Application of Least Squares and Kriging in Multivariate Optimization sof Field Development Scheduling and Well Placement Design


Yan Pan







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This study applied two multivariate interpolation algorithms, Least Squares and Kriging, to interpolate a limited number of data obtained from simulation in order to predict the optimal strategies in a field development scheduling project and a waterflood project with a significant reduction in the simulation efforts required.

The two projects were application examples with known answers. The objective of this study was to examine the feasibility and efficiency of multivariate interpolation in solving optimization problems by reducing the simulation effort required.

The net present value was used as the objective function in both projects. The field development scheduling simulation was achieved by an economic model taking acount of all the costs and profits during the time period being studied. The waterflooding simulation was achieved by solving the Laplace equation and generating streamlines within the specified pattern. The movements of the waterfront were tracked and then the oil and water production at each producer was calculated.

The results obtained by interpolation showed that the multivariate algorithms are able to provide a global sketch of the objective function surface, to avoid possible failure at local optima, and to reach the absolute optimum by refining the grids near the intermediate optimum. The approaches were shown to be practical techniques in optimization, and are likely to be useful in full scale problems in which simulation costs would be prohibitive for iterative nonlinear optimization methods.

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