Jetted radial wells are a relatively new form of hydraulic stimulation for oil and gas wells, where small diameters holes extend radially from a wellbore. This technique for increasing well connectivity could also be applied to geothermal wells. Radials can be freely placed along a backbone well, making the design of an economically viable well plan time intensive. Numerical optimization has been extensively applied to well design and will be applied for the design of a radial well plan. A simple optimization case is used to compare gradient-based and gradient-free optimization for jetted radial optimization, the gradient-free CMA-ES algorithm is chosen for the workflow. In addition to CMA-ES, mixed integer CMA-ES and uncertainty-handling CMA-ES are incorporated in the workflow. Three reservoir cases are evaluated for optimization using these algorithms. The workflow is able to determine well plans with higher NPV in each of these cases though finding a global optimum remains difficult.

This study discusses the potential of the in-depth water diversion (IDD) process to enhance oil recovery from subsurface reservoirs and investigates IDD strategies through an ensemble optimization approach. Pilot studies in the North Sea performed in recent years have shown that Sodium Silicate can be applied as blocking agent, diverting water to unswept zones of the reservoir. On the other hand, numerical simulation studies have tried to simulate the IDD behaviour with methods based on weak coupling of a reservoir flow simulator and an external chemical module. This study presents a fully implicit coupled chemical-compositional-flow implementation to simulate the permeability reduction through silicate gels, since IDD is essentially a coupled flow-chemical process. In addition, this study discusses the impact of resolution in space and time on the simulation performance for 2D subsurface petroleum reservoir models. Sensitivity of the oil recovery, and IDD characteristics such as moles of silicate, to design parameters of the IDD process is discussed as well. Since adjoint gradients are not typically available for the parameters describing in-depth divergence and the uncertainties are expected to be large, the optimization study uses an ensemble-based methodology to find optimal IDD reservoir management strategies. In addition to discussing IDD strategies in a deterministic setting, the design of optimal IDD strategies under geological uncertainty is investigated. This study will demonstrate that the in-depth divergence process can be used to extend the reservoir field production life time when timing, size of the Sodium Silicate batch and concentration is optimized. Finally this study discusses the issue of computational costs associated with modeling high resolution required for accurate simulation of this coupled process.

Model based optimization of reservoir water flooding is an ill-posed problem where significantly different control strategies deliver near identical Net Present Values (NPVs). Discovering and exploiting the existence of "redundant" control strategies - particularly those in close proximity to an optimal strategy - is valuable since this offers operational flexibility in reservoir management. To identify such 'flexible strategies' this thesis proposes a workflow to characterize the space of feasible solutions. The feasible region or feasible solution space consists of all control strategies that deliver an NPV within some threshold from an optimal value. Ensemble-based optimization is performed with strong Wolfe line search to identify an optimal control strategy. The BFGS scheme is used to iteratively approximate the Hessian matrix. One dimensional exploration is performed along the singular vector directions that characterize the null space of the Hessian. A thorough exploration results in an accurate characterization of the feasible region. Such an approach however is computationally intractable in case of realistic reservoirs with multiple hundred controls. To address this, a high-dimensional polytope is first defined using the end points from the exploration step. Subsequently, an innovative cross-section constrained maximum volume ellipsoid is inscribed within this polytope to generate an ellipsoidal approximation of the feasible region. Validation results are then presented which show that even one ellipsoid centred at the optimum control vector coordinate provides a conservative description of the feasible solution space.

The Netherlands has set the ambitious goal to be CO2 neutral by 2050 and signed the Paris Treaty in 2015. The contribution of geothermal energy to reaching this goal are outlined in the Masterplan in 2018 which attempts to reduce CO2 emissions. It is imperative to enhance geothermal participation in renewable energy resources, so this thesis proposes a consideration of large scale geothermal field development in order to meet these requirements. For these large scale projects, large scale geological heterogeneities must be taken into account in order to propose a development strategy that honours subsurface variability in properties like porosity or permeability of an aquifer. Furthermore, the nature of the large scale operations, inherently requires the consideration and application of well patterns typically used in oil and gas developments. Operating in these extensive domains, carries a lot of uncertainty in the final economical output of the project, so modelling the process could indicate the optimal conditions that would deliver the best possible operational outcome. Conceptual 2D model approaches were adopted to demonstrate the main ideas behind large-scale geothermal well pattern optimisation. The main objective of this project is to model, evaluate and optimise the performance of large scale geothermal field development. The proposed strategy is based on the use of well patterns as are frequently used in the oil industry. The heterogeneity in geological properties that may be expected to be encountered at larger spatial scales is addressed by the concept of a flexible well density function. This density function allows the well patterns to be resized (or ultimately, reshaped) and adapt to spatial variations in geological characteristics. The flexible well pattern is fed to an objective function created with embedded simulator. The output of the function is the net present value (NPV) of the project. Four test cases are created, starting with a homogeneous static model and building up more heterogeneous aquifer models, aiming to test the performance of the flexible well density function. The aquifer property models are representative of the West Netherlands Basin and specifically the Delft Sandstone Member. Per each aquifer model, line drive and 5-spot development strategies are assessed. Each development scenario is modeled in an objective function and optimised. The optimisation algorithm chosen is the Simplicial Homology Global Optimisation, suitable for black-box functions that show multiple local optimum solution and among them, a global optimum pattern size is found. The NPV of each project realisation is calculated based on the energy recovered and an economic model under Dutch fiscal conditions. The results suggest that, the flexible well placement is successfully aligning with the different aquifer geological properties. Pattern size is inversely correlated to porosity which corresponds to higher volume of pore fluid from which heat can be recovered. The optimisation algorithm managed to identify the global optimum solution of pattern size that delivers the highest possible positive NPV. The most efficient in terms of profitable strategy, is suggested to be the 5-spot pattern. The optimal pattern size ranges between 500 - 2160m depending on the aquifer model. The sweep efficiency, in terms of energy recovery, is also assessed per aquifer model and development strategy. The most efficient is the 5-spot pattern. The performance of the adopted optimisation algorithm, on the fully homogeneous aquifer, is tested with an exhaustive response curve of NPV. It is confirmed that the algorithm manages to identify the global optimum. The character of the NPV as a function of well pattern size/density proved the complexity of the system with respect to the amount and well types introduced. Different sensitivity analyses in the context of the uncertainty of the aquifer thickness, thermal conductivity, thermal heat capacity and full economic model are conducted in order to show the impact on the optimal patter size. The performance of the optimisation algorithm is assessed as well, indicating that further investigation on the tuning meta-parameters could potentially lead to better global optimum solutions in more heterogeneous aquifer models.

The oil industry is a high risk high reward venture. The capital and operating expenses runs into tens of millions of dollars with oil production being the primary source of revenue. During the initial development phase of the field, few wells are completed. Data collection during this period verifies assumptions made during the modelling phase and forms the basis for future development. History matching can play a significant role in these plans since it can determine uncertainties in future production. History matching algorithms must be able to make an accurate estimates of uncertainty in future production while being computationally light. Towards this end, a number of history matching methods have been developed with emphasis being on the ensemble Kalman filter (EnKF) in recent times. While the variants of the EnKF seek to improve different aspects of the method, few have been successful in addressing all of these concerns. The Distributed Gauss Newton (DGN) was developed with the same goal- accurate uncertainty prediction at low computational cost. It is not a variant of the EnKF but uses a sensitivity matrix determined through linear regression which decreases the computational load compared to existing gradient based techniques. In their tests, the authors report superior performance of the DGN compared to a Gauss-Newton scheme. This thesis aims to provide a detailed understanding of the method and its dependencies. This is followed up with a comparison of the DGN with an EnKF variant known as the ES-MDA.