Estimating Oil Reservoir Permeability and Porosity from Two Interacting Wells

Sutawanir¹, Agus Yodi Gunawan², Nina Fitriyati³, Iskandar Fahmi⁴, Anggita Septiani⁵ & Rini Marwati^6
1Statistics Research Division Institut Teknologi Bandung Indonesia,
Jalan Ganesa 10, Bandung 40132, Indonesia 
²Industrial Financial Research Division, Institut Teknologi Bandung Indonesia,
Jalan Ganesa 10, Bandung 40132, Indonesia
³Mathematics Department, UIN Syarif Hidayatullah, Jl Ir. H. Juanda No 95,  Ciputat, Tangerang Banten 15412, Indonesia
⁴Oil & Gas Drilling, Production & Management Research Division,
Institut Teknologi Bandung, Jalan Ganesa No. 10, Bandung 40132, Indonesia
⁵Undergraduate student of Mathematics Study Program, Institut Teknologi Bandung, Jalan Ganesa 10, Bandung 40132,  Indonesia
⁶Universitas Pendidikan Indonesia Bandung Indonesia,
Jalan Dr. Setiabudi No. 229, Bandung 40154, Indonesia
Email: sdarwis@math.itb.ac.id

Abstract. The Ensemble Kalman Filter (EnKF) can be used as a method to estimate reservoir parameters, such as permeability and porosity. These parameters play an important role in characterizing reservoir performance. The EnKF is a sequential estimation method that uses the parameters at t – 1 (called prior) to estimate the parameters at t adjusted by observations at t (called posterior). In this paper, the EnKF was used to estimate the reservoir parameters for the case of a linear flow of two interacting production-injection oil wells. The Laplace transform was used to obtain an analytical solution of the diffusivity equation. A state space representation was generated using the analytical solution. A simulation study showed that the proposed method can be used successfully to estimate the reservoir parameters using well-pressure observations. 

Keywords: ensemble Kalman filter; flow model; interacting well; sequential estimation; Laplace transform.