The attenuation of chemical elements in acidic leachates from coal mineral wastes by soils

The chemical attenuation of acidity and selected elements (aluminum, arsenic, cadmium, cobalt, chromium, copper, fluorine, iron, manganese, nickel, and zinc) in acidic leachates from coal mineral wastes by four natural subsurface soils has been investigated using laboratory column methods Leachate solutions were allowed to percolate through the soils under simulated natural flow conditions, and the elemental concentrations in the influents and effluents were measured periodically Elemental retentions were substantial for all species except managanese, which was eluted in excess from all soils except the most calcareous Two processes appeared to operate in decreasing influent concentrations: (1) precipitation of solid phases caused by increased pH of the leachate as it percolated through the soil, and (2) adsorption of elements onto exchange and sorption sites naturally present in the soil and on iron and aluminum oxide precipitates formed in situ from leachate components because of the increased pH The soil property most important in retention was its alkalinity Thus, carbonaceous soils provide the best control material for acidic leachates from coal mineral wastes. Results show that natural soils can substantially reduce pollutant fluxes to the environment from acidic coal waste dumps and should be considered when selecting waste disposal sites Performed under the auspices of the U.S. Department of Energy     

Modelling quartz cementation of quartzose sandstones

Cementation of quartzose sandstones is modelled assuming that the main source of silica is quartz dissolved at stylolites. The cementation process is shown to operate in one of two different regimes depending on the Damköhler number for diffusion. The regime, where diffusion of silica from the stylolites is a faster process than precipitation, is characterized by a nearly constant supersaturation between the stylolites. This regime, which spans the depth interval of quartz cementation for close stylolites, allows for approximate analytical expressions for the porosity evolution as a function of time and temperature. An expression is derived for the temperature where half the initial porosity is lost during constant burial along a constant thermal gradient. This expression is used to study the sensitivity of all parameters which enter the cementation process. The cementation process is shown to be particularly sensitive to the activation energy for quartz dissolution. The expression for the porosity decrease under constant burial is generalized to any piecewise linear burial and temperature history. The influence of the burial histories on the cementation process is then studied.     

TWO-PHASE OIL MIGRATION IN COMPACTING SEDIMENTARY BASINS MODELLED BY THE FINITE ELEMENT METHOD

The upstream-weighted finite element method with lumped mass matrix is applied to the modelling of oil migration in compacting sedimentary basins. An implicit formulation is made in Lagrangian co-ordinates of a pressure, saturation and a temperature equation, which is based on immiscible two-phase flow of oil and water. The formulation accounts for the compaction of the sediments, the generation of oil from solid organic material (kerogen), the eventual pore space generated by kerogen breakdown, and the density variations of the fluids which may set up thermal convection. The model is validated by comparison with results from a one-dimensional (1D) fractional flow-based migration model. A 2D case example showing oil expulsion from source rocks, and the filling of a trap is presented. The mass balance of the model is easily checked because all oil in the basin originates from breakdown of kerogen. Compared with other alternatives, the simple upstream-weighted finite element method is suggested as a possible first choice for a numerical method for the modelling of oil migration in compacting sedimentary basins. It easily deals with the complex geometry of a basin, it yields reasonably good results, is simple to implement, and the same implementation applies to all spatial dimensions. © 1997 by John Wiley & Sons, Ltd.     

Modelling thermal transients from magmatic underplating—an example from the Vøring margin (NE Atlantic)

The thermal impact of several kilometre-thick magmatic underplating in the lower continental crust is studied with analytical and numerical methods. Simple analytical solutions are derived for the thermal transient in the case of an infinite depth below the underplate and also for the case of a finite depth (down to the asthenosphere). It is shown that these solutions lead to simple approximations for when the transient surface heat flow is at its maximum, what the maximum is, and for how long the transient lasts. Even though these solutions assume that the underplate is emplaced instantaneously, they are useful in the interpretation of underplating over finite time spans. A numerical scheme is suggested for the modelling of underplating that handles both short time intervals as well as long intervals. The scheme treats magmatic underplating in a mass and energy conservative manner, and it is compared against the analytical solutions. Finally, the analytical and numerical results for thermal transients are applied to a transect from the Vøring margin (NE Atlantic), with respect to various degrees of early Cenozoic magmatic intrusion. It appears that more than half of the lower crustal body (LCB) in the Vøring margin must be magmatic underplating for the vitrinite reflectance to be substantially higher than for the non-magmatic case, where the LCB is assumed to comprise Caledonian crust.     

A simple model of pressure build-up caused by porosity reduction during burial

The fluid-pressure build-up due to porosity reduction in sedimentary basins during burial is studied. The model assumes that the void ratio decreases exponentially with depth, and that the permeability is proportional to the void ratio to an arbitrary exponent. Simple analytical solutions are obtained for the Darcy velocity and the fluid excess pressure. The pressure build-up during burial is studied with these solutions, and it is found to be inversely proportional to the gravity number. The importance of the permeability exponents on the fluid pressure is also studied. Gravity numbers much less than 1 are shown to yield high excess pressures during burial. A reasonable approximation for the maximum Darcy velocity is found to be the product of the surface void ratio and the burial rate. Hydrofracturing is discussed in relation to the pressure build-up, and cases characterized by gravity numbers much less than 1 are found to yield hydrofracturing over large depth ranges. It is suggested that the average permeability of hydrofractured sediments during burial corresponds to a gravity number equal to 1.     

Modelling heat and fluid flow in sedimentary basins by the finite element method

In this article we solve the equations for a 2D model of compaction of sedimentary basins saturated with water by the finite-element method. This compaction model considers the rock described by the porosity as a function of effective stress, and both the anisotropic permeability and the anisotropic heat conductivity as functions of porosity. The water density is approximated linearly in the water pressure and temperature, and the water viscosity is a function of temperature. The main variables in the model are the water excess pressure and the temperature, and we account for an implicit solution scheme where we solve for both main variables simultaneously. The non-linearities in the model are either dealt with by the Newton method or by fixed-point iterations. We compare the coupled solution of temperature and pressure with the same decoupled equations. Then we study the contribution to the temperature by convection, the effect of the non-constant water density, and some anisotropic case examples.     

The extension of the Vøring margin (NE Atlantic) in case of different degrees of magmatic underplating

The nature of the Lower Crustal Body (LCB) underneath the western part of the Vøring margin (NE Atlantic) is studied with three scenarios of its extension history: (a) The LCB is Caledonian crust. (b) Half the LCB is Caledonian crust and the other half is emplaced as magmatic underplating in Late Palaeocene. (c) The entire LCB is emplaced as magmatic underplating. The extension of the margin transect is obtained with a procedure that accounts for the extension and thinning of the sedimentary basins. This procedure has been extended to include magmatic underplating. The lithosphere is modelled with deposition of sediments and four rift phases since the Early Devonian until today. The forward modelling is mass conservative and the present‐day thicknesses of the formations, crust, LCB and magmatic underplate are reproduced. The state of the lithosphere and the sedimentary basins are shown and compared at the beginning and at the end of the rift phases. It is concluded that the scenario with the LCB as only underplating requires an unrealistic amount of extension. A scenario where underplating accounts for maximum half the LCB is more likely. Two different interpretations for the Moho underneath the Utgard High are tested: one with a shallow base‐crust and another with a deeper and flatter base‐crust. Tectonic modelling of the two versions favours the latter interpretation. The modelling shows that the Late Jurassic rift phase was much more prominent than the Late Cretaceous and Palaeocene rift phase for all cases of underplating. A strong Late Jurassic rift phase is consistent with the accumulation space needed for the thick Cretaceous formations. There are no observations of magmatism from the Late Jurassic, although this rift phase is stronger than the Cretaceous and Palaeocene rift phase.     

A finite element formulation in Lagrangian co-ordinates for heat and fluid flow in compacting sedimentary basins

This article presents a numerical model of heat and fluid flow in compacting sedimentary basins formulated in Lagrangian co-ordinates. The Lagrangian co-ordinates are the sediment particle positions of the completely compacted basin. A finite element formulation of excess water pressure and temperature in these Lagrangian co-ordinates is presented, in addition to an equivalent formulation in the real co-ordinates. The later formulation is also Lagrangian of nature, since the elements of the grid in the real co-ordinates always frame the same sediment particles. In other words, it is the Lagrangian grid mapped to the real space. This is done in an iterative loop which solves for excess water pressure, and then updates the real co-ordinates of the sediment particles. By comparing the two finite element formulations it is concluded that the one in real space is the simplest, most efficient and most precise. The model is validated by comparison with two dimensionless one-dimensional solutions, one analytical for the linear case, and one numerical for the non-linear case. Both these one-dimensional solutions are obtained on the unit interval, where the moving top boundary caused by continuous sedimentation is incorporated.