Fahim Forouzanfar

Well placement and control optimization for WAG/SAG processes using ensemble-based method

Abstract Compared to the CO2 flooding, the alternative injection of water/surfactant solution and CO2 gas (WAG/SAG) can provide good control over the mobility ratio, stabilize the displacement front and improve the macroscopic sweep efficiency of the flooding. We show that the performance of a WAG/SAG flood can be significantly improved by optimizing the locations and optimizing rates or pressure in order to avoid gas/water channelling and improve sweep efficiency. To maximize the life-cycle net present value (NPV) for a WAG/SAG process, we implemented a steepest ascent algorithm combined with a simplex stochastic gradient to find the optimal well trajectories and controls. Both simultaneous and sequential approaches for the joint optimization of well locations and controls are investigated for a synthetic channelized reservoir model. Well spacing constraints are also included in the optimization process using the penalty method in order to keep the distance between wells greater than a specified minimum value. Four synthetic reservoir problems are studied and optimized to illustrate the viability of the methodology.

Estimation of Optimal Well Controls Using the Augmented Lagrangian Function with Approximate Derivatives

Abstract When efficient adjoint code for computing the necessary gradients is available, the augmented Lagrangian algorithm provides an efficient and robust method for constrained optimization. Here, we develop an augmented Lagrangian algorithm for constrained optimization problems where adjoint code is not available, and the number of optimization variables is so large that the approximation of gradients with the finite-difference method is not computationally feasible. Our procedure applies a pre-conditioned steepest ascent algorithm to maximize an augmented Lagrangian function which directly incorporates all bound constraints as well as all inequality and equality constraints. The pre-conditioned gradient of the augmented Lagrangian is estimated directly using a simultaneous perturbation stochastic approximation (SPSA) with Gaussian perturbations where the preconditioning matrix is a covariance matrix selected to impose a degree of temporal smoothness on the optimization variables, which, for the specific application considered here, are the well controls. Our implementation of this augmented Lagrangian method is applied to estimate the well controls which maximize the net present value (NPV) of production for the remaining life of a given oil reservoir.

History matching of multi-facies channelized reservoirs using ES-MDA with common basis DCT

History matching a channelized reservoir with multiple facies has always posed a great challenge to researchers. In this paper, we present a workflow combining the ensemble smoother with multiple data assimilation (ES-MDA) method with a parameterization algorithm referred to as the common basis discrete cosine transform (DCT) and a post-processing technique in order to integrate static and dynamic data into multi-facies channelized reservoir models. The parameterization algorithm is developed to capture the critical features and describe the geological similarity between different realizations in the prior ensemble by transforming the discrete facies indicators into continuous variables. And the ES-MDA method is employed to update the continuous variables by assimilating the static and dynamic data. Finally, a post-processing technique based on a regularization framework is used to improve the spatial continuity of facies and estimate the non-Gaussian distributed reservoir properties. We apply this automatic history matching workflow to two synthetic problems that represent complex three-facies (shale, levee, and sand) channelized reservoirs. One is a 2D three-facies reservoir with a relatively high number of channels and the other is a 3D three-facies five-layer reservoir containing two geological zones with different channel patterns. The computational results show that the proposed workflow can greatly reduce the uncertainty in the reservoir description through the integration of production data. And the posterior realizations can well preserve the key geological features of the prior models, with a good history data match and predictive capacity. In addition, we also illustrate the superiority of the common basis DCT over the traditional DCT algorithm.

Uncertainty Reduction in Reservoir Geostatistical Description Using Distributed Temperature Sensing (DTS) Systems Data

Downhole temperature measurements provide valuable data for characterizing the flow between the reservoir and wellbore, which in turn is a function of the individual reservoir layer properties. In this paper we investigate the use of downhole temperature profile data, provided from Distributed Temperature Sensing (DTS) systems, as a cost effective and robust alternative to other common approaches, such as using data from production logging tools, for estimating the formation properties and production profile along the wellbore. Previous applications of history matching techniques using downhole temperature profile data have been mostly limited to simple reservoirs, and the quality of their results were unacceptable for more complex cases. In this work, we present the evaluation and application of temperature profile data from DTS systems for the purpose of uncertainty reduction in the reservoir description. We focus on the characterization of multi-layer multi-phase reservoir cases with a high degree of vertical heterogeneity. First, using the principles of information theory we investigate the information content of the temperature profile data regarding various reservoir properties. By computing the mutual information between the reservoir parameters and the temperature profile data, the reservoir properties with higher influence on the reservoir and wellbore temperature profile data are identified. The associated uncertainty in these reservoir properties can be reduced by assimilating the downhole temperature profile data. Through these analysis, we also present an estimation for the expected reduction of uncertainty in the reservoir properties by assimilating the temperature data. Then, we apply the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) algorithm to estimate the reservoir properties selected based on our previous analysis. The set of observed data contains the wellbore temperature profile, the temperature profile of the reservoir adjacent to the wellbore, and the flowing bottomhole pressure (BHP) of the well at a reference depth. We investigate the performance of the history matching algorithm using various combinations of these observed data for estimating the properties of a synthetic layered reservoir. Additionally, the implementation of a doubly stochastic model is also investigated to account for possible uncertainties in the prior mean of the reservoir properties. Our results show that the downhole temperature profile data contain significant amount of information about the permeability and porosity of the reservoir layers. Moreover, the use of temperature profile data within the ES-MDA history matching algorithm is able to provide a good estimation of these properties and significantly reduce the uncertainty in the reservoir description.