Geothermal Modelling Ruggero Bertani Geothermal Innovation & - PowerPoint PPT Presentation

Geothermal Modelling Ruggero Bertani Geothermal Innovation & Sustainability Enel Green Power Trieste, December 2015

Geothermal Modelling THERMAL FLUX   K  T q ˚ W C W    q 2 0 . 03 0 . 06 ˚ 2 m C m m In 1 km 2 , standard thermal flux radiated is 60 kW 1

Geothermal Modelling Natural circulation model: convective cells. T 0 T 0 recharge zone cold (cold water) g discharge zone (hot water) hot T 1 T 2 > T 1 2

Numerical modeling of geothermal fields Input Reservoir characteristics Physico-chemical data Geological / conceptual model Well testing Monitoring of existing / exploratory wells - Fluid monitoring in existing wells - Injection test - WHP monitoring in observing wells - Build Up - Monitoring of water level in wells - Drawdown - Build-up temperature and T&P Logs Reservoir geometry 3D distributions of temperature and - extension - system geology pressure in the reservoir - thickness - faults Reservoir geology and characteristics of the rocks Initial conditions System evolution in - permeability - thermal conductivity the time - porosity - density - comprimibility 3

Geothermal Modelling 4

Geothermal Modelling TAP  PERMEABILITY CAPACITY  VOLUME*POROSITY 5

Geothermal Modelling 1.2 II 0 e  t /t R 1 t = RC 0.8 I 0 I(t)63%I 0 CORRENTE 0.6 C 0.4 V 0.2 t 0 + - 0 0.5 1 1.5 2 2.5 TEMPO RESISTENCE  PERMEABILITY CAPACITY  VOLUME*POROSITY VOLTS  PRESSURE 6

Geothermal Modelling The driving force of the a fluid through the porosity b from a to b is the A Pressure Difference L 3 ] [s -1 ] q=[m D = [Pa] = [kg] [m -1 ] [s -2 ] p D P A K  2 ] q A= [m L = [m] m L m  [Pa] [s] = [kg] [m -1 ] [s -1 ] Permeability [m 2 ] K= 7

Geothermal Modelling Pressure Reduction is proportional to the Extracted Mass V Comprimibility= (DV/V)/DP f f c t = f c fl +(1- f )c r M= [kg] V= [m 3 ] D M = f c t V r D P c t c fl c r = [Pa -1 ] D M r = [kg] [m -3 ] C M  D M / D P C M = [kg] [Pa -1 ] D M C M = f c t V r D P  f c t V r f = Porosity 8

Geothermal Modelling Darcy Law (Henri Darcy, 1856)  k r ( )  m  P  r g F k k     mf mf c c t t   D P D x  F x   k r      D P D y  F y    m     D P D z r g F z 9

Geothermal Modelling Radial Solution G From draw down test m D 10 h; P k hk= 2.3*q* m /4 p /m 10 Log 10 D t From drainage cone P t 1 t 2 P static a P Drawn r i1 r i2 down ln (r) r i = 2  (  t/  ) P  = 1.781 f r r= distance l w 10

Geothermal Modelling Moto radiale Radial Solution   2 m   q r D    p E     p  1 4 hk  4 t        y   E ( x ) ( 1 / y ) e dy 1 x     m   t    q 4 t D  2   10 p ln   p 2   2  r 4 hk   r       11

Geothermal Modelling Linear Solution G From draw-down test surface m r D P coverage reservoir 1/2 G 2A  k = q*  ( m /  *c)/ m r 1/2 G  t Afracture surface[m 2 ] P t 1 t 2 k= permeability [m 2 ] P Q= flow rate[m 3 /s] statica m r = slope [Pa/  s] m viscosity [Pa*s]   porosity r pozzo c= comprimibility [Pa -1 ] X i2 X i1 X 12

Geothermal Modelling Linear Solution   m   2 q x D     p t ierfc      Ak 2 t       m x q D   p t  0 2 t p kA 13

Geothermal Modelling SHALLOW Sezione NW-SE • Shallow reservoir in “ tuscany series” • Top: 400 - 1000 m • Thickness 800 - 1000 m LIGURIDI SERIE TOSCANA Formaz. argillitico – • Temperature 170 - 200° carbonatiche SERIE TOSCANA Formaz. anidritiche VERRUCANO SERBATOIO SUPERFICIALE FORMAZIONE DEL FARMA Basamento DEEP metamorfico • Metamorphic Basement depth 2000 - 3000 m • Top: 300° C isotherm • There is no particular SERBATOIO lithological signature PROFONDO 14

Geothermal Modelling Space and Time discretization Energy and Mass balance Darcy Law Recalculation of Pressure and Temperature 15

Geothermal Modelling They address six categories, namely reservoir geometry, formation parameters, boundary/initial conditions, sinks and sources and computational parameters Simulation input data group (source: Pruess, 2002). 16

Geothermal Modelling FOR EACH CELL:  density (2800 kg/m 3 )  porosity (1.3 %)  permeability (m 2 , X,Y,Z)  conducibility (3.5 W/m°C)  specific heat(850 J/kg°C)  comprimibility (3 x 10 -11 m 2 /N)  expansivity (10 -5 1/°C) 17

Geothermal Modelling log T and P Natural State Model pressure Bagnore_25 Bagnore 25 Bagnore 22A temperature Bagnore 22A 1000 1000 1000 Equilibrium match of 1000 500 500 500 Pressione Pressione bar Temperatura °C bar Temperatura 500 Temperature 0 0 0 0 50 100 150 200 250 300 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 400 °C -500 -500 -500 0 Pressure 0 50 100 150 200 -1000 -1000 -1000 Da Petrasim quota s.l.m.[m] quota s.l.m.[m] quota s.l.m.[m] quota s.l.m.[m] Da estrapolazione Da grafico -500 -1500 -1500 Da tavole -1500 Da Petrasim Da estrapolazione Da tavole -2000 -2000 -2000 -1000 -2500 -2500 -2500 Da Petrasim Da Petrasim BG_3bis BG_3bis -3000 -3000 -3000 BG_25 -1500 BG_22 BG_22 -3500 -3500 BG_23 BG_23 -3500 -4000 -4000 -2000 -4000 18

Geothermal Modelling Modeling grid and the recharge area (F) Permeability as assumed from the drawdown analysis for radial model 19

Geothermal Modelling 20

PetraSim: TOUGH2 Basics Thunderhead Engineering Consultants, Inc. www.thunderheadeng.com +1.785.770.8511

Phases and Components Phases Components • • Homogeneous continuum Chemical species • • May consist of one or more Can be present in several chemical components different phases • • Examples: aqueous phase, non- Examples: H 2 O, NaCl, CO 2 aqueous phase (oil), gas, solid • Distribution of components in • In a closed system, amount of phases determined by chemistry different phases may change • All components in a phase flow • Phase change usually involves together substantial heat effects • In a closed system, components are conserved. 22

Relative Permeability Saturation regime: The porous medium is completely saturated with one phase. Pendular regime (a): One phase occurs in the form of pendular bodies that do not touch each other so that there is no possibility of flow for that phase. Fenicular regime (b): The porous medium exhibits an intermediate saturation with both phases. 23

Implications for Solution • Must start with reasonable physical assumptions • Getting correct initial conditions often requires a steady- state solution • In our experience, it is rare to find an error in TOUGH2, but getting solutions can require several iterations 24

Equations of State • EOS1 – Water, water with tracer • EOS2 – Water, CO 2 • EOS3 – Water, air • EOS4 – Water, air (vapor pressure lowering) • EOS5 – Water, hydrogen • EOS7 – Water, brine, air • EOS7R – Water, brine, air, radionuclides • EOS8 – Water, “dead” oil, gas • EOS9 – Saturated/unsaturated water flow 25

Materials  Materials are used to define the permeability and other properties in an analysis.  Each cell is associated with a material.  Information stored in this Material Editor are listed in the ROCKS section of a TOUGH2 input file. 26

Materials Parameters include:  Name – limited to 5 characters  Description - A longer description for user clarity.  Color – used for display  Rock Density (kg/m3)  Porosity  X, Y, and Z Permeability - only define 1 value for xy direction when working with polygonal mesh  Wet Heat Conductivity  Specific Heat  Relative Permeability  Capillary Pressure  A few others 27

Relative Permeability  Accessed through the Additional Material Data button.  You select the preferred RP function and enter desired parameters.  Plot displays the curves (gas in magenta and blue is liquid)  Curves can drastically affect model results, so look in literature for accepted parameters 28

Capillary Pressure  Similar process for Capillary Pressure 29

Materials Parameters include:  Pore Compressibility – defines how the pore volume changes as a function of pressure. This can be important during injection.  Pore Expansivity - defines how the pore volume changes with temperature.  Dry Heat Conductivity - used with the wet heat conductivity to change the thermal conductivity of the rock.  Tortuosity Factor – related to diffusion, details in the TOUGH2 manual  Klinkenberg Parameter – related to gas phase permeability, details in the TOUGH2 manual 30

Materials Materials can be assigned to:  Layers (through the Layer Manager)  Regions (right click on the Region in the data tree)  Cells or groups of Cells (selected through the 3D View)  Or… 31