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Ensemble based History Matching
Prepared by: Konul Alizada BSc Petroleum Engineering
Baku Higher Oil School/Heriot-Watt University
Supervised by: Lecturer Farad Kamyabi MSc Reservoir Engineering
Norwegian University of Science and Technology
Outline of Presentation
• Reservoir modelling and simulation• History matching problem and uncertainty prediction• Ensemble Kalman Filtering (EnKF)• Field case example
What the Reservoir Simulation is…
A computer run of a reservoir model over time to examine the flow of fluid within the reservoir and from the reservoir!
Simulation is done by calibration of “reservoir and production data” in a process called HISTORY MATCHING.
Reservoir data• Static parameters: Porosity and permeability• Dynamic parameters: Pressure and phase saturations
Production dataWell production rate, bottomhole pressure, water cut, gas oil ratio…
• Challenges impede history matching performance
– Unknown parameters– Measurements (too much data)– Uncertainty quantification.
Ensemble Kalman Filtering vs Traditional History Matching
● Updates both static and dynamic quantities (such as pressure and saturations)● Suitable for updating non-linear reservoir simulation models
● One flow simulation for each ensemble member
● No need of sensitivity coefficients
● Fully automated
● Ensemble members updated sequentially in time and reflecting latest
assimilated data
● Uncertainty of prediction always up-to-date and straightforward from the
ensemble members
● Updates only static quantities (such as porosity and
permeability)
● Repeated flow simulations of the entire production history
● Sensitivity coefficient calculations
● Not fully automated
● History matching repeated with all data when new data are available
● Not suitable for real-time reservoir model updating
● Difficult for uncertainty assessment
OUTLINE OF THE ENKF ALGORITHM
𝑦 𝑘 , 𝑗=[𝑚𝑠
𝑚𝑑
𝑑 ]𝑘 , 𝑗
Ensemble matrix
Methods to solve the assimilation step:• Direct Inverse Calculation• Standard EnKF Assimilation Calculation• Square Root Algorithm with Measurement Perturbations• Square Root Algorithm without Measurement Perturbations
Reference permeability field for 1 injector and 4 producing wells
Field Case Example
Mean represents the most probable modelVariance depicts the change rate called uncertainty
Which assimilation solving is better?
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