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 Core Perm vs DST Probe Perm vs DST 800 800 700 700 600 600 500 500 m m arith arith 400 geom 400 geom k-core/ 01:01 01:01 300 k-probe/ 300 200 200 100 100 0 0 0 200 400 600 800 0 200 400 600 800 k-DST/mD k-DST/mD 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 Lorenz Plot 7.0 6.0 5.0 Unit 2 e 4.0 Unit 4 U 4 ideal storag 3.0 U 2 ideal 2.0 1.0 0.0 0 10000 20000 30000 40000 Flow capy 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 Connectivity and Permeability. 1 0.9 0.8 0.7 x(2D) 0.6 a x(3D) y(2D) 0.5 y(3D) vertical 3D Connected S 0.4 Kv(3D) 0.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 Sand/Shale Sand connectivity for 2D and 3D realisations. After M. D. Jackson (et al) AAPG Bull 89(4) p507-528 Moving from 2D to 3D 1.1 0.9 0.7 flas x n falz y flas z 0.5 het x het y connected sa het z 0.3 0.1 2D 3D -0.1 model 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.