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Abstract
In this article, a new intelligent approach has been developed to modify relative permeability, absolute permeability, well skin factor, and end points saturation properties around the wells and within the specified uncertainty range of history matching of an Iranian field. This field is a highly faulted under-saturated oil reservoir with a long production history from 1968 with serious water production problems with some of its wells. The proposed technique, supervised genetic algorithm for history matching, combines the advantage of detecting and analyzing well-by-well production history data with the advantages of genetic algorithm for final optimization. The supervised genetic algorithm for history matching uses the results of perturbation runs in the preprocessing stage and genetic algorithm local optimization in the last stages for faster and more accurate prediction of genetic algorithm variables during optimization. Separate variables are considered for every layer in each well. It is shown that good estimation of selected variables can be obtained (based on the assumptions of optimization) by integration of the observed oil rate, water cut, and bottom-hole pressure of the production wells. The newly developed method (supervised genetic algorithm for history matching) uses a well-by-well diagnostic engine and conditions these results to genetic algorithm workflow with no need for calculation of the objective function in gradient mode usually performed in classical history matching methods.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the Petroleum Engineering and Development Company (PEDEC), which is a total subsidiary of the National Iranian Oil Company (NIOC), and also the Institute of Petroleum Engineering (IPE, Tehran University) for their support of this work.
NOMENCLATURE
| I | = | well number index, grid index in x direction |
| j | = | reservoir layer index, grid index in y direction |
| k | = | variable index in the well i and layer j, grid index in z direction |
| z | = | number of variable matrix for solution of optimization |
| t | = | time index |
| ts | = | number of time step |
| o | = | index of observed data |
| c | = | index of calculated data |
| Fpi | = | weight factor for bottom-hole pressure of well i |
| Fwi | = | weight factor for water cut of well i |
| Kro | = | end point value of oil relative permeability curve |
| Krw | = | end point value of water relative permeability curve |
| ln | = | total layer number |
| mijk | = | one element of variable matrix of Vz |
| = | the chosen path of variable matrix for hill climbing process | |
| nk | = | number of variable type in each well |
| OFz | = | total objective function (non-fitness) |
| OFDz | = | dimensionless form of OFz |
| Pz | = | part of objective function related to bottom-hole pressure |
| Swc | = | connate water saturation |
| Sor | = | residual oil saturation |
| Vz | = | Zth solution of optimization variable matrix |
| wn | = | total well number |
| Wz | = | part of the objective function related to water cut |
| = | error in measurement for water cut | |
| = | error in measurement for bottom-hole pressure |
