## Abstract

In reservoir modelling, the main aim is to create a reliable model that honours data from various sources. The importance of a reservoir model is highlighted most especially in this downturn period in the oil industry where informed decision by management is vital in the location of hydrocarbon crude oil. The production dynamics of a reservoir is largely dependent on its rock properties. There are rock units in the reservoir that have distinct properties; these units are known as facies. Properties such as permeability and porosity in each facies are similar which have a significant influence on fluid flow in

the reservoir. In order to make an appropriated reservoir assessment, a real knowledge of where the boundaries separating this different facies is critical for future oil production forecasting. In recent times, various history matching methods are being applied to oil recovery. In this work, we will focus on a typical water injection process where water is injected into one injector well with the aim of increasing the production at another well known as the producer. The reservoir is termed as a porous media through which the fluids flow. The fluid flow, in this case, is modelled as a two-phase (oil-water) compressible fluid flow.In this work, we will present a modified algorithm employing the Ensemble Kalman Filter (EnKF) to solve the inverse problem rather than the adjoint method. The production data that will be assimilated are the water and oil production rates as well as saturation values gotten from low-frequency Electromagnetic values. The basic idea of the work is as follows; firstly we generate initial permeability and porosity ensemble guesses which will honour the prior geostatistical knowledge of the reservoir using standard geostatistical software packages. The Kalman Gain multiplied by the innovation (the difference between the observed and simulated value from Schlumberger's ECLIPSE

100) is stored and saved from every EnKF data assimilation step. Then the facies of permeability values (two facies system, one for sand and the other for shale) are generated using Multiple point statistics(MPS) conditioned to a training image and the well data at the producer and the injector. This facies indicator functions (which is 0 for facies 1.shale and 1 for facies 2, sand) are parametrized

using the signed distance function about the boundary separating the two facies system. The previously calculated Kalman gain multiplied with the innovation and a new parameter called the narrow band is added to this signed distance function to get a new signed distance function. Areas with positive signed distance value will be assigned facies code one while areas with negative signed

distance value will be assigned facies code 0.Facies observation from the original data will be added as a constraint to the other facies realizations gotten from this re-parametrization. Saturation values from EM reconstruction will be assimilated with each saturation value from each realization in the ensemble and the mismatch added to improve the estimation of the location of the boundaries between the two facies. The level set representative function will change the topology automatically during the reconstruction process to reduce the mismatch between the observed and simulated data. Reservoir history matching is the process of constraining the reservoir model to mimic actual historical dynamic production data of the reservoir to make bold assumptions about the future production behavior of such reservoir and reduce uncertainty with those assumptions. We will show in this work numerical experiment for realistic 3D situations which show the effectiveness of the EnKF method for history matching over the adjoint method as no gradient calculation is required and can easily be applied in conjunction with any reservoir simulator.

the reservoir. In order to make an appropriated reservoir assessment, a real knowledge of where the boundaries separating this different facies is critical for future oil production forecasting. In recent times, various history matching methods are being applied to oil recovery. In this work, we will focus on a typical water injection process where water is injected into one injector well with the aim of increasing the production at another well known as the producer. The reservoir is termed as a porous media through which the fluids flow. The fluid flow, in this case, is modelled as a two-phase (oil-water) compressible fluid flow.In this work, we will present a modified algorithm employing the Ensemble Kalman Filter (EnKF) to solve the inverse problem rather than the adjoint method. The production data that will be assimilated are the water and oil production rates as well as saturation values gotten from low-frequency Electromagnetic values. The basic idea of the work is as follows; firstly we generate initial permeability and porosity ensemble guesses which will honour the prior geostatistical knowledge of the reservoir using standard geostatistical software packages. The Kalman Gain multiplied by the innovation (the difference between the observed and simulated value from Schlumberger's ECLIPSE

100) is stored and saved from every EnKF data assimilation step. Then the facies of permeability values (two facies system, one for sand and the other for shale) are generated using Multiple point statistics(MPS) conditioned to a training image and the well data at the producer and the injector. This facies indicator functions (which is 0 for facies 1.shale and 1 for facies 2, sand) are parametrized

using the signed distance function about the boundary separating the two facies system. The previously calculated Kalman gain multiplied with the innovation and a new parameter called the narrow band is added to this signed distance function to get a new signed distance function. Areas with positive signed distance value will be assigned facies code one while areas with negative signed

distance value will be assigned facies code 0.Facies observation from the original data will be added as a constraint to the other facies realizations gotten from this re-parametrization. Saturation values from EM reconstruction will be assimilated with each saturation value from each realization in the ensemble and the mismatch added to improve the estimation of the location of the boundaries between the two facies. The level set representative function will change the topology automatically during the reconstruction process to reduce the mismatch between the observed and simulated data. Reservoir history matching is the process of constraining the reservoir model to mimic actual historical dynamic production data of the reservoir to make bold assumptions about the future production behavior of such reservoir and reduce uncertainty with those assumptions. We will show in this work numerical experiment for realistic 3D situations which show the effectiveness of the EnKF method for history matching over the adjoint method as no gradient calculation is required and can easily be applied in conjunction with any reservoir simulator.

Original language | English |
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Publication status | Published - 2016 |

Event | 78th EAGE Conference and Exhibition 2016 - Vienna, Austria Duration: 30 May 2016 → 2 Jun 2016 |

### Conference

Conference | 78th EAGE Conference and Exhibition 2016 |
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Country/Territory | Austria |

City | Vienna |

Period | 30/05/16 → 2/06/16 |

## Keywords

- Electro-magnetic induction tomography
- Level set
- History matching
- Inverse problems
- Ensemble Kalman filter