In this work an analytical solution for the inverse problem of a heterogeneous reservoir, composed by several infinite acting homogenous layers, is presented. The solution comprises a small set of ordinary algebraic equations, providing an explicit solution for the inverse problem. The layers may differ in thickness, porosity, fluid viscosity, total compressibility and initial pressure, which are input data. The proposed Method calculates the radial permeability and the wellbore skin factor for each individual layer and requires Production Logging data.

The Method's outcomes are important for both mature fields and new discoveries, providing valuable information for enhanced oil recovery techniques and accurate data for geological modeling. In addition, the method is a useful tool for assessing acid job diversion performance, especially on carbonate reservoirs, where acidizing procedures are largely employed.

The proposed Delta Transient Method focuses on providing simple calculations and delivering robust results. Operational feasibility of data acquisition has also been taken into account for the development of the Method. The main features of the present work are:

  1. The Method calculates the permeability and skin for each individual layer, for an unlimited number of layers;

  2. The Method has been designed to be applied to a relatively short single rate flow period (only few hours of drawdown/injection);

  3. There is no need for rate changes. Nonetheless, the Method works with rate changes, as long as the principle of superposition is considered;

  4. Only two PLT (production-logging tool) flow profiles at distinct times are required for full application of the Method. No stationary data are needed;

  5. The calculations for each layer are performed with a small set of algebraic equations, which can be easily modeled in any ordinary spreadsheet software. No graph analyses are required.

The Method has a strong operational-practical drive, which consists of demanding only few hours of rig time for data acquisition. Moreover, once permeability and skin for each layer are obtained, a reasonableness check is provided as a final step to the Method. The purpose of this check is to guarantee reliability on the resulting outcomes. Issues concerning formation crossflow, wellbore storage and high transmissibility systems are also addressed. A successful case study is presented, where it took only 10 hours to acquire all necessary data.

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