Mathematical Extrapolation Technique For Predicting And Evaluating Production Performance

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Appendix B – Mathematical Extrapolation Technique for Predicting and Assessing Production Performance
In this section developments in graphical methods of assessing water drive performance are presented. An extensive number of graphical and mathematical extrapolation techniques is available in the literature. A number mathematical extrapolation methods were also assessed (not presented here). Mathematical extrapolation technique presented by Dake (1994) was found to be quite effective in predicting future production performance and in assessing the effects of any remedial actions which has taken place. The method was tested on two fields, namely Miller and Maureen. Description of method proposed by Dake is presented below.
Examination of
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Conversion from surface volumes to reservoir pore volumes is performed using the following relationships:
N_pd=(N_p B_o)/(NB_oi )(1-S_wc)
W_id=W_i/(NB_oi )(1-S_wc)
Since 1PV=(NB_oi)/(1-S_wc )
Finally, the dependence of fractional flow at the producing end of the system on fractional flow at reservoir conditions is expressed using the classical Buckley-Leverett fraction flow function: f_we=1/(1+B_o/B_w (1/f_ws -1))
It must be noted that in most water drive reservoirs before the water breakthrough, there is an initial period of depletion. The fractional flow calculations, only take into account the oil recovered by water injection. Therefore calculations can be performed only after the water breaks through in the producing wells.
Prediction of final oil recovery
If injection rates during the latter part of the flood are relatively stable, then 1/Wid function can be approximated by a straight line, which can be fitted by equation of the form:
(δf_we)/(δS_we )=aS_we+b
Where a and b are constants. Integrating the equation results in quadratic function: f_we=a^2/2 S_we^2+bS_we+c
Where c is constant. Predicted values of fwe and Swe obtained by extrapolation of the quadratic equation above are then can be used in Welge equation for predicting Npd as a function of fwe, which are then should be converted to surface conditions.
Miller Field
The data
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