SUTRA Flow Modelling in Heterogeneous Poroperm Media –

1. TIG-10 –Adelaide 15 November 2010 SUTRA Flow Modelling in Heterogeneous Poroperm Media– • ~ Meter scale: Correlated temperature gradient T(z) & wellbore porosity (z) • > Km scale: Spatial affinity of Waikato River & Taupo Volcanic Zone geothermal outcrops Peter Leary & Peter Malin IESE/UnivAuckland

2. Some geothermal/flow numbers: • 1 MWth ~ 4T(oC)/1000  V(ℓ/s) • 1 MWe ~ 4/100  V(ℓ/s)  V(ℓ/s) ~ 25ℓ/s @ T=100oC • 10ℓ/s ~ 5400bbl/day • 50yr average US oil well production ~ 15±5bbl/day • 1ℓ oil ≡ 50¢ • 1ℓ hot water ≡ 0.5¢

3. Geothermal energy ≡ in situ fluid flow Flow rate/MWe ~ 25ℓ/s ~ 1000 times > oil formation flow rate Need to understand in situ flow.......

4. ‘Laws’ of in situ fluid flow • Well-log ‘law’: power spectra scale inversely with spatial frequency: • S(k) ~ 1/k (=1/f-noise) • ~1/km < k < ~1/cm • Well-core ‘law’: porosity φ controls permeability κ: • δφ ~ δlog(κ)

5. Combine well-log & ‘well-core ‘laws’ in 3D realisation of in situ permeability distributions (where to aquifer access drill wells?)

6. Second realisation of well-log & ‘well-core ‘laws’ for in situ permeability distributions (where to drill wells?)

7. Fault realisation of well-log & ‘well-core ‘laws’ for in situ permeability distributions -- can geophysical methods tell where to drill?

8. SUTRA detailed flow modelling • M-scale spatial poroperm fluctuations: • Correlated temperature gradient T(z) & wellbore porosity (z), MWX field site, Colorado tight gas sands • KM-scale spatial poroperm fluctuations: • Spatial affinity of Waikato River for Taupo Volcanic Zone geothermal outcrops – evidence for joint fault control of geothermal circulation & river course?

9. MWX well spatial correlation of wellbore temperature gradient (red) with wellbore neutron porosity (blue) Temperature Gradient Porosity 1700m DEPTH IN WELL 2450m

10. Analytic solution: T(z)pred Pe(T(z)–T0)/h(z)obs T(z)obs (z)obs

11. T(z) = CUMSUM(T(ζ)) h 

12. Conductive + Advective heat flowQKT - C(T–T0) • Constant heat flow: δQ  0 δTC(T–T0)/Kδ • Darcy flow: /P g/δ (g/) δ • In situ permeability:   0exp() = 0exp() =  • Pe= C2gh0/K ~ 1: • T(z)  (T(z)–T0)/h(z)

13. SUTRA flow/transport solver computes temperature field fluctuations due to heat advected by water percolating through in situ (1/f-noise) poroperm medium.Find: • Thermal field fluctuates with porosity field • Wellbore fluctuations reflect 1/f-noise poroperm spatial fluctuations • Flow simulations with invalid synthetic fracture distributions give • inaccurate flow results

14. 1/F-NOISE POROSITY DISTRIBUTION 20 40 60 80 100 120 0 20 40 60 80 100 120 140

15. 0 0 0 0 0 0 0 0 0 0 0 0 20 20 20 20 20 20 20 20 20 20 20 20 40 40 40 40 40 40 40 40 40 40 40 40 60 60 60 60 60 60 60 60 60 60 60 60 80 80 80 80 80 80 80 80 80 80 80 80 100 100 100 100 100 100 100 100 100 100 100 100 120 120 120 120 120 120 120 120 120 120 120 120 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 Advective Heat Flow Conductive Heat Flow T(z) (red) --(z) (blue)

17. 0 0 0 0 0 0 0 0 0 0 0 0 20 20 20 20 20 20 20 20 20 20 20 20 40 40 40 40 40 40 40 40 40 40 40 40 60 60 60 60 60 60 60 60 60 60 60 60 80 80 80 80 80 80 80 80 80 80 80 80 100 100 100 100 100 100 100 100 100 100 100 100 120 120 120 120 120 120 120 120 120 120 120 120 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 -5 0 5 Advective Heat Flow in Poroperm Noise Gaussian Brownian T(z) (red) --(z) (blue)

18. T(z)obs T(z)pred Pe(T(z)–T0)/h(z)obs T(z)pred T(z)obs (z)obs

19. Synthetic Fracture Set Invalid Observed spatial correlation of in situ fractures requires porosity fluctuation power to scale inversely with spatial frequency (1/f-noise poroperm distribution): S(k) ~ 1/k, 1/km < k < 1/cm Synthetic fracture sets fail this spatial correlation criterion

20. Outcrop-based fracture-intercept basis for 3D synthetic fracture distribution

21. Sample Fourier power-spectra S(k) ~ kβ of borehole spatial fluctuations through synthetic fracture distribution with estimated exponents β

22. Distribution of Fourier power-spectra S(k) ~ kβ exponents β Synthetic data exponents: β ~ -0.4 +/- 0.3 Observed data exponents: β ~ -1.1 +/- 0.15

23. SUTRA detailed flow modelling • M-scale spatial poroperm fluctuations: • Correlated temperature gradient T(z) & wellbore porosity (z), MWX field site, Colorado tight gas sands • KM-scale spatial poroperm fluctuations: • Spatial affinity of Waikato River for Taupo Volcanic Zone geothermal outcrops – evidence for joint fault control of geothermal circulation & river course?

29. XFlt No XFlt

32. M-scale Summary/Conclusions • Sutra fluid flow/transport simulator reproduces spatial correlation between fluctuations in thermal gradient and porosity observed in MWX well  advective/percolation heat transport • Thermal gradient fluctuations track in situ porosity fluctuations • Observed thermal gradient fluctuations ~ 1/f-noise spatial correlation • Observed advection shows bulk permeability fluctuations ~ 1/f-noise • Standard fracture simulation S\W fail to meet the observed 1/f-noise spatial correlation criterion • Flow simulators operating with incorrect fracture spatial correlations cannot give accurate flow/transport results

33. > KM-scale Summary/Conclusions • Sutra fluid flow/transport simulator indicates increased fault-borne • heat transport where faults cross • Thermal diffusion from crossed-fault ‘thermal plumes’ may account for the circular geometry and location of TVZ geothermal outcrops • Faults that (may) control the location of TVZ geothermal outcrops may also guide the course of the Waikato River in the central TVZ • Detailed physically-based flow modelling of fracture/fault borne heat advection in the central TVZ may help understanding of geothermal fields in general • If faults are key structures in TVZ geothermal outcrops, faults are also likely to be key structures in, say, Australian HSA plays; locating in situ buried faults could be important to HSA economics.