Critical pore pressure

Figure 7 Orientation of multiplet structure and pre-existing joints. Orientation of multiplet structure and critical pore pressure calculated from stress data (left), and orientation of natural joints before the stimulation detected by FMI in GPK-1 (right).

ESTIMATION OF CRITICAL PORE PRESSURE FOR SHEAR SLIP OF FRACTURES AT THE SOULTZ HOT DRY ROCK GEOTHERMAL RESERVOIR USING MICROSEISMIC MULTIPLETS... 

CALCULATION OF CRITICAL PORE-PRESSURE FOR SHEAR SLIP OF FRACTURE... 

We estimate distribution of critical pore-pressure of fractures for shear slip during hydraulic stimulation. 

We introduce the fracture planes derived from the source locations of multiplets. The procedures for calculation of the critical pore-pressure are described as follows. 

The estimated critical pore-pressure for shear slip suggests that the fluid pressure in fractures is higher value near the fractured zones 1 and 2 around 2,900 m, and declines as the fractures are away from the zones. 

Figure 5. Calculated critical pore-pressure for shear slip of fractures versus depth of estimated fractures. The zone of permeable fracture, which are detected by well loggings are indicated by shaded rectangles.

It is considered that some fractures opened with increasing pore-pressure maybe after shear slip because the maximum wellhead pressure is about lOMPa. However, Mode I fractures can not radiate seismic events having enough energy, and we can not detect these seismic events. Therefore, we consider only shearing fractures for estimation of critical pore-pressure using induced microseismic events. 

The result in Figure 5 implies that the fluid pressure was transmitted into fractures, and that the pore-pressure around zones 1 and 2 increased up to near maximum fluid pressure in fracturing well. It is reported that the fractures in zones 1 and 2 are permeable under low flow rate (Evans, 2000). Then, the distribution of critical pore-pressure in Figure 5 is reasonable. 

On the other hand, the Pc becomes below zero around 3,200m. The same result can also obtained when the critical pore-pressure is calculated using the orientation of fractures... 

For Ca < 0.1 in Figure 7 the critical capillary pressure is also independent of the initial film thickness. In this case, the hydrodynamic resistance to fluid filling or draining is small enough that the film reaches the periodic steady state in less than half a pore length. Figure 7 confirms the trend observed by Khatib, Hirasaki and Falls that P falls with increasing flow rate (5). c... 

Figure 9 reports the effect of the pore-body to pore-throat radius ratio, R /R, on the critical capillary pressure for... 

For transporting foam, the critical capillary pressure is reduced as lamellae thin under the influence of both capillary suction and stretching by the pore walls. For a given gas superficial velocity, foam cannot exist if the capillary pressure and the pore-body to pore-throat radii ratio exceed a critical value. The dynamic foam stability theory introduced here proves to be in good agreement with direct measurements of the critical capillary pressure in high permeability sandpacks. 

As discussed in Section 1.4.2.1, the critical condensation pressure in mesopores as a function of pore radius is described by the Kelvin equation. Capillary condensation always follows after multilayer adsorption, and is therefore responsible for the second upwards trend in the S-shaped Type II or IV isotherms (Fig. 1.14). If it can be completed, i.e. all pores are filled below a relative pressure of 1, the isotherm reaches a plateau as in Type IV (mesoporous polymer support). Incomplete filling occurs with macroporous materials containing even larger pores, resulting in a Type II isotherm (macroporous polymer support), usually accompanied by a H3 hysteresis loop. Thus, the upper limit of pore size where capillary condensation can occur is determined by the vapor pressure of the adsorptive. Above this pressure, complete bulk condensation would occur. Pores greater than about 50-100 nm in diameter (macropores) cannot be measured by nitrogen adsorption. 

The adsorption in mesopores is characterized by two sequential processes (i) monolayer formation on the pore surface and (ii) filling of the remaining pore space when a critical filling pressure is reached. The first process can be modeled, for example, with the BET equation, and the second one with the Kelvin and related equations. 

Fig. 14.6. Filtration flux as a function of time of filtration for the filtration of O.Oi g/L silica particles in 0.001 M NaCI solution at pH 6 at a membrane of mean pore diameter 84 nm. The particle size was very close to the pore size. The critical transmembrane pressure for these conditions was calculated as 130 kPa. Operation below this pressure gives only a gradual decline in filtration flux with time. Operation above this pressure gives an initially higher filtration flux which declines rapidly with time. In the latter case the intial hydrodynamic force exceeds the electrical double layer repulsion between the membrane and the particles, causing the particles to block the membrane pores.

If a dry microporous hydrophobic hollow fiber membrane with air-filled pores was surrounded by water there would not be any penetration by water into the pores until the water pressure exceeds a certain critical breakthrough pressure. The magnitude... 

For a hydrophobic porous material with contact angle greater than 90°, the APc is >0 and depends on the liquid surface tension and the membrane pore size. As an example, considering water-air-polypropylene system, one can calculate that for a dry membrane with a pore size of 0.03 pim (30 nm) the critical entry pressure of water is more than 300 psi (>20 bar). 

The same principle of operation as described above is applicable also to liquid-liquid extraction where an aqueous liquid and an organic liquid contact each other inside the contactor for extraction of a solute selectively from one phase to another [6-8]. The critical breakthrough pressure for liquid-liquid system could be calculated by Equation 2.1, except that the term A would now be the interfacial tension between the two liquids. Further variation of membrane contacting technology is called gas membrane or gas-gap membrane where two different liquid phases flow on either side of the membrane, but the membrane pores remain gas filled [9-10]. In this situation two separate gas-hquid contact interfaces are supported on each side of a single membrane. 

A novel approach is reported for the accurate evaluation of pore size distributions for mesoporous and microporous silicas from nitrogen adsorption data. The model used is a hybrid combination of statistical mechanical calculations and experimental observations for macroporous silicas and for MCM-41 ordered mesoporous silicas, which are regarded as the best model mesoporous solids currently available. Thus, an accurate reference isotherm has been developed from extensive experimental observations and surface heterogeneity analysis by density functional theory the critical pore filling pressures have been determined as a function of the pore size from adsorption isotherms on MCM-41 materials well characterized by independent X-ray techniques and finally, the important variation of the pore fluid density with pressure and pore size has been accounted for by density functional theory calculations. The pore size distribution for an unknown sample is extracted from its experimental nitrogen isotherm by inversion of the integral equation of adsorption using the hybrid models as the kernel matrix. The approach reported in the current study opens new opportunities in characterization of mesoporous and microporous-mesoporous materials. 

It is well established that the pore space of a mesoporous solid fills with condensed adsorbate at pressures somewhat below the prevailing saturated vapor pressure of the adsorptive. When combined with a eorrelating function that relates pore size with a critical condensation pressure, this knowledge can be used to characterize the mesopore size distribution of an adsorbent from its adsorption isotherm. The correlating function most commonly used is the Kelvin equation [1], Refinements make allowance for the reduction of the physical pore size by the thickness of the adsorbed film existing at the critical condensation pressure [1-2]. Still further refinements adjust the film thickness for the curvature of the pore wall [3]. 

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