Permeability Estimates & Saturation Height Functions: A talk of two halves. Dr Joanne Tudge LPS Petrophysics 101 Seminar 17 th March 2016

Transcription

1 Permeability Estimates & Saturation Height Functions: A talk of two halves Dr Joanne Tudge LPS Petrophysics 101 Seminar 17 th March 2016

2 Permeability: What is it? How do we measure it? Why do we need it? Saturation Height Functions: What are they? How do we use them? Some field examples Outline

3 Permeability (k): The ease of flow of a Newtonian fluid through a medium under pressure Permeability Estimates

4 Permeability (k): The ease of flow of a Newtonian fluid through a medium under pressure A rocks ability to conduct fluids Permeability Estimates

5 A rocks ability to conduct fluids Darcy s Law Units: Darcy (D) or millidarcy (md) Breaks down under certain circumstances: Turbulent Flow (high flow velocity) Gas flow at low pressure (Klinkenberg effect) Q = ka P μl Where: Q = volumetric flow rate A = cross sectional area ΔP/L = pressure drop µ = the viscosity of the fluid Permeability - k

6 A rocks ability to conduct fluids Depends on: Effective Porosity Grain Size Grain Shape Grain Size distribution (sorting) Grain Packing Cementation / Consolidation Clay type Primary Permeability Deposition & Lithification Secondary Permeability Compaction Cementation Fracturing Solution Permeability - k [after Schlumberger]

7 A rocks ability to conduct fluids 3 Types of permeability: Absolute (k) rock fully saturated with one fluid type (e.g. water, or oil) Effective (k o, k g, k w ) immiscible fluids present permeability of each fluid Relative (k r ) ratio of Effective to Absolute for each fluid phase: e.g.: k ro = k o /k (oil) k rg = k g /k (gas) k rw = k w /k (water) Permeability - k [after Schlumberger]

8 Log measurements Stoneley waves Formation Testers (not going to talk about these) NMR (not going to talk about this) Core measurements: Permeability measurements NMR (not going to talk about this) Porosity Permeability relationships Methods to estimate k

9 Log: Stoneley waves Measures dynamic permeability: because fluid is moved through the formation As Stoneley wave passes a permeable formation there is fluid movement between the formation & the borehole Attenuates the wave & changes the velocity Magnitude of effects are frequency dependant Models based on Biot poro-elastic theory relate the above Impermeable Permeable Rx Tx Methods to estimate k

10 Core Permeability measurements: Q = ka P μl Methods to estimate k Where: Q = volumetric flow rate A = cross sectional area ΔP/L = pressure drop µ = the viscosity of the fluid

11 Porosity permeability relationships: Relationships can be variable Often good for specific beds / formations Methods to estimate k

12 Field Example #1

13 Field Example #1

14 Several uses: Predicting flow in the subsurface Interaction of fluids (Relative Perm curves) Inputs into numerical simulator's reservoir behaviour Cut-offs RQI s One use in particular is for Saturation-Height Functions Why do we need it?

15 What are they? How do we use them? Some field examples Saturation Height Functions

16 A method of estimating Saturation based on the height above the free-water-level and capillary pressure Height above FWL h h h Free Water Level (FWL) What are they?

17 Height above FWL A method of estimating Saturation based on the height above the free-water-level and capillary pressure Various different types: Skelt-Harrison Leverett-J Functions FOIL Functions To name a few Saturation - v/v What are they?

18 Leverett-J function: Based on capillary pressure, porosity & permeability Calculated on Core data Transferable to the wireline-log scale J = J-function J 0.217Pc cos res res x k Pc res = Capillary Pressure σ = Interfacial (surface) Tension k = Permeability (Core-derived) Φ = Porosity (Core-derived) Leverett J-Functions (Leverett, 1941)

19 P C = h ρ w ρ oil Height above FWL h h h Free Water Level (FWL) Capillary Pressure

20 Capillary Pressure Brine Saturation Capillary Pressure Brine Saturation Porosity 0.09 Permeability Field Example #2

21 Capillary Pressure Sw Brine Saturation J-Function Porosity 0.09 Permeability 0.59 Capillary Pressure Brine Saturation C.P. Res Height J-Function Field Example #2

22 Sw J-function S w = J Field Example #2

23 Sw Sw Sw Sandstone # J-function Sandstone # J-function Sandstone 1: S w = J Sandstone 2: S w = J Sandstone 3: S w = J Sandstone # J-function Field Example #2

24 FWL (3349.3m) Field Example #2

25 SW? (3330.5m) FWL (3349.3m) Field Example #2

26 SW? (3330.5m) Porosity = Permeability = 1913 md FWL (3349.3m) Field Example #2

27 SW? (3330.5m) Porosity = Permeability = 1913 md FWL (3349.3m) ρ o = ρ w = Field Example #2

28 P C = h ρ w ρ oil P C = SW? (3330.5m) FWL (3349.3m) Porosity = Permeability = 1913 md h ρ o = ρ w = Field Example #2

29 P C = J 0.217Pc cos res res x k SW? (3330.5m) FWL (3349.3m) Porosity = Permeability = 1913 md h ρ o = ρ w = Field Example #2

30 P C = J 0.217Pc cos res res x k J = SW? (3330.5m) FWL (3349.3m) Porosity = Permeability = 1913 md h ρ o = ρ w = Field Example #2

31 P C = J 0.217Pc cos res res x k J = SW? (3330.5m) FWL (3349.3m) Porosity = Permeability = 1913 md h ρ o = ρ w = Sandstone 1: S w = J Field Example #2

32 P C = J 0.217Pc cos res res x k J = SW? (3330.5m) FWL (3349.3m) Porosity = Permeability = 1913 md h ρ o = ρ w = Sandstone 1: S w = J Field Example #2 S w = 0. 65

33 Permeability: Permeability is the ease with which a fluid flows through a rock Estimated from core, often estimated from porositypermeability relationships for rock-types Used in saturation height functions Saturation Height Functions: Saturation height functions method of estimating Sw based on height above the FWL & Capillary Pressure Core & Log scale options Summary

34 Questions?