Graphical Solutions for Laminated and Dispersed Shaly Sands
- Richard Bootle (Lukoil Overseas UK Ltd.)
- Document ID
- Society of Petrophysicists and Well-Log Analysts
- Publication Date
- February 2016
- Document Type
- Journal Paper
- 51 - 59
- 2016. Society of Petrophysicists & Well Log Analysts
- 3 in the last 30 days
- 253 since 2007
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Shaly sand equations are a well-established petrophysical principle. However the solutions to these equations are complex and there is a lack of clarity regarding their optimal implementation and numerous input parameter assumptions. This paper considers the ΔSw impact of shaly sand equations relative to the Archie equation.
An accurate graphical solution for the Rh-Rv laminated-shale model is established. All that is needed to solve for ΔSw is the logged anisotropy, the Archie equation inputs and an estimate of the shale porosity. The graphical solution is a simple and accurate way of using the Rh-Rv laminated-shale model without onerous mathematical computation. The magnitude of Rh-Rv laminated-shale ΔSw is potentially much greater than for Waxman-Smits/Juhasz (the Juhasz solution to the original Waxman-Smits equation).
The Waxman-Smits/Juhasz ΔSw solution is less exact due to the greater number of independent parameters this equation uses. The principal dependencies are the Waxman- Smits saturation exponent n*, the formation water salinity and the Archie equation inputs. Cation exchange capacity and clay volume also impact the solution but are of lesser significance. It is demonstrated that except in low porosity rock, Waxman-Smits/Juhasz cannot exceed -0.10 ΔSw (for the assumption m* = n*). The Waxman-Smits/Juhasz charts allow for a quicklook or screening solution only.
The presence of shale in reservoir rock suppresses the high resistivities that are the primary petrophysical characteristic of hydrocarbons. To account for this, a large number of shaly sand equations have been devised by the industry (Worthington, 1985). Shaly sand equations are modified forms of the Archie equation that account for this extra shale conductivity; two of the most widely used are the Rh-Rv laminated-shale model and the Waxman-Smits/Juhasz equation.
The practical implementation of both these models follows broadly similar principles: a number of additional parameters are added to the standard Archie equation. These parameters are either measured or estimated, in one way or another, and the validity and robustness of the resulting shaly sand Sw is ultimately dependent on the strength of this characterization. Both models have nonlinear mathematical solutions. Both shaly sand models and their input parameters are also of sufficient complexity for multiple versions of their solutions to be in common practice (e.g., the Juhasz solution to the original Waxman-Smits equation).
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