John O'Sullivan

John O'Sullivan
  • PhD
  • Lecturer at University of Auckland

About

135
Publications
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782
Citations
Current institution
University of Auckland
Current position
  • Lecturer
Additional affiliations
July 2011 - present
University of Auckland
Position
  • Lecturer

Publications

Publications (135)
Article
Enhanced geothermal energy production requires the stimulation of natural fracture pathways to increase fluid flow within a reservoir while still effectively recovering the heat. During injection/production, reservoir permeability exhibits various degrees of enhancement or degradation with time. These changes are generally attributed to various mul...
Article
The Rotorua geothermal field (RGF) in the North Island of New Zealand is renowned for an abundance of natural geothermal manifestations and contains one of New Zealand's last remaining areas of major geyser activity at Whakarewarewa. Close proximity of the geothermal resource to a population centre and ease of access for end-users resulted in inten...
Article
The application of the adjoint and direct methods to inverse modeling of the natural state of a convective geothermal system is discussed. The methods have been applied to other subsurface modeling problems, but they have seldom been used in the geothermal context and not at all for high-enthalpy, two-phase systems. There are two important feature...
Article
Full-text available
We consider geothermal inverse problems and uncertainty quantification from a Bayesian perspective. Our main goal is to make standard, `out-of-the-box' Markov chain Monte Carlo (MCMC) sampling more feasible for complex simulation models by using suitable approximations. To do this, we first show how to pose both the inverse and prediction problems...
Article
Waiwera is a new reservoir simulator designed to address the current and future challenges posed by modelling geothermal systems. It incorporates several innovations aimed at improving the robustness of phase transitions and steady-state model convergence, including a modified treatment of the multi-phase gravity term. The Waiwera code is paralleli...
Article
Numerical models of geothermal reservoirs typically depend on hundreds or thousands of unknown parameters, which must be estimated using sparse, noisy data. However, these models capture complex physical processes, which frequently results in long run-times and simulation failures, making the process of estimating the unknown parameters a challengi...
Conference Paper
Full-text available
The Lithium Valley Project has pinpointed a significant domestic U.S. source of brine-hosted lithium located in the deep geothermal reservoir beneath the Salton Sea in Imperial County, California (Dobson et al., 2023). The project's first phase focused on assessing the key opportunities and challenges associated with developing this lithium resourc...
Conference Paper
Full-text available
The Massepe Geothermal Field in South Sulawesi, Indonesia, presents sufficient geothermal energy potential as a promising greenfield site. This study focuses on assessing its resource capacity through uncertainty analysis and a natural state model, despite limited direct subsurface exploration. A comprehensive three-dimensional (3D) geological mode...
Conference Paper
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Evaluating geothermal potential is an essential step in determining the sustainability of a geothermal project, both technically and economically. This study assesses the Mount Ciremai Geothermal Field in Indonesia to determine its feasibility for clean electricity generation through 3D reservoir modelling and numerical simulations. A 3D conceptual...
Conference Paper
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The Salton Sea Geothermal Field (SSGF) is one of the world's largest geothermal resources with an estimated resource potential of nearly 3 GW and dissolved minerals such as lithium of high interest. Despite a long history of production from and reinjection into the deep geothermal system, the brine's complex high salinity is challenging in assessin...
Conference Paper
Full-text available
Geothermal reservoir modelling requires detailed historical extraction data to predict a geothermal system's future state accurately. However, this data is rarely available to modellers. Often, wells are sparsely measured, while grouped measurements, such as mass flow at a separator, occur more frequently. Previously, this data history was manually...
Article
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Geothermal energy in the Paris urban area has been exploited since the early 1970s. Deep drilling in the Paris sedimentary basin has targeted hot brine in the Dogger formations from a mid-Jurassic carbonate rocks series. More than a hundred wells have been drilled to depths ranging from 1400 to 2000 m and decades of production and reinjection have...
Article
Models of geothermal reservoirs used for power generation need to simulate the production of multiphase fluid via a complex network of sources, as well as the reinjection of some of this fluid back into the system. The use of standard numerical methods to model such systems with interacting sources typically gives poor non-linear solver convergence...
Conference Paper
Full-text available
Geothermal power production is a renewable form of base-load electricity generation. However, it is not an emissions-free process due to non-condensable gases, such as CO₂ found naturally underground that are mixed into the working fluid. With the global push toward more sustainable operation of infrastructure, good management of the CO₂ emissions...
Conference Paper
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In geothermal resource developments, resource assessment has an important role especially for the decision making, since the assessment determines the possible production capacity of the field. However, because of its invisibility underground, there are many uncertainties which affect the reliability of the resource assessment. They include quality...
Conference Paper
Full-text available
We have set up a numerical model of a supercritical geothermal system and used it to carry out numerical experiments on the natural state of the system and its response to various production/injection scenarios. The model is based on a synthetic geothermal system that we use in teaching various courses on geothermal modelling, but we have extended...
Conference Paper
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The National Energy General Plan (RUEN) of Indonesia targets the production of 10 GWe from geothermal by 2030 and further increases to 17.5 GWe by 2050. Robust assessments of Indonesia's undeveloped geothermal resources are required to help prioritize systems for development. A new method for resource assessment has been developed by the Geothermal...
Preprint
Numerical models of geothermal reservoirs typically depend on hundreds or thousands of unknown parameters, which must be estimated using sparse, noisy data. However, these models capture complex physical processes, which frequently results in long run-times and simulation failures, making the process of estimating the unknown parameters a challengi...
Conference Paper
Full-text available
Maritaing is one of the potential geothermal areas in the eastern part of Indonesia, located in Alor Island, East Nusa Tenggara. Previous studies indicate that the green field has 17 MW of hypothetical resources. This study aims to create a conceptual model of the geothermal prospect area by combining geology, geophysics, and geochemistry data. The...
Conference Paper
Full-text available
The Massepe Geothermal Field in South Sulawesi, Indonesia, presents promising geothermal energy potential. This study outlines a three-dimensional (3D) digital conceptual model and a numerical reservoir model of the Massepe field. A 3D digital conceptual model was developed utilizing geological, geophysical, and geochemical data. The model incorpor...
Article
Full-text available
Plain Language Summary Earthquakes can strongly affect circulating fluids within the Earth's crust, mainly where faults bend or split into different fault segments and produce dilatant areas. In these areas, earthquakes play an important role in forming ore deposits, because the co‐seismic volume change can produce a pressure drop that drives boili...
Preprint
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The ability to make accurate predictions with quantified uncertainty provides a crucial foundation for the successful management of a geothermal reservoir. Conventional approaches for making predictions using geothermal reservoir models involve estimating unknown model parameters using field data, then propagating the uncertainty in these estimates...
Conference Paper
Full-text available
Geothermal fields are a valuable resource in the energy sector. However, there is significant cost and risk involved in determining the viability of a field for production. We have, therefore, improved a method to assess the potential of a geothermal resource using numerical modelling and uncertainty quantification. We have further conducted a stud...
Conference Paper
Full-text available
The Ohaaki geothermal field (OGF) is a gassy two-phase geothermal field in the volcanic and sedimentary accumulation basin at the eastern margin of the Taupo Volcanic Zone in the central North Island of New Zealand. The long history of exploration and development of Ohaaki started with the drilling of the first well in 1965. Large-scale testing of...
Conference Paper
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The Tikitere geothermal field is one of the 21 high-enthalpy geothermal fields in the Taupo Volcanic Zone (TVZ) in New Zealand. The field is renowned for the tourist attraction Hell's Gate, which consists of many natural geothermal surface features. Based on geoscientific data from the open-source literature, a conceptual model was set up in Leapfr...
Conference Paper
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A typical geothermal model requires significant computational resources to simulate and can contain hundreds of unknown parameters. The process of estimating these parameters, often referred to as model calibration, is a difficult task; traditional methods such as Markov chain Monte Carlo generally require running a prohibitively large number of si...
Conference Paper
This work presents a novel approach for inference in geothermal reservoir models that leverages simulation-based methods and approximate Bayesian computation (ABC) to integrate various types of data to constrain the model. Geothermal reservoir models are complex systems that require a combination of different types of data to be accurately characte...
Conference Paper
Full-text available
Simulation of transient flow in geothermal wells is an important reservoir engineering task. Previously, we discussed the development of a wellbore simulator capable of modelling complex transient flows of water and non-condensable gases in geothermal wells. However, this simulator used productivity models to represent the reservoir. While this rep...
Conference Paper
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This paper discusses the development of a 3D natural state model of Los Humeros Geothermal Field (LHGF), based on numerical simulations with AUTOUGH2. The model gives a good representation of the temperature distribution and the groundwater system. Hence it can be used for simulation of the production history and subsequently for simulation of prop...
Article
Full-text available
A new transient geothermal wellbore simulator is presented. It is based on a mathematical model consisting of three conservation equations (mass, momentum and energy) and a slip model describing how the liquid and vapour phases move differently. The three conservation equations are discretised using the finite volume method with thermodynamic varia...
Conference Paper
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Indonesia has the second highest geothermal power installed capacity worldwide and expects to develop more geothermal energy in the future. In the northeast of the Sulawesi Island, the high temperature geothermal system of Lahendong has a current installed capacity of 80 M We. It lies in the Minahasa-Sangihe Volcanic Arc resulting from the subducti...
Conference Paper
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Indonesia has the second highest geothermal power installed capacity worldwide and expects to develop more geothermal energy in the future. Kamojang is a vapour-dominated geothermal field located 40 km to the southeast of Bandung in West Java, Indonesia. It was the first geothermal project to be developed in Indonesia. In this paper we discuss a mu...
Conference Paper
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There remains a large economic risk in the exploration and development of a green field geothermal resource. M anaging the economic risk of a green field project is done by assessing the potential of the new geothermal energy source. This is currently still done by stored heat calculations and applying an approximate recovery factor. The uncertaint...
Conference Paper
Full-text available
Reservoir modeling is a vital tool in the sustainable management of geothermal reservoirs. A key component of the modeling process is model calibration, in which parameters, including permeabilities and mass upflows, are adjusted until there is an adequate match between the model outputs and collected data. The Bayesian approach to model calibratio...
Article
Full-text available
In a recent paper we discussed the development of a new transient geothermal wellbore simulator. In the present paper we discuss the application of this simulator to the modelling of challenging and interesting flows that occur in a geothermal wellbore. The first group of problems involve the opening and closing of hot geothermal wells with rapid t...
Conference Paper
Full-text available
The East African Rift (EAR) is one of the largest rifts in the world. In various regions on the rift, volcanic activity occurs, which makes it a place with great potential for harnessing geothermal energy. Currently, there are only a few geothermal power plants on the EAR, with the largest ones in Ethiopia and Kenya, and the main focus is on high-t...
Conference Paper
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Standard approaches to geothermal model calibration typically assume independent, identically distributed Gaussian measurement noise about the model. However, in practice, models usually exhibit systematic errors, such as well-to-well offsets between measured data and the best-fit (calibrated) simulation model. Failure to account for these systemat...
Conference Paper
Full-text available
Waiwera is a new open-source, parallelised geothermal reservoir simulator developed through a collaboration between the University of Auckland (UoA) and GNS Science. It is designed to address the current and future challenges of modelling geothermal systems. The Waiwera development was part of the New Zealand Geothermal Supermodels programme to dev...
Conference Paper
Full-text available
Geothermal fields naturally emit greenhouse gasses through surface expression. When a geothermal power plant is installed on a geothermal field, the fluid extracted contains these gases, but generally, the reinjected fluid does not. For this reason, power companies producing from geothermal fields are considered an 'emitter' within the Emissions Tr...
Conference Paper
Full-text available
Geothermal reservoir modelling is essential for the successful development of geothermal fields. It assists geothermal companies in decision making and planning for the development of a geothermal resource. However, the approach used for generating a geothermal reservoir model depends on the company, university, or consultant involved as there is n...
Conference Paper
Full-text available
Geothermal reservoirs are a valuable source of sustainable energy. The economic viability of harnessing geothermal energy is dependent on the size of the energy resource. However, determining the energy potential of a geothermal reservoir is generally complicated and uncertain due to a low availability of data. The estimation of the energy resource...
Article
Full-text available
The Krafla area in north Iceland hosts a high‐temperature geothermal system within a volcanic caldera. Temperature measurements from boreholes drilled for power generation reveal enigmatic contrasts throughout the drilled area. While wells in the western part of the production field indicate a 0.5–1 km thick near‐isothermal (∼210°C) liquid‐dominate...
Conference Paper
Full-text available
Geothermal reservoir modelling is a complex and time-consuming task. While the theoretical background is generally reserved for professionals and academics, with the right training geothermal modelling is more generally accessible. Here we discuss practical and advanced simulation exercises, including idealised case studies, that can be used to int...
Conference Paper
Full-text available
One of the main constraints of geothermal reservoir model development is the time it takes to calibrate geothermal models. Model calibration requires running the model for each change in parameters made to improve the match to available data. In recent years, Waiwera, a parallelised geothermal simulator, has been under development with the aim of s...
Conference Paper
Full-text available
The first well was drilled at the Ohaaki geothermal field in 1965 and not long afterwards the University of Auckland began a long collaboration with Contact Energy and its predecessors in modelling the Ohaaki reservoir. The succession of models has been used to inform decision making and aid consent applications. The permeability distribution in th...
Conference Paper
Full-text available
Developing an accurate geothermal model requires model calibration to match available data. The data is expensive to gather and, therefore, usually sparse. We use geothermal models to make predictions that aid in managing the geothermal field sustainably. However, these model predictions are uncertain due to model complexity and sparse data. This p...
Conference Paper
Full-text available
The ability to make accurate predictions with quantified uncertainty provides a crucial foundation for successfully managing a geothermal reservoir. The standard, state-of-the-art approach to delivering accurate predictions for a geothermal model requires two steps. First, the underlying uncertain parameters (such as subsurface permeability, streng...
Article
We present case studies on two methods for quantifying uncertainty in predictions for highly parameterised geothermal models. One method is fully linear, while the other is nonlinear as it requires sampling model parameters and additional simulations but can handle non-differentiable quantities of interest. We test both methods on a Leyte (Philippi...
Article
A wellbore simulator is an important tool for understanding flow in geothermal wells, however, the literature on the topic is confusing because previous wellbore simulators have been based on a variety of versions of the equations for conservation of mass, momentum and energy. This lack of consistency in describing the behaviour of flow in a geothe...
Conference Paper
Full-text available
Simulation of transient flow in geothermal wells is an important reservoir engineering task. Previously, we discussed the development of a wellbore simulator capable of modelling complex transient processes in geothermal wells. However, its applicability was restricted to flows of pure water. This paper discusses the implementation of an air-water...
Conference Paper
Full-text available
Geothermal reservoir models require suitable bottom boundary conditions to account for the influence of deep geothermal energy sources. When applying mass-and heat-flux boundary conditions to a model, it is standard practice to assign mass upflows to fixed locations on the bottom boundary. That is, during automatic model calibration, each boundary...
Conference Paper
Full-text available
One of the complex transient phenomena that can occur within geothermal wellbores is counter-flow. In geothermal wells, counter-flow occurs when steam flows up the well while water flows down. Here we discuss numerical experiments with a recently developed transient geothermal wellbore simulator that is capable of modelling counter-flow scenarios....
Conference Paper
Full-text available
Weh Island is located in the westernmost part of Indonesia. It has a geothermal field in the south part and a high intensity of submarine volcanic activities in its middle coastal area due to the existence of the active Sumatran Fault and current volcanism, producing hydrothermal mineralisation in the fault zone. Submarine volcanic activities contr...
Article
Geothermal is commonly considered to be a clean, green energy source but it does produce some greenhouse gas emissions, particularly CO2. The amount of CO2 is usually measured as an emission intensity of kg of CO2 emitted per MWh of electricity produced. However, the quantity that is measured for the calculation of emission intensity is the waste C...
Conference Paper
Full-text available
Simulation of the flow in a geothermal wellbore is an important reservoir engineering task, however, most existing geothermal wellbore simulators can only deal with steady-state conditions. This paper discusses the theoretical background and numerical implementation of a transient geothermal wellbore model that is currently under development. The s...
Conference Paper
Full-text available
Computational modelling and calibration can play a vital role in various geophysical settings, including the management of geothermal reservoirs. The calibration process typically involves perturbing model parameters, such as subsurface permeabilities, so that the resulting simulator outputs match field data, usually consisting of noisy surface or...
Conference Paper
Full-text available
Computational reservoir models are commonly used to inform management decisions in the geothermal energy sector. With a well-calibrated model, a range of future scenarios can be simulated and informed decisions can be made. However, the task of calibrating large-scale geothermal models is challenging, both from a conceptual standpoint and in terms...
Conference Paper
Full-text available
The model of the geothermal field on Montserrat Island, developed at the University of Auckland in 2018, has been updated in the following three ways. First, the model grid was extended to the southeast to include more of the area around the Soufrière Hills Volcano, and the grid was refined. Secondly, temperatures inferred from a seismic velocity a...
Conference Paper
Full-text available
Two improvements have recently been made to the model of the Rotorua Geothermal Field, developed at the University of Auckland. First, a finer, regular rectangular model grid is used. Secondly, a Leapfrog-based geological model and an alteration model are used to better define the permeability structure of the computer model. With a new regular rec...
Conference Paper
Full-text available
Transient flow in a geothermal wellbore is modelled using equations for conservation of mass, momentum and energy. Additional constitutive equations that describe phase slip, heat transfer and frictional effects are also required for model closure. The transient wellbore simulator described in this paper solves discrete two-phase conservation equat...
Conference Paper
Full-text available
Simulation of the flow in a geothermal wellbore is an important reservoir engineering task, but most existing geothermal wellbore simulators can only deal with steady-state conditions. This paper discusses the theoretical background of a transient geothermal wellbore model that is currently under development. The simulator is capable of modelling t...
Article
In this work, we present an update for the conceptual model of the El Tatio-La Torta geothermal system, one of the most studied geothermal fields in the Central Andes of South America. Using the structural model reported by Veloso et al. (2019) for northern Chile, the conceptual model proposes a reservoir architecture and heat transfer modes at dif...
Conference Paper
Full-text available
The calibration of geothermal simulation models involves inferring the permeability structure of the system and the location of the deep upflow of heat and mass. Available data typically includes noisy temperature, pressure and enthalpy measurements from pre-existing wells. Mathematically, model calibration is an ill-posed inverse problem. Solving...
Conference Paper
Full-text available
A numerical simulation representing the natural state of a geothermal system commonly involves finding an approximate solution to a mass and energy balance equilibrium problem; that is, solving a steady-state simulation. Solving this type of natural-state simulation problem is often problematic, and geothermal simulators regularly struggle or are u...
Article
Full-text available
This project aims to develop a new natural state model of Jaboi geothermal area to obtain an improved understanding of the subsurface conditions and behavior of the reservoir. This paper describes the progress that has been made in the project so far which includes a new geological model developed in LEAPFROG Geothermal and the reservoir model setu...
Conference Paper
Full-text available
Mathematical and computational modelling of geothermal fields plays a key role in effective management of geothermal reservoirs. Central to the management of such reservoirs is the ability to predict future behaviour. In the case of geothermal reservoir modelling, available data consists of noisy temperature, pressure and enthalpy measurements from...
Conference Paper
Full-text available
This project aims to develop a new natural state model of Jaboi geothermal area to obtain an improved understanding of the subsurface conditions and behavior of the reservoir. This paper describes the progress that has been made in the project so far which includes a new geological model developed in LEAPFROG Geothermal and the reservoir model setu...
Article
The Levenberg-Marquardt (LM) method is commonly used for inverting models used to describe geothermal, groundwater, or oil and gas reservoirs. In previous studies LM parameter updates have been made tractable for highly parameterized inverse problems with large data sets by applying matrix factorization methods or iterative linear solvers to approx...
Preprint
The Levenberg-Marquardt (LM) method is commonly used for inverting models used to describe geothermal, groundwater, or oil and gas reservoirs. In previous studies LM parameter updates have been made tractable for highly parameterized inverse problems with large data sets by applying matrix factorization methods or iterative linear solvers to approx...
Article
The Rotorua geothermal field is a shallow geothermal reservoir lying directly beneath Rotorua City in New Zealand. It is renowned for an abundance of natural geothermal manifestations including the geysers and hot springs at Whakarewarewa. Over-exploitation of the geothermal resource in the 1970s leading to the decline of many active surface featur...
Chapter
The three simple methods for geothermal resource estimation, namely power density, stored heat, and exergy, are reviewed and their shortcomings are discussed. It is concluded that computer modeling should be used instead of these simple methods.An overview is presented of the theory and numerical methods used in computer modeling of geothermal syst...
Conference Paper
Full-text available
Gradient based inversion of high-enthalpy geothermal reservoir models is a demanding task even for just a handful of model parameters. Moreover, as more parameters are included the inverse process becomes slower and parameter uniqueness is a concern. These issues can, nevertheless, be lessened by using appropriate mathematical tools to obtain geolo...
Conference Paper
Full-text available
Manual calibration to adjust parameters to produce a model that best represents the actual behaviour of a geothermal system is a tedious and frustrating process. This paper discusses automatic calibration of a geothermal reservoir model employing inverse modelling techniques. Inverse modelling simulators, namely PEST and iTOUGH2, are utilized to id...
Conference Paper
Full-text available
Significant localised ground subsidence related to geothermal production has been experienced within Wairakei geothermal field since the 1950s. Much of current knowledge of the cause of this subsidence anomaly has come from data gathered recently during an intensive subsidence investigation program. This anomaly is understood to be caused by both a...
Conference Paper
Full-text available
The Leyte geothermal production field is among the largest developed geothermal system in the world. It has a total installed capacity of 700MWe and more than 180 production and injection wells have been drilled over its more than 30 years of production life. Several numerical models have been developed in the past for use in managing the productio...
Conference Paper
Full-text available
Arjuno-Welirang geothermal field is one of the geothermal fields in Indonesia, located in Mojokerto Regency, East Java. It is a high terrain volcanic geothermal system, with a high reservoir temperature of 260oC. The upflow zone of the system is located around the peak of Mt. Welirang, indicated by the manifestation of several fumaroles. The outflo...
Conference Paper
Full-text available
The Kerinci geothermal system is located in Jambi Province, Indonesia. The study area is located on part of the Great Sumatra Fault which means it is a fault-controlled system. Many surface manifestations are found along the faults, such as steaming ground, fumaroles, hot springs and mud pools. The development of Kerinci is problematic as the Sikai...
Conference Paper
Full-text available
The proper management of geothermal resources relies heavily on computational and mathematical modelling. Given a sufficiently complete description of the physical processes governing a geothermal field we can, in principle, predict future values of the field's measurable outputs. This is typically called the 'forward problem'. All models, especial...
Conference Paper
Full-text available
The “Geothermal Supermodels” project is a four-year New Zealand-based research programme, a major part of which is the development of a new open-source, parallelised geothermal reservoir flow simulator. This paper describes progress on flow simulator development over the past year, including the implementation of a modified multi-phase gravity term...
Conference Paper
Full-text available
The Rotorua Geothermal Field is a shallow high enthalpy geothermal reservoir lying directly beneath the Rotorua city in New Zealand. It is renowned for an abundance of natural geothermal manifestations including the geysers and hot springs at Whakarewarewa. However surface geothermal activity waned in the 1970s and a decline in surface discharge of...
Conference Paper
Full-text available
We are using full-scale three dimensional numerical model of the Rotorua geothermal system to generate temperature and pressure time series in model blocks where a surface features is located. The Pearson correlation factors between the time series, rainfall, and recorded temperature variations in surface features are calculated which allows us to...
Conference Paper
Full-text available
Matching the pre-exploitation or natural state of a geothermal field is often problematic. The natural state is approximated by a steady state, achieved by running a geothermal model forward in time until the system is unchanging. The final simulation time may have to be many millions of years to achieve the goal, and therefore, steady state geothe...
Article
Orakeikorako is one of several protected geothermal systems in the Taupo Volcanic Zone (TVZ) in the centre of the north island of New Zealand. Its beautiful surface features are highly valued for both their cultural significance and for tourism. Many other geothermal systems in the TVZ have been developed for energy utilisation including Ngatamarik...
Conference Paper
Full-text available
At Wairakei geothermal field in New Zealand, subsidence has occurred since the onset of production in the 1950's. A good understanding of the stress-deformation behaviour of materials is important for understanding the phenomenon and being able to predict future subsidence. For many of the materials found in the Wairakei geothermal field simple, li...
Conference Paper
Full-text available
The Wairakei geothermal field in New Zealand has experienced a significant amount of production related subsidence in the last 50 years. Therefore, the region has been subject to a significant amount of data collection and rock characterization work. However, the rock properties associated with mechanical deformation are often overly simplified in...
Conference Paper
Full-text available
Model sensitivities are a measure of how specific model results vary with selected model parameters (such as permeability and porosity). They are important for parameterizing numerical models, automatic history matching and uncertainty quantification of model predictions. However, the current way of evaluating model sensitivities using finite diffe...

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