Adiministracion integral de yacimientos.

The Holistic Approach to Reservoir Mechanics

Criticism of these practices may perhaps be regarded as too harsh. It is reasonable to ask whether alternatives to them can be suggested. It is held that such alternatives do exist but that their use requires some rethinking by reservoir engineers. It would seem that a worthwhile approach to the problem of evaluating reservoirs sensibly and simply might have as its basis the philosophy of "holism". This philosophic doctrine was created by the late Field Marshal J. C. Smuts and holds that, in nature, determination is by wholes and not by constituent parts. Translated into reservoir parlance, it would say that what matters is the rock unit and not samples of arbitrary size that may have been taken from it. This approach may be exemplified particularly by the use of special well tests. Thus, pressure build-up or falloff analyses give directly the fluid transmissibility of a reservoir as a unit which exists in situ. Such a measurement represepts an approach to reality which, as Warren, et aI, have shown, is often very different from conventional arithmetic averages of permeability measurements made on cores. On a holistic basis, the optimum method of estimating the average porosity of a formation would be to integrate the appropriate log readings over the interval of interest and to divide this area by the interval selected. It is instructive to apply this technique to the velocity logs shown in Fig. 5. It turns out that the travel time from the actual CVL is 385.3 microseconds and from the synthetic log made on cores, 384.0 microseconds. The percentage difference between these two figures is 0.34 per cent. Actually, such a percentage is less than the precision of either log, and the two travel times may be regarded as being identical. The fact that the two logs are significantly different in detail but show the same transit times may be interpreted as further support for the validity of the theory of random block distribution of reservoir heterogeneities. The holistic approach to saturation and relative permeability estimation would be the following. For saturation, the average resistivity of the formation would be determined and the average formation factor found, either from the average porosity or by integrating under a proximity-log curve. The former method is to be preferred. From the average saturation, average relative-permeability curves for either consolidated or unconsolidated formations can be determined immediately by Corey's excellent approximate method. In this regard, it is pertinent to note that, when the simple holistic scheme is applied to the laboratory and field relative-permeability data of the Rosenwald pool which were presented by Smith and Henderson in 1957, the comparison is reasonably favorable. This is shown in Fig. 6. The divergence between the field and calculated data is in the direction that would be expected if nonuniform saturations exist in the vicinity of the producing wells. Further evidence for the validity of using the average interstitial water saturation of a formation to characterize its relative-permeability characteristics is given in Fig. 7. Here, a comparison is shown between curves calculated by the Corey method and ones found by Wahl, Mullins and Elfrink of Socony Mobil by correlating field measurements of the gas-oil ratios of producing sandstone reservoirs. The agreement between the two sets of curves can only be described as remarkable. The holistic approach specifically excludes from consideration in unitization hearings elaborate arguments concerning cut-off porosities and cutoff permeabilities. It does not seem to be generally known that the cutoff approach has no validity unless a reservoir is ideally stratified and unless the effective mobility ratio is unity. Thus, it can be fairly argued that the present piecemeal approach to reservoir characterization is not only elaborate and complex, but one which is more often than not downright wrong. The holistic approach, by putting its faith in physical measurements made in situ, is likely to lead to participation factors in water floods or other unitization proceedings which are not only more realistic than those found by present methods, but also ones which are fairer. The influence of the human element will not be eliminated, but it will he sensibly reduced.

...