Joint Structural and Petrophysical History Matching of Stochastic

Joint Structural and Petrophysical History Matching of Stochastic Reservoir Models Thomas SCHAAF* & Bertrand COUREAUD Scaling up and modeling for transport and flow in porous media Conference Dubrovnik, 13 -16 October 2008

Outline ü Motivation : Getting reliable production forecasts ü Current methodology ü Focus on the History Matching process ü Proposed workflow to perform joint HM ü Test case : Synthetic 3 D waterflooding model ü History Matching process & results ü Conclusions & Perspectives Dubrovnik, 13 -16 october 2008 2

Motivation Decision taking in uncertain environment Getting reliable production forecasts Dubrovnik, 13 -16 october 2008 3

Current Methodology CPU intensive, non linear Uncertain Input Parameters Numerical Modeling Steps Outputs of interest Decision Making Objective Function Data Assimilation Under-determinded Problem 3 steps approach: § Sensitivity study with respect to the OF (ED+proxy model) § Multiple History Matching processes with remaining parameters § Propagation of uncertainties to forecasts using those HM models Dubrovnik, 13 -16 october 2008 4

History Matching Process 1. Updating simultaneously geological and simulation models 2. But structural and petrophysical uncertainties are seldom tackle at the same time; leading to sub optimal History Matched models All the ingredients are currently available to go ahead (Rivenæs & al. (2005) ; Suzuki & Caers(2008)) Dubrovnik, 13 -16 october 2008 5

Proposed workflow (1/2) 1. Assisted History Matching (AHM) softwares are mature & versatile 2. Geomodeling softwares have powerful internal workflow managers CONDOR (IFP R&D version) 3. Geomodeling softwares can be launch in batch mode GEOMODELER Generic component : launch any exe file in the workflow Geomodeler workflow manager 4. Capitalize on existing geomodeling projects Dubrovnik, 13 -16 october 2008 6

Proposed workflow (2/2) From a practical point of view : § Condor writes a text file with current inversion parameters value 1 § Condor launches the geomodeler that : § reads that file § assigns the values to its own internal variables § launchs its internal workflow : § Structural modeling, § Facies modeling, poro/perm modeling, § Upscaling, export of the data file 2 § 3 § § § 1 2 3 Condor launches the fluid flow simulator Condor get the simulation results, computes the OF value Parameters updating Next iteration Dubrovnik, 13 -16 october 2008 7

Synthetic 3 D waterflooding model Geological Model : 50 38 100 Simulation Model : 20 16 20 3 zones : § Top : Sequential Gaussian Simulation for poro/perm § Middle : Object based stochastic modeling § Bottom : SGS for poro/perm Dubrovnik, 13 -16 october 2008 8

Inversion Parameters set Fault throw Fault transmissivity Channels orientation Channels proportion kvkh ratio Mean k value for SGS Geological Model : 50 38 100 + Sorw = 7 parameters Dubrovnik, 13 -16 october 2008 9

Synthetic 3 D waterflooding model Final oil saturation field Observation Data § 2 oil producers, 1 injector : 12 years of production history § Observation data : Fine scale fluid flow simulation results BHP & WCT Dubrovnik, 13 -16 october 2008 10

History Matching Process § 7 parameters : Channels (%, dir), Fault (throw, T), kvkh, Sorw, Mean_kx CONDOR Condor inversion parameters GEOMODELER Condor inversion parameters have their counterpart in the geomodeler internal workflow (Initial value, lower & upper bounds) Dubrovnik, 13 -16 october 2008 11

History Matching Process § Concrete view of the Geomodeler workflow runs : GEOMODELER WORFLOW MODELED GEOLOGICAL MODEL $throw = 15 m $Chan_dir = 90° Dubrovnik, 13 -16 october 2008 12

History Matching Process § Concrete view of the Geomodeler workflow runs : GEOMODELER WORFLOW $throw = 25 m $Chan_dir = 110° Dubrovnik, 13 -16 october 2008 MODELED GEOLOGICAL MODEL Grid modified @ each iteration ! 13

Fault Throw Management § Freeze NW seismic horizons § Apply the throw to SE horizons Dubrovnik, 13 -16 october 2008 14

History Matching Results § Gradients based constrained optimization (not optimal, P. King work) § Numerical gradients computation (no adjoints …) Initial OF value Dubrovnik, 13 -16 october 2008 15

History Matching Results § Gradients based constrained optimization § Numerical gradients computation «Optimal» OF value Dubrovnik, 13 -16 october 2008 16

History Matching Results Summary Initial value Optimal value + bounds (coarse scale simul) Chan_frac(%) Reference case (fine scale simul) 20 [15; 35] 34. 16 30 Tfault 0. 05 [0. 01; 0. 5] 0. 0138 0. 2 Sorw 0. 3 [0. 15; 0. 35] 0. 229 0. 25 throw(m) 30 [10; 40] 18 15 Mean_kx(m. D) 50 [40; 200] 177. 28 120 0. 005[0. 001; 0. 05] 0. 001 0. 01 110 [80; 120] 99. 31 90 Kvkh Chan_dir(°) Dubrovnik, 13 -16 october 2008 17

Conclusions & perspectives 1. Full History Matching Process : technicaly & operationnaly ok 2. Lead to more robust integrated geological stochastic reservoir models 3. More reliable production forecasts 4. Ongoing work : 1. Better integration of the HM process in the global Geophysics / Geology / Reservoir Engineering Process eg. (fault throw / velocity model updates) Geologicaly realist updating of the reservoir structure ! 2. Parameterization/updating of the geological scale fields (facies, poro, perm) eg. gradual deformation, geomorphing techniques. 3. Prior sensitivity study should be done 4. Test gradients free algorithms : GA, simplex, PSO, VFSA, NEWUOA, hybrid Dubrovnik, 13 -16 october 2008 or even better, Bayesian Approach! 18

Joint Structural and Petrophysical History Matching of Stochastic Reservoir Models Thomas SCHAAF* & Bertrand COUREAUD Scaling up and modeling for transport and flow in porous media Conference Dubrovnik, 13 -16 October 2008

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Gradual Deformation Method Dubrovnik, 13 -16 october 2008 26

Outline ü Motivation : Getting reliable production forecasts ü Current methodology: § Sensitivity study § Multiple History Matching (HM) processes § Propagation of uncertainties to forecasts ü Focus on the History Matching process : § Updating both geological and simulation models § Necessity to tackle both types of uncertainty : structural and petrophysical ü Proposed workflow : § Versatile assisted HM softwares § Geomodeling software internal workflow manager ü Test case : Synthetic 3 D waterflooding model ü History Matching process & results ü Conclusions & Perspectives Dubrovnik, 13 -16 october 2008 27