Direct forecasting without full model inversion Jef Caers

Transcription

1 Direct forecasting without full model inversion Jef Caers Professor of Geological Sciences Stanford University, USA

2 Why moving to Geological Sciences? To attract a greater diversity of students To be able to attract funding for SCRF in addition to current affiliate funding To broaden the scope of SCRF by tackling other applications that involve Quantifying uncertainty for decision making Geostatistics for quantitative geological modeling Integration and aggregation of diverse data with different scales To be able to do what Andre Journel was able to do with 2 years of SCRF

3 Forecasting in subsurface: a need to change paradigms? Common paradigm: causal analysis future Forecast (r) h Proposed paradigm: evidential analysis future Forecast (r) h Data-model inversion Data (d) past Model (m) present Data (d) past Model (m) present Piecemeal approach Integrated approach

4 Real field examples Platform planned Seismic cross-section billion dollar investment decisions: will cash-flow be positive? r: recovery over time / production of water d: seismic data, well/core data, geological information m: structural, petrophysical and fluid flow models

5 Another example: Karst Vuilleumier et al, 212 r: vulnerability to waste water injection d: airborne geophysics, cave mapping data m: karst network, reactive transport model

6 The calibration trap Seismic data calibration using geostatistical models Structure/Facies Porosity/permeability models Correct the problem with more calibration!

7 Sources of uncertainty may be ignored Uncertainty in 3D seismic velocity Due to uncertainty in salt body boundaries Rugosity of salt 1 km Talk of Lewis Li

8 Leading to significant variations in amplitudes

9 How to solve such forecasting problems? Machine learning for sensitivity analysis in geological systems Only variables that affect forecasts matter Bayesian machine learning for inversion in geological systems A Popper-Bayes approach of probabilistic falsification with data Machine learning of prior geological uncertainty Understand and capture natural variability in geological systems

10 Learning sensitivity for forecasting Sensitivity: what of the input impacts the output? Input Computer Model Data Experiment Output Characteristics of forecasting for decision making Input is complex (spatial, multi-variate, discrete, continuous) #models << dim(models) dim(input,model) >> dim(forecast)

11 Input/models are complex Structural geological models Property + fluid models 627 faults in an offshore gas reservoir 3D porosity in 5 million cell model

12 Output/Forecast is simpler 8 Oil Rate 25 Water Rate Oil Rate (stb/day) Water Rate (stb/day) Time(days) Time(days)

13 Learning sensitivity: a simple idea Vary the input Classify the output Analyze distribution between classes i = 1 p i = p i,1, p i,n Class A cdf F(p B) p.,i F(p A) sensitivity 1 i = L L computer models or data experiments Class B cdf no sensitivity p.,j

14 1 Non-linear systems: interaction 1 In Class A.8 Class A Class B.8 For high p j.6 Class A&B.6 cdf cdf SOWCR p i SOWCR watexp p i p j parameter p i is not a sensitive parameter for a given level of parameter p j, parameter p j is a sensitive parameter

15 How to classify? distances & kernels for dimension reduction 22% of variance 8 Oil Rate 1 x 16 2D map of high-dimensional Oil Rate 8 Oil Rate (stb/day) Multi-dimensional scaling Time(days) % of variance x 1 7 (multi-variate extentions, Ogy s talk) Classification by k-medoid or kernel k-medoid

16 Application: forecasting in unconventionals Dallas What affects production in Shale Gas/Oil systems? Geological factors Completion factors response r

17 Bayesian machine learning in geological systems How can data reduce uncertainty on sensitive parameters? Bayesian learning P( )P( ) P( m d) d m m P( d m)p( m) P( d) Popper s philosophy: not see a best solution m implied by the data (inversion), but use data d to falsify possible solutions. In a Bayesian sense this becomes a probabilistic falsification.

18 Example: appraisal in deep-water reservoirs Depth (m) Seismic Data Target Zone Gamma Ray P-impedance Resistivity (Deep) Top and Base surfaces Target reservoir zone Canyon d Infill-Channels Data courtesy of Hess

19 Talk by Celine Scheidt on flume experiments Geostatistics: the quantification of prior P(m) Geological Studies of Similar Systems Multiple Geostatistical Facies Models Mayall et al. (26) - Geological studies for the channelized turbidite reservoirs in West Africa Abreu et al., 23; Adedayo et al., 25; Anderson et al, 26; Babonneau et al., 22; Navarre et al. 22 etc. P(m) Infinite possibilities (realizations)

20 Next talk by Celine Scheidt Multiple prior geostatistical facies models Probabilistic Falsification What set cannot be falsified with seismic? Seismic Data Important: falsification proceeds without inversion

21 Bayesian learning on parameters Multi-dimensional scaling plot Calculate updated uncertainty using Bayes rule.4 2nd dimension (21 %) PDF Width (m) Channel width prior PDF.1 1st dimension (44 %) = field seismic survey Proportion Oil Sand - RP1 Proportion of pay facies

22 Illustrative example: Location + Geology Brief overview of the PhD of Addy Satija Old New Source: Peter Suess (WintersHall)

23 Uncertainty on geological & fluid parameters Structural geological Number faults Fault throw Fault transmissibility Oil-water-contact Depositional (sedimentological) Type of depositional system Reservoir porosity & permeability (spatial) Fluid flow parameters Relative permeability (functional) Oil viscosity Full data-model inversion is not practical

24 Illustrative example: data and prediction + notation OilRate(stb/day) 8.5 x Historical Decline WaterCut% 5 d obs 4 h t(day) Quartiles (Bayesian Inversion) Prior Posterior t (days) Based on declining oil rate observations in old well over last 3 days, Forecast the water cut % in a new well over the next 3 days 1. runs for history match by Markov chain sampling

25 Reduce model complexity with sensitivity analysis x, y, z: scalar variables uniformly valued between and 1 Naïve engineering practice: set y to median value Intuitive Assessment: z has large impact on f y has small impact on f Reducing y uncertainty shouldn t affect f uncertainty

26 Reduce model complexity with sensitivity analysis Even though y is not a sensitive parameter, its interactions are the most sensitive

27 Model Uncertainty Reduction: simple example Effect of other parameters preserved For a minimum change in response uncertainty, the parameter to which the response is least sensitive must be fixed to a value (or range) that maximizes its conditional sensitivity

28 Application to Libyan Reservoir Old New Source: Peter Suess (WintersHall)

29 One way sensitivity: Prediction vs. Data Prediction Variable: Water cut in new well Data Variable: Oil rate decline in old well Based on 5 scoping runs

30 Conditional Sensitivity of Training image for Prediction variable Largest conditional sensitivity minimizes response uncertainty distortion

31 Prediction: Uncertainty reduction in TI Quartiles with only ellipsoids Uncertainty MDS with of Uncertainty TI>=2 without TI>=2 Quartiles with only channels Uncertainty without TI>= predicted Watercut in new well predicted Watercut in new well time(days) time (days) Blue indicates both training images Red indicates only one training image used

32 Oil rate in old well Oil rate in old well Data variable: uncertainty reduction in TI x 1 4 Quartiles with only ellipsoids Uncertainty MDS of Uncertainty with TI>=2 without TI>=2 x 1 4 Quartiles with only channels Uncertainty without TI>= time (days) time (days) Blue indicates both training images Red indicates only one training image used

33 Prediction Focused Analysis 1 Scoping runs CFCA h 1 c Prediction Response (h) h 2 c d c obs,1 CFCA d 1 c d c obs,2 d 2 c Data Response (d) CFCA = Canonical functional component analysis

34 Prediction Focused Analysis 2 h c 1 d c obs,1 Line of Regression d 1 c Linear Gaussian Regression f(h 1c ) f(h 1c d c obs,1) Inv CFCA Prediction Response (h) -1 1

35 Temperature C Scores on PC2 Temperature C Functional data analysis Canadian Weather Stations 4 2 B y( t) b( t) c b 1 b Functional Principal Component Scores Resolute Iqualuit Prin. Rupert Victoria Vancouver M y( t) h( t) sc i 1 i Day of Year Montreal -4 Ottawa Dawson Winnipeg Scores on PC1

36 Functional decomposition is bijective h t = h 1 f φ h,1 t + h 2 f φ h,2 t + Physical Data FCA Functional Components Inverse FCA Reconstructed Data

37 Relating FPCs of data and forecast variables Corr =.94 Corr =.81 Co h c 1 4 h c 2 1 h c 3 1 Canonical correlation analysis d c 1, obs= d c, obs= d c 3, Corr =.94 Corr =.81 Corr =.47 h c d c = d f A T and h c = h f B T h c 2-1 h c Clearly, we are not extrapolating d c 1, obs= d c 2, obs= d c 3, obs=.1

38 Gaussian regression model for direct forecasting d c = Gh c h c = G T C d c 1 1 G + C 1 H G T C d c 1 c d obs + C H 1 h c 9 8 =97.34%, =57.53% C H = G T C d c 1 G + C H =-.32, = Posterior h c 1 Posterior h c 2 Contaminant concentration h(t) 6 Reconstructed Posterior Posterior h c Time (days) 1 Prior Rej CFCA-based PFA t (days) Extended rejection sampler ~1. flow simulations Method ~ 3 flow simulations, all in parallel on cluster

39 Summary Full data-model inversion in the subsurface is impractical for most real field cases Full data-model inversion may not be needed to obtain a good forecast Establish a direct statistical relationship between forecast (h) and data variables (d) by means of model (m) randomization for given prior geological uncertainty Establish research: what dimension reduction method work best for what situation? Computer vision? Statistics? Machine Learning?