Knowledge of the theory underlying the behavior of mixtures of fluids inreservoir rocks is essential to the proper solution of certain types ofproblems in petroleum production, but is as yet incompletely developed. Theobject of this paper is to show the application of well establishedthermodynamic and physical principles to these problems, and thus to assist inthe development of the basic theory. For convenience the problems to beconsidered here may be divided into two groups:

  1. Static problems, involving only the static balance between capillary forcesand those due to the difference in densities of the fluids; i.e., gravitationalforces.

  2. Dynamic problems, involving analysis of the motion of mixtures of immisciblefluids in porous media under the influence of forces due to gravity, capillarity, and an impressed external pressure differential.

Capillary Equilibrium in Sands

Under this heading the static type of problem will be discussed and the resultsof experimental investigations on the capillary properties of unconsolidatedsands will be presented. Although the discussion of this section is, in asense, prefatory to the treatment of problems of mixture flow, the conceptsdeveloped here have considerable intrinsic importance apart from theirapplication to flow problems. For, it is reasonable to postulate that thereservoir fluids are, owing to their long existence in undisturbed mutualcontact prior to exploitation, in substantial equilibrium. It follows thattheir distribution in the reservoir at the time of tapping should be entirelypredictable from the theory of capillary equilibrium, provided certainexperimentally measurable properties of the reservoir rock are known. Knowledgeof the distribution of the several fluids in the reservoir is, of course, helpful in the estimation of reserve, and in other problems.

It is to be emphasized that throughout the discussion of capillary statics itis assumed that the fluids are in equilibrium from the capillary standpoint.Thus, water, where it is referred to as being in a reservoir, will beunderstood to be interstitial water, present at the time of drilling thereservoir, commonly termed "connate" water.

The theory developed here is perfectly general for any porous solid, whether acarefully prepared unconsolidated sand or a natural sandstone from an oilreservoir. At present, however, only problems involving clean, unconsolidatedsands can be made to yield numerical solutions, since only such sands have beenadequately investigated experimentally. Experimental evaluation of thepertinent properties of natural reservoir rocks will permit the extension ofthe numerical treatment to problems involving these materials. We shall nowconsider in some detail the static equilibrium of fluid mixtures in poroussolids; that is, the manner in which the reservoir fluids are distributedvertically when the forces due to capillarity are just balanced by those due togravitation.

T.P. 1223

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