Near-well effects can have a strong impact on many subsurface flow processes. In oil production, because dissolved gas is released from the oil phase when the pressure falls below the bubble point, the detailed pressure field in the immediate vicinity of a production well strongly impacts gas (and thus oil) production. This effect is complicated by the interplay of fine-scale heterogeneity and two-phase flow physics, and can be difficult to capture in coarse-grid simulations. In this article, we develop and apply a new upscaling (coarsegraining) procedure to capture such near-well subgrid effects in coarse-scale flow simulation models. The method entails the use of preprocessing computations over near-well domains [referred to as local well models (LWM)] for the determination of upscaled single-phase and two-phase near-well parameters. These parameters are computed by minimizing the mismatch between fine and coarse-scale flows over the LWM. Minimization is accomplished using a gradient-based optimization procedure, with gradients calculated through solution of adjoint equations. The boundary conditions applied on the LWM can impact the upscaled parameters, but these boundary conditions depend on the global flow and are not, therefore, known a priori. In order to circumvent this difficulty, an adaptive local-global procedure is applied. This entails performing a global coarse-scale simulation with initial estimates for well-block parameters. The resulting pressure and saturation fields are then used to define local boundary conditions for the near-well computations. The overall procedure is applied to several example problems and is shown to provide results in close agreement with reference fine-scale computations. Significant improvement in accuracy over existing near-well upscaling treatments is demonstrated, particularly for a heavy oil case with oil viscosity of ∼10 4 cp.

Large-scale flow models constructed using standard coarsening procedures may not accurately resolve detailed near-well effects. Such effects are often important to capture, however, as the interaction of the well with the formation can have a dominant impact on process performance. In this work, a near-well upscaling procedure, which provides three-phase wellblock properties, is developed and tested. The overall approach represents an extension of a recently developed oil-gas upscaling procedure and entails the use of local well computations (over a region referred to as the local well model (LWM)) along with a gradient-based optimization procedure to minimize the mismatch between fine and coarse-scale well rates, for oil, gas, and water, over the LWM. The gradients required for the minimization are computed efficiently through solution of adjoint equations. The LWM boundary conditions are determined using an iterative local-global procedure. With this approach, pressures and saturations computed during a global coarse-scale simulation are interpolated onto LWM boundaries and then used as boundary conditions for the fine-scale LWM computations. In addition to extending the overall approach to the three-phase case, this work also introduces new treatments that provide improved accuracy in cases with significant flux from the gas cap into the well block. The near-well multiphase upscaling method is applied to heterogeneous reservoir models, with production from vertical and horizontal wells. Simulation results illustrate that the method is able to accurately capture key near-well effects and to provide predictions for component production rates that are in close agreement with reference fine-scale results. The level of accuracy of the procedure is shown to be significantly higher than that of a standard approach which uses only upscaled single-phase flow parameters.

Appropriate modeling of naturally fractured reservoirs is one of the most important and challenging issues in reservoir characterization. In simulation, a double porosity or dual permeability model is applied when fractures are well developed to form a fracture network. On the other hand, the single-continuum approach, where the fracture system is represented by effective permeability, is commonly used if fractures are discrete or disconnected. Focusing on the latter case, this paper proposes a semi-analytical technique to evaluate effective permeability for periodically or randomly fractured media including infinitely thin, infinite-conductivity fractures. The complex variable boundary element method is used to compute potential and stream functions in the two-dimensional space for discretely distributed fracture system under the periodic boundary conditions. Effective permeability is evaluated first for discrete fracture systems of regular patterns as well as a single inclined fracture to demonstrate the validity of the method. 500 distributions of stochastic fractures are next generated to establish correlation between effective permeability and the fracture statistics, i.e., total length L, mean length m, and standard deviation of fracture length s. Sensitivity to the parameters shows that the incremental gain of effective permeability is proportional to L, that the larger m, the larger effective permeability, and that non-zero s increases effective permeability. The effective permeability tensors are also determined for oriented fractures. Analyses by non-parametric regression show that the diagonal elements, kxx and kyy are highly affected by the angle between the oriented fractures and the pressure gradient, while the off-diagonal elements kxy and kyx are strongly affected by both the total length and the angle. Introduction Simulation of naturally fractured reservoirs is conducted commonly by either the continuum or the discrete fracture method. The double porosity or dual permeability method is a typical approach of the continuum model where fractures are assumed to distribute regularly and to be well connected1. The discrete fracture method2 assumes zero matrix permeability, though a fracture system can be modeled more realistically. Naturally fractured reservoirs often comprise irregularly distributed and disconnected fractures which are developed in matrix rock of non-zero permeability. The single-continuum approach, where the fracture system is represented by effective permeability, is more appropriate and flexible to simulate behaviors of naturally fractured reservoirs. Durlofsky3 presented a numerical procedure for computing the effective permeability of a region of periodically distributed heterogeneity. The method first solves the pressure equation over the periodical unit subject to periodic boundary conditions, and then upscales the velocity field to yield the effective permeability. Lough et al.4,5 proposed a method to estimate the effective permeability of grid blocks used in continuum simulation of naturally fractured reservoirs. The boundary element method was employed to solve the boundary integral equations for the pressure under periodic boundary conditions. They applied the method to a fracture system generated using statistical data of fracture length, orientation, and intensity from an actual reservoir. In calculations of the effective permeability for various sedimentary structures, Pickup et al.6 investigated effectiveness of the periodic boundary condition method, and necessity of the tensor permeability. According to them, the periodic boundary condition method is computationally fast, and robust to always produce a symmetric, positive definite tensor. They also concluded that permeability tensors are required for layers of a high bedding angle, high permeability contrast, and comparable thickness.

Hydrocarbon gas injection projects are undertaken in order to maintain reservoir pressure, produce oil through swelling and reduce residual oil saturation by decreasing the interfacial tension (IFT). Along with local displacement efficiency, macroscopic sweep efficiency plays a dominant role in the success of gas injection projects, as recovery from the field depends strongly on reservoir geology and petrophysical properties.In this paper, a procedure to screen the best injectant for implementation of a successful gas injection pilot project is discussed. To determine the microscopic sweep efficiency, PVT experiments and coreflood tests are conducted. First, minimum miscibility pressure (MMP), oil solubility and IFT values are measured through PVT experiments, which is followed by unsteady-state coreflood experiments on 200 cm long cores to evaluate the sweep efficiency at miscible and immiscible conditions. Data from the experiments are used to evaluate oil recovery in a sector model extracted from the full field model. The sector model analysis for different injection scenarios provides sweep efficiency and guidelines for the implementation of the gas injection pilot project.The coreflood experiments show improvement in recovery in immiscible conditions due to oil swelling and reduction in IFT, while higher recovery is achieved in miscible conditions due to multiple-contact miscibility. Evaluation of the macroscopic sweep efficiency in the sector model highlights the issue of gas override, and suggests improving the sweep by gas enrichment, as well as water-alternating-gas injection (WAG).

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