cokriging to improve geomodels and hydrogeological models · matrix solutions inc. 1 cokriging to...

Matrix Solutions Inc. 1

Cokriging to improve geomodels and hydrogeological models

Maxime Claprood, Alexander Haluszka, Louis-Charles BoutinWater Technologies Symposium, April 2017


Objective

• Integration of available data to best represent the regional groundwater flow


Outline

• Background–Why do we talk about cokriging at Water Tech?

• Kriging and Cokriging–Simple approach to cokriging

• Examples–Mapping a structural unconformity

–Mapping net isopach in aquifers


Background - Why is this important?


Background – Why is this important?• Hydrogeology assessment for:

• Any project application

• Water supply

• Environmental Assessment

• Regional scale: 10’s to 100’s km


Background – Why is this important?• Hydrogeology assessment for:

• Any project application

• Water supply

• Environmental Assessment

• Regional scale: 10’s to 100’s km

• Typical workflow:

Regional Characterization and Conceptual

Model Development

3D GeomodelDevelopment

Numerical Model

Construction and Calibration


Background – Why is this important?

• Well logs

• Regional maps • coarse spatial resolution

• Local maps at fine spatial resolution• Seismic derived maps

• Geological and hydrogeological interpretation (soft knowledge)


Model Development


Numerical Model




• To represent major hydrostratigraphic units into a 3D frame

• To consider different levels of confidence in the available data

• Interpolation of units structure can play an important role in numerical model of groundwater flow


Model Development


Numerical Model




• To represent:

• conceptual model of groundwater flow

• hydraulic connection between aquifers

• transmissivity of aquifers


Model Development

3D Geomodel Development

(GOCAD)

Numerical Model



Cokriging


Cokriging

• Kriging:– Learn from your initial data:

• To define the spatial structure for interpolation

–Apply optimal weights to your data points–Take into account:

• Distance between data points and points to interpolate• Structure of variable through:

– the trend– the variogram


Cokriging

• Kriging:

– Limits when sparse control points

from Dubrule (2003)


Cokriging

• Kriging:– Limits when

sparse control points

–Consider other data correlated to initial control points

from Dubrule (2003)


Cokriging

• Extension of kriging using correlated variables

from Dubrule (2003)• Z1 : primary data• Z2 : secondary data


Cokriging

• Extension of kriging using correlated variables

–Collocated cokriging to simplify the equation system

from Dubrule (2003)


Example 1 – Mapping a Structural Unconformity


Mapping a Structural Unconformity• Need to represent local features in regional model

of groundwater flow

100km

Freshwater aquifer

Targeted aquifer forgroundwater supply

your project

Brown to grey: Structural Unconformity


Mapping a Structural Unconformity• Need to represent local features in regional model

of groundwater flow– Small-scale valleys can play an important role for

groundwater flow and hydraulic connection between aquifers

100km

Freshwater aquifer


2km

your project


Mapping a Structural Unconformity

• Data available:Regional Map 500m resolution

• Well markers from well logs (circles)

• Interpreted thalweg(squares)

• Coarse resolution map



Conventional Workflow - Regional map only

Conventional workflow - Well markers only

Blue surface is modeled freshwater aquifer



• CoKriging

–Primary Data: Elevations at well markers

–Secondary Data: Elevations from regional map



• CoKriging - Simplified approach1. Define variogram for primary data only

2. Compute coefficient of correlation (r2) between primary and secondary data– Easy parameter to evaluate

3. Variance of secondary data– Easy parameter to evaluate

r2 = 0.7

Var(Z2) = 3158 m2



• CoKriging

–1st step: Define variogram on primary data:

• variation of variance with distance between data points

• Learn from the data to find best function for interpolation


Mapping a Structural Unconformity• Variogram:

– Variance with distance between control points

– Computed on 4 directions

0°45°

90°

135°



Kriging using well markers only

• CoKrigingCoKriging using well marker and map


Mapping a Structural Unconformity• North-South cross-sections through valleys

Conventional workflow –Well markers only

Freshwater aquifer


• Deep channel:• Hydraulic connection

between aquifers



Conventional workflow –Well markers only Conventional workflow –

Regional Map


between aquifers

• Unconformity at high elevation:• absence of channels



CoKrigingConventional workflow –Well markers only Conventional workflow –

Regional Map

• Shallow channel:• No hydraulic

connection between aquifers


between aquifers

• Unconformity at high elevation:• absence of channels


Mapping a Structural Unconformity• CoKriging:

– Considers correlation between 2 sets of data– In this example, cokriging best integrate the data to map the

structural unconformity:• Ensure proper representation of the hydraulic connection in the next-to-

be-built numerical model of groundwater flow.


Example 2 – Mapping Net Isopach


Mapping Net Isopach

dZgross

• Gross isopach vs Net isopach– Well markers identify top and bottom of major

hydrostratigraphic units (gross isopach)• Small effort to pick, 100 to 1000 picks for a typical project


Mapping Net Isopach• Gross isopach vs Net isopach

– Well markers identify top and bottom of major hydrostratigraphic units (gross isopach)• Small effort to pick, 100 to 1000 picks for a typical project

– but if we look at the well logs within that unit


Mapping Net Isopach

• Interlayering of shale and sand–Net Isopach (dZnet): portion of sand within the unit

• Only sand portion contributes to groundwater flow

–dZnet is complex to pick:• To save effort, picks at

10-50 wells for a typical project


Mapping Net Isopach

• hydraulic conductivity (K) is not constant within a single hydrostratigraphic unit–Transmissitivity (Kxy * dZnet) affected by net isopach

• We would like to represent all shale and sand layers in model, but…


Mapping Net Isopach

–Can have 30+ hydrostratigraphic units in regional model of groundwater flow

–Represent regional groundwater flow in major aquifers


Mapping Net Isopach• Possible to represent all sub-units for local-scale projects

– Transport in single aquifer

• and we have the expertise to do it!

• From WaterTech 2015 presentation


Mapping Net Isopach

• In regional models, limit the number of layers, but we still need to represent the net isopach

• 2 options:

1. Scale transmissivity by net isopach

2. Represent the aquifers in one layer where:

• layer thickness = net isopach


Mapping Net IsopachMap: Gross isopach from geomodel

Dots = Net isopach

0m (blue) to 60m (red)


Mapping Net IsopachMap: Gross isopach from geomodel

Dots = Net isopachR2 = 0.6 between gross and net isopach

Perfect for Cokriging!


Mapping Net IsopachGross Isopach from geomodel Cokriged Net Isopach

Both maps: 0m (blue) to 60m (red)


Mapping Net Isopach

• What impact does it have on regional groundwater flow?– Let’s assume the aquifer’s horizontal conductivity:

• Kxy = 5x10-5 m/s

–… and we compute the transmissivity (T) of the aquifer• T = K * dz


Mapping Net Isopach

• What impact does it have on regional groundwater flow?Transmissivity scaled by gross isopach

* All maps: Transmissivity from 0 (blue) to 250 (red) m2/day


Mapping Net Isopach


* All maps: Transmissivity from 0 (blue) to 250 (red) m2/day

Transmissivity scaled by net isopachinterpolated from well markers only


Mapping Net Isopach


* Color scale for all maps are transmissivity from 0 (blue) to 250 (red) m2/day

Transmissivity scaled by net isopachcokriged with gross isopach

Transmissivity scaled by net isopachinterpolated from well markers only


Conclusions


Conclusions• Cokriging was successfully used to:

– Map structural unconformity • integrated all available data

– local well markers, regional low-resolution map (and high-resolution local map, not presented)

• better represented conceptual model of regional groundwater flow

• improved hydraulic connections between aquifers

– Map aquifer’s net isopach• improved representation of transmissivity

of aquifer• More realistic flow system into a

regional groundwater flow model


Matrix Contacts

• Maxime [email protected]

• Alexander [email protected]

• Louis-Charles [email protected]

mailto:[email protected]



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