Presentation by Wouter Kranenburg, Deltares, at the Delft3D - User Days (Day 2: Hydrodynamics), during Delft Software Days - Edition 2019. Tuesday, 12 November 2019, Delft.

1. Lake Kivu
3D hydrodynamic modelling
of a deep and strongly stratified lake
to study methane extraction
Wouter Kranenburg
Delft Software Days
November 12, 2019

2. Introduction: Lake Kivu
Lake Kivu:
• Deep, strongly stratified lake
• Trapped dissolved CO2 & CH4
• Increasing gas extraction
Pilot methane extraction plant

3. Introduction: the Project
Title:
• ‘Study on water levels, deep currents and waves in Lake Kivu’
Aim:
• Increase understanding of the physical processes in the lake
… relevant for safe, sustainable and optimal methane extraction
• Tool development
• Capacity building
Approach:
• Overview literature
• ADCP measurements
• 3D hydrodynamic modelling
• Wave modelling
• 3D + methane modelling
Team:
• Client: Lake Kivu Monitoring Program
• Partners: Deltares, Hydro-Key,
EAWAG, Deep, EPFL, VUBrussels

4. Introduction: this Presentation
Title:
• 3D hydrodynamic modelling of the deep and strongly stratified Lake Kivu
Approach:
• Overview literature
• ADCP measurements
• 3D hydrodynamic modelling
• Wave modelling
• 3D + methane modelling
Authors:
• Meinard Tiessen, Reimer de Graaff, Jelmer Veenstra (Deltares), Rob Uittenbogaard
(Hydro-Key), Wim Thiery (VUB), Jonas van de Walle (KULeuven), Damien Bouffard
(EAWAG), Gaetan Sakindi (LKMP), Augusta Umutoni (LKMP)

5. Lake Kivu: Stratification
• Deep lake (475 m) in volcanic area
• Subaquatic discharge warm & saline water
• Strong and stable stratification
• CO2 & CH4 from subaquatic sources and
production
• Trapped dissolved CO2 & CH4
Salt = dominant

6. Lake Kivu: Gas extraction
• Problem? Fear for limnic eruption (has happened in Lake Nyos & Lake Monoun)
• Solution: Extract methane and use for energy supply!

7. Lake Kivu: Saturation?
Kusakabe (2017)
Close to 100%
Gas Saturation
Schmid et al. (2019)
Required Uplift to
100% Saturation
Hydrostatic
Pressure
Lake Kivu

8. Lake Kivu: Questions
Questions:
• How does the lake presently behave?
• What are the typical flow velocities and patterns in the lake?
• How will reinjected water (saline & nutrient rich deep reinjection and CO2 rich
shallow reinjection) spread through the system?
Considerations:
• Strongly spatially variable wind forcing (lake effect) and the spatial non-uniform
plume dispersion require 3D hydrodynamic modelling
Aim:
• Development of 3D hydrodynamic model of Lake Kivu for study of spatial patterns
in flow & concentrations, at time scales up to ~2 years

9. Characteristics:
• Hydrostatic Reynolds-Averaged Navier-Stokes modelling framework
• Solves eq.’s for hor. momentum transport, continuity & transport of constituents
• Equation of state includes effects CO2, CH4 on density
• Model accounts for meteo-forcing:
wind, atmospheric pressure, evaporation, precipitation, heat exchange (solar and
atmospheric radiation, back radiation, latent heat fluxes, sensible heat fluxes)
Set-up: Modelling framework
Delft3D-FLOW of Delft3D 4 Suite:
• In-house code of Deltares
• Process-wise state-of-the-art code for
3D hydrostatic flow
• Options for coupling to Water Quality
(Delft3D-WAQ), Waves (Delft3D-WAVE)
and Near-Field modules

10. Set-up: Modelling framework
Equation of state:
substance β-coefficient Reference
salinity 0.75 10-3
Wuest et al. 1996
CO2 0.284 10-3
Ohsumi et al., 1992
CH4 -1.25 10-3
Lekvam and Bisnoi, 1997
( ) ( )( )2 42 4 CO 2 CH 4, ,CO ,CH , 0 1 CO CHsT s T s s    = = + + +

11. Set-up: Modelling framework
Wind drag and heat fluxes:
‘Both related to turbulent fluxes, so should have the same form’
Wind drag coefficient wind speed dependent, but heat flux coefficients constant
Lorke & Wűest, 2003 Verburg & Antenucci 2010
Wind drag coefficient Dalton number (evaporation)
( ) 10eva E a w a latQ C U q q H= −10 10w D aC U U =

12. Set-up: Schematization
• Horizontal grids:
Coarse and refined version
• Vertical layers:
0.5 m thick near surface and
around pycnocline, increasing
with max. factor 1.15
• Computation time:
depends on grid and
computer
124 x 75, size ≈ 750 m;
Approx. 2 day for 1 yr
on 8 cores
369 x 231, size ≈ 250 m;
Approx. 8 days for 1 yr
on 8 cores

13. Set-up: Schematization
Bathymetry:
• Bathy info from Ross et al. (2012):
side scan sonar in North + older data
Lahmeyer and Osae (1998)
• Interpolated on grid

14. River outflows:
• Ruzizi (3.6 km3/y → 114 m3/s)
Set-up: Schematization
River inflows:
• 21 measured river inflows (Muvudja,
2009) = approx. 25% of total inflow.
• 20 rivers, spread around basin, 2.4
m3/s each, to account for remaining
75% of total inflow

15. Set-up: Schematization
Subaquatic discharges:
Measurements (Ross et al., 2015) → Calculations (Schmid, ‘05/’18) → Model

16. Initial conditions:
• Vertical profiles for temperature, salinity, CO2 and CH4 from Schmid et al. (2004)
• Applied horizontally uniform over the lake
Set-up: Schematization

17. For accurate modeling of forcing conditions: Highly detailed and spatially
variable wind information required.
Set-up: Meteo forcing
Wind conditions:
• Show a daily recurring wind pattern
• Pattern variable over the seasons (wet and dry)
• Strong spatial differences in (particularly) wind-direction (“lake effect”)
day→

18. Set-up: Meteo forcing
Wind forcing:
• Spatially variable wind (and other meteo)
from the COSMO-CLM model
• Provided by Van der Walle & Thiery
COSMO model:
• Nonhydrostatic limited-area atmospheric
model
• Compressible flow in a moist atmosphere
• thermo-hydrodynamic equations (Doms
2011)
• Applied in climate mode (CLM)
• Runs provided 1-hourly output with a
spatial resolution of 0.025º (about 2.75
km) for the years 2012-2016.

19. Set-up: Simulation
Simulations:
• Simulated time period: 1/1/2012 – 31/12/2013;
• First half year considered spin up time
• Time step: 1 minute
• Computation time: 2 days per year

20. Validation: Used data
Temperature: →
• Mooring lines near Gisenyi and
Kibuye (10m interval)
• Vertical profiles near Gisenyi,
Kibuye, Ishungu
• Acknowledgement: “Eagles”,
“Biological Baseline”, J.-P. Descy
Flow velocities: →
• Recent ADCP measurements
• Not synchronous with COSMO-CLM
info

21. Validation: Used data
Temperature: →
• Mooring lines near Gisenyi and
Kibuye (10m interval)
• Vertical profiles near Gisenyi,
Kibuye, Ishungu
• Acknowledgement: “Eagles”,
“Biological Baseline”, J.-P. Descy
Flow velocities: →
• Recent ADCP measurements
• Not synchronous with COSMO-CLM
info

22. Validation: Temperature (LKMP Gisenyi)
17 december 2019
Figure: Vertically interpolated temperature data from mooring lines
Observation: July → Sept. mixing of biozone, related to stronger winds
Temperature
wind speed →

23. Validation: Temperature (LKMP Gisenyi)
17 december 2019
mooring
model + casts
Temperature

24. Validation: Temperature (LKMP Gisenyi)
17 december 2019
mooring
model + casts

25. Validation: Temperature (near Kibuye)
17 december 2019
mooring
model + casts

26. Validation: Temperature (near Ishungu)
17 december 2019
Model-data comparison shows:
• Good reproduction of temperatures in Biozone
• Good reproduction of Biozone mixing
• Good reproduction of level of temperature interface
• Slight underestimation of temperatures below Biozone
model + casts

27. Validation: ‘Deep’ currents (interior zone)
ADCP 1 @ 162 m:
• Flow velocities very
small
• No clear directional
preference in either data
or model
 measured
 simulated
ADCP 2 @ 76 m:
• Flow velocities >2 times
as large
• N-S preference in both
data and model

28. Validation: Near surface currents
Measured →
Simulated →
ADCP 2 @ 8.5 m:
• Comparable magniuted
• Part SW smaller for model,
but for both all in NW + SW
quadrants
ADCP 3 @ 13 m:
• Data: N preference
• Model: small and no
preference.
• Role strong shear in wind?

29. Validation: Near surface currents
Measured →
Simulated →
ADCP 2 @ 8.5 m:
• Comparable magniuted
• Part SW smaller for model,
but for both all in NW + SW
quadrants
ADCP 3 @ 13 m:
• Data: N preference
• Model: small and no
preference.
• Role strong shear in wind?
Conclusion validation: model quality sufficient to use the model for further analysis

30. Exploration: Surface currents
January:
• Strong clock-wise
circulation
July:
• E → W across the
center; reversed comp.
Jan @ East side
July:
• Stronger difference
over the day

31. Exploration: Surface currents
Generally, surface
currents seem to
quite well follow
the wind
Valuable to explore
further together with
field measurements

32. Exploration: ‘Deep’ currents
Power
spectrum
Observations:
• Peaks in East-
ward velocity
• Seem to reflect
diurnal wind
pattern
f = 0.042 h-1 → 1day
f = 0.082 h-1
Depth ≈ 60 m
f = 0.12 h-1

33. Exploration: ‘Deep’ currents
Power
spectrum
Observations:
• Also present at
larger depth
f = 0.042 h-1
f = 0.082 h-1
Depth ≈ 180 m

34. Exploration: ‘Deep’ currents
Power
spectrum
Observations:
• Also present at
larger depth
f = 0.042 h-1
f = 0.082 h-1
Depth ≈ 300 m

35. Exploration: ‘Deep’ currents
Power
spectrum
Observations:
• Also present at
larger depth
f = 0.042 h-1
f = 0.082 h-1
Depth ≈ 420 m
 ↓NB: Also peaks at lower f

36. Exploration: ‘Deep’ currents
Power
spectrum
Observations:
• Peaks in East-
ward velocity
• Seem to reflect
diurnal wind
pattern
f = 0.042 h-1
f = 0.082 h-1
Depth ≈ 420 m
Wind influence penetrates to larger depths, beyond mixed zone directly
influenced by wind shear. Might indicate the presence of internal waves.

37. Exploration: Temperature structure
North side South sideCross section
July
January

38. Exploration: Temperature structure
North side South sideCross section
July
January
Observations:
• thermocline much more
hor. uniform in Jan.
• In July, first break up
thermocline on South
side
Remark:
• Latter is remarkable, as
wind strongest at North
side
• But also directed to
North
• Possibly upwelling of
cold water at South side

39. Exploration: Temperature structure
North side South sideCross section
July
January
Observations:
• thermocline much more
hor. uniform in Jan.
• In July, first break up
thermocline on South
side
Remark:
• Latter is remarkable, as
wind strongest at North
side
• But also directed to
North
• Possibly upwelling of
cold water at South side

40. Discussion: Wind forcing
Wind forcing:
• COSMO-CLM gives spatially variable info
• Compares well with available wind data in general; More precise look:
slight underestimation of the lowest wind speeds, mainly occurring during
the night
• This might explain why wind speed dependent coefficients in heat flux
model didn’t work that well:
• Low wind speed → increase of coefficient → increase of heat flux →
increased cooling during night → underestimated temperature
Good meteo info is of utmost importance for the model!
Acquisition of additional meteo data recommended, also for additional
validation atmosphere model.

41. Discussion: Future applications
3D hydrodynamic model of Lake Kivu: horizontal dimensions included.
Opportunities:
• Present model is a valuable tool to further study Lake Kivu currents
• Provides basis to study hor. effects of extractions, reinjections, mutual interactions
• Can be coupled to Near-Field module to introduce entrainment and initial spreading
• Can be coupled to Water Quality module to include more bio-chemical processes.
• This would allow to study fate of reinjected water and dissolved gasses as result of
advection, mixing, biochemical production and destruction combined
• Can be used to track plastics and pollution, and to identify sources
• Operational applications
Challenges / limitations:
• Time scale up to about 1-3 years
• Limited number of scenarios

42. Conclusions
• A 3D hydrodynamic model of Lake Kivu has been developed for study
of spatial patterns in flow & concentrations, at time scales up to ~2 years
• The model has been validated with temperature and flow velocity
measurements
• Shows good reproduction of Biozone temperatures, wind-induced ‘deep
mixing’, thermocline levels, flow speed & directions (‘deep’ / near surface)
• Based on the validation results the model quality is considered sufficient to
use the model for analysis of Lake Kivu hydrodynamics
• Lessons from exploration:
• Near-surface currents: different patterns January – July
• Wind influence seems to extend far beyond Biozone: internal waves?
• First break-up of thermocline on South side → upwelling?
• Opportunities for future:
• Extraction, reinjection, potential interactions methane extractions
• Water quality modelling (bio-chemical and tracking)
• Recommendation: continue / extend data acq. meteo & flow for validation

43. Questions?