64:
the slippage velocity, as obtained from the
Klinkenberg's approach, captures the contribution of molecule-wall interactions and when this velocity is zero, the Poiseuille velocity profile (which results from molecule-molecule interactions) is recovered. However, Klinkenberg's formulation ignores the transition flow region, where neither molecule-molecule nor molecule-wall interactions can be neglected because both are playing a relevant role. The feasibility of Klinkenberg linear function of the reciprocal pressure depends on the Knudsen number. For Knudsen numbers from 0.01 to 0.1 the Klinkenberg approach is acceptable.
63:
When
Klinkenberg defined the interactions to be considered, he supposed the existence of a layer (sometimes called Knudsen layer), thinner than molecular mean free path, adjacent to the pore's wall where only molecules-wall collisions would occur and collisions among molecules could be ignored. Thus
96:
will be higher than brine permeability. This is because gas does not adhere to the pore walls as liquid does, and the slippage of gases along the pore walls gives rise to an apparent dependence of permeability on pressure. This is called the
Klinkenberg effect, and it is especially important in
445:
Obviously what can be obtained from minipermeameter measurement is gas permeability. Gas slippage will occur during the measurement because nitrogen is injected quickly from probe to core and it is very difficult to get to equilibrium in very short time span. Therefore, to get the permeability
76:
is injected into the core plug while mounted in a steel chamber. The samples are either full diameter core samples that are intervals of whole core cut, typically 6 inches long, or 1-in plugs drilled from the cores. The pressure drop across the sample and the flow rate are measured and
104:. The gas flows from the end of a small-diameter tube that is sealed against the core surface. The pressure in the probe and the corresponding volumetric gas flow rate is measured together. The gas permeability is determined by the equation:
224:
44:
measurements, the
Klinkenberg correction is usually necessary due to the so-called Klinkenberg gas slippage effect. This takes place when the pore space approaches the mean free path of the gas
373:
344:
315:
286:
257:
439:
417:
395:
455:
Klinkenberg, L. J.: 1941, The permeability of porous media to liquids and gases, Drilling and
Production Practice, American Petroleum Inst., pp. 200–213.
72:
Permeability is measured in the laboratory by encasing a core plug of known length and diameter in an air-tight sleeve (the
Hassler Sleeve). A fluid of known
458:
Ziarani, A. S., and
Aguilera, R.: 2012, Knudsen's Permeability Correction for Tight Porous Media, Transport in Porous Media, Volume 91, Issue 1, pp 239–260
470:
Klinkenberg, L. J.: 1941, The permeability of porous media to liquids and gases, Drilling and
Production Practice, American Petroleum Inst., pp. 200–213
110:
60:
condition, Klinkenberg demonstrated that the permeability of porous media to gases is approximately a linear function of the reciprocal pressure.
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In probe permeametry (mini-permeameter) measurement nitrogen gas is injected from the probe into core through a probe sealed to a core slab by a
479:
Bravo, M.C. Effect of transition from slip to free molecular flow on gas transport in porous media, J. Appl. Phys. 102, 074905 _2007.
495:
25:
41:
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can be used as a fluid. When high rates of flow can be maintained, the results are comparable. At low rates,
505:
446:
equivalent to the brine permeability at formation condition
Klinkenberg calibration is necessary.
500:
351:
33:
93:
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264:
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29:
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219:{\displaystyle K_{g}=Cq_{1}\mu _{g}{\frac {P_{1}}{a}}G(P_{1}^{2}-P_{2}^{2})^{2}}
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85:
37:
101:
89:
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device. A more accurate correction factor can be obtained using
427:
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419:: Geometric factor (halfspace solution)
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24:is a procedure for calibration of
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77:permeability is calculated using
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1:
397:: Internal radius of tip seal
441:: Constant (unit conversion)
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368:{\displaystyle \mu _{g}}
435:
413:
391:
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346:: Atmospheric pressure
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282:
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220:
22:Klinkenberg correction
496:Petroleum engineering
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414:
392:
370:
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339:{\displaystyle P_{2}}
312:
310:{\displaystyle P_{1}}
283:
281:{\displaystyle q_{1}}
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252:{\displaystyle K_{g}}
221:
97:low-permeable rocks.
28:data obtained from a
425:
403:
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317:: Injection pressure
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431:
409:
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259:: Gas permeability
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34:Knudsen correction
434:{\displaystyle C}
412:{\displaystyle G}
390:{\displaystyle a}
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84:Normally, either
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94:air permeability
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375:: Gas viscosity
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30:minipermeameter
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36:. When using
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506:Porous media
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58:laminar flow
54:steady state
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26:permeability
21:
18:Petrophysics
15:
288:: Flow rate
79:Darcy's law
68:Application
490:Categories
450:References
501:Petrology
357:μ
189:−
142:μ
74:viscosity
42:core plug
86:nitrogen
40:gas for
38:nitrogen
229:Where,
102:gasket
52:Under
48:Theory
90:brine
56:and
88:or
16:In
492::
81:.
20:a
429:C
407:G
385:a
361:g
332:2
328:P
303:1
299:P
274:1
270:q
245:g
241:K
212:2
208:)
202:2
197:2
193:P
184:2
179:1
175:P
171:(
168:G
163:a
158:1
154:P
146:g
136:1
132:q
128:C
125:=
120:g
116:K
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