The confined flow of multiphase fluids is relevant in a range of applications in both science and engineering. For example, the two-phase flow of gas and liquid can commonly be observed in boilers used for power production, nuclear reactors (particularly in a loss-of-coolant accident) as well as in the transportation of hydrocarbons in the oil and gas industry. The optimal design and operation of these systems relies on an understanding of how the phases interact and the behaviour emergent from these interactions. This thesis studies multiphase flows in the field of natural gas extraction from unconventional reservoirs, with a focus on coal seam gas (CSG). In this context, the bottom hole pressure (BHP) in a natural gas well is an important parameter in the effective design of well completions and artificial lifting systems. Poor estimation of this can lead to liquid loading in the wellbore and reduced efficiency of the extraction process. The complex interaction of production gas and the associated water can increase the uncertainty in pressure gradients and ultimately impact the BHP estimation. A significant body of research has explored pressure gradients in the co-current multiphase flows found in conventional gas extraction, but these are not expected to hold for the counter-current regimes present in CSG production. Therefore, this research aimed to develop a fully resolved-numerical model for the simulation of simultaneous gas and liquid transport in scenarios applicable to CSG extraction. When two-phases flow in a confined environment such as a pipe or conduit, the topology of the interface is described by commonly observed flow regimes. When the pipe is in a vertical configuration, the typical regimes include bubble, slug, churn and annular flow. The models that describe the liquidgas interactions are typically dependent on the flow regime and can significantly impact the accuracy of pressure predictions. As a result, knowledge of the flow regime is required a priori to predicting the pressure gradient. Once this has been determined, the uncertainty associated with the phase interaction models can still deteriorate the practical use of predictive tools. The rise velocity of elongated bubbles in the slug flow regime has recently been identified in the literature as impacting greatly on the estimation of liquid hold up and pressure gradients in a piping system. Understanding the behaviour of these bubbles, termed Taylor bubbles, allows operators to reduce pressure oscillations in the wellbore and more accurately forecast production over the life of the well. This work seeks to capture the behaviour of these bubbles in flow configurations applicable to CSG extraction. This involves modelling annular pipe systems at a range of inclinations as well as with fluids propagating in co-and counter-current directions. This thesis presents the development, verification and validation of a phase-field lattice Boltzmann method (PFLBM) that allows for the simulation of dynamic liquid-gas flows with density ratios on th...