Oil & Gas: Exponential Decline Model

The risk analysis model below examines the familiar production forecasting model for oil and gas
wells, the exponential decline curve. The standard equation, q = qie-at
(3.3), can be used with random variables for both qi (the
initial production rate, sometimes called IP) and a (the constant decline rate).
Here the model has an additional parameter, t (time), which makes the output
(Rate, STB/YR) more complicated than the volumetric reserves output.

No longer do we just want a distribution of numbers for output. Instead we
want a distribution of forecasts or graphs.  The worksheet has two input cells,
IP and Decline, and a column of outputs for the Rate of production in STB/YR
over 15 years.

After simulation you can generate a summary graph like that shown in the
model. This graph shows uncertainty over the 15 year period. The shaded region
represents one standard deviation on each side of the mean. The dotted curves
represent the 5th and 95th percentiles. Thus, between these dotted curves is a
90% confidence interval. We can think of the band as being made up of numerous
decline curves, each of which resulted from choices of qi and a.

» @RISK Example model: Band.xls

This example was taken from Decisions
Involving Uncertainty: An @RISK Tutorial for the Petroleum Industry
by James Murtha, published by Palisade Corporation, where a
detailed, step-by-step explanation can be found.

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