Imbibition Relative Permeability in Unconsolidated Porous Media
Authors: Naar J. , Wygal R.J. , Henderson J.H. 
Published: December 2007

Abstract
Experimental work is reported which shows that consolidated rocks and unconsolidated porous media exhibit different imbibition flow behavior. At a given saturation the imbibition nonwetting permeabilities for a rock are smaller than the drainage permeabilities. The contrary happens for unconsolidated aggregates - imbibition nonwetting permeabilities are larger than drainage ones. A similar difference is observed for the wetting phase. Imbibition permeabilities are larger than drainage ones for a consolidated rock but smaller than drainage permeabilities for an unconsolidated medium. The results of these differences are examined for two cases.Flooding Efficiency - Craig's scheme for the computation of production history of a five-spot water flood is shown to agree extremely well with experimental results obtained when using a system packed with glass spheres if imbibition relative permeability curves are used.Alcohol-Slug Displacement - Published theory on oil displacement by alcohol slugs bas been questioned despite the apparent agreement between predicted and observed results.
The present work suggests that, if imbibition relative permeability curves characteristic of the unconsolidated media used in the early experiments had been available to make the predictions, the inadequacy of the theory would have been immediately evident. The experimental work shows that poorly consolidated formations tend to behave like unconsolidated media. Finally, it is shown that the difference in imbibition behavior is directly related to pore-size distribution and cementation.

PART 1 - THE FLOW BEHAVIOR OF UNCONSOLIDATED AGGREGATES

Introduction
Experiments on scaled models of field reservoirs are useful for studying new displacement processes which are incompletely understood. Even when a mathematical description is possible, the solution might be difficult and complex. An answer obtained from a scaled model is extremely valuable in such cases. A great amount of work, therefore, has been devoted to the derivation of scaling laws. Similarity groups have been defined which assumethat the relative permeability curves of the prototype and the model are the same whether the displacement is an imbibition or a drainage process andthat there is a linear relationship between the capillary pressure of the model and the prototype.
For practical reasons (simplicity in the preparation of models, duration of the experiments, etc.), the porous media of laboratory models are usually unconsolidated packs of sand or glass particles. Hence, unless the capillary and flow characteristics of unconsolidated and consolidated systems are identical, the model data are applicable only to unconsolidated formations. The usefulness of scaled-model studies may then be seriously restricted since most oil-bearing sands are consolidated. Perkins and Collins suggested the use of model and prototype curves normalized with respect to both relative permeability and saturation to improve compliance with scaling criteria. Even this technique does not give a satisfactory model-prototype match. This paper reports an observation of two-phase flow in unconsolidated sands which shows that, for most displacements, "scaling" in the strict sense of the word is not even qualitatively feasible with a sand model. It provides, however, a firm foundation for testing a theory by matching it with observed performance of laboratory-size models.

EXPERIMENTAL
As a part of a basic study of packed aggregates, the relative permeability of glass-spheres and sand-grain packs was measured with capillary control. The fluids were oil and air.
SPEJ