A generalized approach for fast estimation of reservoir permeability distribution from analysis of pressure transient data

• Published in: Journal of petroleum science & engineering 2019-11, Vol.182, p.106240, Article 106240
• Main Authors: Heidari Sureshjani, Mohammadhossein, Ahmadi, Mohammad, Fahimpour, Jalal
• Format: Article
• Language: English
• Subjects: Inverse problem; Permeability heterogeneity map; Pressure transient analysis
• ISSN: 0920-4105; 1873-4715
• DOI: 10.1016/j.petrol.2019.106240

Estimation of permeability variation from analysis of pressure transient data is very challenging. Such problem may not have a unique solution and cannot be analyzed with classic well-test models. The available models for fast estimation of permeability map are restricted to several assumptions such as existence of pure radial or linear flow in an infinite medium. Such assumptions may be violated in real applications. To handle pressure transient analysis in heterogeneous reservoirs, more flexible models are needed to be applicable for majority of real well tests. In this work, a generalized approach is developed to estimate reservoir permeability variation from analysis of pressure transient data. For non-radial flow regimes, we show that the permeability rings should be defined non-circular. In flow geometries other than radial, we may not be able to use radius of investigation. Accordingly, we propose the use of pressure drop at the boundary of region of investigation instead. The average permeability in non-circular rings can produce satisfactory derivative predictions. Inspired by this observation, we developed an inverse procedure to estimate equivalent average permeability along with appropriate inner and outer ring boundaries. After estimation of equivalent permeabilities from the inverse procedure, the 2D permeability map is estimated through a minimization process. The defined objective function represents the difference of geometric average of realizations and equivalent average permeabilities from the inverse procedure. Using such form of definition, there is no need to perform any flow simulation during minimization process. We applied the procedure to back calculate the permeability variation around a horizontal well from analysis of its pressure derivative data. In addition, the uncertainty of the estimation and prediction was evaluated. The results reveal the strength of the proposed methodology for pressure transient analysis of heterogeneous reservoirs. •A methodology is developed for fast estimation of permeability map using pressure transient data.•The developed approach is general and can be used for different well/reservoir geometries and flow regimes.•Using this approach, there is no need to flow simulation runs during the minimization process.•The methodology for uncertainty quantification without running flow simulation is described.