Fractional flow for reversed flow boundary condition in foam improved oil recovery (IOR)

Student thesis: Doctoral Thesis

Abstract

Due to the special flow properties of foam compared to those of conventional liquids and gases, injecting foam into oil reservoirs can be an excellent way of extracting the oil in place. This ability of foam as an efficient IOR mechanism is made possible by its tendency to cause a reduction in the mobility of the injected gas; consequently increasing the gas sweep efficiency. In addition, foam helps to suppress viscous fingering that conventional CO2 or gas injection could cause. In foam improved oil recovery (IOR), it is usually the dispersed gaseous phase (that is, gas within foam) that displaces the residual oil left behind by primary and secondary oil recovery methods. It is also possible to envisage a reverse case in which the liquid phase (partly oil, but usually containing a significant amount of water plus some surfactant), pushes invading fluid back; hence allowing for flow reversal. This could happen at depth on a foam front if, for example, the gas injection pressure declines or alternatively as a new injection well comes online downstream of the foam flow. In that situation, initially foam will be displacing water. Then at a certain time, flow reversal takes place. Thesimplest model for this is qt(t > tr) = −qt(t < tr); where 'tr' is the instant in time at which reversal takes place, 'qt' is total fluid flow rate and 't' is any arbitrary time other than 'tr'. Hence, foam displaces water up to 'tr', then water starts displacing foam for t > tr. This study is focused on how multiphase (i.e. foam and water) flow in porous media as described by the fractional flow model, behaves when this sort of reversal happens. Using the fractional flow model and the method of characteristics (MOC), this study has shown that during flow reversal, there is a shock - that is, a jump in water or liquid saturation 'Sw' between foamed gas with a small amount of water (downstream of the shock) and water with a small amount of foamed gas (upstream of it). The magnitude of the jump in water saturation at the shock grows over time. Depending on how quickly over time the water saturation 'Sw' decreases downstream of the shock and how quickly 'Sw' grows upstream of it, the speed of the shock (itself determined by a Rankine-Hugoniot condition or integral mass balance) is found to vary in different ways over time. Typically, the tendency is that the shock speed decreases with time, at least initially. The position of the shock can also be updated provided the speed is known. Moreover, once an updated position of the shock is specified at any instant in time, so called characteristic fans ahead of and behind it can be used to determine water saturations on either side of the shock. Characteristics are lines of constant liquid saturations in a distance-time plot, while fans are sets of characteristics with different liquid saturations spreading out from a point in the plot. Thus, it is possible to iterate between determining water saturations across the shock (based on intersections of characteristic lines at the current shock location) and determining (based on those saturations) how fast the shock moves at any given instant and where it will be at a later time. This study also suggests that during flow reversal in foam IOR, characteristics that start off behind the shock will collide with the shock as they move downstream, whilst the shock itself will collide with characteristics ahead of it. Ultimately, the overall solution to the foam IOR problem during flow reversal will depend on the interaction between the two characteristic fans. The solution for the propagating shock also makes it possible to contrast the mobility of the foam front during the forward and reverse flow stages.
Date of Award23 Aug 2021
Original languageEnglish
Awarding Institution
  • University Of Strathclyde
SponsorsUniversity of Strathclyde
SupervisorPaul Grassia (Supervisor) & Leo Lue (Supervisor)

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