Permeability in the Eye of the Beholder

Martin Kennedy FESAus and SPE Lecture Tour 2009 Contents

• Definitions • Fundamentals • Measurements • Estimation • Reconciliation

Definitions

COMPLEXITY Single phase Gas Single Phase Gas Reservoir Fluids ‘Ambient’ (Kair) Overburden/Reservoir Pressure(kinf) keff/krel

Thin Section Directional Properties Probe kmax Core Plug k90

Whole Core

SCALE WFT kv

Well Test

EWT Characteristics

• Permeability • Porosity – Dimensions L2 – Dimensionless – 10-14 to 10+>7 mD – 0 to 0.5 – Tensor (Anisotropic) – Scalar (Isotropic) • Resistivity, acoustic • density, neutron properties capture – Dominated by largest – All pores contribute pores equally

1 D = 0.99 um2 Permeability and Fluid Flow

A

Q = Δp.a4 8Δl.μ

= kAΔp Δl.μ

k = a4 So… 8A

Δl Porosity-Permeability (Capillary Bundles) Permeability-Porosity

10000

1000

100 1mm tubes D 0.1mm tubes k/m 0.01mm tubes 10 Permeability-Pore Size

10000 1

1000

0.1 0.000 0.050 0.100 0.150 0.200 100

D tube pore 3% porosity porosity

k/m tube pore 30% por 10

1

0.1 0.00001 0.0001 0.001 pore diameter/m Fracture Permeability

Q = Δp.h.w3 Flow through a slot A 12Δl.μ

= kAΔp permeability equation Δl.μ w 3 h k = h.w 12A

Δl kif = w2 Intrinsic permeability of a fracture 12

Permeability Controls in Real Rocks

Field A Field B Realisations of SEM Images from the Plover sands in the Browse Basin. (2mmx2mm). Although coarser grained, the B sand has fewer paths that are more tortuous.

Porosity = 0.18 Porosity = 0.16 Kh = 470mD Kh = 2 mD Pore network models constructed from the SEM images Measurement

• Fluid has to move… – Laboratory – Test (including WFT) • Uncertainty and Errors. – Measurement. – Geological. • Scale. – Probe <1cm – Plug 5cm – Whole Core 10 – 20cm – WFT – DST 10 5 cm – EWT 10 6 cm

Laboratory

Q = k.L.ΔP A.η P1 η is viscosity of the fluid used for the measurement Confining Rubber Pressure Sleeve

Uncertainty Issues P2 Simple Geometry A, L – high accuracy Q η – known for simple fluids Q – cc/min can be difficult to measure P – high accuracy but normally low.

Wireline Formation Testers. The tools are primarily designed to measure formation pressure. Permeability is actually mobility (permeability/viscosity)

Typical flow-rate 5-50cm3/min.

0.05 – 0.5 BOPD (100 – 1000scf/d). (through a single 1cm diameter hole) Drill Stem Test

10 Cm3/min 500 cm3/min 2-3 m in) (at well)

Uncertainty Issues Unknown Geometry A, L – low accuracy η – un-reliable and variable Q – ca 1000cc/min (at well) P – high accuracy/precision.

Estimation Methods • LOG BASED – Empirical Correlation. • Field Specific (probably based on core) • K = k(Ø, Swir) • CUTTINGS BASED – Image Analysis of Pore System. – Rock Typing. – Model the Pore System.

Estimation: the pitfalls

10000

1000

100 core data D Model model Data kh/m logy on x 10 Range Range

1 0 5 10 15 20 25 30

0.1 porosity

Available core data is used to generate a porosity-permeability transform. This is applied to log porosity in un-cored intervals. IT WILL NOT REPRODUCE THE FULL VARIABILITY Relationships between Properties.

0.8

10 0.7

1 0.6

0.1 0.5 Warro-ob Torosa-2 Kh/mD T- 4 0.01 0.4 Cal-1 Bn-2

0.001 0.3

0.0001 051015 0.2 Phi

Porosity and Permeability 0.1

0 0.01 0.1 1 10 100 1000 10000

Kh/MD

Saturation and Permeability Published Porosity, Swir - Permeability Relationships (Used to produce the NMR log Permeability)

K(PHI) Sw fixed at 20% K(Sw) Phi fixed at 25%

10000.0 10000.0

1000.0 1000.0

Wyllie-Rose Wyllie-Rose 100.0 Timur 100.0 Timur

D Coates

D Coates

k/m Morris & Biggs

k/m Morris & Biggs 10.0 grain size 10.0 Timur (10pu) KOZENY-CARMEN Morris-Biggs(10pu) 1.0 1.0 0 20 40 60 80 100 0.1 0102030 0.1 poro Sw /%

Often quite robust but they can only be used above the Transition Zone (unless you have an NMR log). Grain Size Relations

Permeability (Grain Size)

10000

1000

100

medium fine 10 vf

k/mD mg(Shell) fg(Shell)

1 0 10203040

0.1

0.01 poro

The Shell models were developed in the GOM so buyer beware. The BP/ARCO models are more general but do need a good knowledge of grain size, sorting, cementation/consolidation. Interpretation

• Why don’t my Test Perms match the Core? • What? – Scale (plug, log, layer) – Ambient/overburden. – Effective/Absolute – Air/Brine • Why? – Net/Pay definition. – Well In-flow prediction. – Reservoir Modeling. – Fluid Distribution Modelling.

What Permeability?

Rock: Overburden Correction Fluid: Klinkenberg Correction

Plover 1.20

10000.000

1.00 1000.000

0.80 100.000

Macedon 10.000 0.60 Plover

Plov er Kinf/Kair Kh(3000) 1.000 0.40

0.100 0.20

0.010

0.00

0.001 0.01 0.1 1 10 100 1000 10000 0.001 0.010 0.100 1.000 10.000 100.000 1000.000 10000.000 Kair /m D Kh(800)

These corrections are normally important for low permeabilities (<1mD). For High Permeabilities we are getting into Hair Splitting Territory (>100mD). Up-scaling and Averaging

..and Moving Away from the Borehole Heterogeneity and Anisotropy

• Scale Dependence – aka “My Perms don’t match!” – – May be due to measurement error(s) or… – May indicate heterogeniety. • Heterogeniety can be quantified using some old –unfashionable- methods.. – Cv – Lorenz Coefficient – Dykstra-Parsons • It Determines how the Core Data Should be Averaged. Matching Core to DST Results (Choice of Average)

WELL DST Core Probe H/m K/mD K /mD Cv K /mD Cv arith geom arith geom 19 8 83 77 8.4 3.2 96 38 1.2 22 3.5 190 750 300 1 380 160 0.9 23 9 490 240 49 1.8 310 85 1.3 Shi-Yi Zheng et al (AAPG Bull 84 p1929 (2000) HWU Matching Core to DST Results (Sampling)

WELL DST Core Probe H/m K/mD K /mD plugs Cv K /mD samples Cv arith geom arith geom 19 8 83 77 8.4 28 3.2 96 38 180 1.2 22 3.5 190 750 300 11 1 380 160 39 0.9 23 9 490 240 49 31 1.8 310 85 150 1.3

800 800 Core Perm vs DST Probe Perm vs DST

700 700

600 600

500 500

400 m m arith 400 arith geom geom

k-core/ 300 01:01 300 01:01 k-probe/

200 200

100 0 200 400 600 800 100 0 200 400 600 800 k-DST/mD k-DST/mD 0 0 Matching Test and Core: Indications of Heterogeniety

Core Arith: 200mD 2. Heterogeneous Core Geom: 50mD L = 0.62, Cv = 1.2 TEST: 60mD

Core Arith: 1000mD 4. Homogeneous Core Geom: 700mD L = 0.25, Cv = 0.6 TEST: 1100mD

Heterogeniety Measures

7.0 Lorenz Plot

6.0

5.0

4.0 Unit 2 e 3.0 Unit 4 U 4 ideal storag U 2 ideal 2.0

1.0 0 10000 20000 30000 40000 Flow capy 0.0 An Example: Dolomite Oil Field

Large Oil Field Producing Below Bubble Point

Issues STOIIP (porosity, N/G) Production Profile. Water Flood Behaviour. Perforation Strategy.

Permeability Prediction Silurian Shallow Inland Sea. Dolomite Reservoir: Description Based on Core Plugs

1000.00

100.00

Net Average Poro = 10pu plug data 10.00 N = 71 plugs model Kh/mD 58 with k>1mD

1.00 0.00 5.00 10.00 15.00 20.00 25.00 30.00 But is this representative?

0.10 poro/%

700

600

500

400 IG porosity

flow 300 homog

200

100

0 Lorenz Coefficient 0.55 01234567 pore space Reservoir Rock

Pure Dolomite

3 phases of dolomitisation.

3 Porosity Types: Micro-crystalline Inter-granular Vuggy (or Leached)

3 depositional settings Supratidal - micro-xt Intertidal - intergranular/Vuggy Sub-tidal - intergranular/Vuggy

Dolomite Reservoir: Description Based on Whole Core

por-perm plot

1000 Net Average Poro = 4.3 pu 100 no vugs N = 179 plugs pin point vugs 166 with k>1mD 10 small vugs

Kh/mD medium vugs large vugs 1 0 0.05 0.1 0.15 0.2

0.1 60000

porosity 50000

40000 w hole core 30000 k-phi model homog. 20000 flow capacity

10000

0 0 5 10 15 Lorenz Coefficient = 0.89 pore space Campos Basin: Test and Core Permeability Test Permeability consistently higher than Core (3 wells, 14 DSTs).

Note: This is Unusual in that the core data has not been averaged Campos Basin Field kDST>kcore because… Most Core Data comes from Facies 2, Muddy Sand. The ‘H’ in kH is too small. (Core data averaging is not an issue here)

Fac.2

Fac.1 1 Connectivity and Permeability. 0.9

0.8

0.7

0.6

x(2D) a 0.5 x(3D) y(2D) 0.4 y(3D) vertical 3D Connected S Kv(3D) 0.3

0.2

0.1 0 0.2 0.4 0.6 0.8 1 Sand/Shale 0

Sand connectivity for 2D and 3D realisations. After M. D. Jackson (et al) AAPG Bull 89(4) p507-528 1.1

Moving from 2D to 3D 0.9

0.7

flas x n 0.5 falz y flas z het x het y connected sa 0.3 het z

2D 3D 0.1 model

-0.1 Conclusion

• Permeability is not just another property curve. – It has units and dimensions and is directional. • It cannot be measured as a continuous curve. – Imposes a limit on accuracy. – Probe permeameter is as close as we get. • Different scale measurements need not agree. – Depends on averaging applied to the finer scaled data. – Disagreements may actually be telling us about the reservoir. Post-script: North Sea Chalk

Ekofisk

Tor

1 um