The Material Balance as an Equation of a Straight Line—Part II, Field Cases
Authors: Havlena D. , Odeh A.S. 
Published: December 2007

ABSTRACT
The use of the straight-line method of solving the material balance equation is illustrated by means of six field cases. Also, the application of statistical criteria to arrive at the most probable answer is shown. The theory underlying the straight-line method of solution and the applicability of the statistical criteria was presented in a previous paper.1
The field cases include saturated and undersaturated oil reservoirs with and without water drive. The aquifers discussed are: limited radial, infinite radial, very small aquifer and infinite linear. The field cases also include a gas reservoir producing under water drive.
INTRODUCTION
In a previous paper,1 the authors presented the theory underlying the solution of the material balance as an equation of a straight line. The appropriate equations for various material balance cases as well as the methods of analysis and interpretation with comments and discussion were also included.
To illustrate the various theoretical cases treated previously, five field cases are analyzed in this paper by employing the straight-line method of solving the material balance equation (MBE) and one example previously published is referred to. The use of statistical criteria to arrive at the most probable answer is also shown.
All the field examples presented, except Case 2, are excerpts from complete reservoir studies. To illustrate the method, only sections specifically dealing with the material balance principles are included. Additional geologic information and basic data are reported to better acquire an understanding of the cases and thus to better follow the reasoning that suggested the successful application of the straight-line method of solving the MBE. The six cases are:
saturated reservoir, small gas cap, limited aquifer; saturated reservoir, very small gas cap, infinite aquifer; undersaturated-saturated reservoir, very small aquifer; highly undersaturated reservoir, no water drive; high undersaturated one-well reservoir, limited aquifer; and gas reservoir, infinite linear aquifer.
WATER DRIVE, A KNOWN GAS CAP
THE D4 SAND. GUICO FIELD, VENEZUELA
The D4 sand, which was discovered in 1943, is presented in a depleted state. Since its discovery it has produced under water drive, gas-cap-gas expansion, and solution gas drive. In Nov., 1947, water injection was initiated to arrest further pressure decline.
When discovered, the D4 sand was a saturated reservoir with a gas cap/oil zone volume ratio m estimated volumetrically at 0.0731, an average permeability of 500 md, a porosity value of 25 per cent, and an oil viscosity at reservoir conditions of 0.3 cp. The volumetrically determined stock-tank oil initially in place was 23.1 million bbl. The volumetrically weighted physical data and production data available until Nov., 1953 are reported in Table 1.
In Ref. 1, the effects on the straight-line plot of various values of re/rw for a constant ?tD, or of various dimensionless times for a constant re/rw, were theorized and were illustrated in Fig. 3A of that reference. In this field case, the previously theoretically predicted effects are established. Thus, the MBE calculations using Eq. 3c of Ref. 1 were performed for various re/rw and dimensionless time values. Eq. 3c of Ref. 1 is:
Equation
where F=net production in reservoir barrels, Eo=Bt-Btt, and the other symbols conform to AIME standards.
THE D4 SAND. GUICO FIELD, VENEZUELA
The D4 sand, which was discovered in 1943, is presented in a depleted state. Since its discovery it has produced under water drive, gas-cap-gas expansion, and solution gas drive. In Nov., 1947, water injection was initiated to arrest further pressure decline.
When discovered, the D4 sand was a saturated reservoir with a gas cap/oil zone volume ratio m estimated volumetrically at 0.0731, an average permeability of 500 md, a porosity value of 25 per cent, and an oil viscosity at reservoir conditions of 0.3 cp. The volumetrically determined stock-tank oil initially in place was 23.1 million bbl. The volumetrically weighted physical data and production data available until Nov., 1953 are reported in Table 1.
In Ref. 1, the effects on the straight-line plot of various values of re/rw for a constant ?tD, or of various dimensionless times for a constant re/rw, were theorized and were illustrated in Fig. 3A of that reference. In this field case, the previously theoretically predicted effects are established. Thus, the MBE calculations using Eq. 3c of Ref. 1 were performed for various re/rw and dimensionless time values. Eq. 3c of Ref. 1 is:
Equation
where F=net production in reservoir barrels, Eo=Bt-Btt, and the other symbols conform to AIME standards.