Permeability units

Permeability may be expressed in different units, usually depending on whether liquids or gases are involved in the permeation, and may be on a pointwise or overall basis. 

On an overall basis, we are speaking of a mass, molar, or volumetric flux—that is, the mass, molar, or volumetric flow rate per unit surface area of the membrane normal to flow, per unit pressure difference, for the entirety of the membrane thickness. 

Pressure difference may be in pounds per square inch, atmospheres, bars, pascals, centimeters of mercury, inches of water, or whatever chosen. (It may be noted that pressure is ordinarily expressed in mass-distance units, as mass per unit area, rather than as stress in force-distance units, as force per unit area, with the pascal being an example of the latter.) For convenience, a few conversion factors are supplied in Table 19.8. 

Note If a pointwise permeability value P Is measured in the units of say 10 cm /cm -sec-cm Hg/cm, then multiplying this value of Pi by 76cm Hg/atm will yield the new value of Pi in 10 cm /cm -sec-atm/cm. The new value will be higher since the pressure difference Is now measured in the lower value of atm instead of the highervalue of cm Hg. 

The symbol commonly used for membrane permeability is simply P or P, denoting the permeability of (or to) a component i. The particular units of Pj are best defined merely by its usage, and may pertain either to the pointwise value or the overall value. Moreover, this use of the symbol P is to be distinguished from the usage for the fluid flowing pressure P, which may be further distinguished by Pl for the high-pressure side or reject side of the membrane, and Py for the low-pressure or permeate side, as utilized in Hoffman (2003) and in Section 19.10 of this chapter. 

---

Table 1. Permeability Units with Conversion Factors...

This equation defines the permeability (K) and is known as Darcy s law. The most common unit for the permeability is the darcy, which is defined as the flow rate in cm3/s that results when a pressure drop of 1 atm is applied to a porous medium that is 1 cm2 in cross-sectional area and 1 cm long, for a fluid with viscosity of 1 cP. It should be evident that the dimensions of the darcy are L2, and the conversion factors are (approximately) 10 x cm2/darcy C5 10-11 ft2/darcy. The flow properties of tight, crude oil bearing, rock formations are often described in permeability units of millidarcies. 

Above the water table, groundwater can also occur in perched aquifer conditions. In these instances, groundwater occurs in relatively permeable soil that is suspended over a relatively low permeability layer of limited lateral extent and thickness at some elevation above the water table. Perched groundwater occurrences are common within the vadose zone high-permeability zones overlie low-permeability zones of limited lateral extent in unconsolidated deposits. However, perched conditions can also occur within low-permeability units overlying zones of higher permeability in both unconsolidated and consolidated deposits. In the latter case, for example, a siltstone or clay stone overlies jointed and fractured bedrock such that groundwater presence reflects the inability of the water to drain at a rate that exceeds replenishment from above. 

Table 2.15 Permeability of Various Gases Through Several Polymer Films. Permeability units are in cm3-mil/100in2/24h/atm...

There are several major problems with the described approach. First, the geological maps are prepared by stratigraphic units, and the lithology has to be inferred. In any case, stratigraphic units include, in most cases, alternations of various rock types, often with a wide range of permeabilities. It is almost impossible to translate a geological map into permeability units. 

This paper has highlighted that a number of components, important to fault seal analysis, are often either not included or not quantified in sufficient detail to allow a low risk seal evaluation. The main components which are not always considered in detail are (i) the errors in throw patterns which arise from seismic resolution and fault damage zone structures (ii) the assumption that juxtaposition of reservoir against low permeability units and shale smear are the only sealing mechanisms and (iii) that fault seal data from anywhere is directly applicable to any other sealing problem, i.e., that the geohistory is not critical... 

Perched aquifer A locally saturated zone or lense in the unsaturated zone that may overlay a low-permeability unit. 

In each unit, hydraulic-conductivity values typically vary over a broad range. Some of the highest values are obtained for the Mannville Group, and the Rierdon and Sawtooth formations of the Ellis Group, In this area, these more permeable units are found relatively deep in the stratigraphic sequence. Unfortunately, no data are available for the intervening shale units. However, by analogy with conductivity values reported elsewhere for shale and clay sediments (C.D.W.R., 1971), they should be lower than 5 10 cm/s. 

Calcite cementation in the Zia Formation has greatly reduced potential reservoir/aquifer quality. Most permeable units are extensively cemented with phreatic calcite. Many tabular units are often laterally extensive, forming significant barriers to vertical fluid flow and conceivably resulting in compartmentalization of the reservoir/aquifer. 

Researchers in membrane technology have adopted the special permeability unit called the Barrer ... 

The dimensions of permeability become clear after rearranging equation 1 to solve for P. The permeability must have dimensions of quantity of permeant (either mass or molar) times thickness in the numerator with area times a time interval times pressure in the denominator. Table 1 contains conversion factors for several common unit sets with the permeant quantity in molar units. The unit nmol/(m-s-GPa) is used herein for the permeability of small molecules because this unit is SI, which is preferred in current technical encyclopedias, and it is only a factor of 2, different from the commercial permeability unit, (cc(STP)mil)/(100 in. 2datm). The molar character is useful for oxygen permeation, which could ultimately involve a chemical reaction, or carbon dioxide permeation, which is often related to the pressure in a beverage botde. 

For permeation of flavor, aroma, and solvent molecules another metric combination of units is more useful, namely, (kg-m)/(m2sPa). In this unit the permeant quantity has mass units. This is consistent with the common practice of describing these materials. Permeability values in these units often carry a cumbersome exponent hence, a modified unit, an MZU (10 20 kg-m)/(m2 sPa), is used herein. The conversion from this permeability unit to the preferred unit for small molecules depends on the molecular weight of the permeant. Equation 4 expresses the relationship where MW is the molecular... 

Figure I. Vertical section of the modelled domain. Grey layers labelled by numbers are aquifers, white layers labelled by letters are semi-permeable units.

Other tables including data on permeability of nitrogen, oxygen, and carbon dioxide, and conversion figures for the various permeability units, appear in an article by Lebovits. "... 

Piezometers are installed in the ground in order to monitor and obtain measurements of pore water pressures (Fig. 4.8). Observations should be made regularly so that changes due to external factors such as excessive precipitation, tides, the seasons, etc., are noted, it being important to record the maximum pressures that have occurred. Standpipe piezometers allow the determination of the position of the water table and the permeability. For example, the water level can be measured with an electric dipmeter. Piezometer tips that have leads going to a constant head permeability unit, enable the rate of flow through the tip to... 

The results of the relative permeability tests performed on the sample which had been treated with 2.5% Dri-Film solution are shown in Figures 6 and 7. In this case the first flow of the nonwetting phase (brine) in the drainage test was measured at a saturation of 11% pore volume, the wetting phase (oil) relative permeability was 0.004 at 54% pore volume wetting phase saturation, and the residual brine (connate water) saturation was 13.5% pore volume. The water curve extended to a value of 0.37 relative permeability units, compared with the highest point on the oil curve (in the imbibition test) of 0.185 relative permeability units. 

---