Category: Simulations

Quantitative Analysis of Experimental and Synthetic Microstructures for Sedimentary Rock

Post author By R Hilfer
Post date April 17, 1999

B. Biswal, C. Manwart, R. Hilfer, S. Bakke, P.E. Øren

Physica A 273, 452 (1999)
https://doi.org/10.1016/S0378-4371(99)00248-4

submitted on
Monday, May 17, 1999

A quantitative comparison between the experimental microstructure of a sedimentary rock and three theoretical models for the same rock is presented. The microstructure of the rock sample (Fontainebleau sandstone) was obtained by microtomography. Two of the models are stochastic models based on correlation function reconstruction, and one model is based on sedimentation, compaction and diagenesis combined with input from petrographic analysis. The porosity of all models closely match that of the experimental sample and two models have also the same two point correlation function as the experimental sample. We compute quantitative differences and similarities between the various microstructures by a method based on local porosity theory. Differences are found in the degree of anisotropy, and in fluctuations of porosity and connectivity. The stochastic models differ strongly from the real sandstone in their connectivity properties, and hence need further refinement when used to model transport.

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Tags reconstruction models, sediments

Porous Media Simulations

Reconstruction of Random Media Using Monte Carlo Methods

Post author By R Hilfer
Post date September 8, 1998

C. Manwart, R. Hilfer

Physical Review E 59, 5596 (1999)
https://doi.org/10.1103/PhysRevE.59.5596

submitted on
Tuesday, September 8, 1998

A simulated annealing algorithm is applied to the reconstruction of two-dimensional porous media with prescribed correlation functions. The experimental correlation function of an isotropic sample of Fontainebleau sandstone and a synthetic correlation function with damped oscillations are used in the reconstructions. To reduce the numerical effort we follow a proposal suggesting the evaluation of the correlation functions only along certain directions. The results show that this simplification yields significantly different microstructures as compared to a full evaluation of the correlation function. In particular, we find that the simplified reconstruction method introduces an artificial anisotropy that is originally not present.

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Tags reconstruction models, sand stone, sediments

image analysis Porous Media Simulations

Microstructure Analysis of Reconstructed Porous Media

Post author By R Hilfer
Post date July 15, 1998

B. Biswal, R. Hilfer

Physica A 266, 307 (1999)
https://doi.org/10.1016/S0378-4371(98)00607-4

submitted on
Wednesday, July 15, 1998

We compare the quantitative microstructural properties of Berea Sandstone with stochastic reconstructions of the same sandstone. The comparison is based on local porosity theory. The reconstructions employ Fourier space filtering of Gaussian random fields and match the average porosity and two-point correlation function of the experimental model. Connectivity properties of the stochastic models differ significantly from the experimental model. Reconstruction models with different levels of coarse graining also show different average local connectivity.

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Tags reconstruction models

image analysis Porous Media Simulations

Threedimensional Local Porosity Analysis of Porous Media

Post author By R Hilfer
Post date February 5, 1998

B. Biswal, C. Manwart, R. Hilfer

Physica A 255, 221 (1998)
https://doi.org/10.1016/S0378-4371(98)00111-3

submitted on
Thursday, February 5, 1998

A quantitative comparison of the pore space geometry for three natural sandstones is presented. The comparison is based on local porosity theory which provides a geometric characterization of stochastic microstructures. The characterization focusses on porosity and connectivity fluctuations. Porosity fluctuations are measured using local porosity distributions while connectivity fluctuations are measured using local percolation probabilities. We report the first measurement of local percolation probability functions for experimentally obtained three-dimensional pore space reconstructions. Our results suggest the use of local porosity distributions and percolation probabilities as a quantitative method to compare microstructures of models and experiment.

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Tags local porosity theory

Lattice Models Nonequilibrium Simulations Stochastic Processes

Statistical Prediction of Corrosion Front Penetration

Post author By R Hilfer
Post date August 18, 1996

T. Johnsen, R. Hilfer

Phys.Rev. E 55, 5433 (1997)
https://doi.org/10.1103/PhysRevE.55.5433

submitted on
Wednesday, September 18, 1996

A statistical method to predict the stochastic evolution of corrosion fronts has been developed. The method is based on recording material loss and maximum front depth. In this paper we introduce the method and test its applicability. In the absence of experimental data we use simulation data from a three-dimensional corrosion model for this test. The corrosion model simulates localized breakdown of a protective oxide layer, hydrolysis of corrosion product and repassivation of the exposed surface. In the long time limit of the model, pits tend to coalesce. For different model parameters the model reproduces corrosion patterns observed in experiment. The statistical prediction method is based in the theory of stochastic processes. It allows the estimation of conditional probability densities for penetration depth, pitting factor, residual lifetimes, and corrosion rates which are of technological interest.

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Tags corrosion

Critical phenomena Equilibrium Simulations

Phase Transitions in Dense Lipid Monolayers Grafted to a Surface: Monte Carlo Investigation of a Coarse-Grained Off-Lattice Model

Post author By R Hilfer
Post date April 12, 1996

F. M. Haas, R. Hilfer, K. Binder

The Journal of Physical Chemistry 100 (37), 15290-15300 (1996)
DOI: 10.1021/jp9610980

submitted on
Friday, April 12, 1996

Semiflexible amphiphilic molecules end-grafted at a flat surface are modeled by a bead-spring chain with stiff bond angle potentials. Constant density Monte Carlo simulations are performed varying temperature, density, and chain length of the molecules, whose effective monomers interact with Lennard-Jones potentials. For not too large densities and low temperatures the monolayer is in a quasi-two-dimensional crystalline state, characterized by uniform tilt of the (stretched) chains. Raising the temperature causes a second-order transition into a (still solid) phase with no tilt. For the first time, finite size scaling concepts are applied to a model of a surfactant monolayer, and it is found that the technique in this case again is useful to locate the transition more precisely. For comparison, also a one-dimensional version of the model is studied, and directions for future extensions of this modeling are discussed.

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Tags lipid layer

Critical phenomena Simulations

Continuum Monte Carlo Simulation at Constant Pressure of Stiff Chain Molecules at Surfaces

Post author By R Hilfer
Post date August 31, 1995

F. M. Haas, R. Hilfer

Journal of Chemical Physics 105, 3859 (1996)
https://doi.org/10.1063/1.472206

submitted on
Thursday, August 31, 1995

Continuum Monte-Carlo simulations at constant pressure are performed on short chain molecules at surfaces. The rodlike chains, consisting of seven effective monomers, are attached at one end to a flat twodimensional substrate. It is found that the model exhibits phases similar to the liquid condensed and liquid expanded phases of Langmuir monolayers. The model is investigated here for a wide range of pressures and temperatures using a special form of constant pressure simulation compatible with the symmetry breaking during tilting transitions in the liquid condensed phases. At low pressures the chains undergo a tilting transition exhibiting tilt directions towards nearest and also next nearest neighbours depending on temperature. At elevated temperatures and low pressure the film enters a fluidlike phase similar to the liquid expanded phase observed in experiment.

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Tags lipid layer

Critical phenomena Equilibrium Simulations Statistical Physics

Continuum Monte-Carlo Simulations of Phase Transitions in Rodlike Molecules at Surfaces

Post author By R Hilfer
Post date October 28, 1994

R. Hilfer, F.M. Haas, K. Binder

Il Nuovo Cimento D 16, 1297-1303 (1994)
https://doi.org/10.1007/BF02458816

submitted on
Friday, October 28, 1994

Stiff rod-like chain molecules with harmonic bond length potentials and trigonometric bond angle potentials are used to model Langmuir monolayers at high densities. One end of the rod-like molecules is strongly bound to a flat two-dimensional substrate which represents the air-water interface. A ground-state analysis is performed which suggests phase transitions between phases with and without collective uniform tilt. Large-scale off-lattice Monte Carlo simulations over a wide temperature range show in addition to the tilting transition the presence of a strongly constrained melting transition at high temperatures. The latter transition appears to be related to two-dimensional melting of the head group lattice. These findings show that the model contains both, two- and three-dimensional ergodicity breaking solidification transitions. We discuss our findings with respect to experiment.

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Tags lipid layer

Critical phenomena Equilibrium Simulations Statistical Physics

Layers of Semiflexible Chain Molecules Endgrafted at Interfaces: An Off-Lattice Monte Carlo Simulation

Post author By R Hilfer
Post date July 11, 1994

F.M. Haas, R. Hilfer, K. Binder

Journal of Chemical Physics 102, 2960-2969 (1995)
https://doi.org/10.1063/1.468604

submitted on
Monday, July 11, 1994

A coarse‐grained model for surfactant chain molecules at interfaces in the high density regime is studied using an off‐lattice Monte Carlo technique. The surfactant molecules are modeled as chains consisting of a small number (e.g., seven) of effective monomers. For the modeling of lipid monolayers, each effective monomer is thought to represent several CH2 groups of the alkane chain, but applications of the model to other polymers end grafted at solid surfaces also should be possible. The head segments are restricted to move in the adsorption plane, but otherwise do not differ from the effective monomers, which all interact with Lennard‐Jones potentials. Bond angle and bond length potentials take into account chain connectivity and chain stiffness. The advantage of this crude model is that its phase diagram can be studied in detail. Temperature scans show two phase transitions, a tilting transition at low temperatures between a tilted and an untilted phase, and a melting transition at high temperatures where the lattice of head groups loses its crystalline order.

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Tags lipid layer