The basic mathematical models used to obtain the above
equations have a non-linear form. The presence of second order
terms in the Equations (4) and (5) are due to the correction of the
linear model and better consistency with non-linear mathematical
models.
The rates of oil production have been obtained from design of
experiments model and mathematical model and the results have
been plotted in Fig. 1 and Fig. 2.
As can be seen in Figs. 1 and 2 there is a linear relationship
between the results from design of experiment and mathematical
model versus actual data from field. However there is not a complete
consistency between the results in the mathematical model
and the design of experiment model. In other words, Fig. 1 shows
that in contrast to the very good and fitted results of mathematical
design model, the obtained results from design of experiment do
not totally match the mathematical model results. The reason for