The unsteady flow of a weakly compressible fluid in a thin porous layer II: three-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a three-dimensional layer, composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Numerical solution of this three-dimensional evolution problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l, a situation which occurs frequently in the application to oil and gas reservoir recovery and which leads to significant stiffness in the numerical problem. Under the assumption that $\epsilon\propto h/l\ll 1$, we show that, to leading order in $\epsilon$, the pressure field varies only in the horizontal directions away from the wells (the outer region). We construct asymptotic expansions in $\epsilon$ in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive expressions for all significant process quantities. The only computations required are for the solution of non-stiff linear, elliptic, two-dimensional boundary-value, and eigenvalue problems. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the layer, $\epsilon$, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighbourhood of wells and away from wells.

The unsteady flow of a weakly compressible fluid in a thin porous layer III: three-dimensional computations

We describe a novel method for determining the pressure and velocity fields for a weakly compressible fluid flowing in a thin three-dimensional layer composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Our approach uses the method of matched asymptotic expansions to derive expressions for all significant process quantities, the computation of which requires only the solution of linear, elliptic, two-dimensional boundary value and eigenvalue problems. In this article, we provide full implementation details and present numerical results demonstrating the efficiency and accuracy of our scheme.

Facilities management carbon footprints: an audit of critical elements of management and reporting

Concern for the environmental impact of organizations’ activities has led to the recognition and demand for organizations to manage and report on their carbon footprint. However, there is no limit as to the areas of carbon footprints required in such annual environmental reports. To deliver improvements in the quality of carbon footprint management and reporting, there is a need to identify the main elements of carbon footprint strategy that can be endorsed, supported and encouraged by facility managers. The study investigates carbon footprint elements managed and reported upon by facility manager in the UK. Drawing on a questionnaire survey of 256 facility managers in the UK, the key elements of carbon footprints identified in carbon footprint reports are examined. The findings indicate that the main elements are building energy consumption, waste disposal and water consumption. Business travel in terms of using public transport, air travel and company cars are also recognized as important targets and objectives for the carbon footprint strategy of several FM (facilities management) organizations.

Organocatalytic domino reaction of cyanosulfones: access to complex cyclohexane systems with quaternary carbon centers

When ε-nitro-a,β-unsaturated esters are added to conjugated cyanosulfones in the presence of a bifunctional thiourea catalyst, a highly stereoselective domino reaction occurs to generate complex cyclohexanes with up to four stereogenic centers, one of which is quaternary in nature. Therefore, it is demonstrated that, like nitro compounds, sulfones can undergo an asymmetric intramolecular conjugate addition to r,β- unsaturated esters in the presence of a bifunctional organocatalyst.