Real time monitoring of multiple wells flowing under pseudosteady state condition by using Kalman filtering

Abstract

This work develops a method for the real time monitoring of well performance by using Kalman filtering. A system of two or more wells draining the same reservoir under pseudo steady state condition is monitored simultaneously to estimate both the relative localized skin effects in the individual wells and the reservoir wide relative permeability. The ability to continuously estimate the skin values in the wells offers tremendous value in production decisions. Simultaneous estimation of skin and relative permeability helps to differentiate between near wellbore effects and reservoir wide bulk effects. The dimensionless multiwell productivity index (MPI), which relates the production rate vector to the pressure drawdown vector is used in the calculations. In the modern production environment, the flow rates and the pressures are being monitored continuously and the relationship between them can be used to estimate the skin factors. In order to calculate the relative permeability, which is common to all the wells, an additional equation is introduced by assuming that the sum of the skins is zero. Thus for a system of wells, the skin values and common relative permeability are calculated. Due to the huge volumes of data being collected by the bottomhole gauges and due to the uncertainties in the deterministic method, stochastic tools like the extended Kalman filter are powerful tools to estimate the skin and relative permeability. The Kalman filter is an optimal, recursive state estimation algorithm. A program was created in Matlab® to simulate the different operating conditions and to generate the data required to run the Kalman filter. For a given set of flow rates, the program uses material balance functions to estimate the average pressure and the pseudo steady state equations to estimate the flowing pressures. The data set consisting of flow rates, flowing pressures and average pressure is used as input to the Kalman filter to estimate the skin and relative permeability factors.