Embed Size (px)
Citation preview
These slides are made available for educational purposes only.
No reproduction neither usage of these slides in full or part are allowed, unless a written approval of Dr. Denis Voskov is obtained.
Copyright note:
DARSim thanks Dr. Voskov for providing his slides.
© 2015, Dr. Denis Voskov, All rights reserved.
Visit our event page at: www.Darsim.CiTG.TUDelft.nl/events
Rigorous Coupling of Geomechanics and Thermal-
Compositional Flow for SAGD and ES-SAGD Operations
Denis Voskov
Rustem Zaydullin and Timur Garipov
TU Delft 2 May 22, 2015
Objective
Understand the physical processes of SAGD operations
Account for complex deformation behavior: plasticity, thermal effects etc.
Develop effective numerical schemes
Incorporate models for SAGD into AD-GPRS
TU Delft 3 May 22, 2015
AD-GPRS, version 3.0
Features Current release
Formulations Natural and Molar, full capability for black-oil model, unified restart, tie-line-
based formulation
Physical models Black-oil, fully EoS two- and three-phase, thermal, external libraries, K-value
formulation, solid phases
Properties AD-EoS, AD-PVT, external libraries, hybrid approach
Space approx. Cartesian, unstructured, MPFA, nonlinear MPFA
Time approx. FIM, AIM+, Sequential Implicit
Geomechanics Fully and sequentially coupled, thermo-elasticity and plasticity
Chemistry Kinetics and equilibrium, precipitation and dissolution
TU Delft 4 May 22, 2015
4-5 May 2015
SUPRI-B 4
Target models
Shale-gas/oil, Oil shale
Enhanced Steam Injection
(images: from DTU, ETH Zurich, RII, MIT, Shell, Conoco-Phillips)
CO2 storage in saline aquifers
Enhanced Geothermal Methane Hydrates
Petroleum Reservoirs
TU Delft 5 May 22, 2015
Governing equations
Up – convective flux Jcp – diffusive flux Gp – thermal conductive flux
ϕ – porosity sp – phase saturation vck – stoichiometry coefficients
xcp – phase concentration ρp – phase density rk – reaction mass rate
up – phase energy hp – phase enthalpy ek – reaction energy rate
𝜕
𝜕𝑡𝜙 𝑥𝑐𝑝𝜌𝑝𝑆𝑝
𝑛𝑝
𝑝=1
+ 𝛻 𝑥𝑐𝑝𝜌𝑝𝐔𝑝 + 𝑠𝑝𝐉𝑐𝑝
𝑛𝑝
𝑝=1
+ 𝑥𝑐𝑝𝜌𝑝𝑞𝑝
𝑛𝑝
𝑝=1
= 𝑣𝑐𝑘𝑟𝑘
𝑛𝑒
𝑘=1
1
𝜕
𝜕𝑡𝜙 𝑢𝑝𝜌𝑝𝑆𝑝 + 1 − 𝜙 𝑢𝑟
𝑛𝑝
𝑝=1
+ 𝛻 ℎ𝑝𝜌𝑝𝐔𝑝 + 𝜙𝑆𝑝𝐆𝑝
𝑛𝑝
𝑝=1
+ (1 − 𝜙)𝐆𝑟 (2)
+ ℎ𝑝𝜌𝑝𝑞𝑝
𝑛𝑝
𝑝=1
+ 𝑞ℎ = 𝑣𝑐𝑘𝑒𝑘
𝑛𝑒
𝑘=1
TU Delft 6 May 22, 2015
Thermodynamic equilibrium
𝐹𝑐𝑝 = 𝑓𝑐1 𝑝, 𝑇, 𝐱1 − 𝑓𝑐𝑝 𝑝, 𝑇, 𝐱𝑝 = 0, 𝑐 = 1,… , 𝑛𝑐 , 𝑝 = 2,… , 𝑛𝑝 (3)
• Molar variables:
– Global solve (1)-(2) with unknowns 𝑝, 𝑇, 𝑧𝑐 [𝑛𝑐 + 1]
– Local (3) on each nonlinear iteration (multiphase flash)
• Natural variables:
– Global solve (1)-(3) with unknowns 𝑝, 𝑇, 𝑆𝑝, 𝑥𝑐𝑝 [𝑛𝑐𝑛𝑝 + 1]
– Require local phase stability test (to define 𝑛𝑝)
• Tie-line-based variables:
– Global solve of (1) with unknowns 𝑝, 𝐿, 𝛾𝑐 [𝑛𝑐]
– Interpolation replaces multiphase flash
TU Delft 7 May 22, 2015
Thermal Simulation: Phase-Behavior
K-values K(P, T) Fully EoS
zoil zoil
Non-iterative phase-behavior computation
Based on the assumption of K-values compositional independence
Need to solve systems of nonlinear equations
No assumptions on K-values
TU Delft 8 May 22, 2015
Steam injection: EoS vs. K-values
{C1, C4, Bitumen, H2O}
TU Delft 9 May 22, 2015
Steam-solvent injection: EoS vs. K-values
{C1, C4, Bitumen, H2O}
TU Delft 10 May 22, 2015
Steam Assistant Gravity Drainage (SAGD)
1.E+00
1.E+02
1.E+04
1.E+06
0 100 200 300
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.0
Krw
Krow
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.5 1.0
Krg
TU Delft 11 May 22, 2015
SAGD vs. Expanding Solvent SAGD: dynamic
STRIP-SAGD SAGD
So Sg T
TU Delft 12 May 22, 2015
SAGD: EoS vs. K-values
TU Delft 13 May 22, 2015
ES-SAGD: EoS vs. K-values
TU Delft 14 May 22, 2015
Why geomechnics important for SAGD?
Total E&P Canada Ltd., 2006
TU Delft 15 May 22, 2015
Coupling flow and mechanics
Fluid mass balance:
Momentum balance:
Coupling terms:
𝑑𝑖𝑣 𝜎′ − 𝑏𝑝𝐼 = 0
𝑘
𝑘0=𝜙
𝜙0
𝑁
𝜙 = 𝜙0 +𝑏 − 𝜙0 1 − 𝑏
𝐾𝑑𝑝 − 𝑝0 + 𝑏𝜀𝑣 + 𝛽 − 𝑏 𝜀𝑣
𝑝− 3𝛼 𝑇 − 𝑇0
𝑑
𝑑𝑡𝜙 𝜌𝑓 + 𝑑𝑖𝑣 𝜌𝑓 𝑣 = 𝑞
TU Delft 16 May 22, 2015
SAGD Problem: Model Setup
Thermal compositional model
› C1, C3, Bitumen, H20
Drucker-Prager plasticity
› .
Porosity and permeability update
~5,000 2D elements
𝐽2+𝐴𝐼1 + 𝐵 = 0
TU Delft 17 May 22, 2015
SAGD Problem: Damage Mechanism and Plasticity
Plasticity indicates damage
F = 𝐽2+𝐴𝐼1 + 𝐵
𝜎′ = ∁𝜀 − 𝑏𝑝 − 𝛼𝐾𝑇
𝐼1 = 𝜎′1 + 𝜎
′2 + 𝜎
′3
𝐼2 = 𝜎′1𝜎′2 + 𝜎
′2𝜎′3+𝜎′3𝜎′1
𝐽2 =1
3𝐼12 − 𝐼2
Poro-elastic regime Poro-plastic regime
F < 0 F = 0
TU Delft 18 May 22, 2015
SAGD Problem: Model Parameters
Li P. and Chalaturnyk R. 2007
Rahmati E., Nouri A., and Fattahpour V. 2014
TU Delft 19 May 22, 2015
SAGD Simulation: Deformation Behavior Vertical displacement, m
TU Delft 20 May 22, 2015
SAGD Simulation: Deformation Behavior Horizontal displacement, m
Plastic strain
TU Delft 21 May 22, 2015
SAGD Problem: Deformation Behavior
TU Delft 22 May 22, 2015
SAGD Problem: SAGD vs ES-SAGD Temperature, K Saturation Plastic strain
TU Delft 23 May 22, 2015
Solution Strategies: FIM vs. Sequential (SI)
Flow problem Solve flow problem
Prepare data for mechanics
Mechanics Solve mechanical problem
Prepare data for flow
Convergence?
Solution
Pn+1, Tn+1, Un+1
Pn, Tn, Un
Coupled Problem Flow and mechanics simultaneous solution
Solution
Pn+1, Tn+1, Un+1
Pn, Tn, Un
Kim, Tchelepi, Juanes, 2011
TU Delft 24 May 22, 2015
Sequential Implicit Framework: SAGD example
Water injection Steam injection FIM
SI
TU Delft 25 May 22, 2015
Summary
Developed thermo-mechanical model:
› Thermo elasticity and plasticity
› Thermal EoS and K-values
› FIM and SI schemes
Demonstrated applicability for:
› Steam-assisted gravity drainage problem (SAGD)
Thank You
