An analytic model for computing the countercurrent flow of heat in tubing and annulus system and its application: Jet pump

Shale fields are currently over-reliant on electric submersible pumps (ESPs) in the early stage of artificial lift despite its weakness to sandy flow and often failing within the first three months. Jet pumps are reliable and costeffective alternatives to the ESPs. Current studies on jet pumps have focused on designing parameters for maximizing performance; however, there have been very few investigations on predicting temperature profiles in the wellbore with a jet pump in use. Fluid temperature influences viscosity; hence, the production of heavy oil. Typically, the heavier the hydrocarbon, the greater is the variation in viscosity with temperature. Therefore accurate temperature prediction is essential for the efficient design of heavy oil production facilities. This paper offers an analytic model to compute temperature profiles in the tubing and annulus. Results show a good match with a field data set. Data set from a well in Tah field in China is used to validate the model. In addition, sensitivity analyses were performed that showed that injection temperature affects the annulus temperature profile, leading to significant changes in frictional pressure loss at shallow depths. In contrast, injection rate has less influence on temperature profiles, although, of course, higher fluid velocity causes greater frictional losses. Results show that a hotter and relatively small flow rate leads to lesser pumping cost by reducing frictional pressure drop during the operation. The proposed model ideally requires the bottom-hole temperature as a boundary condition (BC). When subsurface temperature data are unavailable, as often the case due to cost, a computing method is offered in the paper for reliable temperature profile estimation from only two data points at the wellhead.