|Publisher||Society of Petrophysicists and Well-Log Analysts||Language||English|
|Content Type||Conference Paper|
|Title||A MATHEMATICAL COMPARISON OF COMMON SATURATION EQUATIONS|
|Authors||G. A. BROWN, BP PETROLEUM DEVELOPMENT LIMITED|
|Source||SPWLA 27<sup>th</sup> Annual Logging Symposium, 1986|
|Copyright||1986. Society of Petrophysicists & Well Log Analysts|
Steady progress has been made in recent years in the understanding of the ''shaly sand'' response of well log data. This has resulted in the log analyst being confronted with an array of saturation equations, all purporting to solve the ''shaly sand'' problem. This paper recognizes that a comparison of the equations by applying them to given sets of logs is very subjective. Thus a computer model is developed to study the response of the equations over the whole range of shale and saturation possibilities. The equations studied are the Indonesia, Cyberlook, Dual Water and Normalised Waxman and Smits. Positive conclusions are drawn about the applicability of the various equations to specific geological conditions. The study also highlights assumptions made in the formulation of the equations and the effect of these assumptions on the computed saturation. Substantial differences are observed in Sw calculated from the Dual Water and the Indonesia equation especially in fresh formation water. A new equation is developed which is an expansion of the Dual Water concept to allow ''m'' (the cementation exponent) to change from ''m'' clean sand to ''m'' shale, as a function of shale volume. This new equation is termed a ''Dual Mineral'' model because it recognizes that both shale and sand are different minerals each with different pore distributions, whilst shale has in addition the effect of increasing the apparent conductivity of the saturating fluid as described by Waxman and Smits. The Dual Water and Normalised Waxman and Smits equations are demonstrated to be simplifications of the Dual Mineral model. The Cyberlook equation is a simplification of the Dual Water model. The consequences of the assumptions made in the formulation of these different saturation equations is clearly demonstrated.