High-dimensional geostatistical history matching

Hydrocarbon reservoir modelling and characterisation is a challenging subject within the oil and gas industry due to the lack of well data and the natural heterogeneities of the Earth’s subsurface. Integrating historical production data into the geo-modelling workflow, commonly designated by history matching, allows better reservoir characterisation and the possibility of predicting the reservoir behaviour. We present herein a geostatistical-based multi-objective history matching methodology. It starts with the generation of an initial ensemble of the subsurface petrophysical property of interest through stochastic sequential simulation. Each model is then ranked according the match between its dynamic response, after fluid flow simulation, and the observed available historical production data. This enables building regionalised Pareto fronts and the definition of a large ensemble of optimal subsurface Earth models that fit all the observed production data without compromising the exploration of the uncertainty space. The proposed geostatistical multi-objective history matching technique is successfully implemented in a benchmark synthetic reservoir dataset, the PUNQ-S3, where 12 objectives are targeted.     

Constraint energy minimizing generalized multiscale finite element method in the mixed formulation

This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves the flow equation in a mixed formulation on a coarse grid by constructing multiscale basis functions. The resulting velocity field is mass-conservative on the fine grid. Our main goal is to obtain first-order convergence in terms of the mesh size which is independent of local contrast. This is achieved, first, by constructing some auxiliary spaces, which contain global information that cannot be localized, in general. This is built on our previous work on the generalized multiscale finite element method (GMsFEM). In the auxiliary space, multiscale basis functions corresponding to small (contrast-dependent) eigenvalues are selected. These basis functions represent the high-conductivity channels (which connect the boundaries of a coarse block). Next, we solve local problems to construct multiscale basis functions for the velocity field. These local problems are formulated in the oversampled domain, taking into account some constraints with respect to auxiliary spaces. The latter allows fast spatial decay of local solutions and, thus, allows taking smaller oversampled regions. The number of basis functions depends on small eigenvalues of the local spectral problems. Moreover, multiscale pressure basis functions are needed in constructing the velocity space. Our multiscale spaces have a minimal dimension, which is needed to avoid contrast dependence in the convergence. The method’s convergence requires an oversampling of several layers. We present an analysis of our approach. Our numerical results confirm that the convergence rate is first order with respect to the mesh size and independent of the contrast.     

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.