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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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

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

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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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

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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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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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

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 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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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

This study investigates the effect of thermoelastic interactions between multiple parallel fractures on energy production from a multiple-fracture enhanced geothermal system. A coupled thermo-hydro-mechanical finite element model has been developed that accounts for non-isothermal fluid flow within the fractures, conductive heat transfer in the rock matrix, and the mechanical deformation of the matrix. The model results show that the matrix deformation significantly increases the interactions between the two adjacent fractures. Matrix contraction due to the cooling of the matrix increases the fracture aperture in the adjacent fracture, and facilitates the creation of favourable flow pathways between the injection and production wells. These flow paths reduce the energy production from the system. The effects of fracture spacing, reservoir temperature gradient and mechanical properties of the rock matrix on the production temperature and the net production energy are investigated. It is shown that the spacing calculated based on the assumption of rigid matrix (constant uniform aperture) are too small, and in order to account for the thermoelastic interactions, the spacing between fractures should be further increased to maximise the net energy production from the system. Otherwise, the multiple-fracture system fails to improve the energy recovery from the geothermal reservoir, as initially intended.

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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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Thermoporoelastic effects during heat extraction from low permeability geothermal reservoirs are investigated numerically, based on the model of a horizontal penny-shaped fracture intersected by an injection well and a production well. A coupled formulation for thermo-hydraulic (TH) processes is presented that implicitly accounts for the mechanical deformation of the poroelastic matrix. The TH model is coupled to a separate mechanical contact model (M) that solves for the fracture contact stresses due to thermoporoelastic compression. Fractures are modelled as surface discontinuities within a three-dimensional matrix. A robust contact model is utilised to resolve the contact tractions between opposing fracture surfaces. Results show that due to the very low thermal diffusivity of the rock matrix, the thermally-induced pore pressure partially dissipates even in the very low-permeability rocks that are found in EGS projects. Therefore, using the undrained thermal expansion coefficient for the matrix may overestimate the volumetric strain of the rock in low-permeability enhanced geothermal systems, whereas using a drained thermal expansion coefficient for the matrix may underestimate the volumetric strain of the rock. An “effective” thermal expansion coefficient can be computed from the drained and undrained values to improve the prediction for the partially-drained matrix.

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Fracture networks are heterogeneous systems creating anisotropic flow patterns, though field-scale flow models of fractured reservoirs use up-scaling of the fracture network to effective properties to model flow. We study the impact of upscaling aperture from a realistic aperture model, where aperture is defined by a stress-aperture relation that considers aperture variations within single fractures, to an arithmetically averaged distribution. This analysis is done through calculation of the equivalent permeability tensor of a discrete fracture and matrix flow model, taking into account different contrasts between fracture and matrix permeability. Results show that a strong equivalent permeability anisotropy emerges for a low matrix permeability, and that accurate representation of fracture aperture is as important as the fracture topology, particularly when the fracture matrix permeability ratio is large. The orientation of the permeability tensor varies with varying rock matrix permeability, reflecting anisotropy of the permeability that is impossible to extract from the fracture patterns itself. The results also highlight that utilizing a constant aperture for the fracture network may not reproduce the true anisotropy of the permeability. Utilizing an equivalent aperture in flow simulations introduces errors in both the direction and magnitude of principal permeabilities and the equivalent permeability anisotropy.

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A fully coupled thermal-hydraulic-mechanical (THM) finite element model is presented for fractured geothermal reservoirs. Fractures are modelled as surface discontinuities within a three-dimensional matrix. Non-isothermal flow through the rock matrix and fractures are defined and coupled to a mechanical deformation model. A robust contact model is utilised to resolve the contact tractions between opposing fracture surfaces under THM loadings. A numerical model has been developed using the standard Galerkin method. Quadratic tetrahedral and triangular elements are used for spatial discretisation. The model has been validated against several analytical solutions, and applied to study the effects of the deformable fractures on the injection of cold water in fractured geothermal systems. Results show that the creation of flow channelling due to the thermal volumetric contraction of the rock matrix is very likely. The fluid exchanges heat with the rock matrix, which results in cooling down of the matrix, and subsequent volumetric deformation. The cooling down of the rock matrix around a fracture reduces the contact stress on the fracture surfaces, and increases the fracture aperture. Stress redistribution reduces the aperture, as the area with lower contact stress on the fracture expands. Stress redistribution reduces the likelihood of fracture propagation under pure opening mode, while the expansion of the area with lower contact stress may increase the likelihood of shear fracturing.

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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