A Mathematical Model of a Gas Kick

Abstract

This study presents an analysis of annular backpressure variations associated with controlled gas kicks and their pronounced erect on casing strings and exposed underlying formations. A mathematical model describing the volumetric behavior of an extraneous gas as it is transported from reservoir to surface conditions under changing temperatures and pressures has been programmed in a Kingston FORTRAN II language for digital computer analysis. The gases under investigation typify Gulf Coast reservoir gases within a 0.6 to 0.7 specific gravity range. The program output has been substantiated by actual field cases of gas kicks encountered in Gulf Coast wells. The development of empirical equations for calculating suitable gas deviation factors for unique temperatures and pressures was incorporated in the program to provide realistic solutions. An output listing of annular backpressures and corresponding equivalent fluid densities resulting at a predetermined critical depth (casing setting depth) and total depth for selected stages of circulation is provided in a chronological sequence. Additional information including reservoir pressure and temperature, kill mud density, produced gas or surface volume of the expanded gas intrusion, drill pipe and annular volumes can be obtained from the model. This paper illustrates that a precise knowledge of the volumetric behavior of extraneous gases in annular flow and its effect on equivalent fluid densities at a critical depth is significant and should receive serious consideration in controlling threatened blowouts and in the design of drilling programs. Surface pressures in excess of formation limitations are a threat to zones of lost circulation and are potentially injurious to productive intervals. A knowledge of annular backpressure and equivalent fluid density profiles for probable gas kicks aids in a technological accomplishment of drilling programs and provides a sale tolerance in the event a threatened blowout is encountered.