Model Inversion for Induced Seismicity David Castiñeira Research Associate Department of Civil and Environmental Engineering In collaboration with Ruben Juanes (MIT) and Birendra Jha (USC) May 30th, 2017
Outline Slide 2 1. Introduction CCS Induced Seismicity 2. Methodology Forward Modeling Inverse Modeling 3. Results for CO 2 sequestration Model Model description Model uncertainties Bayesian solution for inverse problem 4. Conclusions
CO 2 sequestration and Induced Seismicity Slide 3 Carbon Capture and Storage (CCS) challenges: Economic (and political!) Engineering Risks and uncertainties Risks of Induced Seismicity: Uncertainty is always present (e.g., fault stability) Evaluating impact of CO 2 injection on fault stability is more difficult. Need to quantify the risk of induced seismicity due to CO 2 injection. Source: University of Edinburgh Proposed solution to evaluate seismic risk: To develop (forward) model that simulate the fundamental physics. To implement a (inverse) problem workflow to match observations To deploy model for designing operational constraints. Source: BGR
Forward Modeling: Coupled flow-geo simulation Slide 4 Existing computational solutions for coupling flow and deformation. Numerical simulation framework to couple a multiphase flow simulator with a mechanics simulator. Unconditionally stable fixed-stress scheme for sequential solution of two-way coupling. Rigorous formulation of nonlinear multiphase geomechanics to handle strong capillary effects. Mechanical stability of faults modeled from fluid pressures and multiphase flow behavior. Faults represented as surfaces embedded in a 3D medium by zero-thickness interf. elements (to accurately model fault slip under dynamically evolving fluid pressure and fault strength). Reference: Jha, B., and R. Juanes (2014), Coupled multiphase flow and poromechanics: A computational model of pore pressure effects on fault slip and earthquake triggering, Water Resour. Res., 50, doi:10.1002/2013wr015175. Applications: Algorithms can be used for prediction fault slip, fault activation, subsidence, identification of unswept zones in both real and synthetic reservoirs, etc. Research: Improving forward-model Reservoir Simulation Analytical models Data- driven models
Inverse Modeling: Uncertain parameters Slide 5 Large-scale parameters Tectonic boundary conditions Size of the reservoir. Aquifer description: Size of the aquifer and aquifer/reservoir permeability ratio. Fault description: strike, dip, permeability PVT parameters Rock parameters Permeability, Porosity, NTG... Geomechanical properties Poisson ratio (u ), Static coefficient of fraction, dynamic friction coefficient, compressibility intercept (a), compressible wave velocity (vp), shear wave velocity (vs), etc.
Inverse Modeling: Observations Slide 6 Driving index Samaria (P50) 1 Depletion Drive Index (DDI) Connate water and rock expansion Index (CRI) Water Drive Index (WDI) Gas Injection Drive Index (GIDI) 0.9 0.8 Reservoir flow data Well static bottom hole pressure (WBHP data) Well flow rates (production/injection) Mechanical data Surface deformation (measured from InSAR, GPS, etc) Reservoir compaction (measured using radioactive markers). Seismic data Seismic data reflects earthquake dynamic; it should brings valuable information to the inverse problem. Problem with seismic data: it s massive, noisy, difficult to interpret without specialized knowledge. We need an effective approach to incorporate seismic data into inverse problem workflow: earthquake attributes Driving Index 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 1974 1979 1984 1989 1994 1999 2004 Date SL No Stand Pipe Parasite String TD Ecd Ql Qg Max Cuttings 1 2 3 4 5 6 7 8 13 13 115 115 10 10 10 9 135 12 12 10 10 8 7 8 ECD 5.ppg 4.75 4.81 4.54 4.66 4.35 4.55 4.73 4.85 5.16 5.24 4.97 5.13 4.82 5.09 5.3 4.3 1.0918% 1.1841% 1.2816% 1.4624% 1.6120% 1.9141% 2.1340% 2.0640% 1 2 3 4 5 6 8 8 8 75 7 7 125 11 10 10 9 8 ECD 4.ppg 3.56 3.66 3.75 3.58 3.52 3.67 3.96 4.1 4.23 4.05 4.03 4.25 1.3000% 1.5000% 1.7011% 1.7207% 1.9871% 2.3089% 1 2 3 4 5 55 55 55 55 5 125 10 95 9 9 ECD 3.ppg 2.7 2.86 2.89 2.93 2.71 3.06 3.32 3.37 3.44 3.22 1.2880% 1.8690% 1.9893% 2.1220% 2.1976% Cas Shoe ECD 2009
Inverse Modeling: Bayesian Solution Slide 7 Observations (D) Model parameters (q ) q D) = Posterior Distribution Bayes Rule: q D) = D q ) q ) D) = ò D q ) q ) D q ) q ) dq D q ) q ) D) = Likelihood function = Prior distribution = Evidence (or marginal distribution) Why Bayesian? Challenges: Inference from noise and limited data. Complex structure of the posterior distributions Natural mechanism for regularization Expensive forward model and large dimensionality of Natural framework for uncertainty quantification and the inversion parameters VoI analysis.
Inverse Modeling: Gaussian Processes Slide 8 Gaussian Processes (GP) represents a powerful regression technique for I/O data. GP finds joint distribution of infinite-dimensional multivariate normally distributed random variables. GP is actually a distribution over functions! One needs to define Kernel matrix (i.e., covariance of multivariate normal distribution, e.g., square exponential), which controls the level of smoothness in your non-linear regression model. (It) can be used for multiple input/output data Multivariate Normal Distribution: æ N ç 1 d q ik - q K( q i, q j; a ) = s exp - ç å 2 è 2 k= 1 lk 2 2 jk ö ø
Recap: Modeling Induced Seismicity Slide 9 Source: BGR PHYSICAL MODEL Forward Model Computational Model Predictions Data Science Observations + + - Inverse Problem 1. Updated geological model 2. Risk Analysis and Operational Constraints
Case Study: 3D MODEL FOR CO 2 SEQUESTRATION 2016 Annual Founding Members Meeting 10
CO 2 injection (2D model) Slide 11 CO 2 injection in a deep confined aquifer for the purpose of geologic carbon sequestration. CO 2 is injected at 1500 m Aquifer is bounded on the top and bottom by a low-permeability caprock, and the fault is (in principle) impermeable to flow. Aquifer is hydraulically compartmentalized with a sealing fault that cuts across it. 2D plane-strain model with fault under normal faulting conditions (vertical principal stress due to gravity is the largest among the three principal stresses). Storage capacity of the aquifer is limited by overpressurization and possible slip on the fault. -> Modeling needed (!)
CO 2 injection (3D model) Slide 12 CO 2 injection in a deep confined aquifer for the purpose of geologic carbon sequestration. 3D model with (4 x 4 x 2) km simulation domain. CO 2 is injected at 1500 m in 200m anticlinal aquifer. t Aquifer is hydraulically compartmentalized with a sealing fault that cuts across it. Aquifer is bounded on the top and bottom by a low-permeability caprock. failure stable s Normal faulting conditions (vertical principal stress due to gravity is the largest among the three principal stresses). Storage capacity of the aquifer is limited by overpressurization and possible slip on the fault. -> Modeling needed (!)
CO 2, Uncertain Model Parameters Slide 13 Static coefficient of friction (µ f ) : It s assumed that sliding begins when the ratio of shear to normal stress on contact surfaces reaches the value of static coefficient. Dynamic coefficient of friction(µ d ): after sliding occurs the coefficient of friction decreases and reaches the dynamic friction coefficient. Slip-weakening model (d 0 ): The linear slip-weakening friction model produces shear tractions equal to the cohesive stress plus a contribution proportional to the fault normal traction that decreases from a static value to a dynamic value as slip progresses Rock permeability (k) : Permeability affects how quickly pressure affects the fault stability. 4 permeability multipliers (for 4 reservoir layers) Rock porosity (f ): Rock porosity affects the total volume of fluid in the system. Fault permeability (k fx and k fz ): To model leakage across and along fault.
Sensitivity analysis on 2D Model Slide 14 Parameter (Units) Earthquake Time Earthquake Location Earthquake Magnitude µ s 1.980 0 1.807 µ d 0 0 0.007 d c (meters) 0 0 0.057 k (mdarcy) 0.062 0 0.025 k ft (mdarcy) 0.050 0 0.067 k fl (mdarcy) 0 0 ~ 0 Fault Plane 0.020 0.0584 0.084
Prior Distributions and True (synthetic) Model Slide 15 PRIOR DISTRIBUTIONS TRUE MODEL Parameter Distribution Mean Var Min Max Parameter True Value µ s TruncNormal 0.6 0.03 0.55 0.65 µ d TruncNormal 0.2 0.1 0.1 0.3 d c (meters) TruncNormal 0.1 0.2 0.05 0.3 k 1 (mdarcy) TruncNormal 300 200 100 500 k 2 (mdarcy) TruncNormal 300 200 100 500 k 3 (mdarcy) TruncNormal 300 200 100 500 k 4 (mdarcy) TruncNormal 300 200 100 500 f TruncNormal 0.1 0.01 0.08 0.12 k f,t (mdarcy) TruncNormal 5.00e- 06 2.00e- 06 1.00E- 06 1.00E- 05 k f,l (mdarcy) TruncNormal 5.00e- 06 5.00e- 06 1.00E- 06 1.00E- 05 µ s 0.6 µ d 0.15 d c (meters) 0.16 k 1 (mdarcy) 200 k 2 (mdarcy) 300 k 3 (mdarcy) 250 k 4 (mdarcy) 250 f 0.09 k f,t (mdarcy) 4.33E- 06 k f,l (mdarcy) 4.87E- 06
Observations/Model responses Slide 16 Earthquake Time: This time is defined as the first time when rupture is observed along the fault since the start of the simulation. Earthquake Magnitude: While inertial effects are ignored in our quasi-static simulation, a finite-element integration of the total amount of slip over the fault, and the energy liberation associated to that slip, can be used as an estimate of the earthquake magnitude. ò M = G dg 0 d G f 2 M w = log10 ( M o) - 6.0 3 where Mo = seismic moment Mw = earthquake magnitude G = shear modulus d = magnitude of slip vector Earthquake Location: Hypocenter is defined as the exact location (measured as distance from origin) where faultrupture is first observed (Fixed for this study!) 16
Gaussian Processes (GP) Total of 1000 simulations run to build GP model (80% training, 20% validation) Slide 17 Hyperparameter selection via maximum likelihood and cross-validation
Solution Inverse problem using MCMC + GP Slide 18 2D Model Solution q z) = z q ) q ) = z) ò z q ) q ) z q ) q ) dq Parameter Distribution Mean Std p µs Normal 0.50 0.03 - µd Normal 0.30 0.05 - dc (meters) Normal 0.30 0.01 - k (mdarcy) Normal 600 200 - kf,t (mdarcy) Normal 7e-6 1e-6 - kf,l (mdarcy) Normal 7e-6 1e-6 - Fault Plane Bernoulli - - 0.5
Solution Inverse problem using MCMC + GP Slide 19 3D Model Solution ò = = q q q q q q q q d p z p p z p z p p z p z p ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( µ s µ d d c f k fl k ft
Solution Inverse problem using MCMC + GP Slide 20 k 1 k 3 Converge plots (sampling history and posterior) k 2 k 4 Geweke plots (two-sample test of means)
Solution Inverse problem using MCMC + GP Slide 21 Earthquake Time Earthquake Magnitude
Posterior Predictive Earthquake Risk Assessment Slide 22 Earthquake Magnitude CO 2 injection rate (MSCF/D)
Conclusions Slide 23 1. Uncertainty analysis seems critical for large-scale deployment of CCS 2. Data-fit models (e.g., GP) make inverse modeling (e.g., MCMC) attainable. 3. Earthquake attributes (time, location and magnitude) can be used to infer key geological properties 4. Posterior models can be used to quantify risk envelopes for key operational parameters.
Questions?