Geometry of random sequential adsorption

By sequentially adding line segments to a line or disks to a surface at random positions without overlaps, we obtain configurations of the one- and two-dimensional random sequential adsorption (RSA) problem. We have simulated the one- and two-dimensional problem with periodic boundary condition. The one-dimensional simulations are compared with the exact analytical solutions to give an estimate of the accuracy of the simulation. In two dimensions the geometrical properties of the RSA configuration are discussed and in addition known results of the RSA process are reproduced. Various statistical distributions of the Voronoi-Dirichlet (VD) network corresponding to the RSA disk configuration are analyzed. In order to characterize pores in the RSA configuration, we introduce circular holes. There is a direct correspondence between vertices of the VD network and these holes, and also between direct/indirect geometrical neighbors and these holes. The hole size distribution is found to be a parabola. We also find general relations that connect the asymptotic behavior of the surface coverage, the correlation function, and the hole size distribution.     

Real-Space Renormalization Estimates for Two-Phase Flow in Porous Media

We present a spatial renormalization group algorithm to handle immiscibletwo-phase flow in heterogeneous porous media. We call this algorithmFRACTAM-R, where FRACTAM is an acronym for Fast Renormalization Algorithmfor Correlated Transport in Anisotropic Media, and the R stands for relativepermeability. Originally, FRACTAM was an approximate iterative process thatreplaces the L × L lattice of grid blocks, representing the reservoir,by a (L/2) × (L/2) one. In fact, FRACTAM replaces the original L× L lattice by a hierarchical (fractal) lattice, in such a way thatfinding the solution of the two-phase flow equations becomes trivial. Thistriviality translates in practice into computer efficiency. For N=L ×L grid blocks we find that the computer time necessary to calculatefractional flow F(t) and pressure P(t) as a function of time scales as N^1.7 for FRACTAM-R. This should be contrasted with thecomputational time of a conventional grid simulator N^2.3. The solution we find in this way is an accurateapproximation to the direct solution of the original problem.     

A fast algorithm for estimating large-scale permeabilities of correlated anisotropic media

The problem of estimating large-scale permeabilities of reservoirs based on knowledge of the small-scale permeabilities is addressed. We present an accurate and fast algorithm to calculate the global permeabilities of two- or three-dimensional correlated and anisotropic block samples, thus providing a fast algorithm for obtaining grid block permeabilities for reservoir simulators from small scale data. The algorithm is tested on both two- and three-dimensional tube networks generated from real images and fractal forgeries modeling porous media. In almost all cases, the algorithm estimates the correct global permeability (calculated using exact but slow algorithms) of the network to better than 5%. The new algorithm is comparable in speed to conventional averaging techniques, such as the geometric mean, but the obtained estimates are always much better.List of Symbols K permeability of network (global permeability - K _e estimated permeability - K K×(L_x×L_y)/L_z - K permeability perpendicular to layering - K permeability parallel with layering - L _x, L_y, L_z Network size inx, y andz-directions - L Size of quadratic (cubic) network - Q global flux through network - U Q/(L_x×L_y), Darcy velocity (flux per unit area) - V volume of network - P pressure drop across network - a,b parameters in Equation (4) - P _i pressure at sitei - q _ij flux between nodesi andj - parameter of Pareto distribution - porosity - K(i) permeability at site (block)i - K _ij permeability of bond between nodesi andj - K _min minimumk(i) for sample - K _max maximumK(i) for sample - fluid viscosity     

Lattice gas simulations of osmosis

An analysis of the phenomenon of osmosis within the lattice gas model is presented. The model considered is a two-species version of the Frisch-Hasslacher-Pomeau model with rest particles and a semipermeable membrane which is implemented as a boundary that blocks one species, but lets the other pass freely. In this way the equilibrium between a pure and a mixed subsystem can be studied. Analytic expressions for both the pressure difference and the fluctuations of this quantity are obtained from the entropy function for the lattice gas, and we find that these results are in good agreement with those obtained from simulation. The osmotic flow across the membrane is also studied. We characterize the concentration boundary layer, and an analytic expression for the osmotic permeability as a function of porosity is compared with results from simulations.     

Simulations of migration, fragmentation and coalescence of non-wetting fluids in porous media

A model based on invasion percolation was used to simulate the migration on a non-wetting fluid through a porous medium filled with an immiscible wetting fluid under the influence of a gradient such as that provided by gravity. The migrating fluid clusters undergo both fragmentation and coalescence. The fragment size distribution obtained from two-dimensional simulations in which the gradient g is slowly increased from 0 can be represented by the scaling form N_s(g)s^-2ƒ(s|g|^-z where z=1+(D−1)ν(ν+1). Here D is the fractal dimensionality of invasion percolation, with trapping, and ν is the ordinary percolation correlation length exponent.     

High-resolution measurements of thermal expansion along the uniqueb-axis of squaric acid

The thermal expansion of squaric acid along the uniqueb-axis was measured between 323 K and 418 K with a resolution of 2·10^–7 in strain and 5·10^–4 K in temperature using a capacitance dilatometer. The anomaly associated with the antiferro-electric phase transition occuring atT _c=373.5 K was observed over the rangeT _c–50 K<T<T _c+7 K. The regular lattice expansion follows a generalized Grüneisen's law with a Debye-temperature _D =660 K and a uniaxial pressure-dependence of _D /p _b . The critical behaviour close toT _c was studied with a sweep rate of 36 mK/h. A hyteresis loop of width 23 mK was observed in the strain curve, indicating a 1st order transition. However, no discontinuity in dilatation was observed, and therefore the transition is close to a multicritical point. The anomalous increase in the expansion coefficient can be described with critical exponents ==0.56 in the interval 0.4 K<|T–T _c|<12 K. Closer toT _c the divergence is stronger. A generalized Pippard relation between the expansion coefficient and specific heat holds to within 1 K from the transition point. The inconsistencies apparent closer toT _c are interpreted as a consequence of a weak 1st order transition.