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Summary The impact of steam quality, circulation rate and pressure difference between the well pair during SAGD initialization using steam circulation was explored through the use of numerical simulations employing a discretized wellbore model. These operating parameters appear to affect uniformity of reservoir heating, occurrence of steam breakthrough and time required to establish communication between the well pair. The simulation results indicate that, for the given tubing and liner sizes and reservoir properties, relatively lower circulation rates at high-steam quality are more favourable for faster initialization and development of uniform temperature between the horizontal well pair. At lower steam qualities, however, higher circulation rates appear more favourable. The use of high-steam quality in combination with high-circulation rates leads to slower rates of initialization, less uniform heating along the length of the wells and possibility of premature steam breakthrough at the heel. It was also found that having a higher steam quality in the lower well than in the upper well could lead to faster initialization and more uniform heating between the well pair. A small pressure difference, offsetting the natural hydraulic pressure (50 kPa), appears to be more favourable for faster and more uniform initialization.

It is often claimed that functional programming languages, and in particular pure functional languages are suitable for formal reasoning. This claim is supported by the fact that many people in the functional programming community do reason about languages and programs in a formal or semi-formal way. Different reasoning principles such as equational reasoning, induction and co-induction, are used, depending on the nature of the problem. Using a computer program to check the application of rules and to mechanise the tedious bookkeeping involved can simplify proofs and provide more confidence in their correctness. When reasoning about programs, this can also allow experiments with new rules and reasoning styles, where a user may not be confident about structuring a proof on paper. Checking the applicability of a rule can eliminate the risk of mistakes caused by misunderstanding the theory being used. Just as there are different ways in which formal or informal reasoning can be applied in functional programming, there are different ways in which tools can be provided to support this reasoning. This thesis describes an investigation of how to develop a mechanised reasoning system to allow reasoning about algorithms as a functional programmer would write them, not an encoding of the algorithm into a significantly different form. In addition, this work aims to develop a system to support a user who is not a theorem proving expert or an expert in the theoretical foundations of functional programming. The work is aimed towards a system that could be used by a functional programmer developing real programs and wishing to prove some or all of the programs correct or to prove that two programs are equivalent.