Diffusion sandstone

Fig. 2.7.5 Two-dimensional D—T2 map for Berea sandstone saturated with a mixture of water and mineral oil. Figures on the top and the right-hand side show the projections of f(D, T2) along the diffusion and relaxation dimensions, respectively. In these projections, the contributions from oil and water are marked. The sum is shown as a black line. In the 2D map, the white dashed line indicates the molecular diffusion coefficient of water,...

Fig. 3.6.10 Distributions of diffusivity and relaxation times for partially brine- and oil-saturated Bentheim sandstone [43].

Meade (1966) shows that claystones have a porosity decreasing to 0% at 1 Km depths and sandstones, 20% porosity at the same depth. Manheim (1970) shows that ionic diffusion rates in sediments are 1/2 to 1/20 that of free solutions when the sediments have porosities between 100 - 20%. It is evident that the burial of sediments creates a very different physical environment than that of sedimentation. As a result of reduced ionic mobility in the solutions, a different set of silicate-solution equilibria will most certainly come into effect with the onset of burial. The activity of ions in solution will become more dependent upon the chemistry of the silicates as porosity decreases and the system will change from one of perfectly mobile components in the open sea to one approaching a "closed" type where ionic activity in solution is entirely dictated by the mass of the material present in the sediment-fluid system. Although this description is probably not entirely valid even in rocks with measured zero porosity, for practical purposes, the pelitic or clayey sediments must certainly rapidly approach the situation of a closed system upon burial. 

Experimentally determined effective transport properties of porous bodies, e.g., effective diffusivity and permeability, can be compared with the respective effective transport properties of reconstructed porous media. Such a comparison was found to be satisfactory in the case of sandstones or other materials with relatively narrow pore size distribution (Bekri et al., 1995 Liang et al., 2000b Yeong and Torquato, 1998b). Critical verification studies of effective transport properties estimated by the concept of reconstructed porous media for porous catalysts with a broad pore size distribution and similar materials are scarce (Mourzenko et al., 2001). Let us employ the sample of the porous... 

Diffusional transfers of potassium and silicon between sandstones and shales may be sufficient to accomplish feldspar dissolution, illitization, and quartz cementation (Thyne, 2001 Thyne et al, 2001). Losses of the magnitude observed for detrital carbonates in shales exceed the capacity of diffusion-mediated transfer. Large-scale advection seems required, although our understanding of shale permeabilities seems to preclude this (Bjprlykke, 1989, 1993 and Lynch, 1997). The possibility of convection driven by salinity heterogeneity within thick shale sequences has been demonstrated by Sharp et al (2001), who note that more information for rock properties and fluid compositions within deep basinal shales is needed before the generality of their results can be assessed. 

Certainly, CO2 evolved during late diagenesis must ultimately return to the atmosphere/ocean. It also seems clear that transport of major components such as silicon and potassium between sandstones and shales at a scale of a few meters is required and can perhaps be accomplished by diffusion (Thyne et ai, 2001). New data, especially for shales, must be obtained before simultaneous quantitative balances can be proposed for the reactions in Table 1. The speciation of aluminum in pore fluids, the initial and final quantities of the reactants and products in both sandstones and shales, and the precise volumes of sandstones and shales in the sequences in question are key data needed to ascertain the scale of mobihty for the major elements in late diagenesis. Our abihty to answer basic questions about the rock cycle falls short, in large part, for lack of information about the major mineral components of shale, the most common type of sedimentary rock. 

The item here called a conductivity factor has various names— permeability, diffusivity, etc.— that sometimes emphasize the host material (e.g., permeability of sandstone ) and sometimes emphasize the traveling material (e.g., diffusivity of hydrogen ). The factor in reality always depends on both host and traveler it is a property of the transport situation as a whole. Sometimes it is useful to separate out two components such as mobility of the diffuser and tortuosity of the matrix but for present purposes we shall stay with a single comprehensive factor. The terms permeability and diffusivity may be used from time to time, but we shall try to maintain the view that any conductivity factor is acceptable, under whatever name, as long as its units are clearly in view. 

Fig. 10. Theoretical dolomite distributions from four potential controlling processes. The model represents a sandbody sandwiched between pedogenic dolocrete layers. (A) Pedogenic dolomite cement there would be most dolomite at the top of each sandbody. (B) Dolomite cement sourced from the dolocrete during burial, transported by diffusion cement should be equally abundant at the tops and bases of sandbodies, with a minimum at the centre. (C) Dolomite distribution controlled by high-permeability streaks allowing input from external sources fluvial sandstones usually fine upwards, leading to high-permeability bases and thus most dolomite at sandbody bases. (D) Dolomite distribution controlled by the relative buoyancy of oil (which may have carried dissolved CO2), or a separate CO2 gas phase caused dolomite cementation and thus led to most dolomite at the tops of sandbodies.

Cementation occurred chiefly by diffusive supply of Ca " and HCOj" derived from detrital carbonate grains uniformly distributed in sandstone beds and, in formations with mudrock interbeds, from detrital and biogenic carbonate in mudrocks. Local factors, many of which remain unidentified, influenced the cementation process and resulted in substantial heterogeneity in the distribution and form of calcite cement (Fig. 2). 

Although sandstone dominated, the Ballycastle-Murlough Bay section contains subordinate marine to brackish shales rich in organic detritus (Fig. 4). Microbial reactions in shallow-buried organic-rich mudrocks can produce solutes that, upon diffusion into adjacent sandstones, may precipitate small amounts (c. 10 vol%) of carbonate cement (McMa-... 

Figure 3.3. The concentration of silica in a fluid along a one-dimensional flow path in a quartz sandstone, initially at equilibrium. A pulse of dilute fluid is introduced at time 0 or distance 0, and gradually relaxes towards equilibrium. Reaction toward equilibrium is driven by irreversible dissolution of quartz, diffusion, and dispersion. The small arrows indicate the flow direction (after Knapp, 1989, Figure 1).

In this equation, d is the tortuosity of the porous medium (between 0 and 1 0.5 would be typical for a consolidated sandstone), Z>nuid is the diffusion coefficient in pure fluid and i is a retardation factor, defined as... 

Sandstone grains with a distorted crystal structure (clearly demonstrated by outcrops of dislocations on grain shears and assessed at 4 x 10 cm (Plates gf, 10b) show a much higher coefficient of diffusion and accelerated mass transfer compared to similar processes in perfect crystals. 

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