Page 204 - Principles of Applied Reservoir Simulation 2E

Pan II: Reservoir Simulation 189

context refers to a potential "change in assets associated with some chance
occurrences." Risk analysis generates probabilities associated with changes of
model input parameters. The parameter changes must be contained within ranges
that are typically determined by the range of available data, information from
analogous fields, and the experience of the modeling team. Each model run using
a complete set of model input parameters constitutes a trial. A large number of
trials can be used to generate probability distributions. Alternatively, the results
of the trials can be used in a multivariable regression analysis to generate
analytical expressions, as described below.
One of the most widely used techniques for studying model sensitivity
to input parameter changes is to modify model input parameters in the history
matched model. The following procedure combines multivariable regression and
the results of model trials to generate an analytical expression for quantifying
the effect of changing model parameters.
Assume a dependent variable F has the form

F = K n Xj J
j*\

where {Xj} are n independent variables and K is a proportionality constant that
depends on the units of the independent variables. Examples of Xj are well
separation, saturation end points, and aquifer strength. Taking the logarithm of
the defining equation for F linearizes the function F and makes it suitable for
multivariable regression analysis, thus

InF = InK + £ e /m X j
7 = 1
A sensitivity model is constructed using the following procedure:
4 Run a model with different values of {Xj}
4 Obtain values of F for each set of values of {Xj}
The constants K, {e-\ are obtained by performing a multivariable regression
analysis using values of F calculated from the model runs as a function of {Xj} .
In addition to quantifying behavior, the regression procedure provides
an estimate of fractional change of the dependent variable F when we make