Mathematical model of Baltic artesian basin – version V0

Juris Seņņikovs Laboratory for Mathematical Modelling

of Environmental and Technological

Processes UNIVERSITY OF LATVIA

Introduction

Structure of

presentation

1.Conception of model

system

2.Geometry model

3.Conception of the

modeling task

4.Results

5.Future perspective

Introduction – groundwater modeling

Model –”An object, which is designed to replace the object under consideration,

and which resembles the studied object.“

One of the project objectives is to create mathematical model of the Baltic

artesian basin (BAB).

Model should be able to show:

1.BAB geological structure

2.BAB groundwater flow (groundwater filtration model)

3.BAB flow and transformations of solubles in the groundwater

(groundwater chemistry model)

Model will be created as a computer model. Parrarel to model development

software for data processing and vizualization of the modeling results is

created (HiFiGeo).

All of the objects needed for model operation (data, software, equations,...)

will be denoted as model system.

Information base Geometry model Hydrogeological

model

Closed 3D spatial model, which includes geological structure and properties of geological materials

Geological data monitoring data

•Objects(layers, faults, materials) • Automatic mesh generation • Stratigraphy (hronological generation)

• input • update • storage • access • remote access(web)

• 3D mesh • equations • numerical method • boundary conditions • solutions

• Result: groundwater flow in BAB •Used in activities 4a, 4b, 4c

Scheme of intergrated model system development

Development of 3D geological structure geometry

model

Geometrical model is created in layers.

Creation of each layer geometry involves several data sources, depending

on data availability, usebility....

Borehole data

Other model

data

3D

geological

structure

Layer surface and

thickness data Maps of layer

distribution

(geological maps)

Geological know-how

in areas with no data

Input data – borehole database

D3 gj-am surface

distribution borehole

data

Cm surface distribution

borehole data

Deeper you go, less

data you get...

Input data – structural surface isoline maps

Isolines and

traces of

faults on the

basement

surface

Input data– structural surface isoline maps

Basement surface

data:

In Latvia– isolines

and borhole data

In Lithuania– isolines

In Estonia– Data from

Estonian

hydrogeological

model

Rest of the model

territory–published

data

During the constraction of the model

problems of stitching the heterogenous

data was solved

Input data –geological maps

Input data – other information

Building of geometry structure algoritms

All of the layers are built on the triangular mesh. Each mesh vertex holds

layer surface height value. Triangular mesh plot permits to introduce

variable resolution level within the different meshplot areas.

Triangular meshplot for whole of the BAB area is constructed considering

common lines, such as: coastline, river/lake lines, border of geological

material distribution, traces of the tectonic faults etc.

Each surface is assigned to particular meshplot subarea within the general

meshplot.

Combining all of the surfaces we get 3D volume mesh, which is constructed

of prizm, pyramidal and tetrahetral elements.

Building of geometry structure algoritms

Typical lines Model border

Border of the

geological material

Border of Estonian

hydrogeological

model

Rivers

Building of geometry structure algoritms

Border of the triangular meshplot

coinsides with the line data

Model border

Border of the

geological material

Typical lines

Border of Estonian

hydrogeological

model

Rivers

Geometric structure - mesh

Finite element mesh,

view from the top.

Higher resolution of

mesh in areas with

sufficient geological data

Model construction algoritms

3D geological structure of the model is composed of different data sources. To

implement all of the available data into geometrical model a set of operations is

developed, known as assamblege of algoritms. Algoritms which define individual

geological surfaces are subdivided into individual blocks.

Applied algorithms are implemented using specially developed script language. This

approach has several advantages:

1. Flexibility in choosing ways to build the structure

2. Parallelization in developing/updating of different structure elements

3. Documented and repeatable structure building path

4. Possibility to rebuild the structure with slight or significant modifications at any

time

5. Possibility to build, and maintain several structures of different complexity

simultaneously

In constructing the version 0 model system, main attention was paid to the

design of the model script and its components. Model script allows to run

model construction, calculation and processing results automatically.

Algoritms for model geometry

•Surface data from borehole database

•Surface data from the structural map isolines

•Layer thickness map

To create above listed algoritms all of steps listed below need to be taken:

•Transformation of the data format

•Interpolation

•Extrapolation

•Smoothing

•Triangulation of the point assamblege

Parameters Borderline Isolines Fault lines

Database of boreholes

Filtering (MySQL)

Set of points

3D surface 2D triangulation

2D triangular mesh

3D surface Outer border

Set of 3D surfaces

Geological stratification

Volume mesh

Line

HiFiGeo volume mesh

“Law”

Table

Subquaternary rock data

Set of thicknesses

Layer thickness

DATA/Result

Algorithm

External sources (models)

Model construction algoritms

Skripta moduļa piemērs

SelectMeshRegion( MeshIn=BABRezgisBezLuzFile, EdgeIDMap=EdgDBFile, LineID=1000, ZFileOut=UpesMask.Z, SelectionSide=0 )

InterpolateFromRaster( MeshIn=PamataRezgisFile, RasterIn=SRTMtiffFile, ZFileMask=UpesMask.Z, Op=min, Dist=500, ZvalOut=Upes1.z )

InterpolateFromRaster( MeshIn=PamataRezgisFile, RasterIn=LVDEMtiffFile, ZFileMask=UpesMask.Z, Op=min, Dist=500, ZvalOut=Upes2.z )

InterpolateFromRaster( MeshIn=PamataRezgisFile, RasterIn=IOWtiffFile, ZFileMask=UpesMask.Z, Op=min, Dist=500, ZvalOut=Upes3.z )

MergeZFiles( FileIn1=Upes1.z, FileIn2=Upes2.z, FileOut=Upes.Topo.z )

MergeZFiles( FileIn1=Upes.Topo.z, FileIn2=Upes3.z, FileOut=Upes.Topo.z )

InterpolateFromRaster( MeshIn=PamataRezgisFile, RasterIn=SRTMtiffFile, ZvalOut=topoSRTM.z )

InterpolateFromRaster( MeshIn=PamataRezgisFile, RasterIn=LVDEMtiffFile, ZvalOut=topo25m.z )

InterpolateFromRaster( MeshIn=PamataRezgisFile, RasterIn=IOWtiffFile, ZvalOut=topoiow.z )

MergeZFiles( FileIn1=topoSRTM.z, FileIn2=topo25m.z, FileOut=topo.z )

MergeZFiles( FileIn1=topo.z, FileIn2=topoiow.z, FileOut=BAB.topo.z )

MergeZFiles( FileIn1=BAB.topo.z, FileIn2=Upes.Topo.z, FileOut=BAB.topo.z )

Surface topography generation

Script bloc – secīgs komandu saraksts

Command – data processing tool

Geometric structure

D2 ar-br

distribution area

Cross section A-B

Geometric structure

Cross section A-B

Geometric structure

3D attēli

HiFiGeo software

Software for visualisation of input data and results:

•Visualization of surfaces

•Visualization of vertical sections along any direction

•Visualization of horizontal sections along any level

•3D sections of any configuration

•Visualization pf piezometric head and flow velocity fields (scalar and vector

magnitudes)

•Borehole database (SQL) query definition and query results visualization

•Visualization of borehole stratification and lithology in vertical cross

sections

•Visualization of GIS layer (WMS , SHP format)

•Calculations settings management

HiFiGeo software

Borehole vizualization in cross sections

HiFiGeo software

Western Latvia geological structure, including tectonic faults, in 3D.

HiFiGeo software

SO4 concentration levels in D3 gj-am layer.

Groundwater flow calculation settings

In V0 stationary (e.g. stable and constant on a longer time frame flow )flow is calculated

Boundary conditions:

1.As model covers all of the BAB area, no flow conditions are defined for

the margins

2.Infiltration conditions are set on the surface (infiltration v0 is set constant for the whole

model area)

3.Mean discharge values are set for the water wells (in places where data is

available)

Material properties:

1.Constant horisontal and vertical permeability values for each layer,

determined during the calibration.

2.Quaternary– areally variable permeability settings. For Latvia territory

permeability is calculated using specially designed algoritm.

Calculation results are: piezometric head in each mesh point in each layer

and un flow velocity fields, as a derivative from the piezometric head field.

Material properties

Vertical permeability

(m/diurnal)

distribution of the

Quaternary.

Designed algoritms

for determining

material properties

from the borehole

lithology data

In the area outside

Latvia mean

permeability

parameters are set

Material properties

Permeability koefficent

(m/diurnal) distribution in cross

section A-B

Aquicludes – blue color layers

Aquitards – reddish layers

Boundary conditions – Surface basins

Color field represents

surface topography

Blue lines and fields

denote river betwork

and lakes.

Boundary conditions - Discharge

Water discharge points,

color denotes amount of

the discharge m3/diurnal

Latvia – Latvian

Environment, Geology

and Meteorology Centre

data

Lithuania – Geological

survey of Lithuania data

Estonia – Estonian

hydrogeological model (modified)

Calculating groundwater flow

For automation and repeatibility, similar to geology structure building,

material properties and boundary conditions are defined through script

commands.

Performance of the script can be controlled and edited on-line through a

web browser.

Groundwater flow is calculated on computing cluster. V0 is calculated on 8

core, 16 GB RAM computer.

Visualization and analysis of the calculation results is done in HiFiGeo

software.

During the calibration layer permeability properties were varied resulting in

20 calculations.

Verification of the calculated piezometric head distribution with observed

mean piesometric head in Latvia has been done.

Verification of the piezometric head – D3 fm

For comparision static

water levels obtained

during the borehole

instalation were used

350000 400000 450000 500000 550000 600000 650000 700000

6180000

6200000

6220000

6240000

6260000

6280000

6300000

6320000

6340000

6360000

6380000

-50

-30

-10

10

30

50

70

90

110

130

150

170

Verification of the piezometric head– D3 gj-am

For comparision static

water levels obtained

during the borehole

instalation were used

Vertical cross section Viļņa - Rīga – Kohtla-Järve, geological stucture

Results

Vilnius Kohtla-Järve Rīga

Results

Distribution of the piezometric head in cross section, arrows indicate

groundwater flow direction

Vertical cross section Rucava – Rīga - Pleskava, geological structure

Results

Rucava Pleskava Rīga

Results

Distribution of the piezometric head in cross section, arrows indicate

groundwater flow direction

Piezometric head in

D2 ar-br layer Results

Piezometric head in

D3 gj-am slānī

Results

Horizontal cross section, -100

m level – materials and

groundwater flow directions

Results

Horizontal cross section, -

100 m level– Materials and

isolines of piezometric head

Results

Summary

Model system: A script language is developed for automatization of geometry structure

builing and input data processing.

Geometry model: Geometry model of the BAB geological structure is developed, consisting of

24 layers

Groundwater flow model: Defined boundary conditions.

Several groundwater flow calculations.

Preliminary calibration and verification with observed data.

Software: Updated HiFiGeo software structure for geological structure and calculation

results visualization and postprocessing

Future developments

Model system: Futher development of script, generalization, simplification, documentqaion

and project staff training

Futher development of surface generation algoritms.

Geometry model: Futher integration of Lithuania geology data (faults, water discharge,

material properties).

Contacts with the rest of the model covering countries – Polish GS,...

More precise data of the Baltic Sea area.

Groundwater flow model: Joining with the hydrological model (for improved surface infiltration

modelling).

Development of the solubles transport and reaction model.

Non stationary groundwater flow calculations (including project activity

PALEO).

Software: Futher development of the vizualisation and automatization tools