Pore Pressure Equalization

After pile installation an excess pore pressure exists around the pile. In soft clay the excess pore pressure adjacent to the pile surface is positive. By contrast, in stiff clay the excess pore pressure is negative. At a distance from the pile surface the pressure is positive and equals the increase in total stress. 

The excess pore pressure dissipation results in changes in the effective normal stress acting on the pile surface. This in turn results in changes in shaft resistance. This is known as pile setup. How fast the pore water pressure dissipation occurs is dependent on the soils permeability. In a clay the dissipation of excess pore water pressure may take months to occur. In silty clays, the dissipation may take only minutes. 

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The is the pore gas pressure i> is the average thickness is the porosity a is the maximum gas adsorption coefficient b is the gas adsorption coefficient D is the gas diffusion coefficient e is the deformation rate d is the average coal micro-grain size the / equals one atmosphere and the D is the gas diffusion coefficient when the pore pressure equals P . ... 

If all the pores are equally accessible, only those for which r is greater than y cos 6 p will be filled, i.e. each pressure increment causes a group of smaller pores to be filled and a cumulative pore volume as a function of pore size can be determined, as illustrated in Figure 5.9. 

The cyclic steps of one of the PSA processes using the molecular sieve carbon as the adsorbent consist of (a) flowing compressed air through a packed bed of the carbon so that O2 can diffuse and adsorb into the carbon pores faster than N2 and At and produce a N2 rich product gas at feed air pressure (Pa), (b) pressure equalizing the adsorber with a companion adsorber, (c) counter-currently depressuring the adsorber to near ambient pressure to produce the O2 enriched gas, (d) pressure equalizing with another adsorber, and finally (e) repressurizing the adsorber to Pa with feed air [4]. 

The saturated zone is formed by porous material in which all the pore spaces are filled with water. The water table is defined as the depth at which pore water pressure equals atmospheric pressure. If a hole is dug down to the saturated zone, the location of the water table can be easily determined it is at the depth to which water accumulates in the hole. In coarse porous material, the location of the water table itself very nearly approximates the transition between saturated and unsaturated material in a fine-textured porous material, enough water may move upward by capillarity to cause complete saturation of a measurable thickness above the water table (the capillary fringe). 

The pore-pressure profiles further show that pressure equalization has been reached between the Jurassic reservoirs and the lowermost Cretaceous-Upper Jurassic caprock of the Njord structure as there is no drop in pressure when entering into the Jurassic reservoir units (as seen in many other fields on Halten-banken Koch and Heum, 1995). 

Fig. 13. Pore-pressure for the lie- and Tilje formations extrapolated to the apexes of the defined hydraulic compartments. The red trend-line passing through the aquifer pore-pressure points at the apexes of hydraulic compartment II and III represents the maximum reservoir pore-pressure trend-line. At points along this line pressure equalization is reached between the reservoir units and the counter-pressure of the overlying cap rock.

Fig. 14. Relationships between pore-pressures, the hydrostatic gradient, the fracture pressure gradient (approximation to the minimal horizontal stress, Sf,) and the lithostatic pressure gradient (approximation to the vertical stress, S ). Pore-pressures from sea floor to base Pliocene equals hydrostatic. The yellow, dark blue and red pore-pressure trend-lines represent the pore-pressure versus depth gradients for the Paleocene-Eocene, Mid-late Cretaceous and Upper Jurassic-lowermost Cretaceous, respectively. The portion of the red trend-line below approximately 2550 m MSL equals the maximum reservoir pore-pressure trend-line of Fig. 13 and reflects the counter-pressure of the topseal controlling the pore-pressure distribution of hydraulic compartments II, III and (probably) IV.

These differences in Aphc-water illustrate to what extent the hydrocarbon phase pressure at the weak point/apex of each reservoir reaches above the maximum reservoir pore-pressure trend-line, along which, according to the discussion above, pressure equalization (for the wetting phase) has been reached between the reservoir and cap rock. 

Eor meso- and macro-pore materials, the Laplace [24] equation has also been applied for the determination of pore size distribution with the assumption that the pores are cylindrical, resulting in the equality of the two radii of curvature in the Laplace equation. In practice, the penetration of a non-wetting liquid such as mercury into the pores at a specific pressure is related to the pore radius through the following equation, with the assumption that all pores are equally accessible... 

Careful control of the relative vapour pressure permits the stepwise blocking of pores. Starting from a relative pressure equal to 1, all the pores of the... 

If the advancing contact angle is lower than 90°, wetting is spontaneous inside the pores at a pressure equal or lower than the saturating pressure. Its measurement can be done by capillary rise. Nevertheless, this will only characterize the wettability of the external surface of the particles and not that of the internal surface of the pores. This is why, here again, calorimetric approaches were proposed to get an estimated value of the wettability in the case of powden. For example, Briant and Cuiec [30], showed that for a number of solid-Hquid systems the following approximation holds ... 

The action of capillary pressure underlies the mercury porosimetry method, which is commonly used for the determination of pore size distribution in ceramics, adsorbents, catalysts and other porous materials [15]. Mercury is known to wet non-metallic surfaces poorly, and thus the capillary pressure, equal to 2o/r (where r is the pore radius, or the average radius of pores having complex shape), prevents its spontaneous penetration into the pores. The pore size distribution can be established by measuring the volume... 

Sharma and Yortsos make use of the effective medium theory (83) to evaluate the network flow distribution. The effective medium theory is based on the premise that the pressure difference across a particular pore is equal to the mean pressure difference across the porous medium plus a local fluctuation in pressure. 

We present now the extension of the constitutive equation (7) to partially saturated porous media. The material is assumed to be saturated by a liquid phase (noted by index w) and a gas mixture (noted by index g ). The gas mixture is a perfect mixture of dry air (noted by index da) and vapour (noted by index va). Based on most experimental data of unsaturated rocks and soils (Fredlund and Rahardjo 1993), and on the theoretical background of micromechanical analysis (Chateau and Dormieux 1998), the poroelastic behaviour of unsaturated material should be non-linear and depends on the water saturation degree. We consider here the particular case of spherical pores which are dried or wetted under a capillary pressure equal to the superficial tension on the air-solid interface. By adapting the macroscopic non-linear poroelastic model proposed by Coussy al. (1998) to unsaturated damaged porous media, the incremental constitutive equations in isothermal conditions are expressed as follows ... 

It is of some interest to indicate the rather large pressure changes in pores that reaction can cause. Either eq. (48) or (49) indicate that for gas reactions the total pressure difference between the pore mouth and the interior of a pore (center of a catalyst pellet) is at least of the order of the partial pressure change of A. Thus in fast dehydrogenation reactions at atmospheric pressure, the interior of a pellet may be at several atmospheres pressure. For reactions on small pores in which Knudsen flow is occurring this calculation can be carried out with absolute accuracy. The result is that for the reaction A qB, the pressure increase in the pore is equal to (Ma/Mb) — 1) times the partial pressure drop in A, where Ma and Mb are the molecular weights of A and B. 

Permeability curves measured using He, N2 CH4 and CO2 are shown in the following Figs. 3-6. All the above four permeability was tested under the same temperature of 35°C but different effective stresses. Effective stress here equals confining press minus pore pressure. 

When T becomes equal to fN, gross sliding of the particle contacts occurs. This gross sliding is required for permanent particles reorientation as shown in Figure 9.5. This reorientation of particles results in either volume changes (drained conditions) or excess pore pressures (undrained conditions). If particle reorientation does not occur then neither volume change nor excess pore pressure will occur. 

The applied force to overcome the resistance from the surface tension equals the pressure acting over the surface area of the pore. At equilibrium, just before the mercury enters the pore, the force due to pressure equals that arising from surface tension ... 

The DCMD flux will increase with an increase in the membrane pore size and porosity and with a decrease in the membrane thickness and pore tortuosity. In other words, to obtain a high DCMD permeability, the surface layer that governs the man-brane transport must be as thin as possible and its surface porosity as well as its pore size must be as large as possible. However, it must be mentioned here that there exists a critical pore size equal to the mean free path of the water vapor molecules for the given experimental DCMD conditions. In the DCMD process, air is always trapped within the membrane pores with pressure values close to the atmospheric pressure. Therefore, if the pore size is comparable to the mean free path of the water vapor molecules, the molecules of the water vapor collide with one another and diffuse among the air molecules. In this case, the vapor transport takes place via the combined Knudsen/molecular diffusion flow. On the other hand, if the pore size is smaller than the mean free path of the water vapor molecules, the molecule-pore wall collisions become dominant and the Knudsen type of flow will be responsible for the mass transport in DCMD. It should be noted that for the given experimental conditions, the calculated DCMD flux based on the Knudsen mechanism is higher than that based on the combined Knudsen/molecular diffusion mechanism. 

The efficiency of a soil in supporting a structure is influenced by the effective or intergranular pressure, that is, the pressure between the particles of the soil that develops resistance to applied load. Because the moisture in the pores offers no resistance to shear, it is neutral and therefore pore water pressure also has been referred to as neutral pressure. Since the pore water or neutral pressure plus the effective pressure equals the total pressure, reduction in pore water pressure increases the effective pressure. Reduction of the pore water pressure by drainage consequently affords better conditions for carrying a proposed structure. 

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