A mechanistic model for circulating fluid temperature
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An accurate fluid temperature profile in both tubing and annulus during circulation is desirable to allow computation of circulation rates. However, because the circulating fluid exchanges heat with the formation, fluid temperature changes both with time and depth. Consequently, the fluid's intrinsic properties of density and viscosity would change with an increase in circulation time, thereby influencing the optimal pumping rate. Existing analytic methods for solving the heat transfer problem at hand generally assume a constant fluid inlet temperature plus a constant heat flux (or temperature) at the wellbore/ formation interface. These assumptions ignore the reality that the temperature of the circulating fluid entering the wellbore from the holding tank increases with time because of the heat carried by this fluid from the hot formation. Fluid circulation also causes a gradual decrease in heat flux between the wellbore and the formation. These assumptions inherent in the available methods may reduce their reliability in many situations. In this work, we present a generalized analytical model for circulating fluid temperature in boat conduits, for both forward and reverse circulation cases, as a function of circulation time and well depth. We use an energy balance for the fluid in the tank to express its temperature as a function of time. To account for the changing heat flux at the wellbore/formation interface, the principle of superposition in time is used. The heat flux schedule is represented by adding constant heat sources at successive times. This model is flexible to adapt any transient temperature distribution model, TD, and presupposes unsteady heat transport in the formation while steady heat flow occurs in the tubular. Our results show that, under some circumstances, fluid temperatures estimated using these approaches deviate significantly from that estimated without account for the varying nature of tank temperature or formation heat flux. This difference is especially true when the temperature difference between the bottomhole and the wellhead is large. Thus, varying mud tank temperature and formation heat flux need to be accounted for when estimating flowing fluid or circulating mud temperature in the Arctic. However, when the bottomhole and wellhead temperature difference is small, the extra computation involved in this procedure is probably not worth the marginal gain in accuracy. Field examples illustrate the model's application. Copyright 1996, Society of Petroleum Engineers, Inc.
