The document discusses assessing relative permeabilities in geothermal reservoirs through analyzing the effect of gravity on relative permeabilities, performing laboratory measurements using real geothermal fluids, and calculating relative permeabilities from field data at several geothermal fields in Iceland. The results showed differences in relative permeabilities with flow direction and magnitude, and that wells within the same field can follow different relative permeability curves. Comparisons were made between laboratory and field measurements.

1. Assessing relative permeabilities
in geothermal reservoirs
María Sigríður Guðjónsdóttir, PhD
Reykjavik University
Georg Geothermal Workshop
November 24th-25th 2016
#GGW2016

2. Two phase reservoirs
• Two examples where two phase flow takes place in high temperature
liquid dominated reservoirs
• Relative permeabilities used for modelling two phase geothermal reservoirs

3. Motivation, Objectives and Goals
• Motivation:
• Relative permeabilities
• Important parameters for modelling of two phase geothermal reservoirs
• Used to predict the reservoir performance
• Have to be selected carefully to avoid overestimation of the reservoir
• Overestimation of the reservoir can lead to higher drilling cost and unsustainable
utilization of the reservoir
• Objectives and goals
• Analyse effect of gravity on relative permeabilities
• Perform measurements on two phase flow of water and steam using geothermal fluid
• Compare experimental results with field data
• Use the results to estimate the applicability of the relative permeability curves for geothermal
reservoir modelling

4. Darcy Law and relative permeabilities
• Geothermal reservoirs:
• Darcy‘s law one of the governing equations for steady state flow
• Flow through fractures rather than porous matrix
• Darcy‘s law for a single phase flow:
• Darcy‘s law for a two phase flow: 𝑚 𝑤 = −
𝑘𝑘 𝑟𝑤
𝑣 𝑤
𝐴𝑛 ∙ ∇𝑝 − 𝜌 𝑤 𝑔
𝑚 𝑠 = −
𝑘𝑘 𝑟𝑠
𝑣 𝑠
𝐴𝑛 ∙ ∇𝑝 − 𝜌 𝑠
𝑔
𝑚 = −
𝑘
𝑣
𝐴𝑛 ∙ ∇𝑝 − 𝜌𝑔
Mass flow
Pressure gradient
k Intrinsic permeability
r Density
A Area
kr Relative permeablity
n Kinematic viscosity
s Subscript for steam
w Subscript for water
𝑚 = −
𝑘
𝑣
𝐴𝑛 ∇𝑝 − 𝜌𝑔
𝑚 𝑤 = −
𝑘𝑘 𝑟𝑤
𝑣 𝑤
𝐴𝑛 ∙ ∇𝑝 − 𝜌 𝑤
𝑔
𝑚𝑠 = −
𝑘𝑘 𝑟𝑠
𝑣 𝑠
𝐴𝑛 ∙ ∇𝑝 − 𝜌𝑠
𝑔

5. Relative permeabilities
• The relative permeabilities tell us the phases ability to flow with regard to the
presence of the other
• Relative permeabilities for water and steam in porous media
• Experimental results from literature:
References:
Mahiya, G., 1999. Experimental measurement of steam-water relative permeability. M.Sc. thesis, Stanford University, Stanford, California
Satik, C., 1998. A measurement of steam-water relative permeability. Proc., 23rd Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, pp. 120-126
O’Connor, P., 2001. Constant-pressure measurement of steam-water relative permeability. M.Sc. thesis, Stanford University, Stanford, California
Piquemal, J., 1994. Saturated steam relative permeabilities of unconsolidated porous media. Transport in Porous Media, Vol. 17, pp. 105-120
Verma, A., 1986. Effects of phase transformation of steam-water relative permeabilities. Ph.D. thesis. University of California, Berkeley.
Sanchez, J., Schechter, R., 1990. Steady adiabatic, two-phase flow of steam and water through porous media. SPE Reservoir Engineering, August 1990, pp. 293-300
Corey, A., 1954. The interrelation between gas and oil relative permeabilities. Producers Monthly, Vol. 19, pp. 38-41

6. Part I
• Title:
• The effect of gravity on the application of relative permeabilities in modelling two
phase geothermal reservoirs
• Flow in geothermal reservoir simulated
• Two flow cases:
• Horizontal and vertical upwards
• Fluid starting as saturated liquid (x=0) at 100 bar
• Fluid flashes down to 50 bar and steam fraction x=0.155
• Mass flow in the reservoir calculated for a simple convection cell = 0.0144 kg/m2/s
• Specific enthalpy remains constant
• Flashing of the fluid
• Effect of flow direction on the relative permeabilities
• All properties, other than direction kept the same

7. Part I: Results and conclusions
• Middle: 10x massflow as in Left
• Right: 0.1x massflow as in Left
• Same relative permeability curves apply
• Different water saturations gained
• Different relative permeabilities between flow
cases when all properties and conditions other
than direction are kept the same
• This difference increases with decreasing mass
flow
• Different velocity ratios between the flow cases
result in different water saturations and relative
permeabilities

8. Part II
• Title:
• Water and air relative permeabilities from laboratory experiments. The effect
of gravity on Darcy’s law
• Observe the effect of gravity as seen in results from calculations in Paper I
• Perform measurements on water and air flowing through porous media
• Relative permeabilities calculated from
direct measured parameters
• Horizontal and vertical setup
• Varying flow rates and pressure

9. Part II: Results and conclusions
• Effects of gravity on the relative permeabilities observed in results of
laboratory experiments
• Difference increased with decreasing mass flow which is in
accordance with results from calculations in Part I

10. Part III• Title:
• Calculations of relative permeabilities of water and steam from
laboratory measurements
• Use geothermal fluid in a large scale experiments to assess its relative
permeabilities
𝑘 𝑟𝑠 = −
𝑚 𝑠 𝑣𝑠
𝑘𝐴𝑛 ∙ (∇𝑝 − 𝜌𝑠 𝑔)
𝑘 𝑟𝑤 = −
𝑚 𝑤 𝑣 𝑤
𝑘𝐴𝑛 ∙ (∇𝑝 − 𝜌 𝑤 𝑔)

11. Part III: Results and conclusions
• Horizontal and vertical
setups
• Intrinsic permeability
measured using water only
• Variations in intrinsic
permeabilities
• Silica scaling observed
• Relative permeabilities for water and steam calculated from direct measured values,
using real geothermal fluid
• Variations in intrinsic permeabilities, silica scaling one of the contributers
• The resulting relative permeabilities follow the Corey curves to some extent

12. Part IV
• Title:
• Calculations of relative permeabilities from field data and comparison to laboratory measuremen
• Use data from geothermal fields to assess relative permeabilities in the two phase reservoirs
• Data from three geothermal fields in Iceland
• Hellisheiði, Nesjavellir and Reykjanes
• Mass flow and enthalpy from several wells used
• The Shinohara1 method used to calculate the relative permeabilities
• Assumptions:
• The pressure gradient is constant for a short time for each well
• The product of permeability and flowing area, kA, is constant for each well
• Fluid flows in the reservoir according to Darcy’s law
• Flashing in the reservoir is neglected
• Horizontal flow
1Shinohara, K., 1978. Calculation and use of steam/water relative permeabilities in geothermal reservoirs. M.Sc. thesis, Stanford University, Stanford, California .

13. Paper IV: Results and conclusions
Hellisheidi Reykjanes Nesjavellir
• Generaly less interaction between the two phases for the reservoir
flow than for the laboratory experiments
• Fractured flow rather than flow in porous media
• Wells in same area can follow different relative permeability curves

14. Part III and IV together
• Comparison of field data and laboratory results

15. Summary
Reservoir models
15
Controlled laboratory
measurements
Measurements with real
geothermal fluid
Field data, reality• Effect of gravity on the relative permeabilities was studied
• Difference in relative permeabilities with regard to flow direction
and reservoir flow magnitude
• Measurements using real geothermal fluid were performed
• Silica precipitation affected the results
• Shinohara method was used on data from geothermal fields
• Results show that wells within the same field can follow different
relative permeability curves

16. Acknowledgements
• PhD committee:
• Guðrún Sævarsdóttir, Halldór Pálsson, Jónas Elíasson, Guðni Axelsson
• Funding:
• Landsvirkjun Energy Fund
• Orkusjóður
• Geothermal Research Group (GEORG)
• Íslandsbanki study grant
• University of Iceland equipment fund,
• Housing of experiments:
• HS Orka
• Innovation center Iceland
• Keilir