Céline Scheidt, Pejman Tahmasebi and Jef Caers Updating joint uncertainty in trend and depositional models for exploration and early appraisal stage Céline Scheidt, Pejman Tahmasebi and Jef Caers

Real, turbidite reservoir in appraisal stage Courtesy of ENI Only 1 well, no production yet Low quality 3D seismic w1 Considerable uncertainty in: Geological continuity, architecture, geobody dimensions Trends, target proportions MPS: focus on the depositional scenario  little attention on the trend or proportions How to model properly uncertainty in trend and proportions?

Location of next well to be drilled The company is planning to drill a new well Courtesy of ENI w1 Location of next well to be drilled New well: may provide information on the uncertain parameters How can information from a new well be used to jointly update uncertainties?

Uncertainty in depositional scenario: levee and channel complex Use of 3 different Training Images (TIs) Back Shale Thin-bed Bedded sand Massive sand TI2 TI3 Training case 1: base case Training case 2: Only one channel and lower sand percentages. Training case 3: In some zones levees are missing

Fixed probability maps : unrealistic model of uncertainty Low quality geophysical data: uncertainty in trend 3D seismic data: Inverted into facies probability maps Background shales Thin beds Bedded sand Massive sand w2 ? w1 Fixed probability maps : unrealistic model of uncertainty Width of the belt?

Sub-grid used for the modeling Uncertainty in trend: use of auxiliary variables Channel belt: use simple auxiliary variable Easily parameterized: w defines the width of the belt Uncertainty in the belt width accounted by varying the width of the auxiliary variable Sub-grid used for the modeling w2 w = 3.5km w = 7km w1 AXD Narrow belt AXD Wide belt

Incomplete information: Uncertainty on the proportions What about proportions? Proportion is defined by: Well data: only 1 well Seismic data: low quality Training Image: expresses patterns, proportion is only implicitly defined Incomplete information: Uncertainty on the proportions Auxiliary variable with varying width w accounts for uncertainty in proportion Proportion becomes an output: p = p(w, TI, well) Proposed workflow additionally updates the uncertainty on the proportions

Prior distribution of uncertain parameters Prior Uncertainties: uniformly distributed TI: training images: tik = {1,2,3} TR: trend (width of auxiliary variable) w = U([3.5,7])km

Construction of a set of prior models CCSIM Tahmasebi et al. 2014 w = 3.5 w = 7 TI1 TI2 300 prior models for uncertainty modeling Shale proportion Width TI3

Probability of TI given dobs Updating the prior uncertainties with new well data Prior Uncertainties: uniformly distributed TI: training images: tik = {1,2,3} TR: trend (width of auxiliary variable) w = U([3.5,7])km dobs Updated Uncertainties: distributed according to 2 1 Probability of Trend given dobs and TI Probability of TI given dobs

Updating the prior uncertainties with new well data Prior Uncertainties: uniformly distributed TI: training images: tik = {1,2,3} TR: trend (width of auxiliary variable) w = U([3.5,7])km dobs Updated Uncertainties: distributed according to Update Proportion

Distance-based scenario modeling to update probabilities 1 Park H. et al. (2013) Density of points in metric space at the data location: f(data|TIk) for TI1 for TI2 for TI3 Water rate data Production data TI1 responses TI2 responses TI3 responses

Distance: difference of patterns at the well location 1 Distance: difference of patterns at the well location Extraction of well data at the well location Synthetic well values Observed well values Well location TI3 TI1 MDS  dr Multi-Point Histogram (MPH): Analyze difference in patterns TI2 dr2 Training Image dr1 TI1 TI2 TI3 P(TIk|dobs) 0.2 0.8

Updating probability of TR given TI and dobs 2 Updating probability of TR given TI and dobs Updated Uncertainties: distributed according to 2 1 Probability of Trend given dobs and TI TI1 TI2 TI3 P(TIk|dobs) 0.2 0.8 Challenges: TR is a continuous variable  density instead of probability Joint uncertainty in TR and TI  additional dimension to the problem Distance for distinguishing trends  difference in facies proportion at the well

Distance is difference in proportion 2 Distance is difference in proportion Definition of the distance w = 3.5km w = 7km Narrow w  mostly shale Large w  mostly sand  Proportion at the well is a good indication of w Well location Multi-dimensional scaling  dr fTI(w|dobs) width Training Image Training Image drobs dr1 width

Obtaining the final probability 2 1 TI1 TI2 TI3 P(TI|d) 0.2 0.8 fTI(w|dobs) TI w f(w,ti|dobs) TI w

Updating joint probability of TI and trend given actual well Updated joint probability 1. Actual well: all in shale TI1 TI2 TI3 P(TI|d) 0.3 0.4 2. dobs f(w,ti|dobs) w TI fTI(w|dobs) TI w

Updating joint probability of TI and trend given actual well Updated joint probability Probability map from seismic 6.5km w1 w2 Actual well: all in shale dobs f(w,ti|dobs) w TI

Updating joint probability of TI and proportions given actual well Updated joint probability 1. Actual well: all in shale TI1 TI2 TI3 P(TI|d) 0.3 0.4 2. dobs f(p,ti|dobs) TI fTI(p|dobs) p TI p

What are the updated probabilities telling us? Belt width w Small w and p are most likely For TI1 and TI2: Larger values of w possible Low proportions are most likely For TI3: Narrower channel belt Larger proportion possible New well not very informative on the TIs f(w,ti|dobs) TI w Proportions p f(p,ti|dobs) TI p

Rejection sampling yields similar distributions Rejection sampling (1000s models) Proposed Approach (100s models) frequency f(w,ti|dobs) w TI w TI Rejection Sampling Draw a TI and w from the prior Generate a model m with TI and w Extract the well data If dry well, accept the model

Conclusions Uncertainty in trend: use auxiliary variable AXD Uncertainty in trend: use auxiliary variable Variation of the channel belt width Proportion: output and not input Methodology to update probabilities on uncertain parameters given new well data Fully automated Validated using a resampling procedure d Useful for green fields with considerable uncertainty in depositional system, trend and proportion