Interior boundary-aligned unstructured grid generation and cell-centered versus vertex-centered CVD-MPFA performance

Grid generation for reservoir simulation must honor classical key constraints and be boundary aligned such that control-volume boundaries are aligned with geological features such as layers, shale barriers, fractures, faults, pinch-outs, and multilateral wells. An unstructured grid generation procedure is proposed that automates control-volume and/or control point boundary alignment and yields a PEBI-mesh both with respect to primal and dual (essentially PEBI) cells. In order to honor geological features in the primal configuration, we introduce the idea of protection circles, and to generate a dual-cell feature based grid, we construct halos around key geological features. The grids generated are employed to study comparative performance of cell-centred versus cell-vertex control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulations using equivalent degrees of freedom. The formulation of CVD-MPFA schemes in cell-centred and cell-vertex modes is analogous and requires switching control volume from primal to dual or vice versa together with appropriate data structures and boundary conditions. The relative benefits of both types of approximation, i.e., cell-centred versus vertex-centred, are made clear in terms of flow resolution and degrees of freedom required.     

Ensemble clustering for efficient robust optimization of naturally fractured reservoirs

In the development of naturally fractured reservoirs (NFRs), the existence of natural fractures induces severe fingering and breakthrough. To manage the flooding process and improve the ultimate recovery, we propose a numerical workflow to generate optimal production schedules for smart wells, in which the inflow control valve (ICV) settings can be controlled individually. To properly consider the uncertainty introduced by randomly distributed natural fractures, the robust optimization would require a large ensemble size and it would be computationally demanding. In this work, a hierarchical clustering method is proposed to select representative models for the robust optimization in order to avoid redundant simulation runs and improve the efficiency of the robust optimization. By reducing the full ensemble of models into a small subset ensemble, the efficiency of the robust optimization algorithm is significantly improved. The robust optimization is performed using the StoSAG scheme to find the optimal well controls that maximize the net-present-value (NPV) of the NFR’s development. Due to the discrete property of a natural fracture field, traditional feature extraction methods such as model-parameter-based clustering may not be directly applicable. Therefore, two different kinds of clustering-based optimization methods, a state-based (e.g., s _w profiles) clustering and a response-based (e.g., production rates) clustering, are proposed and compared. The computational results show that the robust clustering optimization could increase the computational efficiency significantly without sacrificing much expected NPV of the robust optimization. Moreover, the performance of different clustering algorithms varies widely in correspondence to different selections of clustering features. By properly extracting model features, the clustered subset could adequately represent the uncertainty of the full ensemble.     

Identifying influence areas with connectivity analysis – application to the local perturbation of heterogeneity distribution for history matching

Numerical representations of a target reservoir can help to assess the potential of different development plans. To be as predictive as possible, these representations or models must reproduce the data (static, dynamic) collected on the field. However, constraining reservoir models to dynamic data – the history-matching process – can be very time consuming. Many uncertain parameters need to be taken into account, such as the spatial distribution of petrophysical properties. This distribution is mostly unknown and usually represented by millions of values populating the reservoir grid. Dedicated parameterization techniques make it possible to investigate many spatial distributions from a small number of parameters. The efficiency of the matching process can be improved from the perturbation of specific regions of the reservoir. Distinct approaches can be considered to define such regions. For instance, one can refer to streamlines. The leading idea is to identify areas that influence the production behavior where the data are poorly reproduced. Here, we propose alternative methods based on connectivity analysis to easily provide approximate influence areas for any fluid-flow simulation. The reservoir is viewed as a set of nodes connected by weighted links that characterize the distance between two nodes. The path between nodes (or grid blocks) with the lowest cumulative weight yields an approximate flow path used to define influence areas. The potential of the approach is demonstrated on the basis of 2D synthetic cases for the joint integration of production and 4D saturation data, considering several formulations for the weights attributed to the links.     

Seasonal variability of oxygen and hydrogen isotopes in a wetland system of the Yunnan-Guizhou Plateau,southwest China: a quantitative assessment of groundwater inflow fluxes

The Caohai Wetland serves as an important ecosystem on the Yunnan–Guizhou Plateau and as a nationally important nature reserve for migratory birds in China. In this study, surface water, groundwater and wetland water were collected for the measurement of environmental isotopes to reveal the seasonal variability of oxygen and hydrogen isotopes (δ¹⁸O, δD), sources of water, and groundwater inflow fluxes. Results showed that surface water and groundwater are of meteoric origin. The isotopes in samples of wetland water were well mixed vertically in seasons of both high-flow (September) and low-flow (April); however, marked seasonal and spatial variations were observed. During the high-flow season, the isotopic composition in surface wetland water varied from ?97.13 to ?41.73‰ for δD and from ?13.17 to ?4.70‰ for δ¹⁸O. The composition of stable isotopes in the eastern region of this wetland was lower than in the western region. These may have been influenced by uneven evaporation caused by the distribution of aquatic vegetation. During the low-flow season, δD and δ¹⁸O in the more open water with dead aquatic vegetation ranged from ?37.11 to ?11.77‰, and from ?4.25 to ?0.08‰, respectively. This may result from high evaporation rates in this season with the lowest atmospheric humidity. Groundwater fluxes were calculated by mass transfer and isotope mass balance approaches, suggesting that the water sources of the Caohai Wetland were mainly from groundwater in the high-flow season, while the groundwater has a smaller contribution to wetland water during the low-flow season.     

Numerical solution and convergence analysis of steam injection in heavy oil reservoirs

In this paper, the numerical methods for solving the problem of steam injection in the heavy oil reservoirs are presented. We consider a 3-dimensional model of 3-phase flow, oil, water, and steam, with the effect of 3-phase relative permeability. Interphase mass transfer of water and steam is considered; oil is assumed nonvolatile. We apply the simultaneous solution approach to solve the corresponding nonlinear discretized partial differential equation in the fully implicit form. The convergence of finite difference scheme is proved by the Rosinger theorem. The heuristic Jacobian-Free-Newton-Krylov (HJFNK) method is proposed for solving the system of algebraic equations. The result of this proposed numerical method is well compared with some experimental results. Our numerical results show that the first iteration of the full approximation scheme (FAS) provides a good initial guess for the Newton method. Therefore, we propose a new hybrid-FAS-HJFNK method while there is no steam in the reservoir. The numerical results show that the hybrid-FAS-HJFNK method converges faster than the HJFNK method.     

Groundwater sustainability and groundwater/surface-water interaction in arid Dunhuang Basin,northwest China

The Dunhuang Basin, a typical inland basin in northwestern China, suffers a net loss of groundwater and the occasional disappearance of the Crescent Lake. Within this region, the groundwater/surface-water interactions are important for the sustainability of the groundwater resources. A three-dimensional transient groundwater flow model was established and calibrated using MODFLOW 2000, which was used to predict changes to these interactions once a water diversion project is completed. The simulated results indicate that introducing water from outside of the basin into the Shule and Danghe rivers could reverse the negative groundwater balance in the Basin. River-water/groundwater interactions control the groundwater hydrology, where river leakage to the groundwater in the Basin will increase from 3,114?×?10⁴ m³/year in 2017 to 11,875?×?10⁴ m³/year in 2021, and to 17,039?×?10⁴ m³/year in 2036. In comparison, groundwater discharge to the rivers will decrease from 3277?×?10⁴ m³/year in 2017 to 1857?×?10⁴ m³/year in 2021, and to 510?×?10⁴ m³/year by 2036; thus, the hydrology will switch from groundwater discharge to groundwater recharge after implementing the water diversion project. The simulation indicates that the increased net river infiltration due to the water diversion project will raise the water table and then effectively increasing the water level of the Crescent Lake, as the lake level is contiguous with the water table. However, the regional phreatic evaporation will be enhanced, which may intensify soil salinization in the Dunhuang Basin. These results can guide the water allocation scheme for the water diversion project to alleviate groundwater depletion and mitigate geo-environmental problem.     

Tracing submarine groundwater discharge flux in Tolo Harbor,Hong Kong (China)

Submarine groundwater discharge (SGD) is an important pathway for groundwater and associated chemicals to discharge to the sea. Groundwater levels monitored along a transect perpendicular to the shoreline are used to calculate SGD flux from the nearshore aquifer to Tolo Harbor, Hong Kong (China). The calculated SGD flux—recharge/discharge measured with Darcy’s Law methods—agrees well with estimates based on geo-tracer techniques and seepage meter in Tolo Harbor during previous studies. The estimated freshwater SGD is 1.69–2.0 m²/d at the study site and 0.3?±?0.04 cm/d for the whole of Tolo Harbor, which is comparable to the river discharge (0.25?±?0.07 cm/d) and precipitation (0.45?±?0.15 cm/d). The tide-driven SGD in the intertidal zone is 13.98–17.59 m²/d at the study site and 2.42?±?0.56 cm/d for the whole of Tolo Harbor. The SGD occurring in the subtidal zone and the bottom of Tolo Harbor is 3.12?±?4.63 cm/d. Fresh SGD accounts for ~5% of the total SGD, while the rest (~95%) is contributed by saline SGD driven by various forces. About 96% of the tide-driven SGD in the intertidal zone occurs in the ebbing tide period because the head difference between the groundwater level and sea level is great during this period. Tide-driven SGD in the spring tide is ~1.2 times that during neap tide. The tidal fluctuation amplitude and tide-driven SGD in the intertidal zone are positively correlated to each other; thus, a spring neap variation of the tide-driven SGD is observed.     

Impact of model complexity and multi-scale data integration on the estimation of hydrogeological parameters in a dual-porosity aquifer

This study investigates the impact of model complexity and multi-scale prior hydrogeological data on the interpretation of pumping test data in a dual-porosity aquifer (the Chalk aquifer in England, UK). In order to characterize the hydrogeological properties, different approaches ranging from a traditional analytical solution (Theis approach) to more sophisticated numerical models with automatically calibrated input parameters are applied. Comparisons of results from the different approaches show that neither traditional analytical solutions nor a numerical model assuming a homogenous and isotropic aquifer can adequately explain the observed drawdowns. A better reproduction of the observed drawdowns in all seven monitoring locations is instead achieved when medium and local-scale prior information about the vertical hydraulic conductivity (K) distribution is used to constrain the model calibration process. In particular, the integration of medium-scale vertical K variations based on flowmeter measurements lead to an improvement in the goodness-of-fit of the simulated drawdowns of about 30%. Further improvements (up to 70%) were observed when a simple upscaling approach was used to integrate small-scale K data to constrain the automatic calibration process of the numerical model. Although the analysis focuses on a specific case study, these results provide insights about the representativeness of the estimates of hydrogeological properties based on different interpretations of pumping test data, and promote the integration of multi-scale data for the characterization of heterogeneous aquifers in complex hydrogeological settings.     

Hybrid Gaussian-cubic radial basis functions for scattered data interpolation

Scattered data interpolation schemes using kriging and radial basis functions (RBFs) have the advantage of being meshless and dimensional independent; however, for the datasets having insufficient observations, RBFs have the advantage over geostatistical methods as the latter requires variogram study and statistical expertise. Moreover, RBFs can be used for scattered data interpolation with very good convergence, which makes them desirable for shape function interpolation in meshless methods for numerical solution of partial differential equations. For interpolation of large datasets, however, RBFs in their usual form, lead to solving an ill-conditioned system of equations, for which, a small error in the data can cause a significantly large error in the interpolated solution. In order to reduce this limitation, we propose a hybrid kernel by using the conventional Gaussian and a shape parameter independent cubic kernel. Global particle swarm optimization method has been used to analyze the optimal values of the shape parameter as well as the weight coefficients controlling the Gaussian and the cubic part in the hybridization. Through a series of numerical tests, we demonstrate that such hybridization stabilizes the interpolation scheme by yielding a far superior implementation compared to those obtained by using only the Gaussian or cubic kernels. The proposed kernel maintains the accuracy and stability at small shape parameter as well as relatively large degrees of freedom, which exhibit its potential for scattered data interpolation and intrigues its application in global as well as local meshless methods for numerical solution of PDEs.