TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractConditioning geologic models to production data is generally done in a Bayesian framework. The commonly used Bayesian formulation and its implementation have difficulties in three major areas, particularly for large scale field applications. First, the CPU time increases quadratically with increasing model size, thus making it computationally expensive for field applications with large number of parameters; second, the sensitivity coefficients that define the relationship between reservoir properties and the production response typically depend on either the number of model parameters or the number of data points; and third, the calculation of the prior covariance matrix (or its inverse) can be time consuming and memory intensive.We propose a fast and robust adaptation of the Bayesian formulation for inverse modeling that overcomes much of the current limitations and is well suited for large-scale field applications. Our approach is based on a generalized travel time inversion and utilizes the adjoint method for computing the sensitivity of the travel time with respect to reservoir parameters such as porosity and permeability. The sensitivity calculations depend on the number of wells integrated which can be orders of magnitude less than the number of data points or the model parameters. The adjoint sensitivities can be computed from the pressure and water saturation distribution that is readily available from the numerical simulator. For solving the inverse problem, we utilize an iterative minimization algorithm based on efficient singular value decomposition. Prior information is incorporated using an approximation of the square root of the inverse of the prior covariance calculated using a numerically-derived stencil applicable to a wide class of covariance models. Our proposed approach is computationally efficient and more importantly the CPU time scales linearly with respect to model size making it particularly well-suited for large-scale field applications.We demonstrate the power and utility of our approach using synthetic and field examples. The synthetic examples show the robustness and efficiency of this algorithm. The field example is from the Goldsmith San Andres Unit (GSAU) in West Texas and includes multiple patterns consisting of 11 injectors and 31 producers. Using well log data and water-cut history from producing wells; we characterize the permeability distribution, thus demonstrating the feasibility of our approach for large-scale field applications. m …………….….………..(7) Substituting Eq. 7 in Eq. 6, e J O T = ∇ ) (m m ………………...…….(8) The Hessian is obtained by taking the gradient of Eq. 8 with respect to the model parameter (m): m T T H J J e J = + ∇ …………….(9) For quasilinear problems or near the solution, we can approximate Eq. 9 as follows J J H T ≅ ……………………..(10)This approximation for the Hessian, Eq. 10, is the same as that of the Gauss-Newton algorithm. Now, substituting Eqs.8 and 10 in Eq. 5; e J J J

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractConditioning geologic models to production data is generally done in a Bayesian framework. The commonly used Bayesian formulation and its implementation have difficulties in three major areas, particularly for large scale field applications. First, the CPU time increases quadratically with increasing model size, thus making it computationally expensive for field applications with large number of parameters; second, the sensitivity coefficients that define the relationship between reservoir properties and the production response typically depend on either the number of model parameters or the number of data points; and third, the calculation of the prior covariance matrix (or its inverse) can be time consuming and memory intensive.We propose a fast and robust adaptation of the Bayesian formulation for inverse modeling that overcomes much of the current limitations and is well suited for large-scale field applications. Our approach is based on a generalized travel time inversion and utilizes the adjoint method for computing the sensitivity of the travel time with respect to reservoir parameters such as porosity and permeability. The sensitivity calculations depend on the number of wells integrated which can be orders of magnitude less than the number of data points or the model parameters. The adjoint sensitivities can be computed from the pressure and water saturation distribution that is readily available from the numerical simulator. For solving the inverse problem, we utilize an iterative minimization algorithm based on efficient singular value decomposition. Prior information is incorporated using an approximation of the square root of the inverse of the prior covariance calculated using a numerically-derived stencil applicable to a wide class of covariance models. Our proposed approach is computationally efficient and more importantly the CPU time scales linearly with respect to model size making it particularly well-suited for large-scale field applications.We demonstrate the power and utility of our approach using synthetic and field examples. The synthetic examples show the robustness and efficiency of this algorithm. The field example is from the Goldsmith San Andres Unit (GSAU) in West Texas and includes multiple patterns consisting of 11 injectors and 31 producers. Using well log data and water-cut history from producing wells; we characterize the permeability distribution, thus demonstrating the feasibility of our approach for large-scale field applications. m …………….….………..(7) Substituting Eq. 7 in Eq. 6, e J O T = ∇ ) (m m ………………...…….(8) The Hessian is obtained by taking the gradient of Eq. 8 with respect to the model parameter (m): m T T H J J e J = + ∇ …………….(9) For quasilinear problems or near the solution, we can approximate Eq. 9 as follows J J H T ≅ ……………………..(10)This approximation for the Hessian, Eq. 10, is the same as that of the Gauss-Newton algorithm. Now, substituting Eqs.8 and 10 in Eq. 5; e J J J

Oil production from the unconventional Vaca Muerta play is increasing as a result of a rigorous appraisal and exploitation strategy. Multiple wells have already demonstrated the potential of the Neuquén Basin, however optimization is still ongoing to determine the best practice for completing wells. A stand out difference of the Vaca Muerta play is its thickness (100 m to 450 m), as such a development strategy based solely on vertical wells is being considered in addition to the horizontal well strategy more commonly applied in other shale plays. The thickness of the Vaca Muerta formation creates new challenges and opportunities due to the stratigraphic variation in petrophysical and mechanical properties which can affect fracture effectiveness and well productivity. Completion design, geology and production performance need to be linked. Specifically, the geology of the Vaca Muerta formation, as is the case in most reservoirs, varies significantly more in the vertical direction in comparison to the horizontal direction. With optimum solutions not necessarily being intuitive, numerical simulation is critical as it enables a large number of variables to be analyzed and their individual impact understood and quantified. The objective of this paper is to present the four different approaches that have been used to build numerical models to represent the vertical wells in Vaca Muerta. These are: A single layer model with a planar fracture placed in a zone of improved permeability to represent the Stimulated Rock Volume (SRV) which is then surrounded by undisturbed matrix.A multilayer model with multiple planar fractures placed in an undisturbed matrix.A multilayer model with multiple planar fractures (one per stage), the SRV surrounding the fractures and the undisturbed matrix behind it.A multilayer model, where the SRV is modeled within a dual porosity model. This work shows how these models were constructed, the measurements that were honored and the estimation and justification of values assumed for unknown parameters. The impact of the different methodologies on the time taken and quality of the history match obtained and subsequent forecasts is also discussed. YPF has collected an extensive data set including PLTs, microseismic surveys, downhole pressure gauges, and pressure build ups, which has been used to constrain the numerical models. Building and history matching these models has been challenging but enables conclusions to be made about rock, fluid and completion interaction that cannot be obtained otherwise. The simpler models, have in some cases, enabled rapid estimates to be made for EUR which have subsequently been supported by the results from the more detailed modeling approaches.

Wells in tight gas reservoirs are often completed with multiple stages of hydraulic fracturing. Eventually, each stage contributes to the commingled well production. This paper presents a stochastic analytic production analysis technique for multistage hydraulically fractured wells*. Based on Bayes's theorem, the new technique integrates production performance data, production logs, and prior information to arrive at the most probable description of the reservoir/completions. After validating results with a numerical reservoir simulator, we systematically used the new technique to investigate the effect of data availability, i.e. the number of production logs and duration of production period, on the accuracy of the results. Introduction The process of inferring reservoir/completion parameters from the commingled production data in a multistage hydraulically fractured gas well involves the solution of an inverse problem. Such inverse problems for production analysis are typically undetermined and can lead to instability and nonuniqueness in the solution. To deal with the situation, we resort to production logs and data-independent prior information that can limit the "plausible" models that satisfy the commingled production data. We make use of Bayes's theorem to integrate prior information, production logs and commingled production performance data into reservoir/completion models for each fracture stage. The outline of our paper is as follows. First, we provide a brief mathematical description of the statistical foundation of the method and the analytical flow model. Second, we illustrate the technique using a well in a Rocky Mountain tight gas reservoir. Third, we validate the results using a coarsegrid numerical reservoir simulation model. Finally, we use simulator-generated data to systematically investigate the effect of data availability, i.e. the number of production logs and the duration of the production period on the accuracy of the computed reservoir/completion parameters. Previous Work Previous studies attempting to give a solution to this problem can be divided into two categories: allocation and non-linear regression methods. The allocation method 1 uses standard techniques for single-layer reservoirs with allocated production rates and reconstructed bottomhole pressures. The allocated production rates at times when there are no production logs are computed by linear interpolation of the observed percent contributions of each stage. If there is only one production log available, it keeps the percent contributions of each stage constant. Spivey 2 presents a concise and clear discussion of the deficiencies and limitations of the allocation method. The non-linear regression method 2 proposes the use of a multilayer analytical simulator (forward model) coupled with a non-linear regression algorithm (Levenberg-Marquardt algorithm) to find values of the individual layer properties that give the best fit to the observed well production history and production log data. Discussion of Non-Linear Regression Method Spivey 2 recognizes that, for hydraulically fractured wells, four different parameters are typically available for use as matching parameters, i.e. permeability, fracture half-length, fracture conductivity, and drainage area. However, instead of using a rigorous flow model, he states that it is often difficult to distinguish the effects of fracture conductivity from fracture half-length. This observation leads him to construct his flow simulator based on two major tenets: first, that the fracture is of infinite conductivity; and second, that the fracture conductivity and the fracture half-length can be merged into a single term, i.e. the effective fracture half-length, an idea that he borrowed from Cinco-Ley, et al3 and is applicable only when the well's flow performance is in the pseudoradial flow regime. Use of Spivey's method 2 to analyze actual data has at least three major problems. First, as stated by Cinco-Ley, et al3: "…for the pseudoradial flow period, a fractured well behaves like an unfractured well with an effective wellbore radius being a function of dimensionless fracture conductivity…"

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