Title: Numerical density diffusivity equation and numerical derivatives - a generalised approach for well test analysis

Authors: Victor Torkiowei Biu; Shi-Yi Zheng

Addresses: London South Bank University, 103 Borough Rd, London SE1 0AA, UK ' London South Bank University, 103 Borough Rd, London SE1 0AA, UK

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.

Keywords: numerical density; statistical derivatives; pressure-density equivalent; phase permeabilities; average permeability k estimation; BPR; PDENO; PDENG; PDENW; PDENA; well test analysis; fluid phase permeability; radial flow; density transient analysis; complex reservoirs; reservoir pressure data.

DOI: 10.1504/IJPE.2016.078816

International Journal of Petroleum Engineering, 2016 Vol.2 No.2, pp.91 - 124

Received: 13 May 2016
Accepted: 08 Jun 2016
Published online: 02 Sep 2016 *

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