A Volumetric-Balance Applicable to the Spectrum of Reservoir Oils From Black Oils Through High Volatile Oils
Authors: Brinkley T.W. 
Published: December 2007

Abstract
The proposed equations are consistent with the law of conservation of matter, and represent a volumetric balance on a reservoir oil bubble-point basis. Mathematically, the equations permit the incorporation of flash-liberation characteristics on all produced fluids and differential-liberation characteristics on remaining reservoir fluids. Although flash - liberation and differential - liberation characteristics are formally stated, deviation from these liberation procedures (such as constant-volume technique in lieu of differential technique) can be incorporated in the equations. The proposed equations permit definition of natural depletion performance for closed reservoirs and are applicable to open reservoirs, i.e., those connected with aquifers. Original volume of bubble-point oil (oil-hydrocarbon pore volume) as well as relative permeability ratios (kg/ko) and reservoir oil and gas saturations can be defined from past reservoir pressure-production information. Laboratory-determined PVT characteristics, along with corresponding solution-gas content and viscosity, all vs pressure are necessary for the use of the equations. The equations are suitable for desk-type calculators or electronic computers. Consistent with other volumetric material-balance procedures, they are solved by trial methods.

Introduction
All material-balance principles are based upon the theory of the law of conservation of matter; i.e., in a hydrocarbon system such as a productive reservoir, all hydrocarbons must be accounted for at all times. This may be stated very simply as follows.
(Original Hydrocarbons) = (Remaining Hydrocarbons)+ (Produced Hydrocarbons)...................(1)
This basic equation may be solved on a weight basis (molal-balance) or on a volume basis (volumetric-balance), or a combination of the two. The volumetric-balance approach permits the basic Eq. 1 to be written on a constant reservoir volume basis, as follows.
(Reservoir Volume of Original Hydrocarbons) =(Reservoir Volume of Remaining Hydrocarbons)....(2)
When the reservoir is geologically open (i.e., the hydrocarbon accumulation is in communication with an aquifer), then provision for water encroachment will modify Eq. 2 for the following volumetric balance.
(Reservoir Volume of Original Hydrocarbons) =(Reservoir Volume of Remaining Hydrocarbons) +(Reservoir Volume of Net Water Encroachment)....(3)
The application of these basic equations, of course, is dependent upon the conversion of reservoir fluids between reservoir and surface conditions consistent with the original intent of the equations as previously published. No particular problems are encountered in applying the volumetric-balance equations when the flash-liberation and differential-liberation fluid behaviors are the same; some reservoir oils closely approach these conditions and generally are referred to as "black oils". In contrast, the use of such equations in the volatile-oil range, without proper conversion of surface produced volumes of gas and liquids back to definitive reservoir production, will lead to non-representative reservoir performance calculations. The problem, therefore, is how to calculate representative reservoir performance when there is a difference between flash-liberation and differential-liberation fluid behavior. One approach presented in several published papers incorporates the molal-balance Eq. 1 together with the volumetric-balance Eq. 2 as follows.

Molal Balance
(Original Hydrocarbons in Place) - (Produced Hydrocarbons)= (Remaining Hydrocarbons) ......................(4)

Volumetric Balance
(Reservoir Volume of Remaining Hydrocarbons) =(Reservoir Volume of Original Hydrocarbons)......(5)
Thus this method incorporates Eqs. 4 and 5 as a combination molal-balance and volumetric-balance technique. The method is recognized as fundamental; however, definitions of hydrocarbon densities as well as equilibrium ratio (K = y/x) at elevated pressures and temperatures are subject to extensive laboratory testing.
JPT
P. 589^