Enhanced Reservoir Parameter Redistribution in Single Well Reservoir Modeling: An Inversion Approach Using Pressure Transient Analysis Data
Authors: Kumar Arvind , Wydiabhakti Tety Benedicta , Nukala Sai Teja , Lopes Velerian Sanjao , Ojha Keka 
Published: April 2024

Abstract
Single Well Reservoir Modeling (SWRM) has been used mainly during the early exploration stage in order to perform productivity estimations and further, to optimize the completion strategy. However, its scope is limited due to the availability of petrophysical and dynamic pressure data from either single or few wells in the block. Variousmethods have been formulated in past to increase the robustness of SWRMs for relatively accurate forecasts. This research introduces a novel technique for the concurrent inversion of pivotal reservoirparameters – horizontal permeability, vertical permeability, skin, and boundary distances – for their spatialarrangement within the grid cells of a three-dimensional single well reservoir model (SWRM). The aim is to harnessthe interpretation results from standard pressure transient analysis of well test data, using it as a prioriinformation for the intricate inversion problem.
Our methodology begins with crafting a layer cake geological model derived from the petrophysical analysis of logging data, calibrated by the interpretation results of well test pressure transient analysis. This is succeeded by a systematic flow simulation of field well test operations in the layer cake model, leading to the generation of model pressure data which mostly differs from the acquired well test pressure data. To ensure convergence, we define a cost function that amalgamates both the well test pressure data and the model pressure data. This cost function depends on the reservoir parameters like horizontal permeability, vertical permeability, skin and boundary distances, which need to be refined to achieve a pressure history match. To do that we introduce an inversion approach, where simultaneous inversion of all these reservoir parameters take place in an iterative manner to minimize the cost function. Crucially, our inversion methodology is tightly regulated by a multiphase fluid flow simulator, which constantly solves the implicit black-oil fluid-flow diffusivity equations at each iteration to calculate the error between model pressure and acquired well test pressure. A range including minima and maxima of each property is provided to the inversion scheme, which ensures that at each iteration, we gain a renewed distribution of reservoir parameters. These parameters, in turn, feed into an error scheme steered by the cost function. A Gauss-Newton (GN) inversion method, complemented by a regularization technique, facilitates inversion-based re-distribution of properties across geomodel grid cells. To enhance the fidelity of inversion outcomes, the a priori parameters provided to the solver are rigorously assessed, and if needed, fine-tuned via uncertainty parameter optimization (UPO).
The proposed technique offers a swifter and more dependable method forredistributing reservoir parameters in a homogenous layer cake geomodel, infusing it with the much-neededheterogeneity. Such methodical redistribution not only augments the reliability and credibility of a geomodel butalso sets it up as a robust foundation for production forecasting strategies.