Evaporation-driven soil salinization

Evaporation-driven soil salinization Vishal Jambhekar 1 Karen Schmid 1, Rainer Helmig 1,Sorin Pop 2 and Nima Shokri 3 1 Department of Hydromechanics and Hydrosystemmodeling, University of Stuttgart 2 Department of Mathematics and Computer Sciences, TU Eindhoven 3 School of Chemical Engineering and Analytical Science, The University of Manchester NUPUS Meeting 18-20 March 2013

Overview Motivation Theory Model Concept First Results Coupling Outlook Slide 2/48

Overview Motivation Theory Model Concept First Results Coupling Outlook Motivation Slide 3/48

Motivation Salinization problem: 9.38 million hectares of land is affected in India 1 1.5 million hectares of land is affected in Tunisia 2 It account approx.10 % of Tunisia s surface Salinization in Tunisia 1 Salinity research in India: An Overview, Dagar, J. C., 2005 2 Les sols sales et leur mise en valeur en Tunisie,Hachicha, M., 2007 Motivation Slide 4/48

Motivation Soil salinization problem across the world Motivation Slide 5/48

Motivation To analyze the flow and transport processes related to the evaporative salinization of a porous-medium To develop a model concept Wind Radiation Evaporation Salinized Soil Unsaturated Zone Evaporative Salinization Porous-media flow and transport processes Salt precipitation Change in porous-media properties Interaction processes at the interface Influence of the atmospheric processes Motivation Slide 6/48

Interface Processes turbulent flow laminar boundary layer free flow mass energy exchange exchange momentum exchange radiation convection conduction gas diffusion advection solid fluid shear stress transfer processes normal forces porous medium interface roughness small scale turbulences vaporization and condensation salt precipitation A coupling concept for two-phase compositional porous-medium and single-phase compositional free flow, Mosthaf et al., 2011 Motivation Slide 7/48

Overview Motivation Theory Model Concept First Results Coupling Outlook Theory Slide 8/48

Volume Averaging Micro-scale Macro-scale (REV) Averaging Liquid Gas Solid Solid Liquid Gas Micro-scale to macro-scale transition Effective parameters: Porosity: φ = Saturation: S α = Intrinsic permeability K Volume of pores in REV Volume of REV Volume of phase α in REV Volume of pores in REV Bulk thermal conductivity λ pm Theory Slide 9/48

Stages of Saline-water Evaporation Liquid Gas Salt (a) SS1 Liquid Gas Salt (b) SS2 Liquid Gas Salt (c) SS3 Stages of evaporation 3 : SS1: High evaporation rate SS2: Evaporation rate falls subsequently SS3: Constant low evaporation rate 3 Infrared thermography of evaporative fluxes and dynamics of salt deposition on heterogeneous porous surfaces, Nachshon et al., 2011 Theory Slide 10/48

Saline-water Evaporation Micro-scale Macro-scale (REV) Averaging Saline water Salt Solid Saline water Air Micro-scale to macro-scale transition Salt Theory Slide 11/48

Overview Motivation Theory Model Concept First Results Coupling Outlook Model Concept Slide 12/48

Model Concept Mathematical and numerical model concept A mathematical/numerical model requires an idealization of the physical processes in a natural system in such a way that their characteristic properties are maintained 4 4 Numerical simulation of non-isothermal multiphase multicomponent processes in porous media.: 1. An efficient solution technique, Class et al., 2002 Model Concept Slide 13/48

Model Concept advection, convection conduction, diffusion gas phase air free flow water transfer fluxes direct evaporation matrix air gas phase water advection, convection conduction, diffusion solid phase vaporisation + condensation dissolution + degassing thermal energy salt precipitation water air salt liquid phase porous media Compartments: Single-phase two-component free-flow Three-phase three-component porous-media flow Model Concept Slide 14/48

Objectives To develop desired model concept primary objectives are defined as follows: Primary objectives To describe dissolved salt transport in a porous-medium under the influence of evaporation flux To account for salt precipitation at saturation concentration To include Free-flow porous-media interaction physics and atmospheric processes To validate against the experimental data Model Concept Slide 15/48

Porous-media Equations Multi-phase multi-component Darcy flow Mass conservation of each component κ: (φϱ mol,α S α xα) κ }{{ t } α α α storage [ krα ] ϱ mol,α x κ µ αk ( p α ρ α g) α }{{} advection [ D κ pm,αϱ mol,α xα κ ] }{{} diffusion = α q κ α }{{} source/sink Model Concept Slide 16/48

Porous-media Equations Salt precipitation 5 : q κ α = { (φϱmol,l S l (xl NaCl xl,max NaCl )) t Conservation of precipitated salt: for κ = NaCl, α = l 0 else (φ NaCl s ϱmol,s NaCl) + q NaCl l = 0 t Porosity change: φ = φ 0 φ NaCl s 5 Analytical solution to evaluate salt precipitation during CO2 injection in saline aquifers, Zeidouni et al., 2009 Model Concept Slide 17/48

Porous-media Equations Permeability K change Zeidouni et al. (2009) 5 : ( ) K φ 3 ( ) 1 2 φ0 = K 0 φ 0 1 φ Tsypkin and Woods (2005) 6 : K = 1 e(ωφ(1 (φ NaCl K 0 1 e (ωφ) s ))) 6 Precipitate formation in a porous rock through evaporation of saline water, Tsypkin and Woods, 2005 Model Concept Slide 18/48

Porous-media Equations Local thermodynamic equilibrium Local thermal equilibrium is assumed: T l = T g = T s = T Chemical equilibrium accounts for the mass transfer between fluid phases: Dalton s law: Raoult s law: Henry s law: p g = κ p κ g p κ g = x κ g p κ sat p κ g = x κ wh κ w Mechanical equilibrium is valid locally. Discontinuities in pressure exists across fluid-fluid-solid interface: p c = p g p l Model Concept Slide 19/48

Porous-media Equations One energy equation (T l = T g = T s = T): α (φϱ α u α S α ) } {{ t } storage I = 0 + α + α + α (φ NaCl s ϱ NaCl s c NaCl s T) } {{ t } storage II (1 φ 0 ) (ϱ sc s T) t }{{} storage III [ ϱ α h α v α ] [ λ }{{} pm T ] }{{} convection conduction Model Concept Slide 20/48

Porous-media Equations where heat conductivity λ pm = λ pm (S l ) 7 : λ pm = λ eff,g + S l (λ eff,l λ eff,g ) with effective heat conductivity λ eff,α 8 : ( ) λ 0.28 0.757 log φ 0.057 log(λs/λα) eff,α λs = λ α λ α 7 High Temperature Behavior of Rocks Associated with Geothermal Type Reservoirs, Somerton et al., 1974 8 Analysis of thermal conductivity in granular materials, Krupiczka et al., 1967 Model Concept Slide 21/48

Capillary presure-saturation relationship Micro-scale Macro-scale (REV) Averaging Liquid phase Solid Solid Liquid phase Brooks-Corey model: Multi-phase compositional flow p c (S l ) = p d S 1 λ e S e = S l S lr 1 S lr Model Concept Slide 22/48

Capillary presure-saturation relationship Micro-scale Macro-scale (REV) Averaging Liquid phase Solid Solid Liquid phase Brooks-Corey model: Multi-phase compositional flow p c (S l ) = p d S 1 λ e S e = S l S lr 1 S lr Model Concept Slide 23/48

Numerical discretization Time and space Implicit Euler method employed for time: x t+ t x t = A t+ t x t+ t t BOX method is used for space: Subdomain from element e in Box Bi (i.e. subcontrol volume associated with node i) B i k k i i e j Barycenter of element e e j Integration points Model Concept Slide 24/48

Overview Motivation Theory Model Concept First Results Coupling Outlook First Results Slide 25/48

First Results Dissolved NaCl distribution in a fully saturated homogeneous sand column First Results Slide 26/48

First Results Initial: Evaporation driven NaCl precipitation in an unsaturated homogeneous sand column First Results Slide 27/48

First Results Initial: Evaporation driven NaCl precipitation in an unsaturated heterogeneous sand column First Results Slide 28/48

First Results 2 cm 4 cm Movie: Evaporation driven NaCl precipitation in an unsaturated heterogeneous sand column First Results Slide 29/48

First Results Evaporation driven NaCl precipitation in an unsaturated heterogeneous sand column First Results Slide 30/48

First Results Initial: Initial: (a) High rate (b) Low rate Evaporation driven NaCl precipitation in an unsaturated sand columns First Results Slide 31/48

First Results Evaporation driven NaCl precipitation in an unsaturated sand columns First Results Slide 32/48

Overview Motivation Theory Model Concept First Results Coupling Outlook Coupling Slide 33/48

Coupling with the free-flow advection, convection conduction, diffusion gas phase air free flow water transfer fluxes direct evaporation matrix air gas phase water advection, convection conduction, diffusion solid phase vaporisation + condensation dissolution + degassing thermal energy salt precipitation water air salt liquid phase porous media Coupling Slide 34/48

Free-flow equations Component mass balance: (ϱ mol,g xg κ ) + [ ϱ mol,g x κ ] g v g [ D κ }{{ t pm,gϱ mol,g x κ ] g = q κ g }}{{}}{{}}{{} storage advection diffusion source/sink Phase mass balance: ϱ g + [ ϱ g v g ] = q g }{{} t }{{}}{{} storage advection source/sink Coupling Slide 35/48

Free-flow equations Stokes equation for momentum balance: (ϱ g v g ) t } {{ } storage Energy balance: + [p g I µ g ( v g + v T g ) ] = ϱ g g }{{}}{{} flux body force (ϱ g u g ) } {{ t } storage + (ϱ g h g v g ) }{{} convection (λ g T) = }{{} q }{{} T conduction source/sink Coupling Slide 36/48

Interface Mechanical equilibrium: Normal traction: gas phase solid phase gas phase water phase Tangential traction: gas phase solid phase gas phase water phase Coupling Slide 37/48

Interface Continuity of mass flux: [ϱ g v g n] ff = [(ϱ g v g + ϱ l v l ) n] pm [(ϱ mol,g v g x k g D g ϱ mol,g x k g) n] ff = [(ϱ mol,g v g x k g D g,pm ϱ mol,g x k g Thermal equilibrium: + ϱ mol,l v l x k l D l,pmϱ mol,l x k l ) n]pm The assumption of local thermal equilibrium at the interface allows continuity condition for a primary variable T: Continuity of heat flux: [T] ff = [T] pm [(ϱ g h g v g λ g T) n] ff = [(ϱ g h g v g + ϱ l h l v l λ pm T) n] pm Coupling Slide 38/48

Interface Chemical equilibrium: gas phase solid phase gas phase water phase = Continuity of chemical potential between phases inside the porous medium Continuity of mass or mole fraction at the interface Coupling Slide 39/48

No flow Outflow No flow Coupled problem Initial: Coupling Initial: No flow Numerical example Drying Salinization Coupling Slide 40/48

Overview Motivation Theory Model Concept First Results Coupling Outlook Outlook Slide 41/48

Outlook Future work: Validation against the experimental data Test alternative models for porosity and permeability description Transport for dissolved salt species (e.g. Na + and Cl ) and reactive precipitation Stability analysis Validity of chemical equilibrium assumption at the interface Effect of turbulence and solar radiation on evaporative salinization Outlook Slide 42/48

Thanks a ton... Thanks a lot for your kind attention... Outlook Slide 43/48

Porous-media Equations Supplementary constraints 9 Total void space within the porous matrix is occupied by liquid and gas phases: S g = 1 S l The secondary phase pressure is determined using the capillary pressure: p c (S l ) = p g p l The mass and mole fractions of all components κ {w, a, s} in each phase α {l, g} sums up to one: (e.g. + Xl a + Xl NaCl = xl w + xl a + xl NaCl = 1) X w l 1997 9 Multiphase flow and transport processes in the subsurface, Helmig, R., Outlook Slide 44/48

Porous-media Equations Constitutive relationships Brooks-Corey model is used for capillary pressure-saturation and the relative permeability-saturation relationships Outlook Slide 45/48

Porous-media Equations Fluid properties 10 Density and viscosity of the liquid phase are defined as: ϱ l = ϱ w + 1000Xl NaCl {0.668 + 0.44Xl NaCl + [300p 2400pXl NaCl + T(80 + 3T 3300X NaCl l 13p + 47pX NaCl l )] 10 6 } µ l = 0.1 + 0.333X NaCl l + (1.65 + 91.9Xl NaCl 3 ) + exp{ [0.42(X NaCl0.8 l 0.17) 2 + 0.045]T 0.8 } 10 Seismic properties of pore fluids, Batzle and Wang, 1992 Outlook Slide 46/48

Porous-media Equations Fluid properties Specific enthalpy of the liquid and gas phases are given below: h g (p g, T) = X w g h w + X a gh a and h l (p l, T) = X w l hw + X a l ha + X NaCl l (h NaCl + h NaCl ) The phase internal energy is determined as: u α (p α, T) = h α p α /ϱ α Outlook Slide 47/48

Primary variables The choice depends on the present phases Primary variables and switch criteria Phase State Phase Present Primary Variables Switch liquid phase liquid p l, xl a, xs l, φs s, T xl a xl,max a gas phase gas p g, xg w, T xg w xg,max w both phases liquid and gas p g, S l, xl s, φs s, T S α 0 Table: Primary variables for different phase states and switch criteria Outlook Slide 48/48