Agus Yodi Gunawan
Industrial & Financial Mathematics Research Group, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia

Published : 3 Documents
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Updating Reservoir Models Using Ensemble Kalman Filter

STATISTIKA: Forum Teori dan Aplikasi Statistika Vol 10, No 1 (2010)
Publisher : Program Studi Statistika Unisba

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Abstract

The Ensemble Kalman Filter (EnKF) has gain popularity as a methodology for real time updates ofreservoir models. A sample of models is updated whenever observation data available. Successfulapplication of EnKF to estimate reservoir properties has been reported. A flow modeling is missing inthis research area. This paper presents the applicability of EnKF in flow modeling for three cases:infinite reservoir, bounded reservoir and one dimensional composite reservoir. The solution of flowequation was derived and used as a modeling component of state space modeling of Kalman filterupdating formula. This three reservoir models shows that the EnKF methodology can be used forupdating the reservoir models.

Updating Reservoir Models Using Ensemble Kalman Filter

STATISTIKA: Forum Teori dan Aplikasi Statistika Vol 10, No 1 (2010)
Publisher : Program Studi Statistika Unisba

Show Abstract | Original Source | Check in Google Scholar | Full PDF (299.924 KB)

Abstract

The Ensemble Kalman Filter (EnKF) has gain popularity as a methodology for real time updates ofreservoir models. A sample of models is updated whenever observation data available. Successfulapplication of EnKF to estimate reservoir properties has been reported. A flow modeling is missing inthis research area. This paper presents the applicability of EnKF in flow modeling for three cases:infinite reservoir, bounded reservoir and one dimensional composite reservoir. The solution of flowequation was derived and used as a modeling component of state space modeling of Kalman filterupdating formula. This three reservoir models shows that the EnKF methodology can be used forupdating the reservoir models.

Approximate Solutions of Linearized Delay Differential Equations Arising from a Microbial Fermentation Process Using the Matrix Lambert Function

Journal of Mathematical and Fundamental Sciences Vol 48, No 1 (2016)
Publisher : ITB Journal Publisher, LPPM ITB

Show Abstract | Original Source | Check in Google Scholar | Full PDF (285.348 KB)

Abstract

In this paper we present approximate solutions of linearized delay differential equations using the matrix Lambert function. The equations arise from a microbial fermentation process in a metabolic system. The delay term appears due to the existence of a rate-limiting step in the fermentation pathway. We find that approximate solutions can be written as a linear combination of the Lambert function solutions in all branches. Simulations are presented for three cases of the ratio of the rate of glucose supply to the maximum reaction rate of the enzyme that experienced delay. The simulations are worked out by taking the principal branch of the matrix Lambert function as the most dominant mode. Our present numerical results show that the zeroth mode approach is quite reliable compared to the results given by classical numerical simulations using the Runge-Kutta method.