Vertical or straight hole drilling that usually has less than 30 degree still is utilized to drilling operations in conventional and even in unconventional resources in nowadays worldwide for increasing recovery i.e. higher rate of penetration where there are kind of challenges that demand investigation of this type of drilling. One key challenge is efficient hole cleaning or cuttings removal which can lead to issues related to hole problems and consequently problems such as high over pull margins and stuck pipe may occur. Furthermore, inappropriate use of drilling fluid properties at different stages of drilling operation causes the hole to collapse due the accumulation of cuttings in the annulus as well as at the wellbore. The present study introduces an analytical and a numerical model for a vertical well that can be used to optimize drilling operations. The transport velocity i.e. the ration of the annular velocity and slip velocity is so vital in hole cleaning. Inefficient hole cleaning may lead to problems such as, slow drilling rates which increase drilling time and costs. For a vertical well, as addressed in the literature, the proper hole cleaning is basically dependent on drilling hydraulics or mud rheology liked rilling fluid density, viscosity and thixotropy or gel strength. Based on the proposed predictions of the above-mentioned parameters that are significant to avoid formation damage while drilling a vertical hole. The present article analysis the data related to efficient drilling operations, hole cleaning for a vertical well and the results revealed that mud rheology, density, transport velocity, pipe rotation and the depth of the well are the controlling factors that influence hole cleaning.