Robert McKibbin

A Model for Deep Geothermal Brines,III: Thermodynamic Properties – Enthalpy and Viscosity

This paper, the third in our sequence on a model geothermal brine based on a H2O-NaCl system, proposes correlations for the thermodynamic properties of specific enthalpy and dynamic viscosity of brine. It follows a similar pattern to the second paper on the density correlations, that is formulae which closely approximate the specific enthalpy and dynamic viscosity are given in terms of the primary variables T (temperature), p (pressure) and X (mass fraction of sodium chloride). These correlations cover the entire T-p-X state-space and together with the density correlations, can be used in subroutines suitable for use in numerical simulation programs.

A Model for Deep Geothermal Brines, I: T-p-X State-Space Description

This paper is the first in a sequence which develops a model of hot, high-pressure geothermal brines based on a common salt solution. In this paper, there are proposals for T-p-X state-space delineations of such a model fluid. Using experimental and calculated data, correlations for these delineations are given for a wide range of temperatures, pressures and solute mass fractions, which are based on the primary variables temperature T pressure p and mass fraction of sodium chloride X. These correlations are approximate, particularly at higher temperatures, but are qualitatively correct and can be used in subroutines suitable for use in numerical simulation programs. Correlations will be presented in subsequent papers for some of the thermodynamic properties of such a brine system.

A Model for Deep Geothermal Brines, II: Thermodynamic Properties – Density

This paper is the second in a sequence which develops a model of hot, high-pressure geothermal brines largely modelled on a common salt solution. The first paper described the T-p-X state-space. This paper proposes density correlations for a wide range of temperature T, pressure p and mass fraction of sodium chloride X. Using experimental and calculated data, formulae which closely approximate the density are given in terms of the primary variables T, p and X. These correlations cover the entire T-p-X state-space and can be used in subroutines suitable for use in numerical simulation programs.

Convection in anisotropic inclined porous layers

Two-dimensional convective flow in a system of fluid-saturated porous layers is considered for small fluid velocities. The layers are inclined at an angle to the horizontal and there is a temperature gradient across them. A mathematical model of the system is constructed and the resulting series solution is numerically summed. The unique features of this model include its ability to represent non-symmetric multi-layered systems and materials whose permeabilities are anisotropic.The model is applied to various physical configurations. System aspect ratios, system symmetry and permeablity anisotropies are found to influence the effect that layers of different materials have on the convective flow.

A simple deterministic model for volcanic ashfall deposition

We describe a simple deterministic model for the dispersion of particulate ash which has been ejected into the atmosphere by a volcanic eruption. In our model the atmosphere is divided into a series of horizontal layers within which the physical parameters involved are constant. This is an effective way to allow for the changing behaviour of the particulate ash and atmospheric flow with height whilst retaining simplicity. From our model we construct an analytical expression for the final deposit which could be incorporated within hazard assessment projections. In particular we show how to allow for variation with height of dispersion (caused by turbulence due to the wind) and settling speed (affected by the agglomeration and fragmentation of particles). doi:10.1017/S1446181108000047

Pollutant Transport and Its Alleviation in Groundwater Aquifers

Dissolved chemicals are transported through groundwater aquifers by a mixture of advection with the underlying fluid flow and dispersion within that fluid. The aquifers can be modelled using a layered structure which simplifies the calculation of vertical transport. This simplified model still allows for the natural stratification which occurs in such systems and the changes in physical properties of the aquifer that occur between different geological layers. Equations are presented to calculate the subsequent concentration of the releases of chemicals into this system. A particular example is considered where an instantaneous release of pollutant occurs and it is subsequently remediated by the downstream release of a suitable pollutant removal agent.

The Impact of Applications on Mathematics

Biological cells require active fluxes of matter to maintain their internal organization and perform multiple tasks to live. In particular they rely on cytoskeletal transport driven by motor proteins, ATP-fueled molecular engines, for delivering vesicles and biochemically active cargoes inside the cytoplasm. Experimental progress allows nowadays quantitative studies describing intracellular transport phenomena down to the nanometric scale of single molecules. Theoretical approaches face the challenge of modelling the multiscale, out-of-equilibrium and non-linear properties of cytoskeletal transport: from the mechanochemical complexity of a single molecular motor up to the collective transport on cellular scales. We will present some of our recent progress in building a generic modelling scheme for cytoskeletal transport based on lattice gas models called “exclusion processes”. Interesting new properties arise from the emergence of density inhomogeneities of particles along the network of one dimensional lattices. Moreover, understanding these processes on networks can provide important hints for other fundamental and applied problems such as vehicular, pedestrian and data traffic, or ultimately for technological and biomedical applications.

Fluid flow and solute transport in unevenly-stratified groundwater aquifers

Chemical species such as tracers or dissolved pollutants are dispersed by water flowing within a permeable matrix. The species move not only “down-stream”, but also spread in all directions. The rate of dispersion depends on the porous structure and the fluid speed. The natural layered structure of groundwater aquifers is used to discretize them into “almost horizontal” layers, where each of them may have different matrix properties such as permeabilities, dispersivities, porosities, etc. The thickness of each layer may be horizontally varying. Steady-state fluid flow is considered here in both confined and phreatic aquifers for illustration.

Mass and Energy Transport in Sloping Low‐Temperature Groundwater Aquifers

Quantitative models for fluid flow in long sloping warm‐water aquifers with layered structures are formulated. The steady‐state profiles for the temperature and the fluid volume flux parallel to the boundaries, as well as the associated heat transport, in a sloping system subjected to a perpendicular temperature gradient, are calculated for low Rayleigh numbers. The movement of a pollutant injected into such a system is also modelled, with a view to estimating passage times to, and concentrations at, fluid sampling or withdrawal points. The mathematical models are solved partly by analytic means; this allows more efficient examination of the effects of parameter variation.