“…where k e (t) is the equivalent filter cake permeability, mD; k 1 is the real situation with time-dependent filter cake permeability, mD; w o is the constant filter cake thickness, m; w(t) is the real situation with time-dependent filter cake thickness, m; and r w is the filter cake inner radius, m. During drilling, many factors such as drill-string rotational speed, annulus velocity, drilling fluid type, solid particle size, formation temperature, formation pressure, and formation permeability, can influence the time-dependent properties of the filter cake (Jaffal et al, 2018;Ma et al, 2020;Ribeiro et al, 2017;Veisi et al, 2020;Yao et al, 2014). Some experimental and mathematical models have been conducted to study the filter cake growth process (Fisher et al, 2000;Hashemzadeh and Hajidavalloo, 2016;Jaffal et al, 2017;Ma et al, 2020;Rabbani and Salehi, 2017), and their results showed that both the thickness and permeability of filter cake obey the exponential changing modes.…”