Abstract
We present an analytical solution to estimate the minimum polymer slug size needed to ensure that viscous fingering of chase water does not cause its breakdown during secondary oil recovery. Polymer flooding is typically used to improve oil recovery from more viscous oil reservoirs. The polymer is injected as a slug followed by chase water to reduce costs; however, the water is less viscous than the oil. This can result in miscible viscous fingering of the water into the polymer, breaking down the slug and reducing recovery. The solution assumes that the average effect of fingering can be represented by the empirical Todd and Longstaff model. The analytical calculation of minimum slug size is compared against numerical solutions using the Todd and Longstaff model as well as high resolution first contact miscible simulation of the fingering. The ability to rapidly determine the minimum polymer slug size is potentially very useful during enhanced oil recovery (EOR) screening studies.
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Acknowledgements
We thank Bilal Rashid for help with modifying the detailed viscous fingering code and advice on postprocessing. We also thank Schlumberger for providing the ECLIPSE software and the Malaysian Government for funding S.A. Abdul Hamid’s PhD.
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Appendices
Appendix A
In this appendix we derive the conservation equations for the water phase and the polymer solution. Consider the conservation of mass for the water phase in one dimension
where we have assumed that water is incompressible. We define the fractional flow F w of the water phase as
where v t is the sum of aqueous and hydrocarbon phase velocities, v t = v w + v h . Substituting (A.2) into (A.1), we then have
Similarly, the conservation of the polymer component C p in the water phase is given by
where v p is the velocity of the polymer component. We can also define the fractional flow of polymer component in the water phase as
We can therefore rewrite (A.4) as
In the absence of fingering then the fractional flow of the polymer solution is simply the dimensionless concentration of the polymer in the water phase, C p , as the polymer solution is first contact miscible with the injected chase water. In the presence of viscous fingering, the average fractional flow f p can be described using the Todd-Longstaff formulation in Eq. 18. A plot of f p as a function of C p for μ p /μ w of 50 is shown in Fig. 14. Note that for ω = 1, we have f p = C p which models a fully-mixed, piston-like displacement.
Appendix B
We present here the estimation of the minimum slug required in order to maintain its integrity. Recall that the slug front travels at velocity v2 = F2S2 and it arrives at the production well when x2 = 1, hence
With no fingering, the back of the slug will have approximately the same velocity as the slug front (as discussed in Section 3.1) so v3 = v2. Hence, we have
To take the fingering into account, we multiply x3 in (B.2) by df p /dC p . The fastest wave occurs when C p = 1, shown as the upper blue line in Fig. 5. At the production well, we have
The minimum slug size needed to ensure that the chase water fingers only just cross the polymer slug by the time the polymer breaks through is found by substituting (B.1) into (B.3)
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Abdul Hamid, S.A., Muggeridge, A.H. Analytical solution of polymer slug injection with viscous fingering. Comput Geosci 22, 711–723 (2018). https://doi.org/10.1007/s10596-018-9721-0
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DOI: https://doi.org/10.1007/s10596-018-9721-0