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In this paper, a recently developed parameterization procedure based on principal component analysis (PCA), which is referred to as optimization-based PCA (O-PCA), is generalized for use with a wide range of geological systems. In O-PCA, the mapping between the geological model in the full-order space and the low-dimensional subspace is framed as an optimization problem. The O-PCA optimization involves the use of regularization and bound constraints, which act to extend substantially the ability of PCA to model complex (non-Gaussian) systems. The basis matrix required by O-PCA is formed using a set of prior realizations generated by a geostatistical modeling package. We show that, by varying the form of the O-PCA regularization terms, different types of geological scenarios can be represented. Specific systems considered include binaryfacies, three-facies and bimodal channelized models, and bimodal deltaic fan models. The O-PCA parameterization can be applied to generate random realizations, though our focus here is on its use for data assimilation. For this application, O-PCA is combined with the randomized maximum likelihood (RML) method to provide a subspace RML procedure that can be applied to non-Gaussian models. This approach provides multiple history-matched models, which Electronic supplementary material The online version of this article (enables an estimate of prediction uncertainty. A gradient procedure based on adjoints is used for the minimization required by the subspace RML method. The gradient of the O-PCA mapping is determined analytically or semianalytically, depending on the form of the regularization terms. Results for two-dimensional oil-water systems, for several different geological scenarios, demonstrate that the use of O-PCA and RML enables the generation of posterior reservoir models that honor hard data, retain the large-scale connectivity features of the geological system, match historical production data, and provide an estimate of prediction uncertainty. MATLAB code for the O-PCA procedure, along with examples for three-facies and bimodal models, is included as online Supplementary Material. Mathematics Subject Classification (2010)15A04 · 49N45 · 60G60 · 78M34 · 90-08 · 94A08 · 90C30

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A significant and unique factor associated with gas-condensate reservoirs is a prominent decrease in productivity once the flowing bottom-hole pressure drops below the dew-point pressure. Gas-condensate reservoirs exhibit complex phase and flow behaviors due to the appearance of a condensate bank in the near-well region, and differ in their behavior from conventional gas reservoirs, especially for low permeability, high-yield systems where the condensate banking is more severe. However, there is still a lack of understanding phase and flow behaviors of gas-condensate reservoirs. The difficulty lies in the variation of the composition of the in-situ fluid due to the accumulation of heavy components in the condensate phase. A good understanding of how the gas condensate reservoirs vary in composition is very important to optimize the producing strategy, to reduce the impact of condensate banking, and to improve the ultimate gas recovery. The composition variation has been observed in the field but its effects have been reported rarely in the literature. This work studied compositional variation of gas-condensate systems through a series of laboratory experiments and supporting numerical simulations. The study verified claims on the effect of flow through porous media on the apparent behavior of a gas-condensate mixture. These include compositional variation during depletion, failure to achieve condensate revaporization upon well shut-in, and the effect of well bottom-hole pressures on condensate banking. The effect of irreducible water saturation on the composition variation was also studied. Results from this study show that composition can vary significantly during depletion. Due to the difference in mobilities and accumulation effect, the composition of the mixture will change locally. The overall composition near the wellbore becomes richer in heavy components. As a result, the phase envelope of fluid will shift. Near-well fluids can undergo a transition from retrograde gas to volatile oil. By taking account of the new understanding of the impact of compositional changes, the liquid dropout can be “controlled” by the production strategy. Also, some common practices, for example shutting wells after condensate drops out to revaporize the condensate can be understood to be ineffective.

Due to numerical difficulties in conducting high fidelity simulation of recovery mechanisms in complex natural fracture systems, there are no published studies that address the impact of preserving details of the fracture networks. We used highly refined grids to conduct fine scale simulations of various recovery mechanisms in different complex fracture settings and compared the results to those obtained on simplified dual porosity dual permeability (DPDK) representations created by applying a consistent upscaling procedure. Our study considers densely connected, sparsely connected, and isolated fracture networks that are extracted from a field-scale fractured carbonate reservoir model. Discrete fracture-matrix (DFM) models were constructed using an unstructured grid with refinement of the matrix rock near fractures. High-resolution simulations of spontaneous imbibition, gravity drainage, and viscous displacement recovery mechanisms were conducted on these DFM models. We also built equivalent DPDK models by using single phase flow-based upscaling and actual fracture geometry and distribution. The recovery mechanisms were simulated on these DPDK models and compared to high-resolution DFM models. The fine scale simulations revealed that lateral viscous displacement recovery depends on the details of the fracture networks and can be significantly higher than those predicted from equivalent DPDK models. The DPDK models all predict the same recovery. For spontaneous imbibition, both fine scale and equivalent DPDK models show dependence on fracture geometry, but the DPDK models predict much higher rates. Fine scale and equivalent DPDK models agree reasonably for gravity drainage. These findings are explained by analyzing the matrix-fracture flows, and implications on efforts to improve shape factors in DPDK models and upscaling efforts in DFM models are discussed.