Risk and Uncertainty in Reservoir Modelling

Transcription

1 Risk and Uncertainty in Reservoir Modelling Mike Christie Heriot-Watt University

2 Outline Oil Fields What are they, what do they look like? Mathematics of Reservoir Simulation Equations, getting it right Uncertainty in Reservoir Modelling Where does it come from? Examples Need for advanced computational techniques

3 Developing Oil Fields

4 Oil Fields

5 What Does an OilField Look Like?

6 Oil Reservoir

7 Wytch Farm Oil Field Image Google Maps

8 Wytch Farm from the Sea

9 The Wytch Farm Reservoir

10 Wytch Farm Geology

11 Close up of Sherwood Sandstone Outcrop

12 Wytch Farm Reservoir Model

13 Outline Oil Fields What are they, what do they look like? Mathematics of Reservoir Simulation Equations, getting it right Uncertainty in Reservoir Modelling Where does it come from? Examples Need for advanced computational techniques

14 Mathematics of Flow in Porous Media Conservation of Mass Conservation of Momentum replaced by Darcy s law k ( x) v = p µ Conservation of Energy most processes isothermal Equation of State

15 Equations governing flow Parabolic equation for pressure p kro( S) krw( S) c =. k( ) p t x + µ o µ w Hyperbolic equation for saturation ( ρ xs ρ ys ) ( ) o i o + g i g φ x +.( ρ ) oxivo + ρgyivg = 0 t

16 Low Rate Bead Pack Experiment Bead pack experiment Direct simulation

17 CT Scanned Rock Slab Experiment Image from Davies, Muggeridge, Jones, Miscible Displacements in a Heterogeneous Rock: Detailed Measurements and Accurate Predictive Simulation SPE (1991)

18 Outline Oil Fields What are they, what do they look like? Mathematics of Reservoir Simulation Equations, getting it right Uncertainty in Reservoir Modelling Where does it come from? Examples Need for advanced computational techniques

19 Uncertainty in Reservoir Description? How do we map between wells?

20 Uncertainty in Reservoir Description

21 Equations governing flow Parabolic equation for pressure p kro( S) krw( S) c =. k( ) p t x + µ o µ w Hyperbolic equation for saturation ( ρ xs ρ ys ) ( ) o i o + g i g φ x +.( ρ ) oxivo + ρgyivg = 0 t

22 Data Collection ( x) φ =? k ( x) =?

23 Model Calibration: Teal South simulated observed time (days) simulated observed time (days) simulated observed time (days)

24 Calibrated Models are Non-Unique data forecast model parameters

25 Range of Possible Values for Unknown Parameters log(kh 1 ) log(kh 2 ) boundary porosity log(kv/kh 1 ) log(kv/kh 1 ) log(c r ) aquifer strength

26 Uncertainty Quantification Generate multiple models that agree with known data Use models to predict future behaviour multiple models that match history BOPD forecast uncertainty

27 Outline Oil Fields What are they, what do they look like? Mathematics of Reservoir Simulation Equations, getting it right Uncertainty in Reservoir Modelling Where does it come from? Examples Need for advanced computational techniques

28 What kind of problems? History matching Generate multiple models consistent with data Forecasting Predicting likely production (including range) Optimisation Decision making, under uncertainty

29 IC Fault Model Injector Producer 3 Parameters k low = [ ] md k high = [ ] md throw = [0.. 60] ft Objectives (rates) obj1 = FOPR obj2 = FWPR Z. Tavassoli, J. N. Carter, and P. R. King, Imperial College, London Misfit = obj1 + obj2

30 Multi-Objective PSO: Pareto Dominance 1) A is not worse than B in all objectives obj 2 2) A is strictly better than B in at least one objective obj 1 dominated solutions non-dominated solutions

31 Convergence Speed 20 Runs SOPSO Iteration 28 MOPSO Iteration 12

32 Diversity of Models SOPSO MOPSO

33 Optimisation Scapa field Used for student projects

34 Field Level History Match Match to first 10 years of history Remaining data used to check forecast

35 Optimisation Multi-Objective Maximise cumulative oil (FOPT) Minimise maximum water rate (FWPR) Optimisation variables Well locations (16 variables i, j for each well) Injection well rates Injection well status ( open vs shut )

36 Optimise Well Locations and Injection Rates Vary injection well rates and locations of wells Well rates in [0,15] MBD

37 Oil Saturation Comparison Model 1 Model 2

38 Comparison with Original MSc Plan 77 models 10% Original MSc development plan (4 injectors, 4 producers) 55%

39 Where Does EQUIP come in? 3 factors Data input is uncertain Models take time to run Decisions are costly Need Fast, effective model calibration techniques Combine maths, stats, computer science, engineering