# DECLINE CURVES IN THE ESTIMATE OF OIL AND GAS RESERVES

Translation of Chapter 25 of the Book of Charles E. Webber – Manual of Petroleum Exploration.

The study of the decline curves are one of the oldest of the various methods of estimating oil and gas reserves. This presents a pictorial history of the records produced from a well, group of wells or reservoir. Before the coming of the distribution, free and uninterrupted production of both gas and oil wells during its early life, can trace a curve that could be extrapolated into the future and serve as a basis for forecasts of productivity and reserves. Today, the decline curves are less useful. Generally the production is distributed in proportion to market demand. The invasion of water in many fields helps maintain reservoir pressure and production is often shortened to facilitate this process. The decline curve mean little until some time has elapsed to establish a definite trend of decline or a radio. If this trend can be established early in the life of the reservoir, exploration geologists and engineers can exploit the same methods for estimating reserves. If many years elapse before such a trend develops, the men of exploration are likely to be separated from the enterprise to the field and will be turned over by engineers reservoristas.

In estimating reserves, the most suitable type of graph is a plot of radio production, ie, barrels per day vs average. Cumulative production. Extrapolating the line to a point of «non-economic return» gives a direct reading of all the latest cumulative production. This becomes recoverable reserves. In all cases the goal is to select graphic scales that will result in almost a straight line possible. Obviously these results are more accurate extrapolations.

There are three types of decline curves, each can be represented by mathematical formulas. (Arps, 1956).

1. Constant percentage decline: The decline in productivity is a constant percentage as a function of time. For example, the beginning of the first year of life of the reservoir is produced on average 1000 barrels per day, at the end of this first year will produce 900 barrels per day and end of the second year will produce 810 barrels a day. These reservoirs decreased by 10% annually. The decrease in average radius curve versus cumulative production is straight graph paper.

2. Hyperbolic decline: The decline in output is proportional to a full rate production. This type of decline with average production radius versus cumulative production plot allows a straight line in a log-log paper. Any change in the scale goes right over the graph.

3. Hyperbolic decline: The decline in output is proportional to a radio production. This type of decline where the average production radius is plotted as a function of cumulative production is straightened in a semi-log paper. The radio production is plotted on a logarithmic scale and cumulative production on a regular coordinate.

Figure 25.5 shows how the decline appear when data is plotted as usual. The radio current average daily production for a small oil field is plotted on three types of graphic scales. The decline rate that is harmonious, and the straight line extrapolation on a graph paper indicates a reserve of approximately 7 million barrels. It is obvious that the other two curves could not be extrapolated with little accuracy.

Until now the subject of the decline curve has been treated based on production vs. radio. Cumulative production. Although this type of curves extrapolated directly recoverable reserves, it does not reveal anything about the productive life of the reservoir and does not always indicate a need for some means of increasing production, such as maintaining pressure or water flow . None of this data reveals about the profitability of the project. There are several different types of curves for these purposes which also provides information on reservations. Some examples will be mentioned briefly. Vs production. Extrapolation of time to show the final productive life and anticipate production radios for years to come. Strokes vs. drawdown. Time indicator whether the pressure maintenance is required or not, vs production radios. income or gain may result in estimates of reserves based on economic factors. In all cases it is convenient to plot the data, whatever it is, for q the trend is a straight line for extrapolation. Excellent detailed topics of these additional types of curves and their interpretations have been published. (Clark, 1951, Menzie, 1953).

FIGURE 25-5. Production decline with information plotted in three types of graph.