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.

+dynamic data

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

Ensemble Kalman Filtering vs Traditional History Matching

General Workflow of Ensemble Kalman Filtering

Illustration of the EnKF from the point view of Bayesian concept

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?

Field Case Example