Appraising Incremental Oil with Numerical Quadrature: A Simpson Rule and Trapezoidal Rule Approach

Abstract

Technically, the performance of any successful enhanced oil recovery
(EOR) project is given by the amount of incremental oil achieved from
it. This paper adapted the Simpson quadrature in predicting the
incremental oil from successful enhanced oil recovery processes. The
error term of the quadrature was accounted for using the Finite difference
approach, unlike in past works where it was neglected. This ensures that
the differential equations component of the error formulae was
adequately catered for numerically. This is important as the data
considered were not defined by a model, typical of field data.
Experimental data were used for the analyses. With the measured
Incremental oil values from the laboratory used as comparative
standards, results from the analyses showed that the Simpson quadrature
gives a better incremental oil estimation among the numerical quadrature
considered. This is lucid from the ‘‘error profile’’ plots for the two case
studies where the Simpson and Trapezoidal recorded 4.567% and 5.41%
for surfactant flooding and 5% and 18% for polymer flooding
respectively. The superiority of the Simpson rule in incremental oil can
be attributed to its adoption of higher order polynomial in modelling data
points.