Optimisation of doublet well spacing in low-enthalpy geothermal systems is addressed by defining a novel objective function that is based on the Coefficient of Performance (CoP) and energy sweep efficiency. The definition of objective function that separates performance-based criteria from economic factors, allows us to better observe the effects of heterogeneity on optimisation. A checkerboard pattern of two doublets (two injection wells diagonally placed and two production wells diagonally placed over corners of a rectangle) is considered for a range of homogeneous to heterogeneous (spatially correlated and fluvial) synthetic low enthalpy reservoirs. Optimal length and width of this rectangle are sought in order to (a) maximise heat recovery from a conventionally-chosen licence area around the rectangular domain, (b) minimise heat recovery from outside this licence area, and (c) maximise CoP. We define fixed (15 years and 30 years) and varying life times of operation (between 15 and 30 years). For optimisation, in addition to a simple-search procedure of optimisation across a mesh of simulation nodes, we also utilise a surrogate response surface model to computationally solve the optimisation problem. Our results consistently show that for a fixed life time of 15 years and a discharge rate of 250 m³/hr, 400 m is the optimal well/doublet spacing. Increasing the life time and the discharge rate will increase the optimal well/doublet spacing. The results show while CoP is sensitive to the heterogeneity, adding energy sweep to the objective function makes the distances found for the homogeneous cases also consistent solutions for the heterogeneous cases.

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This paper presents a mixed finite element framework for coupled hydro-mechanical–chemical processes in heterogeneous porous media. The framework combines two types of locally conservative discretization schemes: (1) an enriched Galerkin method for reactive flow, and (2) a three-field mixed finite element method for coupled fluid flow and solid deformation. This combination ensures local mass conservation, which is critical to flow and transport in heterogeneous porous media, with a relatively affordable computational cost. A particular class of the framework is constructed for calcite precipitation/dissolution reactions, incorporating their nonlinear effects on the fluid viscosity and solid deformation. Linearization schemes and algorithms for solving the nonlinear algebraic system are also presented. Through numerical examples of various complexity, we demonstrate that the proposed framework is a robust and efficient computational method for simulation of reactive flow and transport in deformable porous media, even when the material properties are strongly heterogeneous and anisotropic.

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Direct Use Geothermal Systems (DUGS) are increasing their installed capacity worldwide and denser developments with multiple doublets are becoming more common. Interference between doublets therefore becomes an additional concern to subsurface uncertainties. Faults can be either barriers or conduits to flow and can affect the fluid pathways inside the reservoir. The interference between two doublets that are separated by a fault has not been previously studied for DUGS. In this work considering subsurface uncertainty in a full factorial design using 5184 3D reservoir simulations we show that a fault can reduce the system lifetime of a two-doublet system by more than 40 % if one doublet is at close proximity to it. Further, we identify that the fault can also improve both the system lifetime and generated Net Present Value (NPV) with appropriate development decisions. Contrary to previous results that did not consider reservoir architecture, a tramline well configuration is preferable when the doublets have the fault in the centre, while a checkerboard configuration is preferable as the distance to the fault decreases. The Heat In Place (HIP) recovery shows a linear relationship with flow rate and well spacing that is not affected by the fault distance or flow properties. The dimensions of the Influence Area (IA) previously considered are insufficient to capture the temperature drop at the producer wells and the fault position can increase this discrepancy. Our results show the importance of fault characterisation and well positioning with respect to a fault considering subsurface uncertainty and how this can affect denser field development of DUGS. Our findings suggest to integrate faults and the relative positioning of well doublets with respect to a fault more strongly in field development plans. Such considerations should also be included in future optimization plans of multi-well geothermal systems. Moreover, the regulatory framework should be revised to achieve a better match between the IA boundary and the production well temperature drop to enable better planning for denser development of DUGS.@en

Evaluations and interpretations of reservoir productivity are frequent in geothermal, groundwater and hydrocarbon research and applications. In this study, we consider the closure of fractures around production wells due to compaction that can affect the productivity value, i.e. the ability of subsurface formations for transporting the desired fluid to a borehole. We introduce analytical tools to evaluate and predict changes in the productivity of a deformable fractured porous media. We propose analytical models for three geometries: a rectangular fracture with zero/non-zero orientation and a circular fracture with zero orientation to maximum horizontal stress. An advanced numerical model is utilised to evaluate the impact of spatial variation of fracture aperture induced by the fracture deformation on well productivity. The developed analytical solutions using a uniform fracture aperture always either over- or underestimate the production rate. Hence, an equivalent aperture model is developed for the fracture with aperture distribution under variable contact stresses to circumvent this problem. The proposed equivalent aperture model reduces the average and maximum errors of production-rate prediction from 28% to 0.6% and from 116% to 25%, respectively. We further employ the proposed model for sensitivity analyses to illustrate the impacts of in-situ and human-controlled parameters on productivity reduction. These analyses present that the interactions among initial reservoir pressure, fracture orientation, fracture stiffness, and well pressure control productivity reduction behaviours and the maximum productivity reduction values.@en

Interest in direct use geothermal systems is increasing due to their ability to supply renewable, environmentally friendly heat. Such systems are mostly developed in conduction dominated geological settings where faults are often encountered. Interdependencies between physical, design and operational parameters make it difficult to assess the performance of such systems. Interaction with faults could potentially have adverse effects on system lifetime, generated Net Present Value (NPV) and produced energy. In this work a single doublet system in the enthalpy range of 140 kJ/kg to 350 kJ/kg is analysed using COMSOL Multiphysics. A choice of design (well spacing and placement), physical (layered reservoir, fault flow properties, fault throw) and operational (injection and production flow rates) parameters are considered in a full factorial design that includes 2430 3D reservoir simulations. Results show that fault flow properties characterization is more significant than fault throw structural characterization. For the considered reservoir properties, increasing the flow rate four times results in an NPV increase of a factor seven, despite the shorter system lifetime. A sealing fault renders the system lifetime less sensitive to the doublet positioning. Synthetic model results shown can serve as guidelines to reducing full scale field models. Importance and relevance of these results remains very high for horizontally homogeneous, layered reservoirs. The analysis expands the understanding of interdependencies for direct use geothermal systems and informs on their further development.

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As the code was actively developed during the time of publication, the published data suffer from an error with regards to the discount factor applied during the NPV calculation. The published data NPV has been calculated for periods of 100 days, while the discount rate applied was the quoted Annual Discount Rate (ADR) value of the manuscript, namely 7%. When the NPV is calculated at intervals shorter periods than a year, the discount rate needs to be adjusted accordingly. This adjusted Periodic Discount Rate (PDR) should be calculated according to the following equation: [Formula presented] For our data this means that the PDR should be 0.018697 or 1.8697% for each period of 100 days for which the NPV is calculated. This was not done for the published data, due to different versions of the code being used. As a result, the time value of money was discounted much more than it should be (7% each 100 days when it should be 1.8697% per 100 days), leading to lower NPV values. This affects section 3.3 “Lifetime and NPV” of the published article (Figures 9, 10 and 11). We have re-performed the processing after having addressed this issue and plotted the corrected data in the updated figures below. While the qualitative conclusions that were drawn from the published figures are not significantly different from the corrected ones, the quantitative NPV values of the corrected figures differ substantially. Figure 9 Published. [Figure presented] Figure 9 Corrected. [Figure presented] Figure 10 Published. [Figure presented] Figure 10 Corrected. [Figure presented] Figure 11 Published. [Figure presented] Figure 11 Corrected. [Figure presented]

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This paper presents the enriched Galerkin discretization for modeling fluid flow in fractured porous media using the mixed-dimensional approach. The proposed method has been tested against published benchmarks. Since fracture and porous media discontinuities can significantly influence single- and multi-phase fluid flow, the heterogeneous and anisotropic matrix permeability setting is utilized to assess the enriched Galerkin performance in handling the discontinuity within the matrix domain and between the matrix and fracture domains. Our results illustrate that the enriched Galerkin method has the same advantages as the discontinuous Galerkin method; for example, it conserves local and global fluid mass, captures the pressure discontinuity, and provides the optimal error convergence rate. However, the enriched Galerkin method requires much fewer degrees of freedom than the discontinuous Galerkin method in its classical form. The pressure solutions produced by both methods are similar regardless of the conductive or non-conductive fractures or heterogeneity in matrix permeability. This analysis shows that the enriched Galerkin scheme reduces the computational costs while offering the same accuracy as the discontinuous Galerkin so that it can be applied for large-scale flow problems. Furthermore, the results of a time-dependent problem for a three-dimensional geometry reveal the value of correctly capturing the discontinuities as barriers or highly-conductive fractures.@en

Geothermal projects, as renewable energy projects, are not economically attractive in most places of the world at the current state of development; for this reason, subsidies are required by energy and environmental authorities in order to increase the interest in such projects. In this paper, we assess and model strategies for integration of geothermal energy with oil productions of the Moerkapelle oil field in the Netherlands. To do so, numerical simulations have been employed to analyse the feasibility of a fluvial oil reservoir for the synergy potential of oil and geothermal energy exploitation. In order to implement the simulation studies, single phase and two-phase non-isothermal fluid flow modelling are utilized for the geothermal well doublet system and for water flooding in an oil reservoir (including facies heterogeneity), respectively. A series of simulations have been conducted to investigate how hot water from a geothermal reservoir beneath a heavy oil reservoir in the fluvial sedimentary system of the West Netherlands Basin can be used for Thermal Enhanced Oil Recovery (TEOR) and geothermal energy production. This study finds that the high degree of heterogeneity in fluvial oil reservoirs could significantly affect oil recovery improvement and hence the synergy strategy. High values of a) Net to gross (N/G) b) Bottom Hole Pressure (BHP) and c) horizontal wellbore length are favourable for oil recovery. In contrast, wide horizontal wellbore spacing and high oil viscosity have an adverse effect on oil recovery enhancement. Furthermore, the results display that the enhanced oil production helps to reduce the required subsidy for a single doublet geothermal project up to 100%. Consequently, the extra amount of oil produced by utilising the geothermal energy, could make the geothermal business case independent and profitable.

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In this paper, we assess and model new strategies for integration of geothermal energy with gas production in the Oude Leede Gas Field in the Netherlands. We investigate the injection of cooled geothermal water into a gas field located just few kilometers away from the geothermal reservoir in the Netherlands. This synergy type can be considered for economic natural gas production from a gas field in the proximity of a geothermal doublet project and improved energy production in the geothermal reservoir. A 3-D model including a gas trapping mechanism was built to study the possible production potential of the gas field. Water flooding compensates pressure loss by reducing the pore space, however it complicates the process by introducing trapped gas. We studied the effect of injection rate, permeability, saturation condition before flooding and reservoir pressure on the ultimate gas recovery and the residual trapped gas saturation. Injecting water will increase the ultimate recovery factor for higher abandonment pressure. Higher water injection rates will keep the reservoir pressure up, increase the trapped gas saturation, and hence reduce the maximum recovery. The presence of heterogeneity and capillary forces has minor effects on the gas recovery factor. The exergy recovery factor of a water injection process is higher than a gas compression process due to the large amounts of energy required for compression. Considering net present value (NPV) analysis for a higher abandonment pressure, water injection is economically preferable, however not feasible. At a lower abandonment pressure, natural gas depletion can easily compete with the water injection process due to the higher costs of water injection and drilling.@en

The low-enthalpy geothermal systems are commonly deployed in sedimentary geological settings that feature significant levels of deposition-induced heterogeneity. In this paper, realistic levels of heterogeneity in the form of varying porosity variance and spatial correlation lengths are considered for a 3D geothermal system. Using 2600 computationally intensive numerical simulations of two doublets placed in a checkboard pattern, the influence of well and doublet spacings on performance metrics of low-enthalpy geothermal systems are investigated. The simulations strongly support that in varyingly heterogeneous systems, the lifetimes of operation are shorter, and depending on isotropicity or anisotropicity of correlated heterogeneity, the lifetimes vary. Most notably the anisotropically correlated heterogeneity can lead to either positive impact (by diverting the cold water plume) or negative impact (by facilitating an early breakthrough of cold water plume) on the lifetime of the operation compared to isotropically correlated heterogeneity. We also calculate the boundary of the region around the wells designated as the “license area” (where the cold water front reaches to or where a threshold temperature drop of 1 °C occurs). By doing so, it is found that the operator can assume larger extents (of up to 50%) for the license areas of the aquifer than the ones conventionally assumed. To minimize the impact of heterogeneity on operation, the best practice was found to place the doublets in the same spacings as of the wells. Moreover, it is found that the well distance can be significantly shorter than what is commonly realised for heterogeneous geothermal aquifers.@en

The Netherlands experienced the fastest European expansion of geothermal energy exploitation in the past decade. The first Dutch geothermal sites proved that Hot Sedimentary Aquifers exploitation can play an important role in a future low-carbon energy mix. In this study, we estimate that with the expansion rate of the past four years, geothermal heat production from Lower Cretaceous Hot Sedimentary Aquifers could cover up to 20% of the heat demand in the province of Zuid-Holland by 2050. Although this is a significant amount, we show in this study that only 1% of the potentially recoverable heat will be recovered by 2050. This is because of inefficient doublet deployment on a ‘first-come, first served’ basis with operational parameters that focus on objectives of small decentralised heat grid demands. Instead, similar to the common-practise approach in the hydrocarbon industry, a regional coordinated ‘masterplan’ approach could be used to increase heat recovery. Utilising numerical simulations for flow and heat transfer in the subsurface, we showed that the heat recovery efficiency could be increased by tens of percentages with such coordinated doublet deployment. Based on calculations of the Levelized Costs Of Heat for both deployment strategies, we also show that current financial support schemes do not favour heat recovery optimisation. This study emphasises that although Hot Sedimentary Aquifer resources have the potential to cover a significant part of our energy demand, a radical change in financial support schemes and legislation are required to unlock their true potential.

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A new solution for harvesting energy simultaneously from two different sources of energy by combining geothermal energy production and thermal enhanced heavy oil recovery is introduced. Numerical simulations are employed to evaluate the feasibility of generating energy from geothermal resources, both for thermally enhanced oil recovery from a heavy oil reservoir and for direct heating purposes. A single phase non-isothermal fluid flow modeling for geothermal doublet system and a two-phase non-isothermal fluid flow modelling for water flooding in an oil reservoir are utilised. Sensitivity and feasibility analyses of the synergy potential of thermally-enhanced oil recovery and geothermal energy production are performed. A series of simulations are carried out to examine the effects of reservoir properties on energy consumption and oil recovery for different injection rates and injection temperature. Our results show that total oil production strongly depends on the shape of heat plume which can be affected by porosity, permeability, injection temperature, well spacing and injection rate in the oil reservoir. The favourable oil recovery obtains at high amount of (a) injection rate, (b) injection temperature, (c) porosity and (d) low amount of oil reservoir permeability respectively. Furthermore, our study indicates the wellbore spacing plays an important role in oil recovery and an optimum wellbore spacing can be established. The analyses suggest that the extra amount of oil produced by utilising the geothermal energy could make the geothermal business case independent and may be a viable option to reduce the overall project cost. Furthermore, the results display that the enhance oil productions are able to reduce the required subsidy for a single doublet geothermal project up to 50%.

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Oil production optimization of petroleum reservoirs under uncertainty give rise to large-scale optimization problems. Ensemble-based methods for production optimization are used in combination with gradient-based optimization algorithms. Use of commercial-grade simulators able to handle real-scale reservoir models and compute the gradient by the adjoint method is essential for implementing such methods in real-life. However, the simulation time for a single ensemble model renders the problem computationally intractable. Therefore, model reduction is needed. We introduce a grid coarsening method that maintains the overall dynamics of the flow, by preserving the geological features of the model. In this paper, we present a software tool for oil production optimization and a semi-automated workflow for grid coarsening and property upscaling. The software tool integrates state-of-the-art optimization algorithms, ensemble-based optimization strategies and reservoir simulators with adjoint capability. The software is based on the Eclipse input file-format, which enables use of existing reservoir models for production optimization. This allows for oil production optimization of both black-oil and compositional flow models and brings model based production optimization a step closer to routinely implementation in reservoir management workflow. We present the workflow of the optimization software and numerical examples that demonstrates the application of ensemble-based production optimization.

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This paper evaluates the impact of reduction of doublet well spacing, below the current West Netherlands Basin standard of 1000 to 1500 m, on the Net Present Value (NPV) and the life time of fluvial Hot Sedimentary Aquifer (HSA) doublets. First, a sensitivity analysis is used to show the possible advantage of such reduction on the NPV. The parameter value ranges are derived from West Netherlands Basin HSA doublet examples. The results indicate that a reduction of well spacing from 1400 to 1000 m could already influence NPV by up to 15%. This effect would be larger in more marginally economic HSA doublets compared to the West Netherlands Basin base case scenario. The possibility to reduce well spacing is supported by finite element production simulations, utilizing detailed facies architecture models. Furthermore, our results underline the necessity of detailed facies architecture models to assess the potential and risks of HSA doublets. This factor significantly affects doublet life time and net energy production of the doublet.@en

Fluid flow in naturally fractured reservoirs is often controlled by subseismic-scale fracture networks. Although the fracture network can be partly sampled in the direct vicinity of wells, the inter-well scale network is poorly constrained in fractured reservoir models. Outcrop analogues can provide data for populating domains of the reservoir model where no direct measurements are available. However, extracting relevant statistics from large outcrops representative of inter-well scale fracture networks remains challenging. Recent advances in outcrop imaging provide high-resolution datasets that can cover areas of several hundred by several hundred meters, i.e. the domain between adjacent wells, but even then, data from the high-resolution models is often upscaled to reservoir flow grids, resulting in loss of accuracy. We present a workflow that uses photorealistic georeferenced outcrop models to construct geomechanical and fluid flow models containing thousands of discrete fractures covering sufficiently large areas, that does not require upscaling to model permeability. This workflow seamlessly integrates geomechanical Finite Element models with flow models that take into account stress-sensitive fracture permeability and matrix flow to determine the full permeability tensor. The applicability of this workflow is illustrated using an outcropping carbonate pavement in the Potiguar basin in Brazil, from which 1082 fractures are digitised. The permeability tensor for a range of matrix permeabilities shows that conventional upscaling to effective grid properties leads to potential underestimation of the true permeability and the orientation of principal permeabilities. The presented workflow yields the full permeability tensor model of discrete fracture networks with stress-induced apertures, instead of relying on effective properties as most conventional flow models do.

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Required distance between doublet systems in low enthalpy geothermal heat exploitation is often not fully elucidated. The required distance aims to prevent negative interference influencing the utilisation efficiency of doublet systems. Currently production licence areas are often issued based on the expected extent of the reinjected cold water plume on the moment of thermal breakthrough. The production temperature, however, may not immediately drop to non-economic values after this moment. Consequently, heat production could continue increasing the extent of the cold water plume. Furthermore, the area influenced by pressure because of injection and production spreads beyond the cold water plume extent, influencing not only the productivity of adjacent doublet systems but also the shape of cold water plumes. This affects doublet life time, especially if adjacent doublets have different production rates. In this modelling based study a multi parameter analysis is carried out to derive dimensionless relations between basic doublet design parameters and required doublet distance. These parameters include the spacing between injector and producer of the same doublet, different production rates, aquifer thickness and minimal required production temperature. The results of this study can be used to minimize negative interference or optimise positive interference aiming at improving geothermal doublet deployment efficiency.

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This study finds that the geothermal doublet layout with respect to the paleo flow direction in fluvial sedimentary reservoirs could significantly affect pump energy losses. These losses can be reduced by up to 10% if a doublet well pair is oriented parallel to the paleo flow trend compared to perpendicular. The chance that flow paths are formed perpendicular to this trend strongly depends on the net sandstone volume in the reservoir. Detailed fluvial facies architecture realisations which are used in this study, are generated with a process-based approach utilizing geological data from the Lower Cretaceous Nieuwerkerk Formation in the West Netherlands Basin. Finally, this study emphasizes the importance of detailed facies architecture modelling for the assessment of both risks and production strategies in Hot Sedimentary Aquifers.@en

Predicting equivalent permeability in fractured reservoirs requires an understanding of the fracture network geometry and apertures. There are different methods for defining aperture, based on outcrop observations (power law scaling), fundamental mechanics (sublinear length-aperture scaling), and experiments (Barton-Bandis conductive shearing). Each method predicts heterogeneous apertures, even along single fractures (i.e., intrafracture variations), but most fractured reservoir models imply constant apertures for single fractures. We compare the relative differences in aperture and permeability predicted by three aperture methods, where permeability is modeled in explicit fracture networks with coupled fracture-matrix flow. Aperture varies along single fractures, and geomechanical relations are used to identify which fractures are critically stressed. The aperture models are applied to real-world large-scale fracture networks. (Sub)linear length scaling predicts the largest average aperture and equivalent permeability. Barton-Bandis aperture is smaller, predicting on average a sixfold increase compared to matrix permeability. 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 fracture network on equivalent permeability depends on the matrix hydraulic properties, as in a low-permeable matrix, intrafracture connectivity, i.e., the opening along a single fracture, controls equivalent permeability, whereas for a more permeable matrix, absolute apertures have a larger impact. Quantification of fracture flow regimes using only the ratio of fracture versus matrix permeability is insufficient, as these regimes also depend on aperture variations within fractures.

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Infrared thermography has increasingly gained importance because of environmental and technological advancements of this method and is applied in a variety of disciplines related to non-isothermal flow. However, it has not been used so far for quantitative thermal analysis in saturated porous media. This article suggests infrared thermographic approach to obtain the entire surface temperature distribution(s) in water-saturated porous media. For this purpose, infrared thermal analysis is applied with in situ calibration for a better understanding of the heat transfer processes in porous media. Calibration is achieved with a combination of invasive sensors which are inserted into the medium and non-invasive thermal sensors in which sensors are not inserted to measure temperatures but it works through the detection of infrared radiation emitted from the surface. Thermocouples of relatively thin diameter are used to minimize the disturbance for flow. Thermocouples give the temperature values at specified positions inside the porous medium, and these values are compared with the values suggested by the infrared thermographic device at the same positions, in the calibration exercise. The calibration process was repeated for different temperatures and flow rates to get the temperature distributions of the whole material inside the system. This technique enables us to measure accurate two-dimensional temperature distributions, which is not possible by using thermocouples only. Continuous point heat sources at different flow rates and temperatures are studied experimentally. Additionally, it offers numerical simulations of the experiments utilizing a finite element-based model. A two-dimensional density and viscosity-dependent flow and transport model accounting for thermal dispersion is utilized to simulate the experimental results. Possible small heat losses from the surface are incorporated in the model according to the properties and thickness of the Plexiglass material used for the construction of the experiment tank. The numerical results agree well with the experimental observations.

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