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.

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.

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]

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.

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.

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.

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%.

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.

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.

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.

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.

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.