This paper investigates the effects that rock and fluid properties impose on the production history of a well or lease as revealed by a decline curve. In particular, the effects on the constants of the exponential, hyperbolic, and harmonic decline curve equations are reported. An improved method is presented for analyzing production histories, with two field examples illustrating the method. Introduction The extrapolation of production decline curves to predict future oil production has a long history. The word "decline" is a misnomer; "decline curve" is a descriptive term for a graphical presentation of some aspect of the performance history of a well or lease. The graph may show a decline, an incline, or may remain flat. Through the years, the most commonly used decline curve, and the curve usually maintained by oil companies. is the production rate vs time curve plotted on semilog graph paper.The analysis of a decline curve provides two important items of information:the remaining oil and gas reserves to be expected, andthe remaining productive life of a well or lease. In addition, an explanation of any anomalies that appear on the graph is also useful. In recent years, it has been increasingly important to determine the combination of these items so that an accurate yearly estimate of future production can be made. This information is obtained by an analysis of the past performance as shown on the production rate vs time curve. The curve then is extrapolated into the future, and estimated future yearly production is taken from the extrapolated portion of the curve. Decline Curve Analysis Problems Three basic problems associated with the extrapolation process are connected with the historical development of decline curve analysis and have been considered basic assumptions since being defined by Arps. These assumptions are as follow.1. The extrapolation procedure is strictly empirical, and a mathematical expression of the curve based on physical considerations can be set up only for a few simple cases.2. Whatever causes governed the trend of a curve in the past will continue to govern its trend in the future in a uniform manner.3. The decline exponent b in the equations developed by Arps (Table 1) must have a value of 0.0 less than b less than 1.0.Because of empirical extrapolation, a decline curve usually will have a wide range of interpretations. The range of interpretations depends on the production stage of the property. If there is limited prior production history (i.e., a new well), there is a wider range of interpretations possible than for a well or property in the stripper stage of production. Also, each specific interpretation is a function of the experience, integrity, and objective of the evaluating engineer.Various controllable and uncontrollable influences or causes govern the production performance of a well or lease. Some of these influences are as follow. Controllable1. Prorated production.2. Remedial work on producing wells.3. Fluid or gas injection into the producing reservoir.4. Production problems, shutdowns, etc.5. Problems with scale, paraffin, etc.6. Limitations of producing equipment.7. Changes in operating personnel. JPT P. 1327^

This paper explains a simple and effective method for graphically solving all three types of production decline. The three types of declines are:exponentialhyperbolic, andharmonic. The mathematical development of these curves was by Arps. Decline curves are one of the most extensively used forms of data analysis employed in the evaluation of oil properties. Often future production is extrapolated as a straight line on semilog paper (exponential or constant-percentage decline) because this type of decline is the easiest to handle mathematically and graphical. This is done irrespective of the fact that several investigators have reported that this type of decline is rare and that actual oil production usually follows a hyperbolic decline. production usually follows a hyperbolic decline. However, the hyperbolic decline is difficult to analyze mathematically or graphically. The most recent method utilizes transparencies, as proposed by Slider. The method outlined below greatly simplifies the solution and extrapolation of decline curves. The first four columns of Table 1 list the rate:time and cumulative-production:rate relationships as developed by Arps. The equations are all solutions of the differential equation D = Kq = - (dq/dt)/q. In each instance two unknowns must be calculated from the two relationships. They are the decline exponent n and the initial decline rate Di. The third unknown, qi, can be obtained from the production history of the well. First. the rate:time relationship is manipulated to solve for the value of Dit in terms of the ratio (qi/qt). These relationships are shown in Column 5 of Table 1. Next, the rate:time relationship is solved for Di, and this value of Di is substituted into the cumulative-production:rate relationship. This relationship is then solved for the value of Qt/(qit) in terms of (qi/qt), These relationships are shown in Column 6 of Table 1. Two graphs can then be constructed by selecting a value for n and then substituting values of (qi/qt into the relationships. A curve on each graph for the selected value of n will be produced. This can be done for any desired number of n values from 0 n 1. (See Figs. 1 and 2.) These curves can then be used to analyze and extrapolate decline curves from actual production history. P. 38

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