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How to calculate Rw and m porosity cementation exponent from well logsThe "m" cementation exponent is the adimensional power parameter for porosity in the Archie water saturation equation, the Simandoux equation, the Indonesia equation, and others. The higher the m, the higher SW water saturation.
This parameter m depends upon the pore space structure connectivity, the matrix consolidation, and the grains shape (more than the size). Historically, m has been called cementation exponent, but the term porosity exponent is also used. When the tortuosity factor "a" is fixed to 1.0, a default value of m=2 is usually used (also with n=2), but this is more representative for carbonates. For clastic sandstones, the m value ranges from around 1.3 for completely unconsolidated sands, to 2.2 for very well consolidated or cemented sandstones. Typical values for water wet consolidated sandstones range 1.51.9. The lower the m value, less free movable water saturation is calculated for the rock. The Archie equation involves four variables: SW, φ, R_{w} (formation water resistivity), and R_{t} (true deep non invaded formation resistivity), and three parameters: a, m, and n (the saturation exponent). That means that in the well logging practice, some assumptions must be made or the system would be undetermined. —However, if representative water samples with ionic analyses are available, electrochemical computations of salinity and Rw are usually more reliable and preferred— Since the Archie equation works well for non shaly rocks, the easiest way to estimate some unknowns is to work in clean zones (Vsh=0) embedded in SW=100% water, and collect (φ, R_{t}) log data to solve the unknowns. In some reservoirs, the irreducible water saturation SW_{irr} can be reasonably well known (for example, around 15%) to work with clean rocks in fully oil impregnated zones. The most used methods to estimate parameters from the Archie equation, are the Hingle, the Pickett Plot, and the apparent cementation exponent methods:
Is there an easy way to determine the water saturation exponent n from well logs? Not really. The basic problem is that a log independent knowledge of SW would be required, and core lab water saturation data is not often reliable or accurate. A default value of n=1.9 to n=2.1 is usually an useful approximation implicitly used in many well logging equations and theory. The figure below shows the GeolOil panel to estimate the Rwa apparent water resistivity curve in a shaly sand
Resistivity fails to detect water oil contact, but apparent water resistivity does, confirmed by production




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