## Estimation of Well Productivity Index by Analyzing Formation Tester Data in a Multilayer Reservoir

##### Resumen

A new method was developed to reduce the uncertainty in formation permeability measurements from single probe formation testers. This new method, which basically combines spherical drawdown solution and formation rate, does not require a geometric factor which accounts for the deviation from spherical flow. The method which may be called Spherical Drawdown Analysis estimates permeability from drawdown data rather than buildup data. This new technique can be easily implemented with a simple log-log graph of rate function versus time. A line that has a slope of -1.5 is fitted through the data and from the intercept, the spherical formation permeability may be determined. An Eclipse model was built with many scenarios to test and verify the new technique, as well as other techniques, using numerical simulated data. It was found that the spherical drawdown analysis has a wider range of permeability estimation compared to other methods. In addition, it outperformed spherical buildup analysis in permeability estimation especially in relatively high permeability formations.
The effect of the outer layers, in multilayer reservoir systems, on estimating the permeability in the tested layer was also studied. The effective radius of drawdown and buildup tests of a typical probe-test in a multilayer reservoir was first investigated. Then a dimensionless parameter was defined to present this effective radius. This dimensionless parameter was found to be a function of the vertical permeability of the inner layer and the distance from the probe to the outer layer. This radius indicates that as long as the outer layer does not lie within this effective radius, the permeability estimated is not going to be affected by the outer layer.
Based on the outcome of the spherical drawdown analysis method and the knowledge of the effect of the outer layer on permeability estimation, a new methodology was proposed to estimate the well productivity of a multilayer reservoir from single probe-tests. The estimated well productivity was compared with that from the conventional well tests using simulated data as well as actual test data. The productivities obtained from this methodology and other approaches are acceptably close. And the effective radius may be used to guide the selection of test locations so that the test data can be used later to estimate the PI of a well.