The material balance equation derived in the previous section has been in general use for many years, mainly for the following:
1. Determining the initial hydrocarbon in place
2. Calculating water influx
3. Predicting reservoir pressures
Although in some cases it is possible to solve simultaneously to find the initial hydrocarbon and the water influx, generally one or the other must be known from data or methods that do not depend on the material balance calculations. One of the most important uses of the equations is predicting the effect of cumulative production and/or injection (gas or water) on reservoir pressure; therefore, it is very desirable to know in advance the initial oil and the ratio m from good core and log data. The presence of an aquifer is usually indicated by geologic evidence; however, the material balance may be used to detect the existence of a water drive by calculating the value of the initial hydrocarbon at successive production periods, assuming zero water influx. Unless other complicating factors are present, the constancy in the calculated value of N and/or G indicates a volumetric reservoir, and continually changing values of N and G indicate a water drive.
The precision of the calculated values depends on the accuracy of the data available to substitute in the equation and on the several assumptions that underlie the equations. One such assumption is the attainment of thermodynamic equilibrium in the reservoir, mainly between the oil and its solution gas. Wieland and Kennedy have found a tendency for the liquid phase to remain supersaturated with gas as the pressure declines.7 Saturation pressure discrepancies between fluid and core measurements and material balance evidence in the range of 19 psi for the East Texas Field and 25 psi for the Slaughter Field were observed. The effect of supersaturation causes reservoir pressure for a given volume of production to be lower than it otherwise would have been, had equilibrium been attained.
It is also implicitly assumed that the PVT data used in the material balance analyses are obtained using gas liberation processes that closely duplicate the gas liberation processes in the reservoir, in the well, and in separators on the surface. It is only stated here that PVT data based on gas liberation processes that vary widely from the actual reservoir development can cause considerable error in the material balance results and implications.
Another source of error is introduced in the determination of average reservoir pressure at the end of any production interval. Aside from instrument errors and those introduced by difficulties in obtaining true static or final buildup pressures there is often the problem of correctly weighting or averaging the individual well pressures. For thicker formations with higher permeabilities and oils of lower viscosities, where final buildup pressures are readily and accurately obtained and when there are only small pressure differences across the reservoir, reliable values of average reservoir pressure are easily obtained. On the other hand, for thinner formations of lower permeability and oils of higher viscosity, difficulties are met in obtaining accurate final buildup pressures, and there are often large pressure variations throughout the reservoir. These are commonly averaged by preparing isobaric maps superimposed on isopach maps. This method usually provides reliable results unless the measured well pressures are erratic and therefore cannot be accurately contoured. These differences may be due to variations in formation thickness and permeability and in well production and producing rates. Also, difficulties are encountered when production from two or more vertically isolated zones or strata of different productivity are commingled. In this case, the pressures are generally higher in the strata of low productivity, and because the measured pressures are nearer to those in the zones of high productivity, the measured static pressures tend to be lower and the reservoir behaves as if it contained less oil. Schilthuis explained this phenomenon by referring to the oil in the more productive zones as active oil and by observing that the calculated active oil usually increases with time because the oil and gas in the zones of lower productivity slowly expand to help offset the pressure decline. Uncertainties associated with assessing production from commingled reservoir zones motivate regulatory restrictions for this reservoir management strategy. Fields that are not fully developed may also show similar apparent increase in active oil production because the apparent average pressure can be that of the developed portion only while the pressure is actually higher in the undeveloped portions.
The effect of pressure errors on calculated values of initial oil or water influx depends on the size of the errors in relation to the reservoir pressure decline. This is true because pressure enters the material balance equation mainly as differences (Bo – Boi), (Rsi – Rs), and (Bg – Bgi). Because water influx and gas cap expansion tend to offset pressure decline, the pressure errors are more serious than for the undersaturated depletion reservoirs. In the case of very active water drives and gas caps that are large compared with the associated oil zone, the material balance is useless to determine the initial oil in place because of the very small pressure decline. Hutchinson emphasized the importance of obtaining accurate values of static well pressures in his quantitative study of the effect of data errors on the values of initial gas or of initial oil in volumetric gas or undersaturated oil reservoirs, respectively.8
Uncertainties in the ratio of the initial free gas volume to the initial reservoir oil volume also affect the calculations. The error introduced in the calculated values of initial oil, water influx, or pressure increases with the size of this ratio because, as explained in the previous paragraph, larger gas caps reduce the effect of pressure decline. For quite large gas caps relative to the oil zone, the material balance approaches a gas balance modified slightly by production from the oil zone. The value of m is obtained from core and log data used to determine the net productive bulk gas and oil volumes and their average porosities and interstitial water. Because there is frequently oil saturation in the gas cap, the oil zone must include this oil, which correspondingly diminishes the initial free gas volume. Well tests are often useful in locating gas-oil and water-oil contacts in the determination of m. In some cases, these contacts are not horizontal planes but are tilted, owing to water movement in the aquifer, or dish shaped, owing to the effect of capillarity in the less permeable boundary rocks of volumetric reservoirs.
Whereas the cumulative oil production is generally known quite precisely, the corresponding gas and water production is usually much less accurate and therefore introduces additional sources of errors. This is particularly true when the gas and water production is not directly measured but must be inferred from periodic tests to determine the gas-oil ratios and watercuts of the individual wells. When two or more wells completed in different reservoirs are producing to common storage, unless there are individual meters on the wells, only the aggregate production is known and not the individual oil production from each reservoir. Under the circumstances that exist in many fields, it is doubtful that the cumulative gas and water production is known to within 10%, and in some instances, the errors may be larger. With the growing importance of natural gas and because more of the gas associated with the oil is being sold, better values of gas production are becoming available.
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