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.

Permeability measured with a single fluid in the rock is called absolute or intrinsic permeability (Ka). 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.


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 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: Kg = KL + C * (1 / PM)

The factor C varies with permeability so it must be determined for each core plug. There are generalized iterative equations to solve for C, but they are not widely used.

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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