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Predicting the propagation of fluid-driven fractures in heterogeneous porous materials is critical for the design of engineering operations to sustainably use underground energy resources. In this paper, a computational model is presented using the phase-field theory and in the context of finite strain kinematics. The framework is built upon the use of variational principle to minimise the energy of the fracturing heterogeneous porous system. The material properties are distributed statistically over the domain to consider the heterogeneity of the porous material, and the nonlinearity of flow generated within the cracked zone is modelled by considering the effect of inertial flow. This numerical framework is verified using a benchmark example, and its application is tested by simulating a pressurised cavity in a heterogeneous reservoir to identify the influential parameters in the propagation path, including the degree of heterogeneity in the mechanical properties of the porous media and flow characteristics.

Predicting mutual fluid-solid interactions in subsurface reservoirs is essential to address critical geoscientific challenges related to geoenergy such as geothermal energy, hydrocarbon exploration, underground storage sites. In this work, a mathematical setting is presented on the basis of the variational principle for the minimisation of fracturing system energy in the context of finite strain elasticity. The nonlinear system of equations is solved by employing an iterative Newton method on the finite element mesh to emulate nonlinear hydro-mechanical processes of the subsurface porous materials. The application and robustness of this numerical method is tested by simulating a benchmark example, and particular focus is on investigating the impact of the non-linear flow fields within the fractured zone on propagating fracture pathway and evolution of reservoir transmissivity. The results imply the significant changes of the fluid regime and the pressure drop inside the crack as well as around the crack-tip caused by the development of fracture subjected to fluid injection.

The ever growing interest for higher transmission rates, bandwidth efficiency, coverage, and reliability in the third generation (3G) of wireless communication systems and beyond, has initiated an intensive research in the field of multi-antenna communications. Moreover, orthogonal frequency-division multiplexing (OFDM) has recently emerged as a favorable candidate for future generation of wireless communication systems due to its efficient utilization of bandwidth, simplicity of equalization, and robustness to multipath fading. Motivated by these facts, multiple-input multiple-output (MIMO) systems in association with the OFDM transmission are promising schemes widely adopted in recent wireless network standards such as Long Term Evolution (LTE) and Worldwide interoperability for Microwave Access (WiMAX). Space-time coding (STC) techniques are capable of exploiting the spatial diversity offered by multi-antenna systems. STC techniques have also been combined with MIMO-OFDM wireless communication systems to both improve reliability and to increase higher transmission rates compared to single-antenna systems. In particular, the so-called orthogonal space-time block codes (OSTBCs) represent a popular class of STC techniques which are known to not only maximize the spatial diversity gain, but also offer simple decoding schemes. However, to obtain the theoretical promises of orthogonally coded MIMO-OFDM systems, accurate channel state information (CSI) is required at the receiver. The lack of CSI at the receiver is associated with a severe performance degradation of the MIMO-OFDM system. In practice, the CSI is commonly acquired from known pilot symbols inserted in the transmission at the expense of a reduced bandwidth efficiency and power consumption. Therefore, blind channel estimation methods are of great interest as they avoid the aforementioned penalties. In this thesis, we focus on developing blind channel estimation algorithms for orthogonally coded MIMO and MIMO-OFDM systems. First, we introduce a novel model for orthogonally coded single-carrier MIMO systems. Based on this model, we derive a special subspace property of the channel frequency response (CFR) vector. We then justify a closed-form blind channel estimation method that is also directly applicable to each individual subcarrier of a MIMO-OFDM system. Moreover, we propose two strategies to eliminate channel estimation ambiguities. Next, we generalize the special subspace property of the CFR vector derived for single-carrier systems to the multi-carrier case and propose a new closed-form blind channel estimator for orthogonally space-time coded MIMO-OFDM systems. Moreover, we derive the condition under which unique channel estimates can be obtained. Then, we develop a novel blind channel estimation algorithm for MIMO-OFDM systems under OSTBCs based on the semi-definite relaxation (SDR) technique. We show that the non-convex channel estimation problem can be approximated by a convex semi-definite programming (SDP) problem. Therefore, the channel estimation problem can be solved using modern convex optimization methods. Finally, based on the Relaxed Maximum Likelihood (RML) and the Capon receiver, respectively, we develop blind channel estimators which have closed-form solutions. Both of these algorithms exhibit different performance-complexity trade-offs compared to the SDR-based approach. Assuming a finite delay spread over the wireless channel that falls below the duration of the OSTBC-OFDM symbol in MIMO-OFDM systems allows us to estimate the channel parameters in the time-domain jointly for all subcarriers. This facilitates coherent data processing across all the subcarriers compared to the traditional subcarrier-wise channel estimation methods. The proposed channel estimation methods not only offer a considerable reduced computational complexity, but also result in improved estimation accuracy.