motion that it presents, increases directly proportional to the distance travelled. Previous studies recognised this, but assumed the thickness of this region to be just a small fraction of the distance travelled by the discontinuity. Here, however, we demonstrate that the extent of the low mobility region, in both forward and reverse flow, accounts for a considerable fraction of the distance travelled by the foam, despite what was assumed in previous works.