Indirect unstructured hex-dominant mesh generation using tetrahedra recombination

Corner-point gridding is widely used in reservoir and basin modeling but generally yields approximations in the representation of geological interfaces. This paper introduces an indirect method to generate a hex-dominant mesh conformal to 3D geological surfaces and well paths suitable for finite-element and control-volume finite-element simulations. By indirect, we mean that the method first generates an unstructured tetrahedral mesh whose tetrahedra are then merged into primitives (hexahedra, prisms, and pyramids). More specifically, we focus on determining the optimal set of primitives that can be recombined from a given tetrahedral mesh. First, we detect in the tetrahedral mesh all the feasible volumetric primitives using a pattern-matching algorithm (Meshkat and Talmor Int. J. Numer. Meth. Eng. 49(1-2), 17–30 2000) that we re-visit and extend with configurations that account for degenerated tetrahedra (slivers). Then, we observe that selecting the optimal set of primitives among the feasible ones can be formalized as a maximum weighted independent set problem (Bomze et al. 1999), known to be \(\mathcal {N}\mathcal {P}\)-Complete. We propose several heuristic optimizations to find a reasonable set of primitives in a practical time. All the tetrahedra of each selected primitive are then merged to build the final unstructured hex-dominant mesh. This method is demonstrated on 3D geological models including a faulted and folded model and a discrete fracture network.     

Using a Thermal Proxy to Examine Sediment–Water Exchange in Mid-Continental Shelf Sandy Sediments

Fluid exchange across the sediment–water interface in a sandy open continental shelf setting was studied using heat as a tracer. Summertime tidal oscillation of cross-shelf thermal fronts on the South Atlantic Bight provided a sufficient signal at the sediment–water interface to trace the advective and conductive transport of heat into and out of the seabed, indicating rapid flushing of ocean water through the upper 10–40 cm of the sandy seafloor. A newly developed transport model was applied to the in situ temperature data set to estimate the extent to which heat was transported by advection rather than conduction. Heat transported by shallow 3-D porewater flow processes was accounted for in the model by using a dispersion term, the depth and intensity of which reflected the depth and intensity of shallow flushing. Similar to the results of past studies in shallower and more energetic nearshore settings, transport of heat was greater when higher near-bed velocities and shear stresses occurred over a rippled bed. However, boundary layer processes by themselves were insufficient to promote non-conductive heat transport. Advective heat transport only occurred when both larger boundary layer stresses and thermal instabilities within the porespace were present. The latter process is dependent on shelf-scale heating and cooling of bottom water associated with upwelling events that are not coupled to local-scale boundary layer processes.     

Benthic Carbon Mineralization and Nutrient Turnover in a Scottish Sea Loch: An Integrative In Situ Study

Based on in situ microprofiles, chamber incubations and eddy covariance measurements, we investigated the benthic carbon mineralization and nutrient regeneration in a ~65-m-deep sedimentation basin of Loch Etive, UK. The sediment hosted a considerable amount of infauna that was dominated by the brittle star A. filiformis. The numerous burrows were intensively irrigated enhancing the benthic in situ O₂ uptake by ~50 %, and inducing highly variable redox conditions and O₂ distribution in the surface sediment as also documented by complementary laboratory-based planar optode measurements. The average benthic O₂ exchange as derived by chamber incubations and the eddy covariance approach were similar (14.9 ± 2.5 and 13.1 ± 9.0 mmol m^?2 day^?1) providing confidence in the two measuring approaches. Moreover, the non-invasive eddy approach revealed a flow-dependent benthic O₂ flux that was partly ascribed to enhanced ventilation of infauna burrows during periods of elevated flow rates. The ratio in exchange rates of ΣCO₂ and O₂ was close to unity, confirming that the O₂ uptake was a good proxy for the benthic carbon mineralization in this setting. The infauna activity resulted in highly dynamic redox conditions that presumably facilitated an efficient degradation of both terrestrial and marine-derived organic material. The complex O₂ dynamics of the burrow environment also concurrently stimulated nitrification and coupled denitrification rates making the sediment an efficient sink for bioavailable nitrogen. Furthermore, bioturbation mediated a high efflux of dissolved phosphorus and silicate. The study documents a high spatial and temporal variation in benthic solute exchange with important implications for benthic turnover of organic carbon and nutrients. However, more long-term in situ investigations with like approaches are required to fully understand how environmental events and spatio-temporal variations interrelate to the overall biogeochemical functioning of coastal sediments.     

The Dynamics of Benthic Respiration at a Mid-Shelf Station Off Oregon

Mid-shelf sediments off the Oregon coast are characterized as fine sands that trap and remineralize phytodetritus leading to the consumption of significant quantities of dissolved oxygen. Sediment oxygen consumption (SOC) can be delayed from seasonal organic matter inputs because of a transient buildup of reduced constituents during periods of quiescent physical processes. Between 2009 and 2013, benthic oxygen exchange rates were measured using the noninvasive eddy covariance (EC) method five separate times at a single 80-m station. Ancillary measurements included in situ microprofiles of oxygen at the sediment–water interface, and concentration profiles of pore water nutrients and trace metals, and solid-phase organic C and sulfide minerals from cores. Sediment cores were also incubated to derive anaerobic respiration rates. The EC measurements were made during spring, summer, and fall conditions, and they produced average benthic oxygen flux estimates that varied between ?2 and ?15 mmol m^?2 d^?1. The EC oxygen fluxes were most highly correlated with bottom-sensed, significant wave heights (H _s). The relationship with H _s was used with an annual record of deepwater swell heights to predict an integrated oxygen consumption rate for the mid-shelf of 1.5 mol m^?2 for the upwelling season (May–September) and 6.8 mol m^?2 y^?1. The annual prediction requires that SOC rates are enhanced in the winter because of sand filtering and pore water advection under large waves, and it counters budgets that assume a dominance of organic matter export from the shelf. Refined budgets will require winter flux measurements and observations from cross-shelf transects over multiple years.     

Beyond dual-porosity modeling for the simulation of complex flow mechanisms in shale reservoirs

The state of the art of modeling fluid flow in shale reservoirs is dominated by dual-porosity models which divide the reservoirs into matrix blocks that significantly contribute to fluid storage and fracture networks which principally control flow capacity. However, recent extensive microscopic studies reveal that there exist massive micro- and nano-pore systems in shale matrices. Because of this, the actual flow mechanisms in shale reservoirs are considerably more complex than can be simulated by the conventional dual-porosity models and Darcy’s law. Therefore, a model capturing multiple pore scales and flow can provide a better understanding of the complex flow mechanisms occurring in these reservoirs. This paper presents a micro-scale multiple-porosity model for fluid flow in shale reservoirs by capturing the dynamics occurring in three porosity systems: inorganic matter, organic matter (mainly kerogen), and natural fractures. Inorganic and organic portions of shale matrix are treated as sub-blocks with different attributes, such as wettability and pore structures. In kerogen, gas desorption and diffusion are the dominant physics. Since the flow regimes are sensitive to pore size, the effects of nano-pores and micro-pores in kerogen are incorporated into the simulator. The multiple-porosity model is built upon a unique tool for simulating general multiple-porosity systems in which several porosity systems may be tied to each other through arbitrary connectivities. This new model allows us to better understand complex flow mechanisms and eventually is extended into the reservoir scale through upscaling techniques. Sensitivity studies on the contributions of the different flow mechanisms and kerogen properties give some insight as to their importance. Results also include a comparison of the conventional dual-porosity treatment and show that significant differences in fluid distributions and dynamics are obtained with the improved multiple-porosity simulation.     

Generalized field-development optimization with well-control zonation

Of concern in the development of oil fields is the problem of determining the optimal locations of wells and the optimal controls to place on the wells. Extraction of hydrocarbon resources from petroleum reservoirs in a cost-effective manner requires that the producers and injectors be placed at optimal locations and that optimal controls be imposed on the wells. While the optimization of well locations and well controls plays an important role in ensuring that the net present value of the project is maximized, optimization of other factors such as well type and number of wells also plays important roles in increasing the profitability of investments. Until very recently, improving the net worth of hydrocarbon assets has been focused primarily on optimizing the well locations or well controls, mostly manually. In recent times, automatic optimization using either gradient-based algorithms or stochastic (global) optimization algorithms has become increasingly popular. A well-control zonation (WCZ) approach to estimating optimal well locations, well rates, well type, and well number is proposed. Our approach uses a set of well coordinates and a set of well-control variables as the optimization parameters. However, one of the well-control variables has its search range extended to cover three parts, one part denoting the region where the well is an injector, a second part denoting the region where there is no well, and a third part denoting the region where the well is a producer. By this, the optimization algorithm is able to match every member in the set of well coordinates to three possibilities within the search space of well controls: an injector, a no-well situation, or a producer. The optimization was performed using differential evolution, and two sample applications were presented to show the effectiveness of the method. Results obtained show that the method is able to reduce the number of optimization variables needed and also to identify simultaneously, optimal well locations, optimal well controls, optimal well type, and the optimum number of wells. Also, comparison of results with the mixed integer nonlinear linear programming (MINLP) approach shows that the WCZ approach mostly outperformed the MINLP approach.     

Quantifying fracture geometry with X-ray tomography: Technique of Iterative Local Thresholding (TILT) for 3D image segmentation

This paper presents a new method—the Technique of Iterative Local Thresholding (TILT)—for processing 3D X-ray computed tomography (xCT) images for visualization and quantification of rock fractures. The TILT method includes the following advancements. First, custom masks are generated by a fracture-dilation procedure, which significantly amplifies the fracture signal on the intensity histogram used for local thresholding. Second, TILT is particularly well suited for fracture characterization in granular rocks because the multi-scale Hessian fracture (MHF) filter has been incorporated to distinguish fractures from pores in the rock matrix. Third, TILT wraps the thresholding and fracture isolation steps in an optimized iterative routine for binary segmentation, minimizing human intervention and enabling automated processing of large 3D datasets. As an illustrative example, we applied TILT to 3D xCT images of reacted and unreacted fractured limestone cores. Other segmentation methods were also applied to provide insights regarding variability in image processing. The results show that TILT significantly enhanced separability of grayscale intensities, outperformed the other methods in automation, and was successful in isolating fractures from the porous rock matrix. Because the other methods are more likely to misclassify fracture edges as void and/or have limited capacity in distinguishing fractures from pores, those methods estimated larger fracture volumes (up to 80 %), surface areas (up to 60 %), and roughness (up to a factor of 2). These differences in fracture geometry would lead to significant disparities in hydraulic permeability predictions, as determined by 2D flow simulations.     

A multiobjective steepest descent method with applications to optimal well control

Multiobjective optimization deals with mathematical optimization problems where two or more objective functions (cost functions) are to be optimized (maximized or minimized) simultaneously. In most cases of interest, the objective functions are in conflict, i.e., there does not exist a decision (design) vector (vector of optimization variables) at which every objective function takes on its optimal value. The solution of a multiobjective problem is commonly defined as a Pareto front, and any decision vector which maps to a point on the Pareto front is said to be Pareto optimal. We present an original derivation of an analytical expression for the steepest descent direction for multiobjective optimization for the case of two objectives. This leads to an algorithm which can be applied to obtain Pareto optimal points or, equivalently, points on the Pareto front when the problem is the minimization of two conflicting objectives. The method is in effect a generalization of the steepest descent algorithm for minimizing a single objective function. The steepest-descent multiobjective optimization algorithm is applied to obtain optimal well controls for two example problems where the two conflicting objectives are the maximization of the life-cycle (long-term) net-present-value (NPV) and the maximization of the short-term NPV. The results strongly suggest the multiobjective steepest-descent (MOSD) algorithm is more efficient than competing multiobjective optimization algorithms.     

A semi-implicit method for incompressible three-phase flow in porous media

In this paper, we present a semi-implicit method for the incompressible three-phase flow equations in two dimensions. In particular, a high-order discontinuous Galerkin spatial discretization is coupled with a backward Euler discretization in time. We consider a pressure-saturation formulation, decouple the pressure and saturation equations, and solve them sequentially while still keeping each equation implicit in its respective unknown. We present several numerical examples on both homogeneous and heterogeneous media, with varying permeability and porosity. Our results demonstrate the robustness of the scheme. In particular, no slope limiters are required and a relatively large time step may be taken.