**Key concepts**

Historically, drilling optimization aims to maximize the rate of penetration as an objective function. This is achieved by selecting optimum values of the mechanical parameters and hydraulic factors such as weight-on-bit, rotary speed, flow rate, and nozzle size for drilling bits furnished with nozzles. These variables are affected by uncertainties such as variations in formation lithology, the drill-string configuration, borehole quality, drilling fluid, etc. However, both drill bit hydraulics and drilling mud hydraulics are rig circulating system considerations influenced by pseudoplastic behavior. Similarly, during the life of a well, operating companies desire to maximize production. Nonetheless, some factors tend to retard the process of achieving this goal. An enhanced oil recovery mechanism has been in use to maximize recovery by alteration of the properties that hinder production for improved recovery.

*Advances in Rheology of Materials*
