Fig 3:Superposition of real data to dimensionless theoretical curves
Several charts reporting dimensionless type-curve sets similar to that shown in fig. 3 are provided, each characterized by different values of the invaded zone resistivity and invasion diameter. The selection of the most appropriate chart is aided by the use of another chart (fig. 4) reporting dimensionless curves for both the invaded zone resistivity - set A - and the invasion diameter - set B. Superposition of the interpretation form reporting the apparent resistivity values on this chart provides the most probable values for the invaded zone resistivity and the invasion diameter.
Fig 4:Diagram for the selection of the most suitable value of invaded zone resistivity and
invasion diameter. Apparent resistivity values measured by long spaced lateral tools in thin beds are not representative and, therefore, the number of lateral measurements which can be used in the interpretation process is very limited. As a consequence, the log-analyst needs to subjectively supplement this lack of data to achieve interpretation, strongly jeopardizing the interpretation reliability. It is not advisable to apply the Russian log interpretation procedure to layers that are 2 meter thick or less.
NUMERICAL INTERPRETATION
Automatic interpretation of Russian log measurements to determine the true formation resistivity and
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invaded zone resistivity can be performed by using the Rt-Mod software.
The software generates an ideal, two-dimensional geometrical model of the investigated formation and the corresponding synthetic apparent resistivity profile using a finite differences forward modeling. The model is calibrated according to an inverse modeling procedure, i.e., the geometrical and electric properties of the model are progressively modified until a satisfactory superposition between synthetic and real logs is achieved.
Forward and inverse modeling are iteratively repeated until satisfactory convergence is reached. The resistivity values of the invaded and virgin zones assigned to each layer in the generated geometricalelectric model represent the results of the numerical simulation.
The numerical simulation is based on two different log curves, a curve recorded with a long-spaced tool and curve recorded with a short-spaced tool. A correlation log can also be provided, such as a self potential log or a gamma ray log, to confirm the layer sequence simulated by the software. It is also
possible to generate the true resistivity profile only based on the long-spaced measurements and on the stratigraphic log. The nominal well diameter should be assigned to correct the apparent resistivity values for well bore effects.
It was observed that the calculated mud resistivity values are not always consistent with the reported fluid property and, therefore, the interpretation results might be questionable since mud resistivity
determines the apparent resistivity correction for mud, mud cake and filtrate invasion. However, it is also possible that the reported mud resistivity is not reliable for the logged interval. Sensitivity analyses should therefore be run to evaluate more accurately the true mud resistivity.
Although the invasion diameter is calculated during the modeling process, it is not provided as a simulation result.
CASE HISTORY
Three wells were selected to apply the different methodologies for resistivity log interpretation. The wells are located in a sedimentary basin underlain by a folded and partially metamorphosed Paleozoic
basement. The depositional sequence is mainly made of shaly facies, but partly eroded carbonate and evaporitic sedimentary formations are also present. The carbonate sedimentary sequence originated from Jurassic to Quaternary and represents the most interesting gas bearing formation in the area. The reservoir net pay ranges from about 250 m to 100 m (in some marginal areas of the basin). Porosity
ranges between 13% and 20% and permeability is approximately 100 mD. The clastic carbonate
sequence is bounded by turbidites having porosity of 5 - 8 % and permeability between 0.1 and 5.0 mD. The well selection was based on the availability of a sufficient number of resistivity logs to apply the Russian interpretation approach, core analysis to validate porosity logs and to characterize fluids and rock quality, and well testing results to validate the calculated water saturation profiles. Furthermore, inconsistency had been found for all the selected wells between the water saturation values calculated as a function of true formation resistivity evaluated by the western conventional interpretation and the nature and quantity of produced fluids during well testing.
RESULTS AND DISCUSSION
The true formation resistivity values, Rt, obtained by application of the Russian interpretation are consistent with the apparent resistivity measured by long-spaced tools for layers thicker than 2 meters (fig 5). The stratigraphic sequence apparent from the resistivity values is not consistent with the
concavity changes of the response curve recorded by long-spaced tools due to low vertical resolution. The true formation resistivity profiles generated by numerical simulations are reliable when the synthetic and the real log are superimposed (fig 6). Generally, the superposition is very satisfactory except at the boundary of the analyzed interval where the Rt profile appears to be less reliable. Therefore, it is advisable that shoulder formations are also included when modeling the producing layer.
The comparison among simulations based on different tool combinations is shown in fig 7. In particular, the combination of the half meter- and eight meter-spaced lateral logs is the combination used for interpretation.
Fig 5:Resistivity values obtained by Russian interpretation
Fig 6:Resistivity profile generated by numerical simulation
The results obtained by application of the Russian manual methodology and by simulation were compared in terms of the true formation resistivity and invaded zone resistivity (fig 8). The resistivity values calculated with the Russian methodology are consistent to numerical simulations only when numerous reliable measurements are available, i.e., for layers approximately thicker than 2 meters. Numerical simulations seemed to be reliable for any layer thickness (fig 8 left). The layer subdivision adopted in the numerical simulations is greater than in the western or Russian interpretation because forward modeling attributes each concavity change to a formation anisotropy typical of a layer limit. However, measurement errors can influence the log response curve and induce concavity changes which are not due to the formation layering. A comparison between the invaded zone resistivity
calculated by the two interpretation methodologies indicated that results are in good agreement (fig 8 right).
The invasion diameter could only be calculated when the Russian methodology was applied. The results are reported in Tab 1.
Fig 7:Comparison of different resistivity profiles generated by numerical simulations