Mercury porosimetry volume distribution from

Fig. 3J1 Comparison of pore volume size distributions for Clear Creek sandstone" (courtesy Dullien.) Curve (A), from mercury porosimetry curve (B), from photomicrography (sphere model).

With these facts in mind, it seems reasonable to calculate the pore volume from the calibration curve that is accessible for a certain molar mass interval of the calibration polymer. A diagram of these differences in elution volume for constant M or AM intervals looks like a pore size distribution, but it is not [see the excellent review of Hagel et al. (5)]. Absolute measurements of pore volume (e.g., by mercury porosimetry) show that there is a difference on principle. Contrary to the absolute pore size distribution, the distribution calcu-... 

Rieckmann and Keil (1997) introduced a model of a 3D network of interconnected cylindrical pores with predefined distribution of pore radii and connectivity and with a volume fraction of pores equal to the porosity. The pore size distribution can be estimated from experimental characteristics obtained, e.g., from nitrogen sorption or mercury porosimetry measurements. Local heterogeneities, e.g., spatial variation in the mean pore size, or the non-uniform distribution of catalytic active centers may be taken into account in pore-network models. In each individual pore of a cylindrical or general shape, the spatially ID reaction-transport model is formulated, and the continuity equations are formulated at the nodes (i.e., connections of cylindrical capillaries) of the pore space. The transport in each individual pore is governed by the Max-well-Stefan multicomponent diffusion and convection model. Any common type of reaction kinetics taking place at the pore wall can be implemented. 

Cylindrical pellets of four industrial and laboratory prepared catalysts with mono- and bidisperse pore structure were tested. Selected pellets have different pore-size distribution with most frequent pore radii (rmax) in the range 8 - 2500 nm. Their textural properties were determined by mercury porosimetry and helium pycnometry (AutoPore III, AccuPyc 1330, Micromeritics, USA). Description, textural properties of catalysts pellets, diameters of (equivalent) spheres, 2R, (with the same volume to geometric surface ratio) and column void fractions, a, (calculated from the column volume and volume of packed pellets) are summarized in Table 1. Cylindrical brass pellets with the same height and diameter as porous catalysts were used as nonporous packing. 

The pore size distribution (see Fig. 3) can be obtained from the mercury porosimetry data and the t-plot from N2 adsorption isotherms, using an active carbon with a very low surface area as a reference [13]. It was observed that the volumes of mercury intruded were very small. As a consequence, the volumes of meso (the largest ones) and macropores are low. Thus, the samples studied are mainly microporous, as already mentioned in the N2 and CO2 adsorption isotherm results. 

A) Pressure-controlled mercury porosimetry procedure. It consists of recording the injected mercury volume in the sample each time the pressure increases in order to obtain a quasi steady-state of the mercury level as P,+i-Pi >dP>0 where Pj+i, Pi are two successive experimental capillary pressure in the curve of pressure P versus volume V and dP is the pressure threshold being strictly positive. According to this protocol it is possible to calculate several petrophysical parameters of porous medium such as total porosity, distribution of pore-throat size, specific surface area and its distribution. Several authors estimate the permeability from mercury injection capillary pressure data. Thompson applied percolation theory to calculate permeability from mercury-injection data. 

This experiment confirms the good identification of successive mechanisms responsible for the volume variation. It confirms also that equation (2) proposed to interpret a mercury porosimetry curve when the sample collapses leads to a pore size distribution identical to which obtained from Washburn equation when mercury intrudes the pores. 

Another technique for measurement of pore-size distributions is mercury poro-simetry [9]. Because mercury does not wet the surface of oxides (the contact angle varies from 135 to 143 °), pressure is required to force mercury into the pores. The pressure at which mercury is taken up indicates the diameter of the pores, and the volume of mercury intruding gives the volume of the pores. Modem equipment enables the use of very high pressures, and thus measurement of pore diameters of ca 4 nm. It can therefore be concluded that mercury porosimetry and nitrogen adsorption can both be used to measure pores down to a diameter of about 4 nm mercury porosimetry can, however, be used to determine pore of diameters as large as 200 pm. Modern equipment employs computer programs that enable ready calculation of the pore-size distribution from experimental data. 

From such measurements, surface areas (normalized cumulative and relative), pore radii (choice of three measuring units), pore volumes (raw, normalized, cumulative and relative) and pore-size distribution functions of samples can calculated. Figure 8 presents the graphs of mercury-penetrated volume versus pressure in pores of Na- and La-montmorillonite samples. Figure 9 shows pore-size distribution functions from porosimetry data. 

Figure 21 presents the graphs of mercury-penetrated volume versus pressure in the pores of Na- and La-montmorimllonitamples. Figure 22 shows the pore-size distribution functions calculated from the porosimetry data. 

When using mercury porosimetry, a sample holder is first partially filled with the powder to be tested, which is then evacuated and finally filled with mercury. The volume of mercury intruded into the powder sample, V , is measured as a function of the applied presstrre p. If the pores are assumed to be cylindrical, the value Vi i at any applied pressure p leads to the cumrrlative volume of all pores that have a radius equal to or greater than rj. This corresponds to that in gas adsorption where the cumulative pore volmne is the volume of the pores with a radius to be less than or equal to rj. Therefore, the cumulative pore volume decreases with increasing r, in mercury porosimetry, where it increases with increasing r, in gas adsorption. In both cases, the pore size distribution v(r) is obtained by differentiating the cumulative pore volume curve with respect to r. The pore size distribution can also be obtained directly from the data of versus p by using the following relation ... 

The permeability of the core is 3.10 ym determined by mercury porosimetry. This value is relatively low but not too rare. From the pore size distribution, 80% of the pore volume consists of pores having a diameter greater than 10 A, while 80% of the surface area (7 10 cm g ) is made up of pores having a diameter... 

The observations from the LMPA intruded alumina support samples have clearly indicated the need for consideration of the manufacturing techniques used in the production of catalyst supports and other porous media. The potential for the derivation of an inadequate pore size distribution using solely mercury porosimetry is identified. Without other additional complementary techniques, the pore area and volume distributions will readily be miscalculated. 

Figure 10.15. Pore size distributions (obtained by nonintrusive mercury porosimetry) of polyurethane aerogels coming from supercritical CO2 drying of gels synthesized with pentaerythritol in different solutions of DMSO and etoc volume fraction of DMSO <0.3 (top) and >0.3 (bottom) mercury porosimetry conducted by R. Pirard, LGC, Univervity of Liege, Belgium) [39].

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