Disproportionate Permeability Reduction is not a Panacea
Authors: Stavland A. , Ekrann S. , Hettervik K.O. , Jakobsen S.R. , Schmidt T. , Schilling B. 
Published: December 2007

Abstract
The paper discusses experimental and theoretical studies on the effects of disproportionate permeability reduction (DPR), i.e., the ability to reduce relative permeability to water more than to oil. The theoretical part discusses DPR effects by simple analytical arguments, supported by simulations. DPR causes build-up of water saturation in the treated zone to accommodate the water/oil ratio delivered by the reservoir. Core flooding experiments were also carried out, with a DPR gel placed in one half of the core. There is excellent agreement between theory and core flooding results. It was observed that the water saturation in the treated zone increased. Saturation profiles were measured using a CT scanner and is well matched by simulation.

Introduction
Increasing water production is a growing concern for the maturing North Sea fields. The need for near-wellbore treatments, with the aim to reduce excess water production without sacrificing oil production, has focused on the use of polymer gel systems reported to reduce the permeability to water much more than the permeability to oil. Particularly in wells where water and oil is being produced from the same zone so that the water bearing zones cannot easily be isolated. Homogeneous reservoir formations with significant oil and water production, or reservoirs with significant crossflow between layers are strong candidates for simpler placement procedures i.e., non selective or bullheading, that will lead to significant savings in time and cost for the well treatment.
Polymer and gel have been reported to reduce the relative permeability to water more than the relative permeability to oil. Similarly, foam in porous media is known to reduce relative permeability to gas much more than to water or oil. Such chemicals are referred to as disproportionate permeability reducers or relative permeability modifiers. The literature claims that since the permeability to oil is little influenced, water from watered out zones is held back and thereby the oil production may increase.
The paper discusses the effects of placing such chemicals in the immediate vicinity of a production well. Our concern is the effect of DPR treatments on fluid flow patterns in the reservoir and not the mechanisms actually bringing about DPR. The aim of this paper, is through simple theoretical considerations supported by core flooding experiment and simulations, to understand when, and why, DPR treatment may, or may not reduce excessive water or gas production.
The reasons why some polymers and gels gives DPR are not yet fully understood. In the literature polymer adsorption, gel syneresis and swelling and segregated pathways for oil and water are among the suggested mechanisms. Here, the details of DPR are not important. The essential is the disproportionate reduction of water or gas mobility, by whatever mechanism.
Saturation build-up in treated zone
Consider single layer oil production by water (or gas) flooding, see Fig. 1. Gravity and capillarity are neglected. Capillary effects are less important the larger the spatial scale under consideration, and known to be negligible on the reservoir scale. Even in the well region, such effects are generally unimportant due to the dominance of viscous forces caused by the high flow velocities. Gravity effects, on the other hand, may sometimes be quite important in coning-type situations, as discussed later.
Basic mechanisms, one dimension. The remaining oil saturation at breakthrough of water may be quite large, depending on fluid/rock properties. P. 483^