An optimal viscosity profile in the secondary oil recovery

The secondary recovery process is a manner to produce oil from a porous medium, by displacing it with a second fluid (usually water). If the second fluid is less viscous, then the well-known Saffman-Taylor instability appears, producing the "fingering" phenomenon. An intermediate region with variable viscosity mu, containing a polymer mixed with water can be considered between water and oil. A Sturm-Liouville problem is obtained from the study of the linear stability of the straight initial interfaces between mixture and oil. The eigenvalues of this system are the growth constants sigma (in time) of the perturbations and may be controlled by mu. The surface tension due to the mixture water-polymer gives us a maximum value of sigma in terms of the wave numbers of the perturbations. In this paper the maximum value of sigma is minimized, by giving an explicit upper bound for a "minimizing" viscosity of the mixture water-polymer and also a lower bound for the "optimal" length of the intermediate region (injection length). This bounds are obtained in terms of the jump of the viscosity on the interface with the oil. In this way, an improvement of the stability is obtained. (C) Elsevier, Paris.