Technische Universität Berlin Institut für Bauingenieurwesen, Fachgebiet Wasserwirtschaft und...

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Technische Universität Berlin Institut für Bauingenieurwesen, Fachgebiet Wasserwirtschaft und Hydroinformatik DYNAS Workshop

R. Hinkelmann, S. Pham VanFachgebiet Wasserwirtschaft und Hydroinformatik,

Institut für Bauingenieurwesen, Technische Universität Berlin

M. Paul, H. Sheta, T. Breiting, R. HelmigLehrstuhl für Hydromechanik und Hydrosystemmodellierung,

Institut für Wasserbau, Universität Stuttgart

Multiphase Models for Hillslope Hydrology

Contents

• Introduction

• Basic equations and numerical simulation

• Examples of simulating two-phase flow processes in the subsurface

• Conclusions and outlook

Contents

• Introduction

surface water

coastal areasea

riverestuary

lakereservoir

atmosphere interactionsrainevaporation

interactionsgroundwater springsurface-water infiltration

Systems in the hydrological cycle

subsurface

poreaquifer

fractured aquifer

karsticaquifer

Space scales in a subsurface system

catchment area

hydrogeologicalaquifer structure

localheterogeneity

km m mm m

single pore

Kobus (1995)

Time scales

surface water

groundwater

turbulence

wave velocity

pore velocity

adsorption

desorption

flow velocity

in- exfiltration

Processes

flow (e.g. water, soil air)

mass transport (e.g. contaminants, diffusive sources)

heat transport (e.g. cooling water, thermal soil remediation)

reaction, decay (e.g. adsorption, radioactive decay)

mass transfer (e.g. evaporation, condensation)

complex

coupled

multi-dimensional, space and time dependent

Models in the hydrological cycle

Modeling of hydrosystems

hydro-systems

processes

model approaches, methods, points of view

- discretization and stabilization methods

- parallel and adaptive methods and fast solvers

- information processing

- further methods

Monograph in Springer series

Wasserqualität

Hillslope in an alpine region

# Weir

% Spring

$ Meteorological Station

& Borehole

Unsaturated zone

layers macro-pores

preferential flow path

Contents

• Introduction

Model concept for two-phase flow in porous media

S saturation

volume of fluid phase volume of pore space

Model concepts for fractured-porous media

Hinkelmann (2003)

Basic equations

mass conservation for phase :

extended Darcy law for phase :

2 supplementary conditions:

kqvdivt

gρgrad pKμ

1SS gw cwg ppp

Constitutive relationships

Van Genuchten: n = 4.37 m = 0.77 = 0.37

Brooks-Corey: = 2.00 Pd = 2.00 Sw = 0.10

water saturation Sw [-]

0.2 0.4 0.6 0.8 1.0

capillary pressure -saturation

water saturation Sw [-]re

0.2 0.4 0.6 0.8

relative permeability -saturation

Discretization with Box method

time: implicit Euler method

space: node-centered FVM with fully upwinding for the flux terms

control volumesubdomain Bi

integration path

center of gravityof element e

advantages:

- stable

- locally mass conservative

- monotonous

- unstructured grids

disadvantages:

- 1st order accuray in time and space

- numerical dispersion

Discretization and solvers

non-linearities: Newton-Raphson Method

inner solver: BiCGSTAB with Multigrid preconditioning

idea Box method:

- Use advantages of simple methods.

- Compensate the disadvantages with parallel and adaptive methods

as well as fast solvers.

Lehrstuhl für Hydromechanik und Hydrosystemmodellierung,

Fachgebiet Wasserwirtschaft und Hydroinformatik,

Institut für Wissenschaftliches Rechnen, Universität Heidelberg

Unstructured Grid

Simulator MUFTE_UG

Multiphase Flow, Transportand Energy Model

Simulator MUFTE_UG

problem descriptions constitutive relationships physical model concepts mathematical model concepts discretization methods numerical schemes refinement, coarsening criteria physical interpretation

multigrid data structure local mesh refinement solver (CG, multigrid ...) r, h, p- adaptive methods parallelization user interfaces visualization

Parallel Speedup on Linux-Cluster

theoretical

LH Linux-Cluster2

Ölmann, Hinkelmann, Manthey, Lang, Helmig (2002)

preprocessing

database

geostatisticalmethods

mesh generator

geometry

uncertainties

physical properties

AUTOCAD

SIMSET

processing

numerical smulatorsimulation

heuristicsoptimization

postprocessimg

analyses

results

TECPLOT

visualizationtools

statistical tools

Modeling system MUFTE_UG

Contents

• Introduction

Contents

• Introduction

- dike

- methane

- experimental slope

Contents

• Introduction

- dike

- methane

Dike failure

Coastal defense structure

Experiment ETH Zürich

Hele-Shaw model, ETH Zürich

zone 1

zone 2

zone 3zone 4

zone 1: coarse sandzone 2: fine sand (K2 < K1)zone 3: coarse sandzone 4: gravel (K4 > K1)

infiltration of oil

slot between glass and

Experiment and simulation

Paul, Stauffer, Hinkel-mann, Helmig (2000)

Paul (2003)

Experiment and simulation

Paul, Stauffer, Hinkel-mann, Helmig (2000)

Paul (2003)

Paul, Stauffer, Hinkelmann, Helmig (2000)Paul (2003)

Results of the adaptive simulation

Contents

• Introduction

- dike

- methane

Abandoned coal mine

Problem description

dangers of methane

• pit gas

• combustable, explosive

• danger of suffocation

• negative effects on using of buildings

Problem description

closing coal mine

• stopping of ventilation

• stopping of water pumping

• partially filling of the shafts with

suction devices

duration: several years

gas drainagegas pipe with Protego cab

Practical problem cases

Principle sketch

System, initial and boundary conditions

IC: pw = phyd , sg = 0

BC: top: pw = patm , sg = 0 ; else: qw = 0, qg = 0

seamroad

Finite volume mesh

24672 nodes 136646 elements

Gas saturation

Data Explorer

System with geostatistical fractures, initial and boundary conditions

IC: pw = phyd , sg = 0

BC: top: pw = patm , sg = 0 ; else: qw = 0, qg = 0

coal seamfracture

Gas saturation

Contents

• Introduction

- dike

- methane

Infiltration experiment

surface runoff

macro-pores

surface fixing GWT

rain fall

Sketch of the system: homogeneous case

flow Dirichlet K2

initial conditions: pw = 100000 +gh [Pa], Sg = 1.0, Sgr = 0.01 [-] , Swr = 0.1 [-]

no flow (Neumann) boundary conditions: qw = 0.0, qg = 0.0

Dirichlet boundary conditions: pw = 100000 [Pa], Sg = 0.0 [-]

Computational grid and parameters: homogeneous case

parameters: - permeabilities: K1 = 10-12 [m2], K2 = 10-10 [m2]- Brooks-Corey model: pd = 1000 [Pa], = 2- Van Genuchten model: n = 4.366, = 0.00073

time: 153minPd = 0

time: 153minPd = 1000Pa

time: 153minPd = 10000Pa

Water saturation for different pd: homogeneous case

Pham Van (2004)

Water saturation for different pd: homogeneous case

Water saturation for BC und VG model: homogeneus case

Pham Van (2004)

Sketch of two-layer system

Dirichlet

parameters case 1: - permeabilities: K1 = 10-12 [m2], K2 = 10-10 [m2], K3 = 10-10 [m2] - Brooks-Corey model: pd1 = 1000 [Pa], pd3 = 100 [Pa], = 2

parameters case 2: - permeabilities: K1 = 10-12 [m2], K2 = 10-10 [m2], K3 = 10-14 [m2] - Brooks-Corey model: pd1 = 1000 [Pa], pd3 = 10000 [Pa], = 2

iddi K

Kpp scaling with Leverett-function:

Computational grid and parameters: two-layer system

Water saturation: two-layer system, case 1 (preliminary)

Pham Van (2004)

System with small-scale heterogeneities

flow Dirichlet K2

Geostatistical permeability fields

Bardossy (1992)

Water saturation: system with small-scale heterogeneities

Pham Van (2004)

Water saturation: system with small-scale heterogeneities

Pham Van (2004)

System with fracture

flow Dirichlet K2

Computational grid and parameters: system with fracture

parameters: - permeabilities: K1 = 10-12 [m2], K2 = 10-10 [m2]- Brooks-Corey model: pd = 1000 [Pa], = 2- fracture: Kf = 10-9 [m2], b = 1 [cm], b = 0.1 [cm]

Water saturation: system with fracture (b=1cm)

Pham Van (2004)

Water saturation: system with fracture (b=1cm)

Pham Van (2004)

Water saturation: system with fracture (b=0.1cm, 1cm)

Contents

• Introduction

Conclusions

Different layers, small-scale heterogeneities and fractures

have a strong influence on the water infiltration.

Improved model concepts for simulating water infiltration

into macro-pores should be developed in the future based

on controlled experiments:

- double-continuum model concept

- coupling a porous medium with a pipe

The results should contribute to a model concept for

simulating fluid-structure interaction in a hillslope.

Planned joint project: Coupling of flow and deformation processes for modeling hillslope movements

# Weir

% Spring

$ Meteorological Station

& Borehole

project 1: Numerical modeling of surface runoff coupled to the unsaturated zone and further process identification for a hillslope

movement project 2: Numerical simulation of two-phase flow and mass-transfer

processes in the subsurface

project 3: continuum mechanics of hillslope movements

project 4: Experimental investigation on the technical scale for process identification and for verification of numerical models

hillslope movements

partners: - Institut für Geoökologie, Universität Potsdam - Institut für Mechanik, Universität Stuttgart - Institut für Wasserbau, VEGAS, Universität Stuttgart - Institut für Wasserwirtschaft und Kulturtechnik, Universität Karlsruhe

Planned joint project: Coupling of flow and deformation processes for modeling hillslope movements

Project 2

Numerical simulation of two-phase flow and mass-transfer processes inthe subsurface

subsurface flow:

multi-dimensional two-phase flow model concept

macro-pores: combinded model model concept, double continuum

approach, coupling pipe and porous medium

upscaling, uncertainties: geostatistical methods

later transport, mass transfer:

multi-dimensional non-isothermal two-phase / multicomponent flow

and transport model concept

reduction of event-dependent calibration

Model concept for non-isothermal two-phase / three-component flow and transport

energy

R. Hinkelmann, S. Pham VanFachgebiet Wasserwirtschaft und Hydroinformatik,

M. Paul, H. Sheta, T. Breiting, R. HelmigLehrstuhl für Hydromechanik und Hydrosystemmodellierung,

Multiphase Models for Hillslope Hydrology

Technische Universität Berlin Institut für Bauingenieurwesen, Fachgebiet Wasserwirtschaft und...

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