Dario Grana, Tapan Mukerji Annual Meeting 2013 Stanford Center for Reservoir Forecasting Bayesian inversion of time-lapse seismic data for porosity, pressure and saturation changes Dario Grana, Tapan Mukerji
Introduction In time-lapse studies we aim to estimate pressure and saturation changes Changes in dynamic properties can be measured from well/lab data. The main source of information are time-lapse seismic data. Time-lapse seismic data Seismic dataset records information about the elastic contrasts in the subsurface. Seismic attributes depend on rock properties. Dynamic property changes Inverse problem SCRF 2013
Motivation Inverted data can be used in seismic history matching to improve the reservoir description The probabilistic approach allows to quantify the uncertainty in predicted data SCRF 2013
Introduction In pressure-saturation estimation the physical model is not linear and the dynamic property changes are not normally distributed. Changes in dynamic properties are not independent of initial rock properties (static reservoir model) SCRF 2013
Bayesian inversion We propose a Bayesian approach for the simultaneous estimation of porosity jointly with pressure and saturation changes from time-lapse seismic data. SCRF 2013
Bayesian inversion We propose a Bayesian approach for the simultaneous estimation of porosity jointly with pressure and saturation changes from time-lapse seismic data. SCRF 2013
Bayesian inversion We propose a Bayesian approach for the simultaneous estimation of porosity jointly with pressure and saturation changes from time-lapse seismic data. Seismic data, Changes in seismic data Elastic properties, Changes in elastic properties (velocities or impedances) Reservoir properties (porosity) Changes in dynamic properties (saturation and pressure) SCRF 2013
Bayesian inversion Seismic data S depend on reservoir properties R through elastic properties m We can split the inverse problem into two sub-problems: seismic linearized modeling rock physics model SCRF 2013
Reflection coefficients Physical model Seismic forward model: Wavelet convolution Linearized Aki-Richards approximation of Zoeppritz equations Wavelet Reflection coefficients Seismogram SCRF 2013
P-wave velocity versus effective porosity Physical model Rock physics forward model: Granular media models (Hertz-Mindlin contact theory) Gassmann’s equations Velocity-pressure relations P-wave velocity versus effective porosity SCRF 2013
Outline Introduction Theory and Inversion workflow Application Conclusions SCRF 2013
Inversion workflow We first estimate Buland and Omre, 2003 Buland and El Ouair, 2006 SCRF 2013
Inversion workflow We first estimate We then estimate Buland and Omre, 2003 Buland and El Ouair, 2006 SCRF 2013
Inversion workflow We first estimate We then estimate We combine and using Chapman-Kolmogorov equation Buland and Omre, 2003 Buland and El Ouair, 2006 1 2 Grana and Della Rossa , 2010 SCRF 2013
Inversion workflow Seismic data Elastic properties SCRF 2013
Rock physics likelihood function Inversion workflow Seismic data Rock physics likelihood function Elastic properties SCRF 2013
Rock physics likelihood function Inversion workflow Seismic data Rock physics likelihood function Elastic properties Reservoir properties (Chapman-Kolmogorov) SCRF 2013
Simultaneous Bayesian 4D inversion Combined Inverse problem We estimate the posterior distribution SCRF 2013
Reservoir property estimation Using statistical rock physics we estimate the likelihood We use non-parametric pdfs and we estimate them using Kernel Density Estimation (KDE) SCRF 2013
Outline Introduction Theory and Inversion workflow Application Conclusions SCRF 2013
2D application: synthetic model Porosity injector Net-to-gross producer Pressure Saturation SCRF 2013
2D application: synthetic model Saturation 2012 2017 Pressure SCRF 2013
Assumptions Porosity does not change in time (no compaction effect). Initial pressure and saturation (pre-production) are known. SCRF 2013
2D application: seismic model SCRF 2013
Synthetic seismic surveys SCRF 2013
Time-lapse seismic differences SCRF 2013
Rock physics likelihood Different scenarios: Pressure decreases – Saturation insitu Pressure increases – Saturation insitu Pressure insitu – Water replaced oil Pressure insitu – Gas replaced oil Pressure decreases – Water replaced oil Pressure decreases – Gas replaced oil Pressure increases – Water replaced oil Pressure increases – Gas replaced oil SCRF 2013
Rock physics likelihood SCRF 2013
Elastic property changes % SCRF 2013
Reservoir property changes SCRF 2013
Point-wise posterior probabilities SCRF 2013
Application: Norne SCRF 2013
Application: Norne Seismic differences (2003-2001) SCRF 2013
Application: Norne SCRF 2013
Application: Norne SCRF 2013
Outline Introduction Theory and Inversion workflow Application Conclusions SCRF 2013
Conclusions We presented a full Bayesian methodology to estimate reservoir properties and their changes from seismic data The method allows to assess the uncertainty in the estimation of reservoir properties Inverted data can be used in seismic history matching to improve the reservoir description SCRF 2013
Acknowledgments Prof. Tapan Mukerji and Prof. Jef Caers Stanford University, SRB and SCRF for supporting my research Thank you for the attention SCRF 2013
Backup SCRF 2013
Rock physics model Log of porosity, saturation, Mineral parameters mineralogical fractions, Fluid properties Mineral parameters Mixing laws Voigt-Reuss-Hill Mineral fractions Matrix Moduli Estimated Vp, Vs and Density RP Model Nur, Hertz-Mindlin, Kuster-Toksoz,… Saturation, Fluid properties Batzle Wang Gassmann MacBeth’s relation Dry Rock Moduli SCRF 2013
MacBeth modified We assume that SCRF 2013
Bayesian 3D inversion Seismic Inverse problem SCRF 2013
Bayesian 3D inversion Seismic Inverse problem If the prior distribution of m is Gaussian If the model G is linear Then the posterior distribution is Gaussian Buland and Omre (2003) SCRF 2013
Bayesian 4D inversion Time-lapse Inverse problem SCRF 2013
Bayesian 4D inversion Time-lapse Inverse problem If the prior distribution of Δm is Gaussian If the model G is linear Then the posterior distribution is Gaussian Buland and El Ouair (2006) SCRF 2013
Base seismic and time-lapse inversion We then compute the relative impedance change as ΔIP = 1 - IPrep/IPbase SCRF 2013
Base seismic and time-lapse inversion SCRF 2013
Non-parametric pdfs: KDE Clay Vs (m/s) Sand Shale Vp (m/s) SCRF 2013
Application: Norne Calibration well: well E2 Three angle stacks: near, mid, far Base survey + seismic differences (2003-2001; 2004-2001; 2006-2001) Goal: estimate dynamic property changes in 2003, 2004, and 2006 SCRF 2013
Application: Norne Well E2 SCRF 2013
Application: Norne SCRF 2013
Application: Norne SCRF 2013
Application to Norne SCRF 2013
Application: Norne Prediction of gas saturation pressure: 2003 and 2006 SCRF 2013
Application: Norne Prediction of fluid pressure: 2003 and 2006 SCRF 2013