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.     

Well placement optimization subject to realistic field development constraints

This work considers the well placement problem in reservoir management and field development optimization. In particular, it emphasizes embedding realistic and practical constraints into a mathematical optimization formulation. Such constraints are a prerequisite for the wider use of mathematical optimization techniques in well placement problems, since constraints are a way to incorporate reservoir engineering knowledge into the problem formulation. There are important design limitations that are used by the field development team when treating the well placement problem, and these limitations need to be articulated and eventually formalized within the problem before conducting the search for optimal well placements. In addition, these design limitations may be explicit or implicit. In this work, various design limitations pertaining to well locations have been developed in close collaboration with a field operator on the Norwegian Continental Shelf. Moreover, this work focuses on developing constraint-handling capability to enforce these various considerations during optimization. In particular, the Particle Swarm Optimization (PSO) algorithm is applied to optimize for the well locations, and various practical well placement constraints are incorporated into the PSO algorithm using two different constraint-handling techniques: a decoder procedure and the penalty method. The decoder procedure maps the feasible search space onto a cube and has the advantage of not requiring parameter tuning. The penalty method converts the constrained optimization problem into an unconstrained one by introducing an additional term, which is called a penalty function, to the objective function. In contrast to the penalty method, only feasible solutions are evaluated in the decoder method. Through numerical simulations, a comparison between the penalty method and the decoder technique is performed for two cases. We show that the decoder technique can easily be implemented for the well placement problem, and furthermore, that it performs better than the penalty method in most of the cases.     

Heat tracing to examine seasonal groundwater flow beneath a low-gradient stream in rural central Illinois,USA

The thermal profile of a streambed is affected by a number of factors including: temperatures of stream water and groundwater, hydraulic conductivity, thermal conductivity, heat capacity of the streambed, and the geometry of hyporheic flow paths. Changes in these parameters over time cause changes in thermal profiles. In this study, temperature data were collected at depths of 30, 60, 90 and 150 cm at six streambed wells 5 m apart along the thalweg of Little Kickapoo Creek, in rural central Illinois, USA. This is a third-order low-gradient baseflow-fed stream. A positive temperature gradient with inflection at 90-cm depth was observed during the summer period. A negative temperature gradient with inflection at 30 cm was observed during the winter period, which suggests greater influence of stream-water temperatures in the substrate during the summer. Thermal models of the streambed were built using VS2DHI to simulate the thermal profiles observed in the field. Comparison of the parameters along with analysis of temperature envelopes and Peclet numbers suggested greater upwelling and stability in temperatures during the winter than during the summer. Upwelling was more pronounced in the downstream reach of the pool in the riffle and pool sequence.     

The Influence of Bioturbation on Iron and Sulphur Cycling in Marine Sediments: A Model Analysis

The geochemical cycles of iron and sulphur in marine sediments are strongly intertwined and give rise to a complex network of redox and precipitation reactions. Bioturbation refers to all modes of transport of particles and solutes induced by larger organisms, and in the present-day seafloor, bioturbation is one of the most important factors controlling the biogeochemical cycling of iron and sulphur. To better understand how bioturbation controls Fe and S cycling, we developed reactive transport model of a coastal sediment impacted by faunal activity. Subsequently, we performed a model sensitivity analysis, separately investigating the two different transport modes of bioturbation, i.e. bio-mixing (solid particle transport) and bio-irrigation (enhanced solute transport). This analysis reveals that bio-mixing and bio-irrigation have distinct—and largely opposing effects on both the iron and sulphur cycles. Bio-mixing enhances transport between the oxic and suboxic zones, thus promoting the reduction of oxidised species (e.g. iron oxyhydroxides) and the oxidation of reduced species (e.g. iron sulphides). Through the re-oxidation of iron sulphides, bio-mixing strongly enhances the recycling of Fe and S between their reduced and oxidised states. Bio-irrigation on the other hand removes reduced solutes, i.e. ferrous iron and free sulphide, from the sediment pore water. These reduced species are then reoxidised in the overlying water and not recycled within the sediment column, which leads to a decrease in Fe and S recycling. Overall, our results demonstrate that the ecology of the macrofauna (inducing bio-mixing or bio-irrigation, or both) matters when assessing their impact on sediment geochemistry. This finding seems particularly relevant for sedimentary cycling across Cambrian transition, when benthic fauna started colonizing and reworking the seafloor.     

Recycling of Organic Matter in the Sediments of Santa Monica Basin,California Borderland

Geochemical and isotopic data for the uppermost 1.2 m of the sediments of the central Santa Monica Basin plain were examined to better understand organic matter deposition and recycling at this site. Isotopic signatures (Δ¹⁴C and δ¹³C) of methane (CH₄) and dissolved inorganic carbon (DIC) indicate the occurrence of anaerobic oxidation of CH₄ that is fueled by CH₄ supplied from a relict reservoir that is decoupled from local organic carbon (C_org) degradation and methanogenesis. This finding was corroborated by a flux budget of pore-water solutes across the basal horizon of the profile. Together these results provide a plausible explanation for the anomalously low ratio between alkalinity production and sulfate consumption reported for these sediments over two decades ago. Shifts in Δ¹⁴C and δ¹³C signatures of C_org have previously been reported across the 20-cm depth horizon for this site and attributed to a transition from oxic to anoxic bottom water that occurred ~350 years BP. However, we show that this horizon also coincides with a boundary between the base of a hemipelagic mud section and the top of a turbidite interval, complicating the interpretation of organic geochemical data across this boundary. Radiocarbon signatures of DIC diffusing upward into surface sediments indicate that remineralization at depth is supported by relatively ¹⁴C-enriched C_org within the sedimentary matrix. While the exact nature of this C_org is unclear, possible sources are hemipelagic mud sections that were buried rapidly under thick turbidites, and ¹⁴C-rich moieties dispersed within C_org-poor turbidite sections.     

Variations of Hydrodynamics and Submarine Groundwater Discharge in the Yellow River Estuary Under the Influence of the Water-Sediment Regulation Scheme

The “Water-Sediment Regulation Scheme” (WSRS) is critically important to the hydrologic evaluation of the Yellow River estuary since a huge pulse of water and sediment are delivered into the sea during a short period. We used the natural geochemical tracers radium (²²³Ra, ²²⁴Ra, ²²⁶Ra) and radon (²²²Rn) isotopes as well as other hydrological parameters to investigate the mixing variations and submarine groundwater discharge (SGD) in the Yellow River estuary under the influence of the 2013 WSRS. Dramatically elevated radium and radon isotopic activities were observed during this WSRS compared with activities measured during a non-WSRS period. Radium “water ages” indicated that the offshore transport rate nearly tripled when the river discharge increased from 400 to 3400 m³/s. We calculated the SGD flux in the Yellow River estuary based on a radium mass balance model as well as radium and radon time-series models. The SGD flux was estimated at 0.02~0.20 m/day during a non-WSRS period and 0.67~1.22 m/day during the 2013 WSRS period. The results also indicate that large river discharge tends to lead more intense SGD along the river channel direction with a large amount of fresh SGD.