A unified formulation for generalized oilfield development optimization

Oilfield development involves several key decisions, including the number, type (injection/production), location, drilling schedule, and operating control trajectories of the wells. Without considering the coupling between these decision variables, any optimization problem formulation is bound to find suboptimal solutions. This paper presents a unified formulation for oilfield development optimization that seeks to simultaneously optimize these decision variables. We show that the source/sink term of the governing multiphase flow equations includes all the above decision variables. This insight leads to a novel and unified formulation of the field development optimization problem that considers the source/sink term in reservoir simulation equations as optimization decision variables. Therefore, a single optimization problem is formulated to simultaneously search for optimal decision variables by determining the complete dynamic form of the source/sink terms. The optimization objective function is the project net present value (NPV), which involves discounted revenue from oil production, operating costs (e.g. water injection and recycling), and capital costs (e.g., cost of drilling wells). A major difficulty after formulating the generalized field development optimization problem is finding an efficient solution approach. Since the total number of cells in a reservoir model far exceeds the number of cells that are intersected by wells, the source/sink terms tend to be sparse. In fact, the drilling cost in the NPV objective function serves as a sparsity-promoting penalty to minimize the number of wells while maximizing the NPV. Inspired by this insight, we solve the optimization problem using an efficient gradient-based method based on recent algorithmic developments in sparse reconstruction literature. The gradients of the NPV function with respect to the source/sink terms is readily computed using well-established adjoint methods. Numerical experiments are presented to evaluate the feasibility and performance of the generalized field development formulation for simultaneous optimization of the number, location, type, controls, and drilling schedule of the wells.     

A low-dimensional subsurface model for saturated and unsaturated flow processes: ability to address heterogeneity

A low-dimensional model that describes both saturated and unsaturated flow processes in a single equation is presented. Subsurface flow processes in the groundwater, the vadose zone, and the capillary fringe are accounted for through the computation of aggregated hydrodynamic parameters that result from the integration of the governing flow equations from the bedrock to the land surface. The three-dimensional subsurface flow dynamics are thus described by a two-dimensional equation, allowing for a drastic reduction of model unknowns and simplification of the model parameterizations. This approach is compared with a full resolution of the Richards equation in different synthetic test cases. Because the model reduction stems from the vertical integration of the flow equations, the test cases all use different configurations of heterogeneity for vertical cross-sections of a soil-aquifer system. The low-dimensional flow model shows strong consistency with results from a complete resolution of the Richards equation for both the water table and fluxes. The proposed approach is therefore well suited to the accurate reproduction of complex subsurface flow processes.     

Direct forecasting of reservoir performance using production data without history matching

The conventional paradigm for predicting future reservoir performance from existing production data involves the construction of reservoir models that match the historical data through iterative history matching. This is generally an expensive and difficult task and often results in models that do not accurately assess the uncertainty of the forecast. We propose an alternative re-formulation of the problem, in which the role of the reservoir model is reconsidered. Instead of using the model to match the historical production, and then forecasting, the model is used in combination with Monte Carlo sampling to establish a statistical relationship between the historical and forecast variables. The estimated relationship is then used in conjunction with the actual production data to produce a statistical forecast. This allows quantifying posterior uncertainty on the forecast variable without explicit inversion or history matching. The main rationale behind this is that the reservoir model is highly complex and even so, still remains a simplified representation of the actual subsurface. As statistical relationships can generally only be constructed in low dimensions, compression and dimension reduction of the reservoir models themselves would result in further oversimplification. Conversely, production data and forecast variables are time series data, which are simpler and much more applicable for dimension reduction techniques. We present a dimension reduction approach based on functional data analysis (FDA), and mixed principal component analysis (mixed PCA), followed by canonical correlation analysis (CCA) to maximize the linear correlation between the forecast and production variables. Using these transformed variables, it is then possible to apply linear Gaussian regression and estimate the statistical relationship between the forecast and historical variables. This relationship is used in combination with the actual observed historical data to estimate the posterior distribution of the forecast variable. Sampling from this posterior and reconstructing the corresponding forecast time series, allows assessing uncertainty on the forecast. This workflow will be demonstrated on a case based on a Libyan reservoir and compared with traditional history matching.     

A multi-domain decomposition-based Fourier finite element method for the simulation of 3D marine CSEM measurements

We introduce a multi-domain decomposition Fourier finite element (MDDFFE) method for the simulation of three-dimensional (3D) marine controlled source electromagnetic measurement (CSEM). The method combines a 2D finite element (FE) method in two spatial dimensions with a hybrid discretization based on a Fourier FE method along the third dimension. The method employs a secondary field formulation rather than the total field formulation. We apply the MDDFFE method to several synthetic marine CSEM examples exhibiting bathymetry and/or multiple 3D subdomains. Numerical results show that the use of the MDDFFE method reduces the problem size by as much as 87 % in terms of the number of unknowns, without any sacrifice in accuracy.     

A finite volume scheme with improved well modeling in subsurface flow simulation

We present the latest enhancement of the nonlinear monotone finite volume method for the near-well regions. The original nonlinear method is applicable for diffusion, advection-diffusion, and multiphase flow model equations with full anisotropic discontinuous permeability tensors on conformal polyhedral meshes. The approximation of the diffusive flux uses the nonlinear two-point stencil which reduces to the conventional two-point flux approximation (TPFA) on cubic meshes but has much better accuracy for the general case of non-orthogonal grids and anisotropic media. The latest modification of the nonlinear method takes into account the nonlinear (e.g., logarithmic) singularity of the pressure in the near-well region and introduces a correction to improve accuracy of the pressure and the flux calculation. In this paper, we consider a linear version of the nonlinear method waiving its monotonicity for sake of better accuracy. The new method is generalized for anisotropic media, polyhedral grids and nontrivial cases such as slanted, partially perforated wells or wells shifted from the cell center. Numerical experiments show noticeable reduction of numerical errors compared to the original monotone nonlinear FV scheme with the conventional Peaceman well model or with the given analytical well rate.     

Evaluation of bank filtration as a pretreatment method for the provision of hygienically safe drinking water in Norway: results from monitoring at two full-scale sites

Two case studies were carried out in central Norway in order to assess the performance of bank filtration systems in cold-climate fluvial aquifers relying on recharge from humic-rich surface waters with moderate microbial contamination. Three municipal wells and two surface-water sources at operative bank filtration systems were monitored for naturally occurring bacteriophages, fecal indicators, natural organic matter (NOM) and physico-chemical water quality parameters during a 4-month period. Aquifer passage effectively reduced the microorganism and NOM concentrations at both study sites. Bacteriophages were detected in 13 of 16 (81%) surface-water samples and in 4 of 24 (17%) well-water samples, and underwent 3 ± 0.3 log₁₀ reduction after 50–80-m filtration and 20–30 days of subsurface passage. NOM reductions (color: 74–97%; dissolved organic carbon: 54–80%; very hydrophobic acids: 70%) were similar to those achieved by conventional water-treatment processes and no further treatment was needed. Both groundwater dilution and sediment filtration contributed to the hygienic water quality improvements, but sediment filtration appeared to be the most important process with regard to microbial and NOM reductions. A strengths-weaknesses-opportunities-threats analysis showed that bank filtration technology has a high potential as a pretreatment method for the provision of hygienically safe drinking water in Norway.     

Review: Occurrence of the pathogenic amoeba <Emphasis Type="Italic">Naegleria fowleri</Emphasis> in groundwater

Naegleria fowleri is a thermophilic free-living amoeba found worldwide in soils and warm freshwater. It is the causative agent of primary amebic meningoencephalitis, a nearly always fatal disease afflicting mainly children and young adults. Humans are exposed to the organism via swimming, bathing, or other recreational activity during which water is forcefully inhaled into the upper nasal passages. Although many studies have looked at the occurrence of N. fowleri in surface waters, limited information is available regarding its occurrence in groundwater and geothermally heated natural waters such as hot springs. This paper reviews the current literature related to the occurrence of N. fowleri in these waters and the methods employed for its detection. Case reports of potential groundwater exposures are also included. Despite increased interest in N. fowleri in recent years due to well-publicized cases linked to drinking water, many questions still remain unanswered. For instance, why the organism persists in some water sources and not in others is not well understood. The role of biofilms in groundwater wells and plumbing in individual buildings, and the potential for warming due to climate change to expand the occurrence of the organism into new regions, are still unclear. Additional research is needed to address these questions in order to better understand the ecology of N. fowleri and the conditions that result in greater risks to bathers.     

Investigating the impact of the properties of pilot points on calibration of groundwater models: case study of a karst catchment in Rote Island,Indonesia

A robust configuration of pilot points in the parameterisation step of a model is crucial to accurately obtain a satisfactory model performance. However, the recommendations provided by the majority of recent researchers on pilot-point use are considered somewhat impractical. In this study, a practical approach is proposed for using pilot-point properties (i.e. number, distance and distribution method) in the calibration step of a groundwater model. For the first time, the relative distance–area ratio (d/A) and head-zonation-based (HZB) method are introduced, to assign pilot points into the model domain by incorporating a user-friendly zone ratio. This study provides some insights into the trade-off between maximising and restricting the number of pilot points, and offers a relative basis for selecting the pilot-point properties and distribution method in the development of a physically based groundwater model. The grid-based (GB) method is found to perform comparably better than the HZB method in terms of model performance and computational time. When using the GB method, this study recommends a distance–area ratio of 0.05, a distance–x-grid length ratio (d/X _grid) of 0.10, and a distance–y-grid length ratio (d/Y _grid) of 0.20.     

Mapping of groundwater prospective zones integrating remote sensing,geographic information systems and geophysical techniques in El-Qaà Plain area,Egypt

The geospatial mapping of groundwater prospective zones is essential to support the needs of local inhabitants and agricultural activities in arid regions such as El-Qaà area, Sinai Peninsula, Egypt. The study aims to locate new wells that can serve to cope with water scarcity. The integration of remote sensing, geographic information systems (GIS) and geophysical techniques is a breakthrough for groundwater prospecting. Based on these techniques, several factors contributing to groundwater potential in El-Qaà Plain were determined. Geophysical data were supported by information derived from a digital elevation model, and from geologic, geomorphologic and hydrologic data, to reveal the promising sites. All the spatial data that represent the contributing factors were integrated and analyzed in a GIS framework to develop a groundwater prospective model. An appropriate weightage was specified to each factor based on its relative contribution towards groundwater potential, and the resulting map delineates the study area into five classes, from very poor to very good potential. The very good potential zones are located in the Quaternary deposits, with flat to gentle topography, dense lineaments and structurally controlled drainage channels. The groundwater potential map was tested against the distribution of groundwater wells and cultivated land. The integrated methodology provides a powerful tool to design a suitable groundwater management plan in arid regions.     

Source partitioning of anthropogenic groundwater nitrogen in a mixed-use landscape,Tutuila, American Samoa

This study presents a modeling framework for quantifying human impacts and for partitioning the sources of contamination related to water quality in the mixed-use landscape of a small tropical volcanic island. On Tutuila, the main island of American Samoa, production wells in the most populated region (the Tafuna-Leone Plain) produce most of the island’s drinking water. However, much of this water has been deemed unsafe to drink since 2009. Tutuila has three predominant anthropogenic non-point-groundwater-pollution sources of concern: on-site disposal systems (OSDS), agricultural chemicals, and pig manure. These sources are broadly distributed throughout the landscape and are located near many drinking-water wells. Water quality analyses show a link between elevated levels of total dissolved groundwater nitrogen (TN) and areas with high non-point-source pollution density, suggesting that TN can be used as a tracer of groundwater contamination from these sources. The modeling framework used in this study integrates land-use information, hydrological data, and water quality analyses with nitrogen loading and transport models. The approach utilizes a numerical groundwater flow model, a nitrogen-loading model, and a multi-species contaminant transport model. Nitrogen from each source is modeled as an independent component in order to trace the impact from individual land-use activities. Model results are calibrated and validated with dissolved groundwater TN concentrations and inorganic δ¹⁵N values, respectively. Results indicate that OSDS contribute significantly more TN to Tutuila’s aquifers than other sources, and thus should be prioritized in future water-quality management efforts.