Nonlinear Joint Estimation Of The Down-hole Parameter And State In The Managed Pressure Drilling

Down-hole flow and pressure are important symbols for diagnosing down-hole drilling conditions in managed pressure drilling.First,a three-order down-hole dynamic model of wellbore is established which has some unknown parameters and unmeasured states.For example,friction factor is an unknown parameter variable,and down-hole flow and pressure are unmeasured state variables.Based on this model,a Lyapunov function is established to design a new nonlinear state observer which can estimate down-hole unknown parameter and unmeasured states,thus ensuring estimation errors of the observer can be convergent.Using drilling data and a wellbore simulator,the nonlinear state observer is simulated under the situations with model error or without model error separately.Simulation results under the two situations show that the observer can estimate down-hole flow and pressure in real time rapidly and accurately.Secondly,in the actual managed pressure drilling model,always there are several unknown parameters besides the friction factor,so a nonlinear high-gain observer is designed for the case that there are several unknown parameters in the model.The observer can realize the joint estimation of several unknown parameters and unmeasured states.The high-gain observer also can ensure the estimation error to be convergent.Using drilling data and a wellbore simulator,the nonlinear state observer is simulated under the situations with model error or without model error separately,and simulation results of those observers are analyzed.At last,the observer is used for the actual managed pressure drilling process.The model parameters from the managed pressure drilling field data are applied to the nonlinear observer.The down-hole pressure is observed using the nonlinear observer based on those measured field data such as wellhead back pressure,wellhead flow,standpipe pressure.The change of the down-hole pressure is used to determine whether the down-hole gas cut occurs.The least-squares method is used to estimate the average density of the annulus fluid,if the average density of the annulus fluid decreases larger than a given threshold value,then the gas cut can be confirmed.This method can be used to verify that the nonlinear observer is able to diagnose the down-hole gas cut in advanced,the conclusion is that the nonlinear observer can effectively determine the down-hole gas cut about 16 seconds ahead of time and provides valuable time for controlling the gas cut by MPD operation.