Pumping tests interpretation is an art that involves dealing with noise coming from multiple sources and conceptual model uncertainty. Interpretation is greatly helped by diagnostic plots, which include drawdown data and their derivative with respect to log‐time, called log‐derivative. Log‐derivatives are especially useful to complement geological understanding in helping to identify the underlying model of fluid flow because they are sensitive to subtle variations in the response to pumping of aquifers and oil reservoirs. The main problem with their use lies in the calculation of the log‐derivatives themselves, which may display fluctuations when data are noisy. To overcome this difficulty, we propose a variational regularization approach based on the minimization of a functional consisting of two terms: one ensuring that the computed log‐derivatives honor measurements and one that penalizes fluctuations. The minimization leads to a diffusion‐like differential equation in the log‐derivatives, and boundary conditions that are appropriate for well hydraulics (i.e., radial flow, wellbore storage, fractal behavior, etc.). We have solved this equation by finite differences. We tested the methodology on two synthetic examples showing that a robust solution is obtained. We also report the resulting log‐derivative for a real case.

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This study proposes a new inverse algorithm to estimate the hydraulic conductivity (K) distribution based on a Gaussian Mixture Model that significantly reduces the number of parameters to be estimated during the inversion process. Moreover, a new objective function that increases the sensitivity of parameters using the spatial derivatives of hydraulic heads is introduced, and the algorithm is further improved by including a Bayes estimator that takes advantage of different possible solutions. The developed approach is tested through multiple synthetic experiments consisting of 250 randomly generated K fields resulting in different levels of heterogeneity and the use of different number of pumping tests, with a total of 1,000 cases of two-dimensional configuration. A large number of cases are considered to ensure that our findings and conclusions are not based on a single realization. Results revealed significant improvements to K estimates, computational time, and predictions of independently conducted tests not used in the calibration effort when compared to a geostatistical inverse approach. Overall, our results reveal that the Gaussian Mixture inversion approach is able to achieve similar or higher levels of accuracy using half of the pumping tests and 20% of the computational time compared to a geostatistical inversion approach.

This paper presents the advances on the characterization of Naturally Fractured Vuggy Reservoirs (NFVR) located in the South East Gulf of Mexico. Halos, fractures and vugs were characterized through well tests using the triple porosity–double permeability (3φ-2k) model. Through the analysis of well and imagelogs was determined the predominance of high vuggyporosity producing intervals, so that the pressure data were analyzed using a triple porosity-double permeability (3φ -2k) approach, with total and partial penetration. These NFVRs have vuggy and fracture porosity, with triple porosity, matrix, fractures, and vugs, or matrix, vugs with their halos. In both cases, the 3φ-2k model is appropriate to characterize these fields. These models, recently presented involve the determination of 9 and 13 parameters, for total and partial penetration, respectively, which implies challenges in terms of the uniqueness of the results. In this way, it is suggested to consider information from other sources like cores, well logs, and image logs, in order to select characteristic values for some of the parameters of the model of interpretation, specifically the storage ratios for vugs and fractures, ωv and ωf, and in this way to eliminate the non-uniqueness problem. Thus, the integration of static and dynamic information is a key element for a complete description of NFVR. The 3φ-2k model allows better data fits than the classical dual-porosity model, obtaining more information related to the interactions of the three different media. The sum of vuggy and fracture porosity obtained from 3φ-2k model is not equal to the secondary porosity obtained from the dual-porosity model. If partial penetration effects are present, it is recommended to perform the analysis taking into account these effects because information on the vertical communication of vugs and fractures can be obtained with the 3φ-2k model. It is confirmed through the analysis of well-tests with partial penetration that the vertical communication of vugs can be more important than the horizontal communication. It is crucial to obtain fracture and vug connectivity in both horizontal and vertical direction, mainly because these reservoirs are sharing a common aquifer. The objective of this work is to demonstrate the application of a 3φ-2k model to determine several parameters related to reserves and productivity of NFVR. Vertical connectivity of both vugs and fractures are important parameters when an aquifer is underlying heavy oil NFVR, because these areas could establish preferential routes for the advancement of water.