Pressure permeability

The solid line in Fig. 2 shows the permeability-pressure curve of C02 in polycarbonate calculated by fitting the simplified permeability expression, eq. (14), to experimental data of Wonders and Paul (15). The data fitting procedure, described elsewhere (1 1), gives Do = 1.09 x 10 8 cm2/sec and p = 0.065 cm3(polymer)/cm3(STP). Fig. 2 shows a good agreement between the experimental data and eq. (14) over the entire pressure range. 

Comparing the curves in Fig. 2 shows that representing the permeability versus pressure data by either model provides a satisfactory fit to the data over the pressure range of 1 to 20 atm. However, at pressures less than 1 atm. the two models differ in their prediction regarding the behavior of the permeability-pressure curve [Fig. 2]. While the matrix model predicts a strong apparent pressure dependence of the permeability in this range (solid line), the dual-mode model predicts only a weak dependence (broken line). 

Solvent modifiers and additives can be used to adjust the retention and selectivity of separation in packed-column SFC. Similar effects have been reported with open-tubular capillary SFC. The advantage of capillary column over packed column arises from the differences in permeability. Pressure ramps are much easier to use in capillary columns to modify the solvent strength (via density modification) as compared to packed columns. Therefore it should be entirely feasible, with capillary SFC, to combine the benefit of solvent density (pressure) programming with simultaneous modification of the solvent strength. ... 

Change in permeability Pressure records Pumping tests Change in strength Penetration test Previous data needed... 

The following derivations and calculations avoid any specific assumptions about units. Instead, the quantities have been described as having consistent units. The degree of separation and recovery, moreover, is independent of the units. If, however, numerical values for permeability, pressure, and flow rate are used, then specific units are required, which in turn determine membrane area, given the membrane thickness, or the overall membrane permeability. 

One of the main goals of the GDL is the transport of gaseous species. From an experimental point of view the determination of the gas permeability (pressure-driven flow) is easier than the determination of the diffusion (driving force concentration difference) of gases. This might be the reason that, in the literature, values for the permeability for GDL material can be found much more often than diffusion coefficients or structural parameters of the materials necessary for the determination of the effective diffusion coefficient. Especially when looking in the specification for GDLs provided by manufacturers, one will find values for gas permeation but no data relevant for gas diffusion. 

Though Washburn model [63] is most commonly applied to describe liquid infiltration into textiles, it has got some limitations such as the model cannot be used to model source driven flows without modification and it cannot be applied to describe spreading in two- or three-dimensions. The other equation which is commonly used to model liquid transport in porous material is Richard s equation [64]. Richard s equation is a semi-empirical formulation based on Darcy s law, where the rate of volmnetric liquid flow is proportional to the driving pressure. An essential character of the models based on Richard s equation is that they contain the functional relation between permeability, pressure and moisture. 

An important safety feature on every modern rig is the blowout preventer (BOP). As discussed earlier on, one of the purposes of the drilling mud is to provide a hydrostatic head of fluid to counterbalance the pore pressure of fluids in permeable formations. However, for a variety of reasons (see section 3.6 Drilling Problems ) the well may kick , i.e. formation fluids may enter the wellbore, upsetting the balance of the system, pushing mud out of the hole, and exposing the upper part of the hole and equipment to the higher pressures of the deep subsurface. If left uncontrolled, this can lead to a blowout, a situation where formation fluids flow to the surface in an uncontrolled manner. 

In some cases when drilling fluids invade a very low permeability zone, pressure equalisation in the formation can take a considerable time. The pressure recorded by the tool will then be close to the pressure of the mud and much higher than the true formation pressure. This is known as supercharging. Supercharging pressures indicate tight formation, but are not useful in establishing the true fluid pressure gradient. 

For direct measurement from core samples, the samples are mounted in a holder and gas is flowed through the core. The pressure drop across the core and the flowrate are measured. Providing the gas viscosity (ji) and sample dimensions are known the permeability can be calculated using the Darcy equation shown below. 

Natural water drive occurs when the underlying aquifer is both large (typically greater than ten times the oil volume) and the water is able to flow Into the oil column, i.e. it has a communication path and sufficient permeability. If these conditions are satisfied, then once production from the oil column creates a pressure drop the aquifer responds by expanding, and water moves into the oil column to replace the voidage created by production. Since the water compressibility is low, the volume of water must be large to make this process effective, hence the need for the large connected aquifer. 

The prediction of the size and permeability of the aquifer is usually difficult, since there is typically little data collected in the water column exploration and appraisal wells are usually targeted at locating oil. Hence the prediction of aquifer response often remains a major uncertainty during reservoir development planning. In order to see the reaction of an aquifer, it is necessary to produce from the oil column, and measure the response in terms of reservoir pressure and fluid contact movement use is made of the material balance technique to determine the contribution to pressure support made by the aquifer. Typically 5% of the STOMP must be produced to measure the response this may take a number of years. 

For a single fluid flowing through a section of reservoir rock, Darcy showed that the superficial velocity of the fluid (u) is proportional to the pressure drop applied (the hydrodynamic pressure gradient), and inversely proportional to the viscosity of the fluid. The constant of proportionality is called the absolute permeability which is a rock property, and is dependent upon the pore size distribution. The superficial velocity is the average flowrate... 

The field unit for permeability is the Darcy (D) or millidarcy (mD). For clastic oil reservoirs, a good permeability would be greater than 0.1 D (100 mD), while a poor permeability would be less than 0.01 D (10 mD). For practical purposes, the millidarcy is commonly used (1 mD = 10" m ). For gas reservoirs 1 mD would be a reasonable permeability because the viscosity of gas is much lower than that of oil, this permeability would yield an acceptable flowrate for the same pressure gradient. Typical fluid velocities in the reservoir are less than one metre per day. 

In the simplest case, for a pressure drawdown survey, the radial inflow equation indicates that the bottom hole flowing pressure is proportional to the logarithm of time. From the straight line plot ot pressure against the log (time), the reservoir permeability can be determined, and subsequently the total skin of the well. For a build-up survey, a similar plot (the so-called Horner plot) may be used to determine the same parameters, whose values act as an independent quality check on those derived from the drawdown survey. 

From downhole pressure drawdown and build-up surveys the reservoir permeability, the well productivity index and completion skin can be measured. Any deviation from previous measurements or from the theoretically calculated values should be investigated to determine whether the cause should be treated. 

Consider two distinct closed thermodynamic systems each consisting of n moles of a specific substance in a volnme Vand at a pressure p. These two distinct systems are separated by an idealized wall that may be either adiabatic (lieat-impemieable) or diathermic (lieat-condncting). Flowever, becanse the concept of heat has not yet been introdnced, the definitions of adiabatic and diathemiic need to be considered carefiilly. Both kinds of walls are impemieable to matter a permeable wall will be introdnced later. 

From what has been said, it is clear that both physical and mathematical aspects of the limiting processes require more careful examination, and we will scare this by examining the relative values of the various diffusion coefficients and the permeability, paying particular attention to their depec dence on pore diamater and pressure. 

There is a further simplification which is often justifiable, but not by consideration of the flux equations above. The nature of many problems is such that, when the permeability becomes large, pressure gradients become very small ialuci uidiii iiux.es oecoming very large. in catalyst pellets, tor example, reaction rates limit Che attainable values of the fluxes, and it then follows from equation (5,19) that grad p - 0 as . But then the... 

Let us first consider experiments without composition gradients. These are permeability measurements, in which flow is induced by a pressure gradient Consider first the flow of pure substance 1, setting x = 1, = 0 and... 

The conditloci to be satisfied by the pressure difference, if (10,18) is to be a good approximation, is not so demanding as that needed to ensure that (10.14) is a good approximation, and it does not depend on the permeability of the medium. Thus (10.18), applied at sufficiently high pressure, should provide a method of determining which is more robust than (10.14)... 

At the opposite limit of bulk diffusion control and high permeability, all flux models are required to he consistent with the Stefan-Maxwell relations (8.3). Since only (n-1) of these are independent, they are insufficient to determine all the flux vectors, and they permit the problem to be formulated in closed form only when they can be supplemented by the stoichiometric relations (11.3). At this limit, therefore, attention must be restricted from the beginning to those simple pellet shapes for ich equations (11.3) have been justified. Furthermore, since the permeability tends to infininty, pressure gradients within the pellet tend to zero and... 

It is seen that the pressure variation tends to zero when - , so In coarsely porous pellets with high permeability the pressure change Induced by reaction may be very small compared t/ith the absolute pressure. In this sense, then, the pellet approaches an isobaric system at high values of the permeability. 

Hite s treatment is based on equations (5.18) and (5.19) which describe the dusty gas model at the limit of bulk diffusion control and high permeability. Since temperature Is assumed constant, partial pressures are proportional to concentrations, and it is convenient to replace p by cRT, when the flux equations become... 

These should be con describe the same reaction, s but at the limit of fine Physically the interesting f appearance of the pressure p ablej with the consequence describe the system at the at the limit of fine pores, true that the pressure wit ni sense that percentage variat of the pressure variations i permeability, so convective permeability and pressure gr the origin of the two terms... 

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