EXTENSION OF THE CLASSICAL SKIN-FACTOR THEORY FOR OIL AND GAS WELLS: INCORPORATING RADIAL AND PRESSURE-DEPENDENT PERMEABILITY
M.I. Epov1, N.N. Mikhailov2,3,4, O.E. Aksyutin5, V.N. Sokotushchenko2, O.M. Ermilov2,6
1Trofimuk Institute of Petroleum Geology and Geophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
2Gubkin Russian State University of Oil and Gas, Moscow, Russia
3Oil and Gas Research Institute, Moscow, Russia
4Lomonosov Moscow State University, Moscow, Russia
5PAO Gazprom, Saint Petersburg, Russia
6OOO Gazprom Dobycha Nadym, Nadym, Russia
Keywords: Skin factor, Hawkins model, three-zone model, permeability, radial permeability variation, near-wellbore region, linear permeability variation
Abstract
This study extends the classical skin-factor concept originally proposed by M.F. Hawkins. A fundamental limitation of the Hawkins model is identified: the permeability of the drilling-fluid filtrate invasion zone is assumed to remain constant ( k skin = const). Based on an analysis of recent experimental evidence, an integrated skin-factor model is developed in which the permeability ( k ) of the near-wellbore region is represented as a function of both the radial distance ( r ) from the wellbore wall and pressure ( p ): k = k ( r , p ). The proposed model comprises three characteristic invasion zones, each governed by a distinct mechanism of permeability variation. Comparative simulations reveal substantial differences between the classical Hawkins model and the proposed three-zone model, k = k ( r ), as well as the integrated model, k = k ( r , p ). Assuming a linear radial variation in permeability, comparative relationships are obtained between the normalized production rate and the skin factor, as well as between the skin factor, the production rate, and pressure drawdown. The classical Hawkins model is shown to overestimate the production rate by an average of 15-25%, with deviations increasing to 40-50% in the zone of maximum invasion. The results are of fundamental importance for the theory of flow through porous media and have practical significance for oilfield development planning by providing a basis for selecting well stimulation methods according to the characteristics of individual invasion zones.
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