Assessing relative permeabilities in geothermal reservoirs

María Sigríður Guðjónsdóttir, PhDReykjavik University

Georg Geothermal WorkshopNovember 24th-25th 2016

#GGW2016

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

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

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: 𝑚ሶ𝑤= −𝑘𝑘𝑟𝑤𝑣𝑤 𝐴𝑛ሬሬԦ∙൫∇𝑝−𝜌𝑤𝑔ሬሬԦ൯ (3)

𝑚ሶ𝑠 = −𝑘𝑘𝑟𝑠𝑣𝑠 𝐴𝑛ሬሬԦ∙൫∇𝑝−𝜌𝑠𝑔ሬሬԦ൯

𝑚ሶ= −𝑘𝑣𝐴𝑛ሬԦ∙ሺ∇𝑝−𝜌𝑔ሬሬԦሻ Mass flow Pressure gradientk Intrinsic permeabilityr DensityA Areakr Relative permeablityn Kinematic viscositys Subscript for steamw Subscript for water

𝑚ሶ= −𝑘𝑣𝐴𝑛ሬሺ∇𝑝−𝜌𝑔ሬሻ (2) 𝑚ሶ𝑤= −𝑘𝑘𝑟𝑤𝑣𝑤 𝐴𝑛Ԧ∙൫∇𝑝−𝜌𝑤𝑔ሬ൯ (3)

𝑚ሶ𝑠 = −𝑘𝑘𝑟𝑠𝑣𝑠 𝐴𝑛Ԧ∙൫∇𝑝−𝜌𝑠𝑔ሬ൯

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, CaliforniaSatik, C., 1998. A measurement of steam-water relative permeability. Proc., 23rd Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, pp. 120-126O’Connor, P., 2001. Constant-pressure measurement of steam-water relative permeability. M.Sc. thesis, Stanford University, Stanford, CaliforniaPiquemal, J., 1994. Saturated steam relative permeabilities of unconsolidated porous media. Transport in Porous Media, Vol. 17, pp. 105-120Verma, 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. 293-300Corey, A., 1954. The interrelation between gas and oil relative permeabilities. Producers Monthly, Vol. 19, pp. 38-41

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

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

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

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

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

𝑘𝑟𝑠 = − 𝑚ሶ𝑠𝑣𝑠𝑘𝐴𝑛ሬԦ∙(∇𝑝− 𝜌𝑠𝑔Ԧ)

𝑘𝑟𝑤 = − 𝑚ሶ𝑤𝑣𝑤𝑘𝐴𝑛ሬԦ∙(∇𝑝− 𝜌𝑤𝑔Ԧ)

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

Part IV• Title:

• Calculations of relative permeabilities from field data and comparison to laboratory measurements• 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 .

Paper IV: Results and conclusionsHellisheidi 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

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

15

SummaryReservoir models

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

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