A General Spatio-Temporal Clustering-Based Non-local Formulation for Multiscale Modeling of Compartmentalized Reservoirs

Representing the reservoir as a network of discrete compartments with neighbor and non-neighbor connections is a fast, yet accurate method for analyzing oil and gas reservoirs. Automatic and rapid detection of coarse-scale compartments with distinct static and dynamic properties is an integral part of such high-level reservoir analysis. In this work, we present a hybrid framework specific to reservoir analysis for an automatic detection of clusters in space using spatial and temporal field data, coupled with a physics-based multiscale modeling approach. In this work a novel hybrid approach is presented in which we couple a physics-based non-local modeling framework with data-driven clustering techniques to provide a fast and accurate multiscale modeling of compartmentalized reservoirs. This research also adds to the literature by presenting a comprehensive work on spatio-temporal clustering for reservoir studies applications that well considers the clustering complexities, the intrinsic sparse and noisy nature of the data, and the interpretability of the outcome. Keywords: Artificial Intelligence; Machine Learning; Spatio-Temporal Clustering; Physics-Based Data-Driven Formulation; Multiscale Modelin

Upscaling and Multiscale Reservoir Simulation Using Pressure Transient Concepts

Fluid flow in subsurface petroleum reservoirs occurs on a wide range of length scales and capturing all the relevant scales in reservoir modeling is a cumbersome task. Even with the advent of modern computational resources, reservoir simulation of high resolution fine scale geologic models remain a challenge. Therefore, it is customary to use some kind of upscaling procedure to coarsen the multimillion cell geologic models to a scale feasible for practical reservoir simulation. Existing methods for upscaling of geologic models are based on steady state concepts of flow while the actual flow simulations itself is utilized for the purpose of capturing pressure and saturation transients. However, steady state or pseudo steady state limits may never be achieved for a coarse cell volume during a simulation time step in high contrast low permeability systems introducing a potentially significant bias into an upscaling or downscaling calculation. In this dissertation, a novel formulation is proposed which resolves these dynamic effects using an asymptotic pressure solution. Three principal research contributions are made in this dissertation. First, a novel construction of transmissibility in 1D is derived using pseudo steady state concepts which has the advantage of localization over steady state methods, when applied for upscaling problems. This construction is general for all grid geometries usually utilized in industry standard reservoir simulation codes (block centered, radial, corner point). A new form of pressure averaging is proposed to effectively convert a 3D pseudo steady state upscaling into a 1D calculation. Second, a pressure transient diffuse source upscaling formulation is introduced to identify well-connected sub volume that reaches pseudo steady state especially in high contrast systems. The formulation is based on transients approaching pseudo steady state in the upscaling region which can effectively identify the well-connected sub volume that contributes the flow. Third, the pressure transient diffuse source formulation developed for upscaling is extended to the multiscale framework where the large scale changes in pressure are resolved on the coarse grid while the saturations are resolved on the fine scale using downscaled coarse information. Applications are shown for both incompressible and slightly compressible flow

Nonlinear Acceleration of Sequential Fully Implicit (SFI) Method for Coupled Flow and Transport in Porous Media

The sequential fully implicit (SFI) method was introduced along with the development of the multiscale finite volume (MSFV) framework, and has received considerable attention in recent years. Each time step for SFI consists of an outer loop to solve the coupled system, in which there is one inner Newton loop to implicitly solve the pressure equation and another loop to implicitly solve the transport equations. Limited research has been conducted that deals with the outer coupling level to investigate the convergence performance. In this paper we extend the basic SFI method with several nonlinear acceleration techniques for improving the outer-loop convergence. Specifically, we consider numerical relaxation, quasi-Newton (QN) and Anderson acceleration (AA) methods. The acceleration techniques are adapted and studied for the first time within the context of SFI for coupled flow and transport in porous media. We reveal that the iterative form of SFI is equivalent to a nonlinear block Gauss-Seidel (BGS) process. The effectiveness of the acceleration techniques is demonstrated using several challenging examples. The results show that the basic SFI method is quite inefficient, suffering from slow convergence or even convergence failure. In order to better understand the behaviors of SFI, we carry out detailed analysis on the coupling mechanisms between the sub-problems. Compared with the basic SFI method, superior convergence performance is achieved by the acceleration techniques, which can resolve the convergence difficulties associated with various types of coupling effects. We show across a wide range of flow conditions that the acceleration techniques can stabilize the iterative process, and largely reduce the outer iteration count

FV-MHMM method for reservoir modeling

The present paper proposes a new family of multiscale finite volume methods. These methods usually deal with a dual mesh resolution, where the pressure field is solved on a coarse mesh, while the saturation fields, which may have discontinuities, are solved on a finer reservoir grid, on which petrophysical heterogeneities are defined. Unfortunately, the efficiency of dual mesh methods is strongly related to the definition of up-gridding and down-gridding steps, allowing defining accurately pressure and saturation fields on both fine and coarse meshes and the ability of the approach to be parallelized. In the new dual mesh formulation we developed, the pressure is solved on a coarse grid using a new hybrid formulation of the parabolic problem. This type of multiscale method for pressure equation called multiscale hybrid-mixed method (MHMM) has been recently proposed for finite elements and mixed-finite element approach (Harder et al. 2013). We extend here the MH-mixed method to a finite volume discretization, in order to deal with large multiphase reservoir models. The pressure solution is obtained by solving a hybrid form of the pressure problem on the coarse mesh, for which unknowns are fluxes defined on the coarse mesh faces. Basis flux functions are defined through the resolution of a local finite volume problem, which accounts for local heterogeneity, whereas pressure continuity between cells is weakly imposed through flux basis functions, regarded as Lagrange multipliers. Such an approach is conservative both on the coarse and local scales and can be easily parallelized, which is an advantage compared to other existing finite volume multiscale approaches. It has also a high flexibility to refine the coarse discretization just by refinement of the lagrange multiplier space defined on the coarse faces without changing nor the coarse nor the fine meshes. This refinement can also be done adaptively w.r.t. a posteriori error estimators. The method is applied to single phase (well-testing) and multiphase flow in heterogeneous porous medi