Analytical solutions by the hodograph method to hydrodynamic problems for oil and gas traps

Resting gas, oil and combined traps in equilibrium with moving water are st udied by the methods of complex analysis (conformal mapping of hodograph ci rcular polygons onto the strip in the complex potential plane). For a monoc line dipping at an arbitrary angle and a one-phase trap two regimes (diffus er and confuser) are possible and explicit analytical solutions for the sha pe of a sharp interface between water and hydrocarbon are derived in terms of hypergeometric functions. The free surface is shown to coincide with the Saffman-Taylor finger in the Hele-Shaw apparatus if the monocline axis is vertical. For a gas-oil trap the interface consists of two branches along w hich the isobaric condition (constant pressure in the gas aloft) and the co ndition of a linear increase of pressure with depth (in the oil phase separ ated by a horizontal hydrostatic interface from the gas finger and by a hyd rodynamic interface from water) are reduced to a standard hodograph represe ntation through two touching circles. A critical regime is analyzed when th e free surface does not have an inflexion point. (C) 2001 Elsevier Science B.V. All rights reserved.