This paper analyzes the relation between well spacing and Net Present Value of a Hot Sedimentary Aquifer geothermal doublet. First, a sensitivity analysis is carried out to evaluate the effect of uncertainty of geological and production parameters on the Net present Value. Second a finite-element approach is utilized to study the effect of fluvial facies architecture on geothermal energy production. For this purpose detailed fluvial facies architecture models are created utilizing a process-based facies modelling approach. These models and reservoir properties are based on a geological dataset of the Lower Cretaceous Nieuwerkerk Formation in the West Netherlands Basin (WNB). Results of the sensitivity analysis show that a 10% variation in well spacing from a 1000m base case scenario could vary the NPV by 10%. The minimal required well spacing is dependent on the reservoir thickness, flow rate and the allowed production temperature drop. The simulations results show that the theoretical advantage of a reduction in well spacing could be balanced by a poor well connectivity between the wells because of the characteristic of fluvial reservoir architecture. @en

Predicting equivalent permeability in fractured reservoirs requires an understanding of the fracture geometry and aperture, which cannot be fully sampled from subsurface data. We quantify for a range of aperture-size scaling models and the Barton-Bandis conductive shear model the fractures that are critically stressed at in-situ stress conditions as defined by either Coulomb friction or Barton-Bandis peak shearing. These models are applied to realistic large-scale fracture networks. (Sub-)linear length scaling predicts the largest average aperture, and subsequent equivalent permeability exceeds 1 Darcy in a 10mD matrix. In contrast, Barton-Bandis aperture predicts an equivalent permeability of 60mD. Application of critical stress criteria results in a decrease in the fraction of open fractures. For the applied stress conditions, Coulomb predicts that 50% of the network is critically stressed, compared to 80% for Barton-Bandis peak shear. The impact of the reactivated fracture network on equivalent permeability depends on the matrix properties, as in a low-permeable matrix, fracture connectivity controls equivalent permeability, while for a more permeable matrix, large absolute apertures are more important than network connectivity. Quantification of fracture flow regimes using only the ratio of fracture versus matrix permeability is insufficient, as these regimes also depend on fracture connectivity, controlled by aperture. @en

Fluvial sandstone reservoirs composed of stacked meander belts are considered as potential geothermal resources in the Netherlands. Net-to-gross, orientation and stacking pattern of the channel belts is of major importance for the connectivity between the injection and production well in such reservoirs. Understanding the influence of the fluvial sandstone architecture on the heat recovery is necessary for designing geothermal doublet projects in fluvial reservoirs. A detailed outcrop study of the Huesca fluvial fan is used as an analogue for fluvial reservoir architecture. The study shows meandering fluvial sandstone bodies, laterally amalgamated and vertically stacked within the meander belts. Meander belts in the outcrop have a width of 1 to 1.5 km and are up to 4 km long. Sandstone bodies are surrounded by impermeable floodplain deposits and poorly permeable crevasse splay sandstones (Donselaar & Overeem, 2008). The floodplain deposits decrease the net-to-gross and connectivity in the meander belt. In order to identify the most influential geological features controlling the flow and heat transfer in geothermal aquifers, several reservoir models of fluvial sandstones are constructed with increasing geological detail. These models are based on the results of geological fieldwork on the Huesca fluvial fan in Miocene, Ebro Basin, Spain. Several models with different geometry of the fluvial sandstone bodies, orientation of the channel belts and stacking patterns of the channel bodies are considered. A finite-element approach is utilized to study the geothermal energy production. The effects of different levels of architectural complexity on the geothermal energy production, by conducting several accurate numerical simulations, are discussed. The results show that utilizing simplified reservoir models can lead to a significant error in predictability of the heat recovery from deep fluvial sandstone formations. @en

A fracture network arrangement is quantified across an isolated carbonate platform from outcrop and aerial imagery to address its impact on fluid flow. The network is described in terms of fracture density, orientation, and length distribution parameters. Of particular interest is the role of fracture cross connections and abutments on the effective permeability. Hence, the flow simulations explicitly account for network topology by adopting Discrete-Fracture-and-Matrix description. The interior of the Latemar carbonate platform (Dolomites, Italy) is taken as outcrop analogue for subsurface reservoirs of isolated carbonate build-ups that exhibit a fracture-dominated permeability. New is our dual strategy to describe the fracture network both as deterministic- and stochastic-based inputs for flow simulations. The fracture geometries are captured explicitly and form a multiscale data set by integration of interpretations from outcrops, airborne imagery, and lidar. The deterministic network descriptions form the basis for descriptive rules that are diagnostic of the complex natural fracture arrangement. The fracture networks exhibit a variable degree of multitier hierarchies with smaller-sized fractures abutting against larger fractures under both right and oblique angles. The influence of network topology on connectivity is quantified using Discrete-Fracture-Single phase fluid flow simulations. The simulation results show that the effective permeability for the fracture and matrix ensemble can be 50 to 400 times higher than the matrix permeability of 1.0 · 10^-14 m². The permeability enhancement is strongly controlled by the connectivity of the fracture network. Therefore, the degree of intersecting and abutting fractures should be captured from outcrops with accuracy to be of value as analogue.

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The reactive mixing between seawater and terrestrial water in coastal aquifers influences the water quality of submarine groundwater discharge. While these waters come into contact at the seawater groundwater interface by density driven flow, their chemical components dilute and react through dispersion. A larger interface and wider mixing zone may provide favorable conditions for the natural attenuation of contaminant plumes. It has been claimed that the extent of this mixing is controlled by both, porous media properties and flow conditions. In this study, the interplay between dispersion and reactive processes in coastal aquifers is investigated by means of numerical experiments. Particularly, the impact of dispersion coefficients, the velocity field induced by density driven flow and chemical component reactivities on reactive transport in such aquifers is studied. To do this, a hybrid finite-element finite-volume method and a reactive simulator are coupled, and model accuracy and applicability are assessed. A simple redox reaction is considered to describe the degradation of a contaminant which requires mixing of the contaminated groundwater and the seawater containing the terminal electron acceptor. The resulting degradation is observed for different scenarios considering different magnitudes of dispersion and chemical reactivity. Three reactive transport regimes are found: reaction controlled, reaction-dispersion controlled and dispersion controlled. Computational results suggest that the chemical components' reactivity as well as dispersion coefficients play a significant role on controlling reactive mixing zones and extent of contaminant removal in coastal aquifers. Further, our results confirm that the dilution index is a better alternative to the second central spatial moment of a plume to describe the mixing of reactive solutes in coastal aquifers.

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The influence of in-situ stresses on flow processes in fractured rock is investigated using a novel modelling approach. The combined finite-discrete element method (FEMDEM) is used to model the deformation of a fractured rock mass. The fracture wall displacements and aperture changes are modelled in response to uniaxial and biaxial stress states. The resultant changes in flow properties of the rock mass are investigated using the Complex Systems Modelling Platform (CSMP++). CSMP++ is used to model single-phase flow through fractures with variable aperture and a permeable rock matrix. The study is based on a geological outcrop mapping of a low density fracture pattern that includes the realism of intersections, bends and segmented features. By applying far-field (boundary) stresses to a square region, geologically important phenomena are modelled including fracture-dependent stress heterogeneity, the re-activation of pre-existing fractures (i.e. opening, closing and shearing), the propagation of new fractures and the development of fault zones. Flow anisotropy is investigated under various applied stresses and matrix permeabilities. In-situ stress conditions that encourage a closing of fractures together with a more pervasive matrix-dominated flow are identified. These are compared with conditions supporting more localised flow where fractures are prone to dilatational shearing and can be more easily exploited by fluids. The natural fracture geometries modelled in this work are not perfectly straight, promoting fracture segments that dilate as they shear. We have demonstrated the introduction of several realistic processes that have an influence on natural systems: fractures can propagate with wing cracks; there is the potential for new fractures to connect with existing fractures, thus increasing the connectivity and flow; blocks can rotate when bounded by fractures, bent fractures lead to locally different aperture development; highly heterogeneous stress distributions emerge naturally. Results presented in this work provide a mechanically rigorous demonstration that a change in the stress state can cause reactivation of pre-existing fractures and channelling of flow in critically stressed fractures.

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A modular pore-scale model is developed to assess the response of wellbore cement to geological storage of CO₂. Numerical formulations for modeling of solute transport are presented and a methodology for coupling with geochemical processes is discussed, which includes: (1) advective and diffusive fluxes of solutes within the pore space, (2) aqueous phase speciation, (3) mineral dissolution-precipitation kinetics, and (4) the subsequent changes in pore space geometry. A Complex Pore Network Model (CPNM) is used to discretize the continuum porous structure as a network of pore bodies and pore throats, both with finite volumes. CPNM allows for a distribution of pore coordination numbers ranging between 1 and 26. This topological property, together with a geometrical distribution of pore sizes, enables the microstructure of porous media to be mimicked. For each pore element, transport of solute is calculated by solving the governing mass balance equations. Chemical reaction of the fluid phase with the main reactive solid components (portlandite and calcite) is incorporated through coupling with a geochemical reactive simulator. Average values and properties are obtained by integration over a large number of pores. Using this approach, we investigate how chemical reaction between water-bearing wellbore cement and supercritical CO₂ can create a distribution of porosity in a direction parallel to the CO₂ concentration gradient and transport path, at 50°C. The dynamics of this process involve interaction between diffusion dominated mass transport and the kinetics of dissolution and precipitation of portlandite and/or calcite. Simulation of unconfined chemical degradation, in a fluid of constant composition, shows development of different regions: (1) a zone adjacent to the inlet face, which is characterized by an increase in porosity due to extensive dissolution, (2) a carbonation zone with decreased porosity, (3) the carbonation front which made a thin layer with the lowest porosity due to calcium carbonate precipitation, and (4) dissolution zone. These results are in agreement with laboratory observations under similar conditions. This provides confidence that this pore-scale approach can ultimately be applied to model the progress of coupled CO₂ transport and cement degradation at critical points along the length of cemented wellbore sections at CO₂ storage sites.

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We benchmark a family of hybrid finite element-node-centered finite volume discretization methods (FEFV) for single- and two-phase flow/transport through porous media with discrete fracture representations. Special emphasis is placed on a new method we call DFEFVM in which the mesh is split along fracture-matrix interfaces so that discontinuities in concentration or saturation can evolve rather than being suppressed by nodal averaging of these variables. The main objective is to illustrate differences among three discretization schemes suitable for discrete fracture modeling: (a) FEFVM with volumetric finite elements for both fractures and porous rock matrix, (b) FEFVM with lower dimensional finite elements for fractures and volumetric finite elements for the matrix, and (c) DFEFVM with a mesh that is split along material discontinuities. Fracture discontinuities strongly influence single- and multi-phase fluid flow. Continuum methods, when used to model transport across such interfaces, smear out concentration/saturation. We show that the new DFEFVM addresses this problem producing significantly more accurate results. Sealed and open single fractures as well as a realistic fracture geometry are used to conduct tracer and water-flooding numerical experiments. The benchmarking results also reveal the limitations/mesh refinement requirements of FE node-centered FV hybrid methods. We show that the DFEFVM method produces more accurate results even for much coarser meshes.

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A second order in space accurate implicit scheme for time-dependent advection-dispersion equations and a discrete fracture propagation model are employed to model solute transport in porous media. We study the impact of the fractures on mass transport and dispersion. To model flow and transport, pressure and transport equations are integrated using a finite-element, node-centered finite-volume approach. Fracture geometries are incrementally developed from a random distributions of material flaws using an adoptive geomechanical finite-element model that also produces fracture aperture distributions. This quasistatic propagation assumes a linear elastic rock matrix, and crack propagation is governed by a subcritical crack growth failure criterion. Fracture propagation, intersection, and closure are handled geometrically. The flow and transport simulations are separately conducted for a range of fracture densities that are generated by the geomechanical finite-element model. These computations show that the most influential parameters for solute transport in fractured porous media are as follows: fracture density and fracture-matrix flux ratio that is influenced by matrix permeability. Using an equivalent fracture aperture size, computed on the basis of equivalent permeability of the system, we also obtain an acceptable prediction of the macrodispersion of poorly interconnected fracture networks. The results hold for fractures at relatively low density.

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Accurate numerical simulation of solute transport or multiphase flow through heterogeneous porous media is still a challenge. One reason is that in continuum models, sharp material interfaces are difficult to represent. The finite-element method allows representation of such discontinuities as element-to-element variations of materials; however, result variables are discretized on the finite-element nodes and when a complementary node-centered finite-volume mesh is used to model transport, this discretization smears out potential discontinuities in nodal concentration or saturation. To overcome this dilemma there are two options: either the nodes can be enriched at the interfaces by additional degrees of freedom or the model can be "exploded" along the interfaces. In the latter technique, interface nodes are multiplied so that they match in number the material domains that they join. We develop this latter approach, implementing a transport model that can evolve dependent variable discontinuities at material interfaces. For transport, we developed a new scheme that is higher order accurate in space, even across these discontinuities, and verify that it is consistent with the continuous method. This analysis shows that the new scheme removes a first-order dependence on mesh refinement observed for the continuous method so that coarser meshes can be used for material interfaces.

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Discrete-fracture and rock matrix (DFM) modelling necessitates a physically realistic discretisation of the large aspect ratio fractures and the dissected material domains. Using unstructured spatially adaptively refined finite-element meshes, we find that the fastest flow often occurs in the smallest elements. Flow velocity and element size vary over many orders of magnitude, disqualifying global Courant number (CFL)-dependent transport schemes because too many time steps would be necessary to investigate displacements of interest. Here, we present a higher-order accurate implicit pressure-(semi)-implicit transport scheme for the advection-diffusion equation that overcomes this CFL limitation for DFM models. Using operator splitting, we solve the pressure and the transport equations on finite-element, node-centred finite-volume meshes, respectively, using algebraic multigrid methods. We apply this approach to field data-based DFM models where the fracture flow velocity and mesh refinement is 2-4 orders of magnitude greater than that of the matrix. For a global CFL of ≤10,000, this implies sub-CFL, second-order accurate behaviour in the matrix, and super-CFL, at least first-order accurate, transports in fast-flowing fractures. Their greater refinement, however, largely offsets this numerical dispersion, promoting a highly accurate overall solution. Numerical and fracture-related mechanical dispersions are compared in the realistic DFM models using second-order accurate runs as reference cases. With a CFL histogram, we establish target error criteria for CFL overstepping. This analysis indicates that for extreme fracture heterogeneity, only a few transport steps can be sufficient to analyse macro-dispersion. This makes our implicit method attractive for quick analysis of transport properties on multiple realisations of DFM models.

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Simulation grid blocks of naturally fractured reservoirs contain thousands of fractures with variable flow properties, dimensions, and orientations. This complexity precludes direct incorporation into field-scale models. Macroscopic laws capturing their integral effects on multiphase flow are required. Numerical discrete fracture and matrix simulations show that ensemble relative permeability as a function of water saturation (k_ri[S_w]), water breakthrough, and cut depend on the fraction of the cross-sectional flux that occurs through the fractures. This fracture-matrix flux ratio [q _fqm] can be quantified by steady-state computation. Here we present a new semianalytical model that uses q_fqm and the fracture-related porosity fjf) to predict k_ri(S_w) capturing that, shortly after the first oil is recovered, the oil relative permeability (kro) becomes less that that of water (k_rw), and k _rwk_ro approaches q_f/q_m as soon as the most conductive fractures become water saturated. To include a capillary-driven fracture-matrix transfer into our model, we introduce the nonconventional parameter A_fw/_Sw), the fraction of the fracture-matrix interface area in contact with the injected water for any grid-block average saturation. The A_fw/_Sw) is used to scale the capillary transfer modeled with conventional transfer functions and expressed in terms of a rate- and capillary-pressure- dependent k_ro. All predicted parameters can be entered into conventional reservoir simulators. We explain how this is accomplished in both, single- and dual-continua formulations. The predicted grid-block-scale fractional flow (f _i[S_w]) is convex with a near-infinite slope at the initial saturation. The upscaled flow equation therefore does not contain an S _w shock but a long leading edge, capturing the progressively widening saturation fronts observed in numerical experiments published previously.

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A two-dimensional numerical model is used to study the nonlinear behavior of density gradients on transverse dispersion. Numerical simulations are conducted using d 3 f, a computer code for simulation of density-dependent flow in porous media. Considering a density-stratified horizontal flow in a heterogeneous porous media, a series of simulations is carried out to examine the effect of the density gradient on macro-scale transverse dispersivity. Changing salt concentration significantly affects fluid properties. This physical behavior of the fluid involves a non-linearity in modeling the interaction between salt and fresh water. It is concluded that the large-scale transport properties for high density flow deviate significantly from the tracer case due to the spatial variation of permeability, described by statistical parameters, at the local-scale. Indeed, the presence of vertical flow velocities induced by permeability variations is responsible for the reduction of the mixing zone width in the steady state in the case of a high density gradient. Uncertainties in the model simulations are studied in terms of discretization errors, boundary conditions, and convergence of ensemble averaging. With respect to the results, the gravity number appears to be the controlling parameter for dispersive flux. In addition, the applicability and limitations of the nonlinear model of Hassanizadeh (1990) and Hassanizadeh and Leijnse (1995) (Adv Water Resour 18(4):203-215, 1995) in heterogeneous porous media are investigated. We found that the main cause of the nonlinear behavior of dispersion, which is the interaction between density contrast and vertical velocity, needs to be explicitly accounted for in a macro-scale model.@en