N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

50 Years of Image Analysis

Numerical study of flow through random packing of non-overlapping spheres in a cylindrical geometry is investigated. Dimensionless pressure drop has been studied for a fluid through the porous media at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), and numerical solution of Navier-Stokes equations in three dimensional porous packed bed illustrated in excellent agreement with those reported by Macdonald [1979] in the range of Reynolds number studied. The results compare to the previous work (Soleymani et al., 2002) show more accurate conclusion because the problem of channeling in a duct geometry. By injection of solute into the system, the dispersivity over a wide range of flow rate has been investigated. It is shown that the lateral fluid dispersion coefficients can be calculated by comparing the concentration profiles of solute obtained by numerical simulations and those derived analytically by solving the macroscopic dispersion equation for the present geometry.Copyright © 2006 by ASME

Simulation of Fluid Flow Through a Granular Bed

We study scalar mixing in heterogeneous conductivity fields, whose structural disorder varies from weak to strong. A range of stretching regimes is observed, depending on the level of structural heterogeneity, measured by the log-conductivity field variance. We propose a unified framework to quantify the overall concentration distribution predicting its shape and rate of deformation as it progresses toward uniformity in the medium. The scalar mixture is represented by a set of stretched lamellae whose rate of diffusive smoothing is locally enhanced by kinematic stretching. Overlap between the lamellae is enforced by confinement of the scalar line support within the dispersion area. Based on these elementary processes, we derive analytical expressions for the concentration distribution, resulting from the interplay between stretching, diffusion, and random overlaps, holding for all field heterogeneities, residence times, and Péclet numbers.

Stretching, Coalescence and Mixing in Porous Media

Nano-scale Experimental Investigation of In-situ Wettability and Spontaneous Imbibition in Ultra-tight Reservoir Rocks

Improved segmentation of X-ray tomography data from porous rocks using a dual filtering approach

X-ray computed tomography data from chalk drill cuttings were taken over a series of voxel dimensions, ranging from 320 to 25 nm. From these data sets, standard petrophysical parameters (porosity, surface area, and permeability) were derived and we examined the effect of the voxel dimension (i.e., image resolution) on these properties. We found that for the higher voxel dimensions, they are severely over or underestimated, whereas for 50 and 25 nm voxel dimension, the resulting values (5%–30% porosity, 0.2–2 m2/g specific surface area, and 0.06–0.34 mD permeability) are within the expected range for this type of rock. We compared our results to macroscopic measurements and in the case of surface area, also to measurements using the Brunauer-Emmett-Teller (BET) method and found that independent of the degree of compaction, the results from tomography amount to about 30% of the BET method. Finally, we concluded that at 25 nm voxel dimension, the essential features of the nanoscopic pore network in chalk are captured but better resolution is still needed to derive surface area.

Resolution dependence of petrophysical parameters derived from X-ray tomography of chalk

X-ray computed tomography is useful for providing insight into the internal structure of porous materials. Extracting reliable quantitative information is difficult because the derived properties rely heavily on data resolution, i.e., very different values emerge, depending on the relationship between size of the features in the sample and the resolution of the 3D tomograms. Here, we present a method for testing if resolution is sufficient for determining reliable petrophysical parameters, i.e., with low levels of uncertainty. We derived the physical properties of sandstone and carbonate rocks over a range of voxel dimensions by computationally reducing raw data resolution in our high resolution images. Lower resolution decreases the calculated surface area for all samples and increases the derived permeability for sandstone. The permeability vs change in resolution was not monotonic for carbonates. The differences in trends for the two rock types result from different pore sizes and pore size distributions.

/pdf/effect-of-tomography-resolution-on-the-calculated-m0c9h45t16.pdf

Effect of tomography resolution on the calculated microscopic properties of porous materials: Comparison of sandstone and carbonate rocks

Flow in porous media is a signiﬁcant challenge to many computational ﬂuid dynamics methods because of the complex boundaries separating pore ﬂuid and host medium. However, the rapid development of the lattice Boltzmann methods and experimental imaging techniques now allow us to efﬁciently and robustly simulate ﬂows in the pore space of porous rocks. Here we study the ﬂow and dispersion in the pore space of limestone samples using the unstructured, characteristic based off-lattice Boltzmann method. We use the method to investigate the anomalous dispersion of particles in the pore space. We further show that the complex pore network limits the effectivity by which pollutants in the pore space can be removed by continuous ﬂushing. In the smallest pores, diffusive transport dominates over advective transport and therefore cycles of ﬂushing and no ﬂushing, respectively, might be a more efﬁcient strategy for pollutant removal.

/pdf/simulating-anomalous-dispersion-in-porous-media-using-the-54gcoowk3v.pdf

Simulating Anomalous Dispersion in Porous Media Using the Unstructured Lattice Boltzmann Method

We studied the diffusion of particles in the highly irregular pore networks of chalk, a very fine-grained rock, by combining three-dimensional X-ray imaging and dissipative particle dynamics (DPD) simulations. X-ray imaging data were collected at 25 nm voxel dimension for two chalk samples with very different porosities (4% and 26%). The three-dimensional pore systems derived from the tomograms were imported into DPD simulations and filled with spherical particles of variable diameter and with an optional attractive interaction to the pore surfaces. We found that diffusion significantly decreased to as much as 60% when particle size increased from 1% to 35% of the average pore diameter. When particles were attracted to the pore surfaces, even very small particles, diffusion was drastically inhibited, by as much as a factor of 100. Thus, the size of particles and their interaction with the pore surface strongly influence particle mobility and must be taken into account for predicting permeability in nanopo...

/pdf/particle-diffusion-in-complex-nanoscale-pore-networks-28m2rjxqne.pdf

D. Müter

Papers

Improved segmentation of X-ray tomography data from porous rocks using a dual filtering approach

Resolution dependence of petrophysical parameters derived from X-ray tomography of chalk

Effect of tomography resolution on the calculated microscopic properties of porous materials: Comparison of sandstone and carbonate rocks

Simulating Anomalous Dispersion in Porous Media Using the Unstructured Lattice Boltzmann Method

Particle Diffusion in Complex Nanoscale Pore Networks