Productivity prediction for gravel-packed horizontal well considering variable mass flow in wellbore

According to the principle of mass and momentum conservation theorem,the pressure drop equations of variable mass flow in the gravel-packed horizontal well were derived.The fluid flow in 3-D space was divided into flowing towards vertical fracture in the horizontal plane and radial flowing in the vertical plane near the wellbore.Using pseudo-three dimensional idea,the reservoir seepage model was developed.The model coupling seepage in reservoir with variable mass flow in wellbore was established and the solving method was given.The results show that the calculated results of well production by this model have high precision and the average error with field data was only 3.79%.The calculated flow rate along wellbore is consistent with the logging derived flow rate.The smaller the distance from root end of wellbore,the greater the fluid velocity in wellbore,the acceleration loss,the friction loss and pressure drop.With the permeability of gravel-packed layer increasing,the production increases sharply,after stabilizing,so a reasonable choice for permeability of gravel-packed layer is important to improve horizontal well productivity.