CORE PERMEABILITY BASICS
Permeability is an intrinsic property of a reservoir rock that indicates the flow capacity of the reservoir. Reservoir engineers use permeability, reservoir pressure, and a few other parameters to estimate oil and gas productivity. Petrophysicists use core permeability values to help calibrate permeability derived from well log data.

The Darcy flow equation defines permeability, and after some rearrangement, is used to calculate permeability from laboratory measurements.

1: Q = K * A * (P1 - P2) / (u * L)

Where:
Q = flow rate
K = permeability
A = area
P1 - P2 = pressure drop
L = path length
u = dynamic viscosity (aka absolute viscosity or viscosity)

To measure the permeability in the lab, dry gas is usually used (air, N2, and He) in permeability determination because of its convenience, availability, and to minimize fluid-rock reaction. The measurement of the permeability should be restricted to the low (laminar/viscous) flow rate region, where the pressure remains proportional to flow rate within the experimental error. At low pressures, we assume the gases follow the ideal gas law.

CORE PERMEABILITY DEFINITIONS
Absolute or intrinsic permeability (Ka) is measured with a single fluid in the rock. It is often measured using dry air, giving rise to the term "air permeability" (Kair). Nitrogen and carbon dioxide are also used. When water is used as the single fluid, the result is called "liquid permeability" (Kliq). Air perm is usually a little higher than liquid perm. The Klinkenberg correction is used to reduce air perm to an equivalent liquid perm.

Effective permeability is the permeability of a rock to one fluid in a two phase system. For example, the effective permeability of oil in an oil-water system (Ko) will be less than absolute permeability. In the same rock and fluid system, the effective permeability of water (Kw) could be higher or lower than Ko.

Relative permeability is the ratio of the effective permeability of a fluid at a given saturation to some base permeability. Base permeability is typically defined as absolute permeability (Ka), air permeability (Kair), or effective permeability to non-wetting phase at irreducible wetting phase saturation, for example Ko @ Sw = SWir. Because the definition of base permeability varies, the definition used must always be confirmed before applying relative permeability data noted along with tables and figures presenting relative permeability data.

In laboratory reports, many different measured values and derived values are presented. Here are some of them:
*  Kmax = maximum horizontal permeability at a particular depth, derived by flowing air through the core in various directions and recording the maximum value.
*  K90 = horizontal permeability measured at 90 degrees to the Kmax direction.
*  Kv or Kvert = permeability measured vertically through the core.
*  KHi or K-Hi = individual layer flow capacity, derived by multiplying the thicknes (H) of a layer by its permeability (K). Kmax is usually used but the average of Kmax and K90 may be more representative.
*  KH = reservoir flow capacity, derived by summing all KHi valees, excluding individual layers that failed cutoff criteria.
* Kavg = arithmetic average of permeability = KH / Hnet.
* Kgeo = geometric average of permeability -- see equations HERE.
* Khar = harminuc average of permeability -- see equations HERE.
Kgeo and Khar are used to model radial flow more accurately than Kavg.

LAB PROCEDURE FOR MEASURING AIR PERMEABILITY
Cut core plugs from whole core or use sample from whole core
Clean core and extract reservoir fluids, then dry the core
Flow a fluid through core at several flow rates
Record inlet and outlet pressures for each

Laboratory apparatus for measuring permeability using air and Darcy's Law

LAB PROCEDURE FOR MEASURING LIQUID PERMEABILITY
Measure inlet and outlet pressures (P1 and P2) at several different flow rates
Graph ratio of flow rate to area (q/A) versus the pressure function (P1 - P2) / L
For laminar flow, data follow a straight line with slope of k/μ
At very high flow rates, turbulent flow is indicated by a deviation from straight line

Finding permeability with liquid or high rate gas flow

KLINKENBERG EFFECT
Klinkenberg (1941) discovered that permeability measurements made with air as the flowing fluid showed different results from permeability measurements made with a liquid as the flowing fluid. Air permeability is always greater than the permeability obtained when a liquid is the flowing fluid. On the basis of the laboratory experiments, liquids had a zero velocity at a grain surface, while gases exhibited some finite velocity at the same grain surface (slippage). This slippage results in a higher flow rate for the gas at a given pressure differential. Klinkenberg also found that, for a given porous medium, as the mean pressure  increased, the calculated permeability decreased.

Klinkenberg developed a method to correct gas permeability measured at low mean flowing pressure to equivalent liquid permeability. A plot of measured permeability versus 1/Pm is extrapolated to the point where 1/Pm = 0 (Pm = infinity). This permeability approximates the liquid permeability.

2: Pm = (P1 + P2) / 2
3: Kliquid = Kgas / (1 + B / Pm)

Correction factor B is determined by conducting the test at several flowing pressures and extrapolating to infinite pressure.

Empirical correlations have been reported in the literature for moderate to high permeability
sandstones (Jones 1987):
4: Bhelium = 44.6 * (Khelium / PHIcore) - 0.447
5: Bair = 0.35 * Bhelium
For low permeability (<10mD) gas sands (Jones and Owens 1980):
6: B = 14.7 * (0.86 * Kair - 0.33)
Where:
Kgas = gas permeability (mD)
Kliquid = liquid permeability derived from gas permeability (mD)
P1 = inlet pressure (psi)
P2 = outlet pressure (psi)
Pm = mean pressure (psi)
B = constant for a particular gas in a particular rock type (psi)
PHIcore = core porosity (fractional)

The Klinkenberg correction is quite important for low-permeability rocks and less important or unimportant for high-permeability rocks. The value of kL obtained after applying the correction represents the permeability to a gas at infinite pressure or to a liquid that does not react with the component minerals of the rock.

PERMEABILITY FROM MICRO-CT SCANS
Permeability is traditionally measured in the laboratory on regularly shaped rock samples by forcing a fluid through the rock and recording the resulting fluid flux and pressure drops. CT Scanning complements and vastly expands laboratory permeability data sets by numerically simulating fluid flow through a direct digital representation of a real pore space obtained by high-resolution 3D imaging. Such imaging and simulations can be rapidly and massively conducted on physical samples of irregular shapes and sizes that are impossible to handle in the conventional laboratory. The pore volume and pore size determined from the CT Scan are manipulated mathematically by simu;ating the Navier-Stokes equation using the Lattice-Boltzman Method, as shown below.

The slow viscous flow needed for such permeability estimates is simulated using the lattice Boltzmann method (LBM). LBM mathematically mimics the Navier-Stokes equations of viscous flow by treating the fluid as a set of particles with certain interaction rules. Its great advantage over directly solving the equations of flow is that it directly handles the boundary conditions on a complex realistic pore surface. The outcomes are consistent datasets of permeability versus porosity correlations and pore geometries for various rock types, including tight gas sandstone, carbonates, and friable tar sands.

The absolute permeability is computed in a manner analogous to a laboratory measurement: a pressure head or body force is directly applied to a digital sample. The resulting fluid flux is then computed and permeability is calculated according to the Darcy's equation. Source: www.ingrainrocks.com.

SAMPLE CORE ANALYSIS REPORT

 02181815W4 #23708 731011 NOTE: Accumap has Kvert in K90 Column S# Top Base Len Kmax K90 Kvert Poros GrDen BkDen Soil Swtr Lithology feet feet feet mD mD mD Frac kg/m3 kg/m3 frac frac 1 3499.19 3500.17 0.98 742.0 0.0 180.0 0.283 0 0 0.129 0.448 SS VF-F 2 3500.17 3501.16 0.98 1196.0 0.0 694.0 0.297 0 0 0.123 0.450 SS VF-F 3 3501.16 3502.17 1.02 622.0 0.0 266.0 0.276 0 0 0.111 0.520 SS VF-F 4 3502.17 3503.16 0.98 223.0 0.0 50.5 0.271 0 0 0.129 0.479 SS VF-F 5 3503.16 3503.88 0.72 837.0 0.0 171.0 0.278 0 0 0.110 0.504 SS VF-F PY 6 3503.88 3504.57 0.69 407.0 0.0 113.0 0.287 0 0 0.118 0.466 SS VF-F 7 3504.57 3504.67 0.10 0.0 0.0 0 0 0 0 0 SH 8 3504.67 3505.26 0.59 514.0 0.0 365.0 0.253 0 0 0.151 0.398 9 3505.26 3505.49 0.23 100.0 0.0 2.6 0.201 0 0 0.134 0.358 SS VF-F SH INC 10 3505.49 3505.98 0.49 401.0 0.0 120.0 0.254 0 0 0.143 0.268 SS VF-F SHBKS 11 3505.98 3506.96 0.98 478.0 0.0 302.0 0.282 0 0 0.131 0.471 SS VF-F 12 3506.96 3507.88 0.92 431.0 0.0 100.0 0.243 0 0 0.156 0.399 SS VF-F CARB INC 13 3507.88 3508.47 0.59 777.0 0.0 556.0 0.277 0 0 0.119 0.389 SS VF-F 14 3508.47 3508.87 0.39 831.0 0.0 383.0 0.275 0 0 0.136 0.422 SS VF-F CARB BK 15 3508.87 3509.88 1.02 413.0 0.0 262.0 0.281 0 0 0.132 0.440 SS VF-F 16 3509.88 3510.87 0.98 604.0 0.0 425.0 0.277 0 0 0.131 0.323 SS VF-F SH INC 17 3510.87 3511.88 1.02 320.0 0.0 35.1 0.229 0 0 0.146 0.422 SS VF-F SH INC 18 3511.88 3512.87 0.98 616.0 0.0 437.0 0.239 0 0 0.103 0.354 SS VF-F 19 3512.87 3513.79 0.92 259.0 0.0 62.0 0.261 0 0 0.073 0.418 SS VF-F 20 3513.79 3514.38 0.59 320.0 0.0 26.8 0.219 0 0 0.096 0.441 21 3514.38 3515.07 0.69 431.0 0.0 82.5 0.236 0 0 0.119 0.387 SS VF-F 22 3515.07 3515.16 0.10 0.0 0.0 SH PY 23 3515.16 3516.18 1.02 969.0 0.0 628.0 0.270 0 0 0.044 0.492 SS VF-F 24 3516.18 3516.77 0.59 837.0 0.0 634.0 0.280 0 0 0.042 0.501 SS VF-F 25 3516.77 3517.46 0.69 556.0 0.0 201.0 0.273 0 0 0.050 0.531 SS VF-F CARB INC 26 3517.46 3518.28 0.82 706.0 0.0 338.0 0.262 0 0 0.046 0.487 SS VF-F 27 3518.28 3519.07 0.79 502.0 0.0 377.0 0.238 0 0 0.079 0.494 SS VF-F CARB INC 28 3519.07 3519.99 0.92 1136.0 0.0 183.0 0.263 0 0 0.063 0.501 SS VF-F 29 3519.99 3520.58 0.59 825.0 0.0 291.0 0.265 0 0 0.052 0.563 30 3520.58 3521.46 0.89 1346.0 0.0 706.0 0.274 0 0 0.055 0.516 SS VF-F 31 3521.46 3522.48 1.02 389.0 0.0 102.0 0.246 0 0 0.064 0.450 SS VF-F/M CARB INC 32 3522.48 3523.47 0.98 165.0 0.0 11.9 0.219 0 0 0.058 0.408 SS VF-F/M CARB INC 33 3523.47 3524.48 1.02 586.0 0.0 66.0 0.219 0 0 0.082 0.411 34 3524.48 3525.47 0.98 1035.0 0.0 395.0 0.244 0 0 0.051 0.391 SS VF-F 35 3525.47 3526.48 1.02 514.0 0.0 187.0 0.199 0 0 0.073 0.360 36 3526.48 3527.47 0.98 526.0 0.0 89.0 0.205 0 0 0.046 0.481 SS VF-M 37 3527.47 3528.16 0.69 1375.0 0.0 208.0 0.216 0 0 0.042 0.548 SS VF-M PY CARB 38 3528.16 3528.88 0.72 287.0 0.0 95.0 0.207 0 0 0.066 0.462 Arithmetic Averages 0.78 618.8 0.0 240.7 0.253 0.0 0.0 0.095 0.443

Core data listing for Shaly Sand Example

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