Parameter Estimation in Petroleum Engineering

Offshore drilling costs may exceed similar land operations by 30 to 40 times and hence it is important to be able to minimize the overall drilling time. This is accomplished through mathematical modeling of the drilling penetration rate and operation (Wee and Kalogerakis, 1989). 

The processes involved in rotary drilling are complex and our current understanding is far from complete. Nonetheless, a basic understanding has come from field and laboratory experience over the years. The most comprehensive model is the one developed by Bourgoyne and Young (1986) that relates the penetration rate (dD/dt) to eight process variables. The model is transformably linear with 

The explanation of each drilling parameter (a,) related to the corresponding drilling variable (Xj) is given below  

Parameter in Equation 18.1 accounts for the lumped effects of factors 

The above model is referred to as the Extended Bourgoyne-Yomg model. Similarly, analysis of combined data from more than two wells is straightforward and it can be done by adding a new variable and parameter for each additional well, A large amount of field data from the drilling process are needed to reliably estimate all model parameters. 

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Tan, T.B., "Parameter Estimation in Reservoir Engineering", Ph.D. Thesis, Dept, of Chemical Petroleum Engineering, University of Calgary, AB, Canada, 1991. 

In chemical, biochemical, environmental and petroleum engineering these models are based on the principles of chemistry, physics, thermodynamics, kinetics and transport phenomena. As most engineering calculations cannot be based on quantum mechanics as of yet, the models contain a number of quantities the value of which is not known a priori. It is customary to call these quantities adjustable parameters. The determination of suitable values for these adjustable parameters is the objective of parameter estimation, also known as data regression. A classic example of parameter estimation is the determination of kinetic parameters from a set of data. 

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