TIPS TRICKS AND TRAPS OF MATERIAL BALANCE CALCULATIONS M.R. CARLSON
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Tips, Tricks and Traps of Material Balance Calculations M.R. Carlson Applied Reservoir Engineering Ltd. Abstract The author has encountered a number of situations where drastically different interpretations are possible from oil material balances. The paper focusses on two of these field situations. In the first case, a gas cap could be interpreted which subsequent analysis disproved. In the second case, regression techniques converged to a total of three different combinations of gas cap and oil leg sizes. The existence of multiple solutions was not readily apparent. The discussion is approached from three different perspectives, which are referenced to the two different field examples: 1. How production, geological, PVT (oil, gas and water) and historical information may be used to screen results and to apply the mathematical technique. 2. A new mathematical approach to error analysis for the Havlena and Odeh material balance has been developed, which the author has not seen elsewhere in the literature. Additionally, graphical interpretation can identify situations where multiple interpretations are likely. 3. A spreadsheet has been used to implement the Havlena and Odeh material balance. Using some simple macros it is possible to quickly generate all of the diagnostic plots. This is a cost effective alternative to purchase of a specialty program. Aquifers are also included as well as statistical regression. Convergence is demonstrated as a criteria for confidence in material balance calculations. The new interpretations were significant. In the first case, it was an important factor in deciding to proceed with a string of successful workovers designed to recover attic oil. In the second case, the new interpretation cut short a field extension drilling program which was resulting in unexpected dry holes. Introduction This paper is based on half a dozen material balance studies that the author has prepared on a consulting basis. Four were for carbonate reservoirs and two were for sandstone reservoirs. The contents are based on this experience and thus represent a mixture of field case, theoretical analysis (developed during projects) and an evolving approach to material balance calculations. Two examples are given, however, they represent the combined experience on all of the above reservoirs. Scales have, for the most part, been removed; since the data is from actual studies. The paper has been structured as follows: 1. A quick summary is made of the material balance equations. These are used for the derivation of the error analysis. No derivation of the equations was made since this is comprehensively covered in many reservoir engineering textbooks. A summary of the various Havlena and Odeh plots is also made, since this material is discussed in the paper. 2. An analysis of the effects of errors in pressure measurement is presented. The author uses this for weighting data points. 3. Some practical observations are made on statistical minimization. 4. The general approach used by the author is outlined. 5. Two typical material balance situations are described, which highlight error analysis and data screening. The paper differs slightly from the norm for a technical paper. The conclusions+ are presented as -tips+ and -traps+ since, in many cases, they represent matters of style. For instance, the author chooses to keep some pressure points based on his error analysis, where others might choose to use this (or similar) analysis to weight each point individually. Material Balance Equation The author prefers the method of Havlena and Odeh. Although favoured for its graphical interpretation, it also forces one to think in terms of reservoir conditions, a major benefit. The Havlena and Odeh material balance equation is as follows: (1) The above terms are expanded upon as follows: (2) (3) (4) (5) These symbols are in fairly common usage and may also be found at the end of this paper under Nomenclature.
II Tips, Tricks and Traps of Material Balance Calculations M.R. CARLSON Applied Reservoir Engineering Ltd.
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hensively covered in many reservoir engineering textbooks. A summary of the various Havlena and Odeh plots is also I' , ' ',' ,,'. 1 made, since this material is discussed in the paper. , The author has encountered a number of situations wherel 2. An analysis of the effects of errors in pressure measurement drastically different interpieta~ons 'are possible from oil material is presented. The author uses this for weighting data points. balances. The, paper focusses on;two ,of these field situations. In the first case, a gas cap could be'interpreted which subsequentl 3. Some practical observations are made on statistical minit analysis disproved. In the second case,- regression techniques I mization. converged to a tot,al of ~~e different combinations of gas cap 4. The general approach used by the author is outlined. and oil leg sizes. The 'existence ofmultiple: solutiqns.was not, 5. Two typical material balance situations are described, which !readily apparent. " . '.' . .": .:::;,~.' <' " highlight error analysis and data screening. ! The discussion is approached froii-t three diffeient;'piis~ec~~ The paper differs slightly from the nonn for a technical paper. tives, which are re~erenced to ~he'tW9 diffe~entfiel(ft
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on half a dozen material balance studies that the author has prepared on a consulting basis. Four were for carbonate reservoirs and two were for sandstone reservoirs. The contents are based on this experience and thus represent a mixture of field case, theoretical analysis (developed during projects) and an evolving approach to material balance calculations. Two examples are given, however, they represent the combined experience on all of the above reservoirs. Scales have, for the most part, been removed; since the data is from actual studies. The paper has been structured as follows: 1. A quick summary is made of the material balance equations. These are used for the derivation of the error analysis. No derivation of the equations was made since this is compre-
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These symbols are in fairly common usage and may also be found at the end of this paper under Nomenclature. The Journal of Canadian Petroleum Technology
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Graphical Interpretation /
This form of the equation can be interpreted graphically in a number of different ways(l). The fIrst is for a solution gas drive in which there is no gas cap nor any water influx:
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Re-arranging we get:
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F:=N Eo If F is plotted against Eo, a straight line of slope N is obtained. For a reservoir with gas cap and solution gas drive the following combination may be plotted:
F
Dividing by the drive indices term yields.
a[Eo+mEg+EjW]
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aN ap ap = [Eo + m Eg + E
This will yield a straight line plot with a slope of mN and an intercept of N, the original oil-in-place. For reservoirs that have water influx:
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N
[Eo + mEg + EjW]
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Then dividing through by N,
aF F
1
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ap
Nap:= N[Eo+mEg+EJ-.] which yields a straight line with a slope of Bw and an intercept of
N.
Substituting the Right Hand Side "RHS" of Equation (1) for the LHS in the fIrst term of the RHS of the above equation,
Aquifer Mathematical Technique 'The author has used the approximate water influx theory of Fetkovitch for fInite aquifers in all of the cases described. The method is not quite as accurate as the Van Everdingen and Hurst technique. The largest error is during early times, as demonstrated in the example calculation outlined in Dake(2). In general, this error is not signifIcant.
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--:=
1 aF F ap .............................................(6)
This is a handy form since it shows the change in aOlP is related to the percentage change in underground withdrawals and drive indices.
Error Analysis In this section, the accuracy and precision of the material balance calculation are examined. There will be two parts to the discussion. The fIrst describes sensitivity to pressure measurements and the second describes sensitivities to values of m. The fIrst step is differentiating Equation (1) with respect to the pressure. Note that the water term has been excluded from this analysis. Using the product rule:
PVT Data Almost all the variables (Eo, Eg , and E fw ) are functions of pressure. In order to solve this problem it is necessary to make some simplifying assumptions regarding PVT properties. Based on the author's experience on data from numerous studies, black oil PVT data can usually be reasonably approximated by straight lines.
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FIGURE 1: PVT data used in error analysis.
December 1997, Volume 36, No. 11
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FIGURE 2: PVT data used in error analysis.
.,~ 35
