Development and application of wellbore heat transfer model considering variable mass flow

Dual-gradient drilling technology is being increasingly used in formations with narrow pressure margins. For dual-gradient drilling based on downhole separation, hollow spheres are separated into the annulus at the separator position, resulting in variable mass flow in the wellbore. Thus, existing heat transfer models are no longer suitable for describing wellbore temperature profiles in dual-gradient drilling. This study focused on developing a wellbore heat transfer model that fully considers separated hollow spheres entering the annulus, complex casing programs, and heat sources, for dual-gradient drilling based on downhole separation. The model was solved using an iterative method. Then, the accuracy of the model was verified using temperature data measured from two wells. Finally, the difference in the annular temperature distributions between dual-gradient drilling and conventional single-gradient drilling were investigated, as were the wellbore heat transfer characteristics for dual-gradient drilling. The following major conclusions were drawn: (1) for dual-gradient drilling based on downhole separation, at the separator location, the annular fluid temperature does not decrease, but rather increase in the flow direction because of the inflow of hollow spheres; (2) a clear inflection point exists in the annular fluid temperature curve at the location where the separator would be; (3) the magnitude of the mutation of the temperature curve at the inflection point is considerably affected by the heat capacities of the hollow spheres and the pure drilling fluid; (4) under the same change in separation efficiency, distance between the bit and separator, flow rate, and thermal conductivity of formation, the variation range of the fluid temperature at the bottom hole is greater than that at the wellhead.