Foam front displacement in improved oil recovery in systems with anisotropic permeability

Grassia, Paul

doi:10.1016/j.colsurfa.2017.03.059

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…In what follows, the improvement to the Velde solution is derived: those readers who wish to skip the derivation should turn directly to equations (3.13)-(3.14) and the results in section 3.3.1. The derivation that we follow is similar to one that has already been employed by Grassia (2017) to describe pressure-driven growth within porous media with anisotropic permeability. Here the system is considered to be isotropic, and there are some subtle (albeit significant) differences in the equations obtained: see Grassia (2017) for details.…”

Section: Improving the Velde Solutionmentioning

confidence: 99%

Foam front advance during improved oil recovery: similarity solutions at early times near the top of the front

et al. 2017

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The pressure-driven growth model is used to determine the shape of a foam front propagating into an oil reservoir. It is shown that the front, idealised as a curve separating surfactant solution downstream from gas upstream, can be subdivided into two regions: a lower region (approximately parabolic in shape and consisting primarily of material points which have been on the foam front continuously since time zero) and an upper region (consisting of material points which have been newly injected onto the foam front from the top boundary). Various conjectures are presented for the shape of the upper region. A formulation which assumes that the bottom of the upper region is oriented in the same direction as the top of the lower region is shown to fail, as (despite the orientations being aligned) there is a mismatch in location: the upper and lower regions fail to intersect. Alternative formulations are developed which allow the upper region to curve sufficiently so as to intersect the lower region. These formulations imply that the lower and upper regions (whilst individually being of a convex shape as seen from downstream) actually meet in a concave corner, contradicting the conventional hypothesis in the literature that the front is wholly convex. The shape of the upper region as predicted here and the presence of the concave corner are independently verified via numerical simulation data.

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Section: Improving the Velde Solutionmentioning

confidence: 99%

Foam front advance during improved oil recovery: similarity solutions at early times near the top of the front

et al. 2017

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“…Pressure-driven growth (in 2-D) has been used to describe a number of foam IOR scenarios in reservoirs including effects of reservoir heterogeneity [48] and anisotropy [49,50], the influence of surfactant migrating downward through a reservoir [51], and also the effect of an increase in injection pressure used to drive the foam along [52]. There is however a scenario that pressure-driven growth has not yet tackled successfully, namely a decrease in net driving pressure moving the foam along, net driving pressure here being the difference between an injection pressure and a pressure downstream of the displacing foam.…”

Section: Introductionmentioning

confidence: 99%

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

Eneotu

Grassia

2020

Proc. R. Soc. A.

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The pressure-driven growth model that describes the two-dimensional (2-D) propagation of a foam through an oil reservoir is considered as a model for surfactant-alternating-gas improved oil recovery. The model assumes a region of low mobility, finely textured foam at the foam front where injected gas meets liquid. The net pressure driving the foam is assumed to reduce suddenly at a specific time. Parts of the foam front, deep down near the bottom of the front, must then backtrack, reversing their flow direction. Equations for one-dimensional fractional flow, underlying 2-D pressure-driven growth, are solved via the method of characteristics. In a diagram of position versus time, the backtracking front has a complex double fan structure, with two distinct characteristic fans interacting. One of these characteristic fans is a reflection of a fan already present in forward flow mode. The second fan however only appears upon flow reversal. Both fans contribute to the flow’s Darcy pressure drop, the balance of the pressure drop shifting over time from the first fan to the second. The implications for 2-D pressure-driven growth are that the foam front has even lower mobility in reverse flow mode than it had in the original forward flow case.

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Pressure-driven growth in strongly heterogeneous systems

Grassia

2018

Eur. Phys. J. E

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Abstract. The pressure-driven growth model for advance of a foam front through an oil reservoir during foam improved oil recovery is considered: specifically the limit of strong heterogeneity in the reservoir permeability is treated, such that permeability variation with depth more than outweighs the tendency of the net pressure driving the front to decay with depth. This means that the fastest moving part of the front is not at the top of the solution domain, but rather somewhere in the interior. Moreover the location of the foam front on the top boundary of the system can no longer be specified as a boundary condition, but instead must be determined as part of the solution of the problem. Numerical solutions obtained from the pressure-driven growth model under these circumstances are compared with approximate analytic solutions. An early-time approximate solution is found to break down remarkably quickly (far more quickly than breakdown would occur in the analogous homogeneous system). Numerical solutions agree much better with local quasi-static solutions centred about local maxima in the front shape, each local maximum corresponding to a depth within the reservoir at which a high permeability stratum is found. These individual local solutions meet together at sharp concave corners to cover the entire depth of the foam front. As time continues to progress however, the system evolves towards a long-time, global quasistatic solution, corresponding to the fastest moving of the aforementioned local maxima. Additional key features of the predicted front shapes are elucidated. The foam front is found to meet the top boundary obliquely despite an established convention in pressure-driven growth that the front and top boundary should meet at right angles. In addition, at each sharp concave corner, discontinuous jumps are predicted in the path length that material points travel to reach either side of the corner. Moreover the long-time, global quasi-static solution is found to admit smooth concavities, as opposed to the aforementioned sharp concave corners, which only tend to be prominent earlier on.

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Foam front displacement in improved oil recovery in systems with anisotropic permeability

Cited by 3 publications

References 19 publications

Foam front advance during improved oil recovery: similarity solutions at early times near the top of the front

Foam front advance during improved oil recovery: similarity solutions at early times near the top of the front

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

Pressure-driven growth in strongly heterogeneous systems

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