Published by the DTI Oil & Gas Directorate for the reservoir
engineering and IOR community in the UK.
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by 15 August 2002.
Fractional Flow Approach to Performance Prediction in Mature Water-Flooded Fields
Audrey Miles reviews a recent study undertaken by Senergy Ltd for the DTI Oil and Gas Directorate (co authors David Hughes and Iain Morrison) (a.miles@senergyltd.com)
Despite the widespread use of sophisticated reservoir simulation models, from time to time the reservoir engineer has to make a prediction of future performance using a more pragmatic approach. This is normally achieved using a trend analysis technique such as decline curve analysis or, for example, projecting log WOR v. Cumulative Oil Recovery plots.
The DTI was concerned that the WOR projection or another technique know as the "X" plot were in use by UKCS operators but the validity of these plots was not known, and RML were asked by the DTI to investigate these projections.
It was concluded that linear extrapolation of log WOR v. Cumulative Oil Recovery is likely to lead to erroneous predictions. The only circumstance when this plot is linear is for harmonic decline. However, this cannot occur in reality as a linear log WOR v. Cumulative Oil Recovery plot implies infinite recovery, whereas clearly the recovery is limited to the amount of mobile oil.
The alternative "X" plot, is ln WOR + 1/fw v. Cumulative Oil Recovery. However, linear extrapolation of this is similarly flawed. As fw approaches 1, the function has much the same limiting behaviour as the log WOR plot (figure shows a comparison for exponential decline using natural logs for both plots).
An alternative, fractional flow (FF), prediction technique was proposed by Laurie Dake. He suggested, at least for short term predictions, a linear extrapolation of the gradient of the FF curve. RML has proposed using the FF technique, but rather than using the Dake extrapolation, the FF curve is extrapolated directly by fitting the later points to a curve of the conventional FF shape.
The assumptions built into the method are that there is a general balance between the amount of water injected (including aquifer influx) and the liquids produced, the reservoir behaves as a single interconnected tank, remains above the bubble point, and that fluids and formation are incompressible. However, in practice some deviation from these conditions can be tolerated.
For example, The figures show the FF curve and a number of predictions for the performance during 1998-9 based on curve fits to data ending in December 1997 (the four predictions used different starting values for the various parameters in the curve fit).
The curve fit was then revised to include the latest data and a prediction based on this revised fit compared to the operator's prediction.
A spreadsheet capturing the FF methodology can be downloaded from the DTI SHARP Website (www.dti-sharp.co.uk and click on Dissemination then Software, right click on System Fractional Flow (EXCEL Spreadsheet) and Save Target As file to your desktop). A longer article can also be found on the website (www.dti-sharp.co.uk and click on Dissemination then Journal Publications and Conference Papers)
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