Pore-scale modeling of dispersion in disordered porous media

We employ a direct pore-level model of incompressible flow that uses the modified moving particle semi-implicit (MMPS) method. The model is capable of simulating both unsteady- and steady-state flow directly in microtomography images of naturally-occurring porous media. We further develop this model to simulate solute transport in disordered porous media. The governing equations of flow and transport at the pore level, i.e., Navier-Stokes and convection-diffusion, are solved directly in the pore space mapped by microtomography techniques. Three naturally-occurring sandstones are studied in this work. We verify the accuracy of the model by comparing the computed longitudinal dispersion coefficients against the experimental data for a wide range of Peclet numbers, i.e., 5×10(-2)相似文献   

Determining straining of Escherichia coli from breakthrough curves

Though coliform bacteria are used world wide as an indication of faecal pollution, the parameters determining the transport of Escherichia coli in aquifers are relatively unknown, especially for the period after the clean bed collision phase brought about by prolonged infiltration of waste water. In this research, the breakthrough curves of E. coli after total flushing of 50-200 pore volumes were studied for various influent concentrations in various sediments at different pore water flow velocities. The results indicated that straining in Dead End Pores (DEPs) was an important process that dominated bacteria breakthrough in fine-grained sediment (0.06-0.2 mm). The filling of the DEP space with bacteria took 5-65 pore volumes and was dependent on concentration. Column breakthrough curves were modelled and from this the DEP volumes were determined. These volumes (0.21-0.35% of total column volume) corresponded well with values calculated with a formula based on purely geometrical considerations and also with values calculated with a pore size density function. For this function the so-called Van Genuchten parameters of the sediments used in the experiments were determined. The results indicate that straining might be a dominant process affecting colloid transport in the natural environment and therefore it is concluded that proper knowledge of the pore size distribution is crucial to an understanding of the retention of bacteria.     

Three-dimensional diffusion of non-sorbing species in porous sandstone: computer simulation based on X-ray microtomography using synchrotron radiation

The diffusion pathways of porous sandstone were examined by a three-dimensional (3-D) imaging technique based on X-ray computed tomography (CT) using the SPring-8 (Super Photon ring-8 GeV, Hyogo, Japan) synchrotron radiation facility. The analysis was undertaken to develop better understanding of the diffusion pathways in natural rock as a key factor in clarifying the detailed mechanism of the diffusion of radionuclides and water molecules through the pore spaces of natural barriers in underground nuclear waste disposal facilities. A cylindrical sample (diameter 4 mm, length 6 mm) of sandstone (porosity 0.14) was imaged to obtain a 3-D image set of 450(3) voxels=2.62(3) mm(3). Through cluster-labeling analysis of the 3-D image set, it was revealed that 89% of the pore space forms a single large pore-cluster responsible for macroscopic diffusive transport, while only 11% of the pore space is made up of isolated pores that are not involved in long-range diffusive transport. Computer simulations of the 3-D diffusion of non-sorbing random walkers in the largest pore cluster were performed to calculate the surface-to-volume ratio of the pore, tortuosity (diffusion coefficient in free space divided by that in porous rock). The results showed that (i) the simulated surface-to-volume ratio is about 60% of the results obtained by conventional pulsed-field-gradient proton nuclear magnetic resonance (NMR) laboratory experiments and (ii) the simulated tortuosity is five to seven times larger than the results of laboratory diffusion experiments using non-sorbing I(-) and Br(-). These discrepancies are probably attributed to the intrinsic sample heterogeneity and limited spatial resolution of the CT system. The permeability was also estimated based on the NMR diffusometry theory using the results of the random walk simulations via the Kozeny-Carman equation. The estimated permeability involved an error of about 20% compared with the permeability measured by the conventional method, suggesting that the diffusometry-based NMR well logging with gradient coils is applicable to the in-situ permeability measurement of strata. The present study demonstrated that X-ray CT using synchrotron radiation is a powerful tool for obtaining 3-D pore structure images without the beam-hardening artifacts inevitable in conventional CT using X-ray tubes.     

Distribution and transport of coal tar-derived PAHs in fine-grained residuum

We investigated the distribution and transport of coal tar-derived polycyclic aromatic hydrocarbons (PAHs) in fine-grained residuum and alluvial floodplain deposits that underlie a former manufactured gas plant. All 16 USEPA priority pollutant PAHs are present at this site and have penetrated the entire 4-5m thickness of clayey sediments, which unconformably overly limestone bedrock. Concentrations of less hydrophobic PAHs (e.g., naphthalene, 0.011-384mg kg(-1)) were about 10 times higher than those of highly hydrophobic PAHs (e.g., benzo[g,h,i]perylene -0.002 to 56.03mgkg(-1)). Microscopic examination of thin-sections of the clay-rich sediments showed that fractures and rootholes, which can act as pathways for flow, occur throughout the profiles. Tarry residue was found coating some fractures and rootholes, indicating that coal tar was, in some cases, able to penetrate as an immiscible phase. However, in the vast majority of samples in which PAHs were detected, there was no detectable tar residue, suggesting that much of the transport occurred in the dissolved phase. Examination of thin-sections with an epifluorescent microscope indicated that PAHs, which fluoresce brightly when exposed to UV light, are distributed throughout the soil matrix, rather than being confined to fractures and rootholes. The widespread distribution of PAHs is most likely due to diffusion-controlled exchange between the fast-flow pathways in the fractures and rootholes and the relatively immobile water in the fine-grained matrix. This implies that fractures and rootholes can play a major role in controlling transport of highly hydrophobic compounds in fine-grained sediments, which would otherwise act as barriers to contaminant migration.     

Quantifying the physical and chemical mass transfer processes for the fate and transport of Co(II)EDTA in a partially-weathered limestone-shale saprolite

The objective of the research is to quantify the relative contributions of physical and chemical mass transfer to the movement of Co(II/III)EDTA (chelates of Cobalt and Ethylene Diamine Tetraacetic Acid or EDTA) through a limestone-shale saprolite soil. Saprolite is a collective term referring to partially-weathered bedrock. It exists extensively in the subsurface. Because the parent bedding structures are maintained during the weathering process, saprolite soils are characterized by intensive fractures and secondary deposits of minerals such as Al-, Fe- and Mn-oxides on the fracture surfaces. Movement of reactive species through the soils may be influenced by diffusion into the rock matrix, a physical mass transfer (PMT) process, and interfacial chemical reactions, a chemical mass transfer (CMT) process. The PMT and CMT processes are phenomenologically similar but mechanistically different. In this research, previous laboratory observations from a Br and Co(II)EDTA tracer injection into an undisturbed saprolite soil column were used. Mechanistic reactive transport models were formulated to quantify the PMT and CMT processes. The PMT process was independently characterized by using the non-reactive tracer Br. Model parameters thus obtained were subsequently used as constraints to quantify the CMT processes involving Co(II)EDTA and its oxidation product Co(III)EDTA. Our calculations indicated that the PMT rates of the less reactive Co(III)EDTA were comparable with their theoretical CMT rates. In contrast, for the more reactive species Co(II)EDTA, CMT rates are higher than PMT rates. Evaluations of alternative CMT process models further confirmed one of our hypotheses on the basis of previous experimental understandings. The hypothesis suggested that competition from Fe-oxide for Co(II)EDTA may account for the majority of the decrease of Co(III)EDTA effluent concentrations that resulted in the separation of total Co and Co(III)EDTA breakthrough curves. Because Co(III)EDTA is more mobile than Co(II)EDTA in the subsurface, the results of this research suggest independent quantifications of CoEDTA PMT and CMT processes if laboratory results are to be interpreted correctly and scaled up for field and predictive uses.     

The effects of scale and spatial heterogeneities on diffusion in volcanic breccias and basalts: Amchitka Island, Alaska

Knowledge of the factors that influence the diffusion of contaminants, such as the diffusivity and the connected porosity, is crucial to modeling the long-term fate and transport of contaminants in subsurface systems with small or negligible advective flow, such as in fractured crystalline rock. Fractured rock is naturally heterogeneous, and hence, understanding the diffusivity of a molecule through this material (or the formation factor of the medium) becomes a complex problem, with critical concerns about the scale of laboratory measurements and about the spatial variability of these measurements relative to the scale needed for fate and transport modeling. This study employed both electrical and tracer-based laboratory methods to investigate the effects of scale and pore system connectivity on the diffusivity for volcanic matrix rock derived from the study site, a former underground nuclear test site at Amchitka Island, Alaska. The results of these investigations indicate a relatively well-connected pore system with scale effects generally limited to approximately 6 cm lengths and well-correlated to observed heterogeneous features. An important conclusion resulting from this study, however, is that there is a potential for the estimated diffusivity to be misrepresented by an order of magnitude if multiple samples or longer sample lengths are not used. Given the relatively large number of measurements resulting from these investigations, an analysis of the probability density function (PDF) of the diffusivity was possible. The PDF of the diffusivity was shown to generally follow a normal distribution for individual geologic layers. However, when all of the geologic layers are considered together, the distribution of the subsurface as a whole was shown to follow a lognormal distribution due to the order of magnitude differences amongst the layers. An understanding of these distributions is essential for future stochastic modeling efforts.     

Drop size-dependent S(IV) oxidation in chemically heterogeneous radiation fogs

Six radiation fog episodes were sampled in the Central Valley of California during winter 1998/1999. Drop size-resolved fog samples were sampled using a size-fractionating Caltech active strand cloudwater collector (sf-CASCC). The sf-CASCC collects a large fog drop sample, comprised mainly of drops larger than 17 μm diameter, and a small fog drop sample, comprised mainly of drops with diameters between 4 and 17 μm. The fog pH was found to vary between approximately pH 5.3 and 6.8, with the pH of the large fog drop sample typically several tenths of a pH unit higher than the simultaneously collected small fog drop sample. At these high pH values, dissolved sulfur dioxide can be rapidly oxidized by a variety of chemical pathways and also can react quickly with dissolved formaldehyde to form hydroxymethanesulfonate. The amount of sulfate produced by aqueous-phase oxidation during each fog episode was determined by application of a tracer technique. The ratio of large : small drop S(IV) oxidation was compared with theoretically predicted ratios of large : small drop S(IV) oxidation rates. Although the higher pH of the large fog drops should promote more rapid S(IV) oxidation by ozone, finite rates of mass transport into the large drops and an increasing rate of complexation of S(IV) by formaldehyde at high pH combine to depress theoretically predicted rates of aqueous sulfate production in large fog drops below rates expected for small fog drops. This prediction is supported by the tracer results that indicate the concentration of sulfate resulting from aqueous-phase S(IV) oxidation in small drops generally exceeded the concentration formed in large drops. These findings stand in sharp contrast to observations in acidic clouds at Whiteface Mountain, New York, where hydrogen peroxide was determined to be the dominant S(IV) oxidant and the rate of S(IV) oxidation was found to be independent of drop size.     

Changes in the pore network structure of Hanford sediment after reaction with caustic tank wastes

At the former nuclear weapon production site in Hanford, WA, caustic radioactive tank waste leaks into subsurface sediments and causes dissolution of quartz and aluminosilicate minerals, and precipitation of sodalite and cancrinite. This work examines changes in pore structure due to these reactions in a previously-conducted column experiment. The column was sectioned and 2D images of the pore space were generated using backscattered electron microscopy and energy dispersive X-ray spectroscopy. A pre-precipitation scenario was created by digitally removing mineral matter identified as secondary precipitates. Porosity, determined by segmenting the images to distinguish pore space from mineral matter, was up to 0.11 less after reaction. Erosion-dilation analysis was used to compute pore and throat size distributions. Images with precipitation had more small and fewer large pores. Precipitation decreased throat sizes and the abundance of large throats. These findings agree with previous findings based on 3D X-ray CMT imaging, observing decreased porosity, clogging of small throats, and little change in large throats. However, 2D imaging found an increase in small pores, mainly in intragranular regions or below the resolution of the 3D images. Also, an increase in large pores observed via 3D imaging was not observed in the 2D analysis. Changes in flow conducting throats that are the key permeability-controlling features were observed in both methods.     

A sensibility analysis of model selection in modeling the reactive transport of cesium in crushed granite

We performed a sensibility analysis of model selection in modeling the reactive transport of cesium in crushed granite through model calibration and validation. Based on some solid phase analysis data and kinetic batch experimental results, we hypothesized three two-site sorption models in the LEHGC reactive transport model to fit the breakthrough curves (BTCs) from the corresponding column experiments. The analysis of breakthrough curves shows that both the empirical two-site kinetic linear sorption model and the semi-mechanistic/semi-empirical two-site kinetic surface complexation model, regardless of their complexity, can match our experimental data fairly well under given test conditions. A numerical experiment to further compare the two models shows that they behave differently when the pore velocity is not of the same order of magnitude as our test velocities. This result indicates that further investigations to help determine a better model are needed. We suggest that a multistage column experiment, which tests over the whole range of practical flow velocities, should be conducted to help alleviate inadequate hypothesized models.     

Measurements of ozone and nonmethane hydrocarbons at Chichi-jima island,a remote island in the western Pacific: long-range transport of polluted air from the Pacific rim region

Chichi-jima island is located in the Pacific about 1000 km from the Japanese main island and is an ideal remote observatory from which to assess the long-range transport of polluted air from East Asia. The ozone concentration was measured from August 1997 to August 1998. Owing to the air mass change, the seasonal variation of ozone shows a distinct character: low concentration (about 13 ppbv) for the maritime air mass during the summer, and high concentration (about 40 ppbv) for the continental air mass during the winter. To assess the contribution of the long-range transport of polluted air during winter, nonmethane hydrocarbons were also measured in December 1999. Using backward trajectory analysis, the transport time of the air mass from the source area in the Pacific rim region was calculated for each sample. The concentration of hydrocarbons shows a clear negative correlation against the transport time. This analysis clearly shows the transport of polluted air, emitted in East Asia, to the Pacific during the winter. The plots of suitable hydrocarbon pairs showed that the decrease of hydrocarbon concentrations during winter is mainly caused by the mixing with clean background air.     

Seasonal cycle and composition of background fine particles along the west coast of the US

We used aerosol data from 4 sites along the west coast of the U.S. to evaluate the role of transport, seasonal pattern, chemical composition and possible trends in the marine background aerosol for the Pacific Northwest. For the Crater Lake samples, the data have been segregated using 10 day back isentropic trajectories to evaluate the role of transport. Our analysis of the segregated data indicates that the trajectories can successfully separate “locally influenced” from “marine background” aerosol, but are not able to identify a significant difference in the mean concentrations during marine vs Asian transport pathways.The background marine aerosol has an annual mean and median concentrations of 2.0 and 1.5 μg m⁻³, respectively, for particles less than 2.5 μm diameter. There is a seasonal pattern in all components of the aerosol mass, with a summer maximum and winter minimum. This pattern is most likely due to the strong seasonal pattern in precipitation, which peaks in winter, combined with enhanced sources in summer. The Crater Lake marine aerosol composition is dominated by organics (∼40% by mass), with smaller contributions from sulfates, mineral dust and elemental carbon. Analysis of the background marine aerosol found no apparent trend since 1988. This is in contrast to results reported by Prospero et al. (J. Geophys. Res. 108 (2003) 4019) for nss-SO₄²⁻ samples from Midway Island in the North Pacific. Comparison of the mean concentrations for each site shows that the Midway samples are significantly more influenced by Asian industrial sources of sulfur, compared to Crater Lake, which implies a substantial loss of nss-SO₄²⁻ from Asian sources that occurs during transit across the Pacific to Crater Lake due to precipitation scavenging.     

Effects of pore volume-transmissivity correlation on transport phenomena

The relevant velocity that describes transport phenomena in a porous medium is the pore velocity. For this reason, one needs not only to describe the variability of transmissivity, which fully determines the Darcy velocity field for given source terms and boundary conditions, but also any variability of the pore volume. We demonstrate that hydraulically equivalent media with exactly the same transmissivity field can produce dramatic differences in the displacement of a solute if they have different pore volume distributions. In particular, we demonstrate that correlation between pore volume and transmissivity leads to a much smoother and more homogeneous solute distribution. This was observed in a laboratory experiment performed in artificial fractures made of two plexiglass plates into which a space-dependent aperture distribution was milled. Using visualization by a light transmission technique, we observe that the solute behaviour is much smoother and more regular after the fractures are filled with glass powder, which plays the role of a homogeneous fault gouge material. This is due to a perfect correlation between pore volume and transmissivity that causes pore velocity to be not directly dependent on the transmissivity, but only indirectly through the hydraulic gradient, which is a much smoother function due to the diffusive behaviour of the flow equation acting as a filter. This smoothing property of the pore volume-transmissivity correlation is also supported by numerical simulations of tracer tests in a dipole flow field. Three different conceptual models are used: an empty fracture, a rough-walled fracture filled with a homogeneous material and a parallel-plate fracture with a heterogeneous fault gouge. All three models are hydraulically equivalent, yet they have a different pore volume distribution. Even if piezometric heads and specific flow rates are exactly the same at any point of the domain, the transport process differs dramatically. These differences make it important to discriminate in situ among different conceptual models in order to simulate correctly the transport phenomena. For this reason, we study the solute breakthrough and recovery curves at the extraction wells. Our numerical case studies show that discrimination on the basis of such data might be impossible except under very favourable conditions, i.e. the integral scale of the transmissivity field has to be known and small compared to the dipole size. If the latter conditions are satisfied, discrimination between the rough-walled fracture filled with a homogeneous material and the other two models becomes possible, whereas the parallel-plate fracture with a heterogeneous fault gouge and the empty fracture still show identifiability problems. The latter may be solved by inspection of aperture and pressure testing.     

Toxicity of water and sediment in a small urban river (Store Vejleå, Denmark)

The urban stream Store Vejle? (Denmark), which receives discharges of urban runoff, was investigated using a combination of biological toxicity tests and chemical analysis. The urban stormwater and road runoff gave low, but statistically significant, effects on the reproduction of the alga Pseudokirchneriella subcapitata. In all pre-concentrated water samples toxic effects were found and differences in toxicity depending on time and location of sampling were identified. Undiluted pore water samples from sediments collected in the stream were all toxic towards the algae and dilutions from 4 to 14 times were needed compared to a pore water sample from an unpolluted stream where a dilution factor of only 1.6 was required. A qualitative correlation between the toxicity of the pore water and the degree of pollution as evidenced by the metal concentration was observed, but statistically significant correlations could not be established by ranking procedures of, e.g. metal content or PAH-concentrations versus the observed toxicity.     

Polyfluorinated telomers in indoor air of Japanese houses

The fluorotelomer alcohols (FTOHs) have been detected in various environmental compartments, including indoor and outdoor air, in North America and Europe. In our previous studies, FTOHs were detected at a relative higher concentration in outdoor air in the Keihan (Kyoto–Osaka, one of the major industrial zones) area, Japan compared to reported data. The exposure level of FTOHs in indoor air in the Keihan area remains unclear. In the present study, indoor air FTOH concentrations were investigated using a passive air sampler containing activated carbon felts. The indoor air sampling was conducted in 49 households of the Keihan area, during winter and summer 2008. Most samples contained 6:2 FTOH, 8:2 FTOH, 10:2 FTOH and 8:2 FTOAc. The median concentration of 8:2 FTOH (5.84 ng m^?3) was highest among fluorotelomers, followed by those of 10:2 FTOH (1.12 ng m^?3), 6:2 FTOH (0.29 ng m^?3), and others. Significant correlations among fluorotelomers were observed in collected samples. The association between housing conditions and 8:2 FTOH concentrations showed that samples collected from bed rooms have higher 8:2 FTOH concentrations than those collected from other locations. In addition, samples collected in winter showed lower levels of 8:2 FTOH than those collected in summer. These findings suggest that 8:2 FTOH is the predominant component among fluorotelomers in indoor air, and that there are emission sources of fluorotelomers in indoor environments of the Keihan area. Further investigations into the origins of fluorotelomers are needed to evaluate indoor contamination with fluorotelomers.     

Arsenic in marine sediments from French Mediterranean ports: Geochemical partitioning,bioavailability and ecotoxicology

This work investigates arsenic mobility, bioavailability and toxicity in marine port sediments using chemical sequential extraction and laboratory toxicity tests. Sediment samples were collected from two different Mediterranean ports, one highly polluted with arsenic and other inorganic and organic pollutants (Estaque port (EST)), and the other one, less polluted, with a low arsenic content (Saint Mandrier port (SM)). Arsenic distribution in the solid phase was studied using a sequential extraction procedure specifically developed for appraising arsenic mobility in sediments. Toxicity assessment was performed on sediment elutriates, solid phases and aqueous arsenic species as single substance using the embryo-toxicity test on oyster larvae (Crassostrea gigas) and the Microtox test with Vibrio fischeri. Toxicity results showed that all sediment samples presented acute and sub-chronic toxic effects on oyster larvae and bacteria, respectively. The Microtox solid phase test allow to discriminate As-contaminated samples from the less contaminated ones, suggesting that toxicity of whole sediment samples is related to arsenic content. Toxicity of dissolved arsenic species as single substance showed that Vibrio fischeri and oyster larvae are most sensitive to As(V) than As(III). The distribution coefficient (Kd) of arsenic in sediment samples was estimated using results obtained in chemical sequential extractions. The Kd value is greater in SM (450 L kg^?1) than in EST (55 L kg^?1), indicating that arsenic availability is higher for the most toxic sediment sample (Estaque port). This study demonstrates that arsenic speciation play an important role on arsenic mobility and its bioavailability in marine port sediments.     

Distinguishing the sources of Asian dust based on electron spin resonance signal intensity and crystallinity of quartz

We report a newly developed provenance-tracing method by using a combination of electron spin resonance (ESR) signal intensity of the E₁′ center in quartz and crystallinity index (CI) of quartz, which reflect the formation age and crystallization conditions of quartz in their source rocks, respectively. ESR signal intensity and CI were determined for quartz in fine silt plus clay fraction (<16 μm) of 38 surface samples from nine Gobi and sandy deserts in north China and south Mongolia. Variations in ESR signal intensity and CI are minor within each desert, suggesting that fine-grained quartz in each desert is nearly homogeneous. Differences in ESR signal intensity and CI among the nine Gobi and sandy deserts are significant and, therefore, a combination of these two parameters can be used to effectively differentiate the nine Gobi and sandy deserts in East Asia. Spatial differences in these two parameters suggest that fine silt to clay-sized quartz in these deserts is heterogeneous and derived mainly from the nearby high-altitude mountains in East Asia.     

Determination of sorption properties of intact rock samples: New methods based on electromigration

Two new methods for determining sorption coefficients in large rock samples have been developed. The methods use electromigration as a means to speed up the transport process, allowing for fast equilibration between rock sample and tracer solution. An electrical potential gradient acts as a driving force for transport in addition to the concentration gradient and forces the cations through the rock sample towards the cathode. The electrical potential gradient induces both electromigration and electroosmotic flow with a resulting solute transport that is large compared to diffusive fluxes. In one of the methods, the solute is driven through the sample and collected at the outlet side. In the other, simpler method, the rock sample is equilibrated by circulating the solute through the sample. The equilibration of rock samples, up to 5 cm in length, with an aqueous solution has been accomplished within days to months. Experiments using cesium as a sorbing tracer yield results consistent with considerably more time demanding in-diffusion experiments. These methods give lower distribution coefficients than those obtained using traditional batch experiments with crushed rock.     

Laboratory measurement of the dry deposition of sulfur dioxide onto northern Chinese soil samples

We investigated soil surface resistance R_c to dry deposition of sulfur dioxide (SO₂) onto different types of soils in laboratory experiments, using samples collected from the arid loess plateau and deserts of northern China. We evaluated the factors that affect R_c, which depends on the physical and chemical interaction between a trace constituent and the deposition surface. We observed that the values of R_c for SO₂ decreased with increase of soil weight and increased with SO₂ concentration, although surface coverage had little effect on R_c. The SO₂ uptake rate by all the northern Chinese soil samples seemed to be, on the whole, dependent on relative humidity (RH). In all of the northern Chinese soil samples, R_c was in the range 0.028–0.65 s mm⁻¹, and was exponentially related to the effective surface area of each soil sample, regardless of RH. Wet chemical analysis of sulfur deposited onto the soil samples showed that oxidation ratio of sulfur(IV) to sulfur(VI) was related to RH, which might be related to complex interactions among the amount of water on the soil sample, the pH, and the metallic ions in the liquid phase.     

Interpretation of out-diffusion experiments on crystalline rocks using random walk modeling

Matrix diffusion in saturated rocks with very low permeability is one of the major mechanisms of solute transport. Laboratory out-diffusion experiments on rock samples may provide an estimate of the bulk diffusion coefficient. However, numerous results have shown that this average parameter does not really depict the complex mechanism of diffusion as a function of the internal heterogeneity of crystalline rocks. Two-dimensional images of the porosity distribution in a granite sample were obtained by impregnation with a radioactive resin and autoradiography. Some examples based on these images and synthetic images were used to perform numerical simulations of out-diffusion using two different random walk methods. The simulated shapes of the out-diffusion curves depend on the spatial distribution of the porosity and on the pore connectivity with the border of the sample. Such relations might explain the multiple nested slopes or the convex shapes often observed on real experimental curves.