Numerical density diffusivity equation and numerical derivatives - a generalised approach for well test analysis
by Victor Torkiowei Biu; Shi-Yi Zheng
International Journal of Petroleum Engineering (IJPE), Vol. 2, No. 2, 2016

Abstract: Presented in this paper are two analytical approaches: 1) the pressure-density equivalent algorithm for each fluid phase, which is derived from the fundamental pressure-density relationship and its derivatives used for diagnosing flow regimes and calculating permeability; 2) the density transient analytical DTA solution derived with the same assumptions applicable in 1) above, but the derivatives for each fluid phase plotted on semi-log density versus time to derive permeability for individual phase. These approaches were tested with synthetic and field data. The synthetic studies demonstrated that the calculated numerical density derivatives on the diagnostic plot yielded much clearer reservoir radial flow regime. For field case, it was difficult to identify the radial flow with the conventional pressure derivative method. In contrast, the fluid phase numerical density and pressure-density equivalent derivatives gave very clear radial flow stabilisations on the diagnostic plot, from which the reservoir permeability was derived, which is consistent with scaled core permeability from the same formation. The study also discovered that in the cases investigated, the heavier the fluid, such as water, the better permeability estimation from the weighted average pressure-density equivalent derivatives. Presented approaches provided an estimation of the individual fluid phase permeability, reflecting the contribution of each phase to flow at a given point.

Online publication date: Fri, 02-Sep-2016

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