“…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. Some previous researchers have utilized the empirical equations with the exponential changing modes to investigate the time-dependent filter cake effects on wellbore stresses (Feng et al, 2018a;Tran et al, 2011), but the coefficients of their empirical equations are constant, which can only be used in some special cases.…”