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.*