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<br /> -5 22 AIR-TO-WATER PERMEABILITY RATIO 41-2 PRINCIPLES
<br /> —(k'1,7xdp/ds). [7a] the hydraulic head, or for air, the pressure differential across the sample,
<br /> At steady state and for isothermal flow, the mass flow velocity (v, multi- 0, and the rate of flow of fluid through it. For the steady-state case, this in-
<br /> volves a measure of both the inlet and outlet pressures, and the volume flux;
<br /> pIied by the density p) is constant. From this and the ideal gas law,
<br /> p = pR?', R being the gas constant and T the constant Kelvin temperature, for the non-steady-state method of Kirkham mentioned above this involves
<br /> the permeability equation for gases becomes a measure of pressure change with time. The air-to-water permeability ratio
<br /> is easily obtained from properly determined values for air and water per-
<br /> pv, = const = —(k'/n)p(dp/ds). [81 meability by simply expressing the values as a ratio, k'a/k',,.
<br /> Equation [8] can be integrated for any number of special cases, depend- Either fragmented samples or soil cores may be used; however, with soil
<br /> ing upon the flow geometry and the boundary conditions. Integration of cores there are several problems that are not involved when fragmented
<br /> this equation for a cylindrical tube of length L, with ends at pressures p, samples are used. For example, the higher water content required for se-
<br /> and p2,yields curing and maintaining suitable cores may affect the air permeability de-
<br /> pvBL = (k'/n)(p,2 —p22)/2. [9J1 termination. The effect of water content on air permeability is negligible
<br /> for air-dried soils. Therafore, it is not a problem with fragmented soil sam-
<br /> By taking p — P., the exit pressure of the tube, and v, = Q2/A, where Ales. Also, the problems associated with encasing the sample to eliminate
<br /> Q2 = volume of gas per unit time leaving the tube at the exit pressure, the
<br /> air leakage through channels that occur between the soil and the encasing
<br /> equation for permeability measurements using gases may be written as material,or through cracks that may develop in the soil, must be considered
<br /> k' = 2,7 Q2p2 [10- with soil cores, but are negligible with fragmented soils. For this reason the
<br /> A(p,2 —p22)/L procedures outlined herein are for air-dried, fragmented soils. However,
<br /> If the average flow rate Q,,,, and the average pressure = , + ) 2 the general principle of the air-to-water permeability ratio applies also to
<br /> are substituted,the equation becomes g p p• — (f 1 p / cores if the necessary precautions are taken in making the measurements.
<br /> The effect of water contained in the soil on permeability, where air is
<br /> k' [11 J used as the measuring fluid, is somewhat analogous to the effect of en-
<br /> A(pt — P=)/L trapped air in the soil when water is used. Permeability measurements for
<br /> Thus, the permeability k' may be obtained for gas flow in the same way as two- and three-phase systems have been made as a function of percentage
<br /> for the flow of liquids, provided that the volume outflow rate at the condi- saturation for various liquids and gases (Wyckoff and Botset, 1936; Corey
<br /> tions of measurement is reduced to the equivalent volume at the algebraic 1957;see also Carmen, 1956).These measurements have been made mostly
<br /> mean pressure and constant temperature, and provided that viscous flow for sands and various consolidated sediments in connection with oil produc-
<br /> prevails during the measurement. The steady-state methods for measuring
<br /> tion where absolute values are particularly important and high precision
<br /> air permeability make use of equations [10] and [11]. Such methods are de- is required. The results show that both liquid and gas permeabilities de-
<br /> scribed by Corey (1957), Grover (1955), American Petroleum Institute crease as the percentage saturation with the other fluid increases. In the
<br /> (1956) and Brooks and Reeve (1959). very low water content range, air permeability is affected only slightly; but,
<br /> By use of equation [8] and the ideal gas law, and with a few simplifying beyond a certain water content, depending upon the soil, air permeability
<br /> assumptions, Kirkham (1947) developed an equation and a non-steady- falls off markedly as water content is increased. Likewise, with water per-
<br /> state method whereby the flux and pressure measurements are combined meability, there is a range of water contents slightly below saturation where
<br /> into a single measurement of pressure as a function of time as air is dis- ~' permeability does not change appreci4bly; but, below a certain water con-
<br /> charged through a soil sample from a closed air chamber of constant vol- tent, depending again upon the soil, there is a marked reduction in perme-
<br /> ume. Space does not permit the derivation of this equation here, but Kirk- ability. It is well to keep in mind that these factors are involved in air and
<br /> ham's final working equation, which is used for air permeability in the water permeability measurements, but for purposes of this method, these
<br /> procedure herein described, is given in section 41-3.3. The reader is re- are not major factors, especially where the results are expressed as a ratio.
<br /> ferred to the original paper (Kirkham, 1947) for this derivation. In this case, errors due to blocking of air flow by water in the soil and
<br /> Regardless of the air permeability method used, the measurement of those due to air entrapment for water flow are compensating.
<br /> permeability of soil with either air or water involves the preparation and The permeability of soils to water is greatly affected by the chemistry of
<br /> placement of the soil in a suitable container with provision for determinim; the soil-water system. Both the exchangeable cation status of the soil and
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