This thesis analyzes the effectiveness of bias-aware filtering techniques, particularly the ColKF, in addressing parameter and bias estimation in data assimilation problems. The research explores the ability of this method to differentiate between the impacts of bias and parameter uncertainty, focusing on how the concept of feedback within the filtering process influences the estimation of both bias and parameters.

The study uses the Lorenz-96 model to conduct twin experiments, investigating various scenarios involving parameter estimation, bias estimation, and combined parameter and bias estimation. The experiments reveal that in a feedback filter configuration, where the bias directly influences the ODE system, the forcing parameter F of the Lorenz-96 model becomes indistinguishable from the bias. Conversely, a non-feedback filter configuration allows for the independent estimation of both the parameter and the bias.

In addition, the research highlights the challenges and considerations in implementing a flexible data assimilation framework, particularly in managing state augmentation, stochastic updates, and bias representation. It emphasizes the importance of carefully considering the feedback mechanism in bias-aware filtering, as it significantly impacts the estimation of parameters and bias.

The findings of this thesis offer valuable insights into the application of bias-aware filtering techniques in the presence of parameter uncertainty and provide a foundation for future research in developing robust and versatile data assimilation frameworks. The study encourages further exploration of these methods in real-world applications and with more complex bias structures to advance our understanding and ability to address uncertainties in dynamic systems effectively.

This study investigates the impact of the viscous properties of the Zechstein formation on the state of stress and (a)seismic slip in depleting gas reservoirs. I have put the focus on the Rotliegend and Zechstein-2 Carbonate gas fields in the Northeast Netherlands. Six geomechanical models (four Rotliegend and two Carbonate) different were created in Plaxis, representing a fault in various gas fields. For the Carbonate models and two Rotliegend models, the halite is juxtaposed to the reservoir, while for the other two Rotliegend models, the halite is not juxtaposed to the reservoir. The models were simulated with both elastic and viscous properties for the Zechstein halite. Deformations and stresses were calculated around and on the fault using the finite element method.

The viscous property led to a significant increase in strain deformation in the halite and the reservoir juxtaposed to the halite, resulting in a greater compaction in the reservoir next to the halite. The change in strain in other layers was limited with the viscous property.
With depletion the stress ratio decreased in the reservoir and juxtaposed layers, increasing the risk of fault reactivation. In the layers above and below the reservoir, the stress ratio increased, moving away from criticality. While the pattern of stress change with depletion was similar for both elastic and viscous models, the magnitude differed.
For the viscous model, the stress ratio in the layers next to the halite are larger with respect to the elastic model. The high horizontal stresses of the halite significantly decreased the horizontal stresses and, consequently, the stress ratio in the Basal Zechstein below the Halite. Deeper in the reservoir, the decrease in vertical stress between the elastic and viscous was larger than the decrease in horizontal stress, resulting in a slightly larger stress ratio for the viscous model, moving the fault away from criticality. In some models, a slip patch was identified for the elastic model but not for the viscous model. Therefore, it can be concluded that a larger pore pressure depletion is needed for fault reactivation.
The difference in stress and slip between the elastic and viscous model were more pronounced when the halite was juxtaposed to the reservoir. Smaller stress changes and differences between the elastic and viscous were observed for the Carbonate reservoir compared to the Rotliegend reservoirs, due to the greater resistance to deformation. This results in a lower risk of fault reactivation with reservoir depletion. Fault reactivation is also not identified for the Carbonate models.

Permeability, a key reservoir characteristic, governs the rate of fluid flow through reservoir rocks. Accurate permeability estimates are paramount for robust reservoir simulation, history matching, and production forecasting. Due to limited core data availability and intrinsic heterogeneity of permeability at different scales, establishing reliable permeability models can be challenging. This study aims to overcome these hurdles by predicting lab-measured core permeability from commonly acquired well logs, using various machine learning algorithms such as Support Vector Regression (SVR), Random Forest (RF), XGBoost, and LightGBM.
We examined two diverse datasets, representing a carbonate platform (Costa Field) and clastic formations (Volve Field). The Costa dataset, including 17 wells across a single reservoir, and the Volve dataset, comprising three wells across three different reservoirs, allowed for evaluating the robustness of our approach under different geological conditions. A critical part of our methodology is feature engineering, particularly incorporating vertical variability. We integrated measurements from adjacent well log readings into our models, recognizing the importance of spatial context and the smoothing effect of well logs over small-scale heterogeneities. This improved prediction accuracy by accounting for shared geological history and depositional environments in proximity.
In Costa Field, blind tests showed R2 scores up to 0.64, and validation R2 scores reached up to 0.8 using a leave-one-well-out cross-validation method. For the Volve Field, blind test R2 scores were up to 0.84, 0.76, and 0.78 for Hugin, Sleipner, and Skagerrak formations, respectively. These results, while satisfactory, underscore the potential of machine learning methods in accurately predicting permeability and highlight the need for effective feature engineering.
This work advocates that while machine learning holds promise for automated feature engineering, human intervention, specifically to incorporate spatial context, can still significantly enhance predictions. Future advancements may seek to internalize this spatial awareness within the machine learning algorithms themselves

This research describes how thermal fractures impact the near-wellbore (NWB) region of a depleted gasfield in a carbon sequestration project. As CO2 is usually injected in its supercritical phase, the injection fluid is injected on high pressures and low temperatures. This is in high contrast with the depleted gasfields, which have a low reservoir pressure. The increase in pressure and decrease in temperature causes a thermoporoelastic response, resulting in a reduction of stress inside the reservoir. Once the fracture initiation stress, the so-called fracture stress, is reached, thermal fractures form.

Thermal fractures form only due to extensive cooling of the reservoir. The fractures impact the NWB region; due to opening of fractures there is a drop in pressure in the bottomhole pressure (BHP). This increases the reservoir's injectivity. This research uses CMG GEM to model this. The simulation uses a homogeneous box dual permeability model with the model being initialized as a generalized depleted gas reservoir in the North Sea. To model the fractures, the Barton Bandis model is used. This model changes the permeability in a fracture cell once fracture conditions are met.

From this model, the moment of fracturing (fracture time), the fracture halflength and the injectivity of the reservoir is researched by performing a sensitivity analysis on key parameters. It is found that the thermal fractures propagate conform to the propagation of the coldest part of the thermal front. The thermal front propagates further once the fracture conditions are met sooner due to fluid highways or when the pressure build up in the reservoir is slower.

The sensitivity on the geomechanical parameters showed that only the stress conditions in the reservoir changed, causing the injection constant to change and thus a different fracture time. The way the reservoir reacted to the initiation of fractures was the same; the injectivity was improved similarly for each parameter.

The effective permeability (thickness and permeability) determines, together with the injection rate, the way the pressure builds up in the reservoir changes the increase of injectivity due to fracturing slightly. Increasing the reservoir volume causes a slower pressure build-up inside of the reservoir, allowing the thermal front to propagate further and thus longer fracture lengths.

Lastly, the sensitivity on the thermal effects showed that a higher difference between the reservoir and injection temperature causes the fracture to be less dependent on the increase of pressure to fracture, resulting in earlier fracturing and longer fracture halflength. The pressure build-up is not changed, so the injectivity remains similar to the basecase scenario.

All in all, this thesis gives an insight on how key parameters impact thermal fracture behavior. It also shows what range of parameters can be expected. Combining these two gives an insight on what parameters the focus should be on to better describe the behavior of thermal fractures, to economize the operation by leaving out or including extensive data collection on key parameters. This helps to improve the injection strategy with CO2 injection projects in depleted gasfields.

As a result of the gas extraction in Groningen (the Netherlands) the amount of earthquakes have increased over the past decades. Understanding the induced seismicity in the Zeerijp area is important for the population living in this relatively densely populated region, but also essential to the Dutch governement and the operator of the field; the Nederlandse Aardolie Maatschappij (NAM). One way of gaining the knowledge on the dynamics of the fault systems in the area is by, for example, a full waveform inversion f recorded seismic data that gives us the moment tensor describing the earthquake mechanism. A drawback of this method is that it is computationally expensive and time intensive. In this thesis two different machine learning techniques are investigated that can lead to a faster estimation of the moment tensor. We find that, when using time traces that are modelled from the 1D velocity model of the area, there is a difference in sensitivity of the network to the individual moment tensor components. Besides that, using a feed forward neural network generally yields a better performance, but does not give us the associated uncertainties of the network. This is in contrast with the mixture density network, which performs slightly worse than the feed forward network, but it does give us the involved uncertainties when the algorithm makes the predictions. Adding different levels of Gaussian noise to the data gave us a first insight as to how the precision of the moment tensor estimations would change. It was found that a mixture density network has a more stable prediction when estimating low signal-to-noise ratio data. No test with real data from the Zeerijp area is done, however, we can conclude from our results that the estimation of the moment tensors in this region should be possible with the use of machine learning techniques.

In this thesis, we discuss two pattern recognition techniques, template matching, and neural networks. We discuss how these techniques have been used for the development of two earthquake detection algorithms. The first algorithm is based on template matching and the second is based on deep learning. The algorithms are designed for the detection of small <0.5M events in the subsurface of Zeerijp, Groningen. These two algorithms have been compared to assess their earthquake detectability and practicality. The systems have been compared using field data from Zeerijp. The algorithm based on deep learning (a neural network) produced too many false positives considering the amount of seismic data we would like to use it for. The algorithm based on template matching did not produce any false positives during testing. The template matching system has been fed six months of continuous seismic data fromZeerijp. This resulted in the detection of at least 22 new events.

Geothermal energy can be a great solution for the downscaling fossil fuel society, but it can potentially lead to seismic hazards. A doublet system, with a cold water injection well and a hot water production well, alters the stress situation in the subsurface, which can result in (micro)fracturing and fault reactivation. Even in water filled reservoirs, aquifers, with relatively good permeabilities, the acting in-situ stress on already existing fault can be changed such that there can be a seismic hazard. The three dominant phenomena that influence the fault reactivation and are triggered by geothermal water injection and production are the direct pore pressure change, poro-elastic stress change and thermo-elastic stress change. To predict and subsequently diminish or limit the seismic hazards in geothermal operations, Seismic Risk Analysis (SRA) are to be completed before such operations can take place in an often seismic risky location, like densely populated areas. In the current (Dutch) geothermal environment mainly three SRA’s are used; “Methodiek voor risicoanalyse ontrent geinduceerde beving door gaswinning” by the Staatstoezicht op de Mijnen (SodM), “Defining the Framework for Seismic Hazard Assessment in Geothermal Projects V0.1” by Q-con/IF-technology [6] and an Excel-model created by TNO/Geomech. By investigating and reviewing these three SRA’s in this thesis their shortcoming and limitations are exposed, for example their lack of physical foundation and explanatory results. From the foundation of the currently excising SRA’s a new alternative SRA, which corresponds in some steps with the older SRA’s, is created in this thesis. In order to successfully finish the new SRA one of the three steps should be completed, starting with SRA Step 1. In this first step of the new SRA a new Physical Screening Model (PSM) is created. When completing the SRA an indication of what type of seismic monitoring there should be done during production. This PSM is a fairly quick and simple in its use but provides sufficient informative data to investigate the seismic hazard for most geothermal operations in the Netherlands. In four different steps in the PSM, the potential reactivation of faults over the whole reservoir during production will be evaluated. With the spatio-temporal evolution of ΔP, Δσporo, ΔT (PSM Step 1) this model can predict fault reactivation at any place and time inside the reservoir, while it can also look at which parameter dominated this reactivation. In this thesis the physical background and results of the PSM will be explained step by step. Eventually there are three final results from the PSM; a Mohr plot that predicts if certain faults (at certain locations) are stable or not and the maximum Moment magnitude (Mw) in combinations with the Peak Ground Velocity (PGV), which predict the severity of a possible event. Sensitivity analyses and case studies done with the PSM in this thesis show the influence of dominating parameters, like permeability and injection rate, and what results can be expected when using this model.

The main objective of this thesis is to assess the combined influences of specified reservoir conditions and operational parameters on the profitability of a geothermal project and on the potential for fault reactivation. The aim is to propose potential development strategies to maximize the profitability and minimize the potential for slip and reactivation of pre-existing critically stressed faults. The reservoir conditions of interest in this study include the fault permeability, the fault throw and the friction coefficient of the sandstone. The operational parameters of interest are the flowrate, the injection temperature of the re-injected water and the distance between the wells and the fault. As a case study a simplified homogeneous 3D box-shaped reservoir model is simulated based on the Delft Sandstone Member in the West Netherlands Basin, using the Delft Advanced Research Terra Simulator (DARTS). Reservoir production data and local pore pressure data are generated with DARTS and serve as the input data for the fault stability model and the economic model, which are both built in Python. The fault stability model is built based on the method of Mohr circles, regional stress values in the Delft area and the failure criterion of sandstone and allows to assess the fault slip tendency of a pre-existing fault. The economic model is based on the Dutch fiscal system and policies and includes the costs of the phases of a geothermal project and required energy calculations. The outputs of the model allow to assess the profitability of a geothermal project based on the Net Present Value (NPV). Outcomes of this study have shown that the profitability and the fault stability depend highly on the joint influences of specific reservoir conditions and operational options. Sealing faults generally have a negative influence on both the NPV outcomes and the fault stability as the presence leads to decreasing heat production, higher pumping costs and higher pressure build up near the fault. This influence is strengthened when the wells are placed close to the fault, while it is reduced by placing the wells far from the fault. The flowrate and the used injection temperature are found to be the most important operational options, regardless of the reservoir conditions. Combining the highest possible flowrates and the lowest possible injection temperature maximizes the NPV outcomes. As it is found that NPV outcomes increase by a factor 6 when increasing the flowrate 2.5 times and decreasing the injection temperature by 5 K may increase the NPV values up to 19\% to 43\% depending on the flowrate. With respect to the reservoir conditions the study has shown that the fault permeability and the sandstone friction coefficient are the most important influencing reservoir conditions, compared to the fault throw. The risk for fault instability increases with decreasing value of the friction coefficient and of the fault permeability. With respect to the operational options the potential for fault slip is minimized when the lowest possible flowrate is combined with the highest possible injection temperature. However, the use of a 5 K higher injection temperature allows the use of a 600 m3/day higher flowrate. Placing the wells minimally 200 m from a fault in the homogeneous reservoir and using a minimum flowrate of 7200 m3/day maximizes the NPV outcomes and fault reactivation is reduced as much as possible. The assessment of the fault stability and the profitability is however very sensitive to the reservoir conditions, which is explicitly found from the results comparing a homogeneous and a heterogeneous reservoir. This makes the potential development strategies extremely prone to heterogeneity effects and subsurface conditions which makes them highly dependent on locations specific properties. Though, the general influences of the reservoir conditions and operational options on a heterogeneous reservoir are similar to those found for the homogeneous reservoir.

Geothermal energy is generally seen as a sustainable source of energy and therefore could be part of the solution for the energy transition. However, there is still a lack of clarity about the conditions under which a geothermal system can be used sustainably. This study investigates the sustainable use of a geothermal system. The geothermal production process in a homogeneous geothermal reservoir with one doublet was simulated using SEAWAT. This model provides the possibility to conduct a sensitivity analysis to examine which parameters play an important role in the geothermal production process. The aim of this analysis was to asses the effect on the well temperature and the thermal recharge, i.e. heat flow from the confining layers towards the reservoir. The tested parameters include four geological uncertainties and two production parameters. From the tested geological uncertainties the thickness of the reservoir has the largest effect on the production profile. Also, it has an impact on the effect of all the other parameters tested, especially on the effect of the confining layers. The confining layers play an important role during the simulation of the production process because they control the thermal recharge, and this enhances the lifetime of the geothermal project. The thinner the reservoir, the larger is the effect of the confining layers and the change in its properties and the more impact the thermal recharge has on the production profile. By examining the effect of the production parameters, the aim was to define a sustainable production design and strategy. It was proven that the production rate has a large impact on the lifetime of a geothermal project, and that an increasing well spacing enhances the sustainable use of a geothermal system. To enhance the sustainable extraction of geothermal energy from a geothermal system the production rate should be kept low. When making a production optimisation two rules of thumb apply to maintain a sustainable production. The first rule says that with a doubling of the reservoir thickness, the production rate can be increased by approximately 50%. The second rule says that with an increase of well spacing of 20%, the production rate can be increased by approximately 50%. Overall, this study emphasizes the positive effect of thermal recharge on the production profile and its enhancement on the sustainable use of a geothermal system. We can conclude that with a sustainable production design and strategy the production from a geothermal system can continue for generations.

Subsidence of the ground surface, caused by hydrocarbon production, compaction of soft ground layers or other subsidence causes, is a timely topic in the Netherlands. Geodetic measurements of the surface can help us improve our knowledge of the subsurface; this process is called geomechanical inversion. Improved knowledge on the subsurface is needed for example to improve deformation predictions and to safeguard subsurface and surface infrastructure. Related works in this domain use derivatives of geodetic measurements as input for their inversion methodologies, but not the measurements themselves. Performing geomechanical inversion with derivatives of geodetic measurements introduces correlations in the covariance matrix of the data, making error propagation into the geomechanical estimates more complex. Defining a direct relationship between measurements and geomechanical estimates and subsequently inverting this relationship, makes the error propagation less complex. This thesis presents a new methodology that can be used to estimate reservoir geomechanical parameters through direct inversion using measurements from optical leveling campaigns. In the context of this thesis, a direct inversion is an inversion of a linear relationship between data and measurements. In this thesis, we propose and test a workflow for the estimation of a simplified set of geomechanical parameters. Part of the workflow is an extensive testing procedure of the geodetic data. A Geertsma nucleus-of-strain model is used to express a source parameter term in function of optical leveling measurements. This source parameter term is a lumped term and consists of a volume term, a pressure term, and several elastic rock parameter terms. This system is inverted using a Tikhonov regularization with a spatial penalty term. The methodology is applied to optical leveling data from a case study (the Norg and Roden gas fields in the northern Netherlands) and shows promising results. The RMS between modeled and measured subsidence for the most promising parameterization is 3.0 mm. The proposed methodology leads to geomechanical estimates with formal quality description, that could improve geomechanical models and subsequently leads to a better understanding of the subsurface and better subsidence predictions. The geomechanical parameter that is estimated is lumped and without additional information, it is impossible to differentiate between individual compaction parameter terms. Feeding the problem more information might also relax the need for regularization but can lead to the introduction of bias. We believe that the framework proposed in this work can be a good starting point for further research that uses geodetic measurements directly as input for a geomechanical inversion.

Displacement control is of utmost importance in deep excavation design and is usually based on numerical modelling, e.g. Finite Element Method (FEM). Numerical methods tend to be more conservative when analysing soil behaviour during deep excavation, whereas for practical and economic reasons this is not favoured. The inverse analysis allows for the identification of the soil parameter set that can provide the measurements observed in the monitoring when it is applied in the model. When performed in a probabilistic concept, it reduces parameter uncertainty and enables the stochastic prediction of future soil behaviour. In this thesis, capabilities and limitations of difference advanced constitutive models are investigated. The Generalized Hardening Soil Small strain model (GHS) presents a positive aspect in modelling soil behaviour during deep excavation with its various stress/strain dependency settings. Because of the uncertainties originating from the size of the domain and limitations of site investigation, the soil parameters can only be shown as probability distributions. In order to make that distribution more accurate, comparative selection of several inverse analysis optimization algorithms is performed. Thereafter, choice of the relevant parameters is done based on the conducted sensitivity analysis and engineering judgement. Having the most competitive optimization approach selected, remote scripting with Python is used to utilise Finite Element (FE) modelling in the 2D Plaxis software. The input parameters are iteratively updated with response observation (diaphragm wall deflections) using the Ensemble Kalman filter optimisation algorithm based on a chosen excavation stage. The re-calibrated parameters are checked with the data, which was used to create synthetic measurements made using the same FE, to perform reliability assessment of the developed Python-based algorithm and investigate its capabilities and limitations. The further development of the presented optimisation method is expected to increase certainty in setting alarm thresholds in the applications of the Observational Method.

The main objective of this study is to quantify interference effects between production and injection wells for geothermal projects that operate within the same reservoir. The secondary objective is to study the time it takes for the reservoir unit to thermally recharge after production has stopped. Two reservoir simulators are benchmarked to decide which one to use for reaching these objectives. The Ammerlaan, Duijvestijn and DAP doublets, all targeting the the Delft Sandstone Member in the West Netherlands Basin, serve as a case study. A literature review is presented to gain a better understanding of the geological history and the structural setting. A box-model of the study area is created and used to benchmark the two reservoir simulators. A static reservoir model is developed in Petrel through seismic interpretation, structural modelling, facies modelling and petrophysical modelling. Populating this static model with dynamic properties allows us to perform reservoir simulations in Eclipse100 and study the propagation of pressure and temperature. A discrete parameter analysis aims to capture the uncertainties that are associated with reservoir modelling and simulation. In this study, data is used from seismic surveys, wireline logs, core studies, a cuttings study and the monthly production volumes of the Ammerlaan and Duijvestijn doublets. It is shown that interference on temperature has a long term (20-30 years) effect on the Duijvestijn (positively) and the Ammerlaan and DAP doublets (negatively). The combined total energy production of the three doublets over 100 years is small with a decrease of 3% due to temperature interference, compared to when running the doublets in stand-alone configuration. Interference on pressure has a short term (days) effect on the achieved flow rate when the injection well cannot reach its target injection rate and is constraint on the maximum allowable pressure at which it is allowed to inject. This occurs under the low permeability scenarios and can be observed when the pressure wave arrives at the neighbouring injector. The Duijvestijn, Ammerlaan and DAP doublets all benefit from this through a combined increase in energy production of 8% over 100 years of production, averaged over all scenarios. During thermal recharge after production, the average reservoir temperature increases asymptotically. Temperature recharges to 96.1% to 97.4% of the initial reservoir temperature after 1000 years of recharging under different thickness and conductivity scenarios. The absence of a thermal influx at the bottom of the reservoir model is limiting the capacity of the reservoir to recharge to its initial average temperature. Interviews are conducted to investigate the implications that the findings of this research have on the policy measures for geothermal projects. Suggestions for changes in policy are made to optimize the recovery of heat in the subsurface.

As implementation of deep geothermal energy projects in the Netherlands increases, reservoir simulation for these geothermal systems stands to play a key role in understanding how these systems will behave and how large scale projects can be optimised to save cost and reduce risk. In this thesis, an extensive simulation study has been conducted using a new Operator based linearisation simulator (DARTS) on a geological model of the Delft Sandstone Member within the West Netherlands Basin (a prolific geothermal reservoir). The first section of the study outlines the construction of a representative geological model of the Delft Sandstone in Petrel using core, well log and seismic data.
The model is quality checked by comparing derived model values with both values recorded in the literature and data from well tests. Following this, a sensitivity and uncertainty study was conducted which examines the effect of changing a wide range of model values and inputs on the thermal
performance of production wells. A well placement study was then implemented, examining how well configuration, orientation and distance can affect well performance. Finally, a considerable section of the thesis investigates the role of non-reservoir lithologies in geothermal reservoir simulation and how the heat transfer from these lithologies can be accounted for utilising multi-scale
upscaling. The findings of the uncertainty and sensitivity analysis suggest that the primary uncertainty for simulation in the Delft Sandstone is the porosity and intrinsically linked permeability, with the value and spatial distribution of these properties having the largest effect on thermal performance of wells (10’s of years difference in thermal breakthrough). From the well placement study, it was found that different well configurations performed variably according to local reservoir conditions (especially reservoir dip) and that optimum configuration should be decided on a case-by-case basis. It was also found that both well separation/interference and orientation have a key role in controlling the thermal productivity of wells. Finally, the section on non-reservoir lithologies finds that firstly, thermal recharge of injected water from these rocks can have a very large effect on thermal breakthrough time (10’s of years for low N/G reservoir) and must not be ignored in geothermal simulations and secondly,
of the three multi-scale upscaling methods implemented to more efficiently simulate conductive heat flux from the non-reservoir rocks, only multiple sub-region upscaling shows significant promise in terms of accurately accounting for heat flux and significantly reducing the number of grid cells. However, the quality of the solution for this method is still strongly linked to fluid flow rate, with higher rates resulting in better solutions.

Constitutive models are one of the main building blocks of the Finite Element Analysis that nowadays is used in almost every geotechnical engineering project. Thus, finding realistic stress-strain behaviour models has been one of the main fields of research in Geotechnical Engineering. However, constitutive equations have become increasingly complex featuring 10 or more parameters as inputs with sometimes small correlations to physical properties (Beaty & Byrne, 1998; Bauer, 1996). Thus, a more data driven approach can be determined to account for that issue. In this thesis, that data driven approach will be attempted by using Neural Networks. The main goal of the thesis is to access if Neural Networks can be used to model constitutive soil behaviour. Specifically, two approaches are used to model stress-strain behaviour of soils.
The first approach is classified as a generic approach because the investigation is mostly focused on which techniques of the Neural Network can help with the modelling of stress and strain behaviour. In that way the Network can be thought of as a “black box”. The prediction after the training of the Neural Network is achieved by dataset retrieved inputs and from inputs that are retrieved from the last step of the prediction. The latter has the objective of replicating the prediction as it is achieved from a typical constitutive model. The aim is the minimisation of errors after training. The feedback and the non-feedback predictions do not produce the same results which imply that the network is sensitive towards a certain input. This is further validated by conducting a sensitivity analysis and by looking into the activation of each node for certain loading cases. Dropout and reassessing the inputs and outputs are attempted to resolve this issue but the results remain erroneous.
The second approach is to create a component based Neural Network. In this case a link is created between the function of the neural Network and typical soil behaviour. The linear elastic model is modelled with a linear activation function. In this case the network is successful in reproducing the full linear-elastic matrix. The linear elastic perfectly plastic model is modelled by connected the linear elastic matrix with a ReLU layer as it is seen in continuum mechanics. The Neural Network accurately predicts the stress-strain relationship. And it can be used to also predict the stress path of “noisy” datasets. However, when trained with noise the signal added to the training dataset is recognised as a pattern from the Neural Network. Finally, the work hardening model does not successfully model the stress-strain relationship as it tends to exaggerate the contribution of the stress input versus the strain input. All in all, this is an effort towards the development of a Neural Network constitutive model with the final aim of producing data driven constitutive models.

Data assimilaiton, a procedure in which observed data is combined with prior knowledge, is widely used in geophysical systems and especially popular in atmospheric and oceanic models. In this study a Monte Carlo based data assimilation method referred as a bootstrap Particle Filter (PF) and a time lag sampling technique are combined together to perform Sequential Data Assimilation (SDA) of borehole observation into a Seismo-Thermo-Mechanical model (STM). The aim of this study is to estimate the state of faults in subduction zones. The STM, a strongly non-linear model, is taken to be a perfect model and serves as a source for both observed data and model realizations termed "particles" or ensemble members. The ensemble is being generated by drawing particles out of a seismic cycle with a constant time lag. Results demonstrate that assimilation strongly depends on the choice of time lag since, small time lags provided with better results. Changing the time lag for sampling leads to a trade off between ensemble spread and resolution due to presence of trends in some of the observed state variables. Although the sampling technique in its current setup is computationally efficient, it was found to be insuficient in representing the model errors. Comparison between the current study of the PF and recent work involving the Ensemble Kalman Filter (EnKF) suggests that the success of the EnKF is related to its error covariance matrix correlating the various state variables. Based on the results and comparison to the EnKF improvements and possible next steps are discussed.

This thesis explores the usage of the particle filter as a data assimilation technique to estimate subsurface processes, such as reservoir volume change from space-geodetic PS-InSAR surface measurements. The specific research area is Groningen, where subsidence is induced by hydrocarbon and salt production.
The satellite radar PS-InSAR technique is used for observing subsidence values in the line-of-sight for a Radarsat-2 descending and a TerraSAR ascending set of measurements. A geomechanical model, the Mogi point source, translates subsurface volume changes to surface deformation. The geomechanical model parameters are estimated by the data assimilation technique particle filter from the observed surface measurements.
The particle filter is tested on synthetic data in a couple of test situations with an identical twin experiment. In addition the knowledge of the synthetic data experiments is used in the particle filter application on the PS-InSAR
measurements of the Groningen gas field. A workflow is created in how to apply the steps of the particle filter on the PS-InSAR measurements in Groningen. Several solutions are developed for improving the fit between measurements and model.

The production and injection of fluids from and in reservoirs leads to changes in the in-situ stress in the subsurface. This can cause reservoir compaction, subsidence, fault reactivation and / or seismicity. As these effects may greatly influence society it is of importance to find accurate methods to describe them so they can be predicted or even better, mitigated.

This thesis discusses a new analytical approach to calculate stress in the subsurface which incorporates the effects of differential compaction on the initiation of fault reactivation. This new approach is named Differential Compaction Loading (DCL) and the reason for its development is due to discrepancies observed between calculations using the Mohr-Coulomb failure criterion, also known as Poro-elastic Loading (PEL), and field observations.

Geomechanical modelling was performed to assess fault failure sensitivity to a range of geometrical aspects as well as reservoir and fault properties. From this analysis, focusing on the reactivation pressure at which failure first occurs, an empirical sense of sensitivity was established. It was found that for the examined variations in the geometry the fault dip angle resulted in the largest spread in reactivation pressure. For the examined reservoir and fault properties, the friction angle was found to have the largest sensitivity.

With these results it was possible to improve the estimates of essential parameters within the analytical approach, yielding a better fit between analytical and modelled solutions. These solutions lie closer to field observations. Hence, the new method of DCL shows a great improvement in calculation of stresses in the subsurface, compared to the method of PEL. This calibrated analytical approach allows for a quick assessment of the fault stability within a reservoir. Additionally, through the results from the geomechanical model new insights were obtained into the way stresses change and behave when a reservoir is depleted. The rotation of the principal stresses for each level of depletion was quantified and a new definition of the critical fault angle, the dip angle which will fail first, was derived. This links the depletion pressure and related rotation angle directly to a value of the new critical fault angle when DCL is present.

Ultimately, these new insights into fault failure behaviour of boundary faults could be a useful tool in the step towards prediction and mitigation of production or injection related seismicity.

Parameter and ambiguity estimation in the temporal domain, for arcs of differential phase observations between two persistent scatterers (PS), is a critical part in Persistent Scatterer Interferometry (PSI). Deformation models, used as constraint in the parameter estimation, often do not capture the full extent of the deformation behaviour. This results in a poor separation of signal and noise, and rejection of arcs that do not behave conform the functional model. Previous work assumed that deformation behaviour is stationary and that a full time series can be described with a single set of deformation parameters. In order to develop a more broadly applicable deformation model, this study applies a temporal smoothness constraint during parameter estimation, by assuming that deformation rates are affected by a temporally correlated zero-mean random acceleration. This constraint is implemented using recursive least-squares, similar to Kalman filtering, which also enables efficient updating of arcs when new acquisitions are available.

Various kind of deformation types are simulated to create phase observations based on real TerraSAR-X, Radarsat2 and ERS stacks of interferograms. This simulated data is processed using the new recursive estimator and results are compared to that of a batch estimator using a steady-state assumption, to analyse the impact of adding a priori information about the smoothness of the physical signal. Furthermore, a case study on real data is performed on an area where non-linear subsidence has occurred, due to soil remediation. This study presents a mathematical framework for incorporating a priori knowledge about the smoothness of the deformation signal as constraint for parameter and ambiguity estimation. Especially non-linear deformation is better estimated using this method, resulting in a higher success-rate, better separation of signal and noise, and more PS passing quality thresholds. The framework moreover enables efficient updating of existing datasets when new acquisition are available.

Steam injection is an EOR method, which is mostly used for heavy oil production. This viable method is based on increasing the pore pressure in the reservoir and reducing the viscosity of the heavy oil. In particular cases, the increase in pore pressure and thermal expansion related to the steam injection leads to surface deformation – heave. The results show that the level of heave increases when the reservoir thickness is larger. For a 100 m thick reservoir, with a pressure increase of 5 MPa and temperature increase to 570 K, the heave is 80 mm. Increasing the reservoir thickness by a factor of two (200 m) results in an increase of heave by a factor of 1.6 (130 mm). A similar increase in heave results when we increase the pressure increment in the reservoir. In our experiments, pressure and heave are linearly related. Results depends on rock properties, most noticeably the elastic property, Young’s modulus, and thermal expansion factor. An increase in Young’s modulus leads to decrease in level of heave. An increase of thermal expansion factor leads to increase in heave.
When the water required for the steam is extracted from a shallow aquifer, producing this aquifer leads to a reduction of the level of heave that is caused by steam injection. This reduction depends on the pressure reduction in the aquifer and on its thickness. For realistic dimensions and rock properties of the aquifer, this effect appears to be insignificant. Only with very low Young’s modulus (7 GPa) and very thick aquifer, the subsidence due to water depletion can compensate the expansion caused by steam injection.