Application of estimation and monitoring in drilling industry has found a wide-spread attention among researchers . One of the main areas relates to the efficient supervision and control of drilling operations . For instance , during drilling oil wells , a fluid is pumped into drill string . This fluid is circulated through drill pipe and drill bit to bottom of the well and then is directed to the surface via annulus to transfer cutting material , meanwhile , cooling and lubricating the drilling devices located at the bottom of well . This causes the pressure between the drilling fluid and formation to be varied , leading to kick phenomenon and ultimately resulting into probable blow out if it is left uncontrolled . Therefore , estimation and monitoring of bottom hole pressure is treated as a necessary requirement during well drilling operations [2] , [3]. In this paper , we are interested to investigate the feasibility of using adaptive observer technique to realize monitoring of drilling operations in oil wells from the essential and critical operational problem views , being considered in the work.