The micritic limestone reservoir zones offshore Abu Dhabi have consistently challenged formation evaluation specialists. For years, zones exhibiting very low resistivity and interpreted as water-bearing, by standard or even more advanced interpretation schemes, have been shown to produce significant quantity of oil. Production tests and core studies have confirmed this fact.

Previous work has shown that a saturation equation still based on resistivity but using a triple porosity model improved the quality of the formation evaluation in these very challenging conditions. One limitation of this very valuable approach was that, in order to ensure an easy analytical solution to the equation, a fixed relationship was assumed between the saturations in the various porosity types, primarily macro- and meso-porosity. Similarly, a fixed exponent was used in the mixing law, combining the respective conductivities of macro-, meso- and micro-porosity.

In this paper, we demonstrate that these limitations can very easily be lifted through an original approach: the saturations in the three types of porosity are computed sequentially, faithfully following the oil migration reservoir model, which states that oil migrates first in the macro-pores, those pores rapidly becoming oil-wet, then in the meso-pores, the micropores remaining primarily water-filled.

In addition, the mixing law attempts to model the fact that meso-porosity appears to create a large divergence from Archie's law, which was not fully accounted for by the earlier models, by allowing for a variable exponent, itself function of pore type.

The split between macro-, meso- and micro-porosity is preferably derived from Nuclear Magnetic Resonance logs, but an alternative approach, that can be used when NMR logs are not available, has also been found to give satisfactory results, provided a reliable permeability log is available, which is in itself a challenge in these difficult formations.

This paper describes in details the equations used to arrive at the solution and shows examples of computation, with comparison to core results and to cased hole saturation obtained from a non Archie approach, in particular from pulsed neutron logs.


In reference 1, M.Petricola and M.Watfa introduced a generalized saturation equation for carbonate formations with micro-porosity. This equation was an attempt at quantifying and accounting for the effect of micro-porosity conductivity on the commonly used resistivity or conductivity logs.

It was shown in the paper that introducing an exponent X as shown in equation A-1 (all equations were too cluttered to be displayed in a readable format in the main text and are displayed in appendix instead) allowed a wide range of conductivity mixing laws to be simulated.

S.Asakura, H. Takezaki and coauthors (ref.2) lately proposed equation A-2 comprising three porosity terms, namely macro-, meso- and micro- porosity. The mixing law they adopted, however kept the X exponent at a fixed value of 2. In Ref.2 Asakura and Takezaki assume that the micro-porosity is water-filled, but still have to solve for two different saturations SWM and SWm, saturation in the macro and meso-pores respectively. They assumed a simple relationship between SWM and SWm, namely SWM=(SWm)2, which is convenient since it turns equation A-2 into a quadratic equation in SWm. In this paper however, this relationship is revised following the reservoir model, which assumes that all the macro-pores have to be oil-filled, before oil can migrate into the mesopores. Figure 1 shows a cartoon representation of that model. It will be shown that no relationship between SWM and SWm is needed and that it is not even necessary to assume that SW? is always unity.

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