Michael J. O'Sullivan

State of the art of geothermal reservoir simulation

Computer modeling of geothermal systems has become a mature technology with application to more than 100 fields world-wide. Large complex three-dimensional models having computational meshes with more than 4000 blocks are now used routinely. Researchers continue to carry out fundamental research on modeling techniques and physical processes in geothermal systems. The new advances are adopted quickly by the geothermal industry and have also found application in related areas such as nuclear waste storage, environmental remediation and studies of the vadose (unsaturated) zone. The current state-of-practice, recent advances and emerging trends in geothermal reservoir simulation are reviewed.

The Henry Problem for Saltwater Intrusion

Previous solutions of the idealized saltwater intrusion problem known as the Henry problem are discussed, and possible reasons for the observed discrepancies between them are given. High-accuracy finite difference techniques are used to solve the nondimensionalized equations governing the problem, and a fine grid is used so that the solutions obtained contain only very small truncation errors. Such errors are investigated by means of grid refinement. Comparison of past results with the present solutions indicate, first, the presence of significant inaccuracy in certain earlier results and, second, the effects of numerical dispersion in other previous solutions calculated using relatively few grid points.

Modeling Biogeochemical Processes in Leachate-Contaminated Soils: A Review

During subsurface transport, reactive solutes are subject to a variety of hydrological, physical and biochemical processes. The major hydrological and physical processes include advection, diffusion and hydrodynamic dispersion, and key biochemical processes are aqueous complexation, precipitation/dissolution, adsorption/desorption, microbial reactions, and redox transformations. The addition of strongly reduced landfill leachate to an aquifer may lead to the development of different redox environments depending on factors such as the redox capacities and reactivities of the reduced and oxidised compounds in the leachate and the aquifer. The prevailing redox environment is key to understanding the fate of pollutants in the aquifer. The local hydrogeologic conditions such as hydraulic conductivity, ion exchange capacity, and buffering capacity of the soil are also important in assessing the potential for groundwater pollution. Attenuating processes such as bacterial growth and metal precipitation, which alter soil characteristics, must be considered to correctly assess environmental impact. A multicomponent reactive solute transport model coupled to kinetic biodegradation and precipitation/dissolution model, and geochemical equilibrium model can be used to assess the impact of contaminants leaking from landfills on groundwater quality. The fluid flow model can also be coupled to the transport model to simulate the clogging of soils using a relationship between permeability and change in soil porosity. This paper discusses the different biogeochemical processes occurring in leachate-contaminated soils and the modeling of the transport and fate of organic and inorganic contaminants under such conditions.

Geothermal heat pipe stability: Solution selection by upstreaming and boundary conditions

In a geothermal reservoir, the heat pipe mechanism can transfer heat very efficiently, with vapor rising and liquid falling in comparable quantities, driven by gravity. For a given heat and mass flux that is not too large, there are two possible steady solutions with vapor-liquid counterflow, one liquid-dominated, and one vapor-dominated. Numerical solution of the equations for two-phase vertical counterflow displays intriguing stability behaviour. If pressure and saturation are fixed at depth, and heat and mass flux specified at the top, the vapor-dominated solution is almost always obtained. That is, for a variety of boundary values, the solution settles to the vapor-dominated steady-state, and only for very special values is it possible to obtain the liquid-dominated case. Similarly the liquid-dominated solution is almost always obtained if the boundary conditions are reversed, with pressure and saturation fixed at the top and heat and mass flux specified at depth.This behaviour is here explained in two complementary ways. It is shown to be a consequence of upstream differencing of the flow terms in the numerical method. It is also shown to be expected behaviour for wavelike saturation solutions. Hence the observed behaviour is not only a direct consequence of the numerical method used, but is fundamental to geothermal heat pipes.

INJECTION AND ENERGY RECOVERY IN FRACTURED GEOTHERMAL RESERVOIRS

Numerical studies of the effects of injection on the behavior of production wells completed in fractured two-phase geothermal reservoirs are presented. In these studies the multiple-interacting-continua (MINC) method is employed for the modeling of idealized fractured reservoirs. Simulations are carried out for a five-spot well pattern with various well spacings, fracture spacings, and injection fractions. The production rates from the wells are calculated using a deliverability model. The results of the studies show that injection into two-phase fractured reservoirs increases flow rates and decreases enthalpies of producing wells. These two effects offset each other so that injection tends to have small effects on the usable energy output of production wells in the short term. However, if a sufficiently large fraction of the produced fluids is injected, the fracture system may become liquid-filled and an increased steam rate is obtained. Our studies show that injection greatly increases the long-term energy output from wells, as it helps extract heat from the resrvoir rocks. If a high fraction of the produced fluids is injected, the ultimate energy recovery will increase manyfold.

Numerical Methods for Contaminant Transport in Rivers and Estuaries

Abstract A review is carried out of the wide range of numerical methods available for modelling contaminant transport in rivers and estuaries. Theoretical considerations indicate that Eulerian–Lagrangian methods (ELMs), particularly the Lagrange–Galerkin method, show the most promise for these problems. Such a method is implemented in a contaminant transport simulator flexible enough for modelling realistic problems. Test problems demonstrate the high performance of the simulator in comparison with other methods.

SALSA – a spatially adaptive local smoothing algorithm

We present a nonlinear integer programming formulation for fitting a spline-based regression to two-dimensional data using an adaptive knot-selection approach, with the number and location of the knots being determined in the solution process. However, the nonlinear nature of this formulation makes its solution impractical, so we also outline a knot selection heuristic inspired by the Remes Exchange Algorithm, to produce good solutions to our formulation. This algorithm is intuitive and naturally accommodates local changes in smoothness. Results are presented for the algorithm demonstrating performance that is as good as, or better than, other current methods on established benchmark functions.

Mathematical modelling of non-isothermal silica transport and deposition in a porous medium

Abstract The problem of transport and deposition of silica in non-isothermal flows, either in a porous medium or a single fracture, is investigated. Analytic solutions are obtained using the method of characteristics for both the one-dimensional problem of constant rate injection into a channel or packed column and the radially symmetric problem of the flow away from a reinjection well. Silica deposition is represented by a first order rate equation. Studies on the temperature effects of reinjection into a hot or cold reservoir are undertaken using the one-dimensional model. The strong dependence of the rate of silica deposition on temperature is confirmed by the model. The radial flow model is applied to some field data from the Otake geothermal field, Japan. The model produces a good match to the permeability decline observed in the wells. Mathematical models of silica deposition resulting from non-isothermal flow in a single fracture are successfully tested against some previously reported numerical results.

Modelling of chemical and thermal changes in well pn-26 palinpinon geothermal field, Philippines

Abstract Significant changes in temperature, chloride and silica concentration have occurred in well PN-26 as a result of reinjection fluid returning. Here the chloride changes are modelled by a simple timedependent production-reinjection lumped parameter model. Analytic solutions are derived for both constant and variable production rates. The decline in measured wellbore temperature is then modelled by coupling the chloride mass balance model to a fracture flow model. Production silica changes are also modelled by coupling the silica mass balance model for the production area to a transport and deposition model for the fractured zone. The final model is able to match changes in chloride, temperature and silica.

Modelling the spontaneous combustion of coal: the adiabatic testing procedure

A general approach is described for modelling problems that involve heat and mass transfer in coal, such as spontaneous combustion. It is based on the TOUGH2 code, which is a general-purpose simulator for modelling multi-component, multi-phase, non-isothermal flow in a porous medium. An equation of state (EOS) module for TOUGH2 is developed, which includes accurate physical properties for all of the gases involved (N2, oxygen and carbon dioxide). The new simulator is then used to model the adiabatic method for testing the reactivity of coal samples. An important part of the model development is the selection of the approximate representation of the reaction of coal with oxygen. The results show that (i) using dual Arrhenius parameters and (ii) representing the heat-release as an oxidation reaction rather than a purely thermal reaction both significantly improve the match of the model to the experimental data.