3rd Geothermal Get Together TU Delft

1. 1
Efficient and robust
forward simulation of
complex geothermal
processes
Denis Voskov
Geoscience & Engineering, TU Delft

2. 2
Simulation of low-enthalpy geothermal
Geothermal in the Netherlands has several
specific challenges:
• Co-production of hydrocarbons – requires
treatment of multiphase compositional flow
• Complex chemical interactions – chemical
description coupled with multiphase flow
• Strong heterogeneities in subsurface
properties demand uncertainty analysis –
ensembles of simulation models are needed
Conclusion: the robust and efficient reservoir
simulation capabilities are wanted!

3. 3
ADGPRS: Automatic Differentiation
General Purpose Research Simulator
• First prototype for gas injection EOR (Voskov et al., 2009)
• Capabilities for thermal EOR (Zaydullin et al., 2014)
• Geothermal capabilities (Wong et al., 2015, 2016)
• Fully-coupled geomechanics with fractures and plasticity
(Garipov et al., 2016)
• Current version - flexible multi-physics research platform
(Rin et al., 2018)
• ADGPRS has been the base for 10 PhD and 20 MSc
(including 12 at TU Delft) projects completed so far
Year of project Prototype ADGPRS DARTS
2015 - 3 -
2016 2 7 -
2017 1 2 5
2018 - - 8

4. 4
ADGPRS: acidizing of wells
• High resolution fully implicit solution
• For fully dissolved control volumes, velocity
needs to switch to Stokes – employ DBS model
Shaik et al. (2018)

5. 5
Darcy vs. DBS models
• Obvious differences (delay in DBS) for all regimes
• More interesting in radial geometry
Unstructured radial model Sensitivity to perturbation Darcy vs. DBS models
Tomin and Voskov (2018)

6. 6
ADGPRS: fracture propagation
Gallyamov et al. (2018)

7. 7
Uncertainties in water breakthrough
1 km
2 km
Injection:
T=308
Production:
T=348
Model size:
50 x 100 x 40
Porosity:
0.1 – 0.36
Permeability:
5 – 3360 mD
Heat capacity:
1935 – 4200 kJ/(m3 K)
Thermal conductivity:
58 – 229 kJ/(day m K)
Net to Gross ratio:
~ 35%
Reinjection of cooled water into injection
well which causes cold front propagation
Shetty et al. (2018)

8. 8
Simulation results & performance
Simulation performance
• Comsol : 160 minutes
• ADGPRS : 5 minutes
• DARTS (CPU): 2 minutes
• DARTS* (GPU): 30 seconds
Large uncertainties due to:
• Reservoir geology
• Lack of information
• Boundary conditions
• Exact position of wells

9. 9
• Original mixture of brine (99 mol. %) and methane (1 mol. %)
• Reinjection of almost pure water (99.99%)
Where is the thermal front (sharp gradient of temperature)?
Reduce rock conduction 10 times. What happen with the thermal front?
Quiz – where is the front?
1
2
3

10. 10
Improved performance with DARTS
Delft Advanced Research Terra Simulator
• Discretization in space, time and physics (OBL)
• C++/CUDA implementation of performance-critical
kernels + open-source Python interfaces
• High performance and flexibility of the code
• Adaptive parametrization in space of unknowns

11. 11
Which data involved in simulation?
𝛽𝑐 𝜔 = ෍
𝑗=1
𝑛 𝑝
𝑥 𝑐𝑗
𝑙
𝜌𝑗
𝑙
𝑘 𝑟𝑗
𝑙
𝜇 𝑗
𝑙 .
( )  4
4
3
3
2
210
4/1
40
10 prprprprT aaaaa  ++++=+− −

12. 12
DARTS: high-enthalpy geothermal
20 years 40 years 60 years
Khait and Voskov (2018)
Temperature distribution for reference continuous physics (ADGPRS)
Temperature distribution for OBL solution (DARTS with 16 points)
Absolute error between solutions

13. 13
DARTS: High-enthalpy Geothermal
0
0.2
0.4
0.6
0.8
1
1.2
Ref. 64 32 16 8 4 2
DARTS performance at different resolution
Maximal error Total cost (nonlinear iter.) Linierization cost

14. 14
Mark Khait: DARTS-GPU
1
10
100
1000
10000
Linearization Interpolation
Time,s
ADGPRS
DARTS CPU
DARTS GPU
0.06 s per single Jacobian assembly on GPU
Khait and Voskov (2017)
Linerization of full SPE10 model with 3 components

15. 15
Yang Wang: negative compressibility
Newton’s (left) and continuation (right) convergence from different initial guesses

16. 16
Stephan de Hoop: flow and dissolution
• Formation of hypogenic karst

17. 17
First DARTS workshop (9 Nov 2018)

18. 18
References
• Shetty S., Voskov D., Bruhn D., 2018: Numerical Strategy for Uncertainty Quantification in Low
Enthalpy Geothermal Project, In: 43rd Workshop on Geothermal Reservoir Engineering, Stanford,
California.
• Voskov D.V., Younis R.M. Tchelepi H.A., 2009: “General nonlinear solution strategies for multi-
phase multi-component EoS based simulation”. SPE Reservoir Simulation Symposium 1, 649-663.
• Zaydullin, R., Voskov, D.V., James, S.C., Henley, H. and Lucia, A., 2014: Fully compositional and
thermal reservoir simulation. Computers and Chemical Engineering, 63, 51-65.
• Garipov, T.T., Tomin, P., Rin, R., Voskov, D.V. and Tchelepi, H.A., 2018: Unified thermo-
compositional-mechanical framework for reservoir simulation. Computational Geosciences, online.
• Garipov, T.T., Karimi-Fard, M. and Tchelepi, H.A., 2016: Discrete fracture model for coupled flow
and geomechanics. Computational Geosciences 20 (1) 149-160.
• Shaik, A., Tomin, P. and Voskov, D., 2018: Modeling of Near-Well Matrix Acidization. In: 43rd
Workshop on Geothermal Reservoir Engineering.
• Tomin, P., Voskov, D., 2018: Robust And Accurate Formulation For Modeling Of Acid Stimulation,
ECMOR XVI-16th European Conference on the Mathematics of Oil Recovery.
• Gallyamov E, Garipov T, Voskov D, Van den Hoek P., 2018: Int J Numer. Anal. Methods.
Geomech., Discrete fracture model for simulating waterflooding processes under fracturing
conditions. 42(13) 1445-1470.
• Khait, M., Voskov, D., 2018: Operator-based linearization for efficient modeling of geothermal
processes. Geothermics, 74, 7-18.
• Khait, M., Voskov, D., 2017: GPU-Offloaded General Purpose Simulator for Multiphase Flow in
Porous Media, SPE Reservoir Simulation Conference.