Decline-curve analysis is a fairly straightforward method of predicting the future production of a well, using only the production history of that well. This type of analysis has a long tradition in the oil industry and remains one of the most common tools for forecasting oil and gas production.8–13 In general, there are two approaches to decline-curve analysis: (1) curve fitting the production data using one of three models developed by Arps8 and (2) type-curve matching using techniques developed by Fetkovich.10 We will present a brief introduction to the approach developed by Arps.
The notions of the transient time and pseudosteady-state time periods were discussed. The reader will recall that the transient time during the production life of a well refers to the time before the effects of the outer boundary has been felt by the producing fluid. The pseudosteady-state time period refers to the time that the effects of the outer boundary have been felt and that the reservoir pressure is dropping at a uniform rate throughout the drainage volume of the well. Theoretically, the approach by Arps requires that the producing well be in the pseudosteady-state time period both for the production period in which the engineer is attempting to model and for the future projected production life that the engineer is attempting to predict. Arps predicted that the production decline from a well would model one of three curves (exponential, hyperbolic, or harmonic decline) and could be represented by the following equation:
where
q = flow rate at time t
t = time
b = empirical constant derived from production data
d = Arps’s decline-curve exponent (exponential, d = 0; hyperbolic, 0 < d < 1; harmonic, d = 1)
Example 12.1 illustrates decline-curve analysis by considering the production from a well and assuming that the production data fit an exponential curve. The following steps are performed:
1. The production history of a given well is obtained and plotted against time.
2. An exponential line of the form q = qi* exp (–b*t) is fit to the data.
3. The equation is extrapolated to determine future production of the well.
Example 12.1 Determining the Production Forecast for Well 15-1 Using the Production History Shown in Fig. 12.1
Given
See the production history shown in Fig. 12.1.
Figure 12.1 Actual production and instantaneous GOR for history-matching problems.
Solution
Using Microsoft Excel, estimate the production and time from Fig. 12.1. Plot them in Excel and fit an exponential trend line to the data. Create a new table, adding values for time in excess of the production history, and calculate values for the flow rate based on the equation given by the trend line. Plot these values next to the actual data.
The reader can see the simplicity of decline-curve analysis in the solution of this problem. However, the engineer, in using this technique to predict future hydrocarbon recoveries, needs to be aware of the assumptions built into the approach—the main one being that the drainage area of the well will continue to perform as it had during the time that the history is attempting to be matched. Engineers, while continuing to use simple decline-curve analysis, are becoming increasingly aware that sophisticated models using mass and energy balance equations and computer modeling techniques are much more reliable when predicting reservoir performance.
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