Intelligent well completions are being increasingly used in complex wells (horizontal, multilateral, or multibranching). Such completions are equipped with permanent sensors to measure temperature and pressure profiles, which then must be interpreted to determine the inflow profiles of the various phases produced. Distributed temperature measurements using fiber optics in particular are becoming increasingly applied.
The value of an intelligent completion hinges on our capability to extract such inflow profiles, or, as a minimum, to locate the entry locations of undesirable water or gas entries. In this paper, we develop a model of temperature behavior in multilateral wells. The model predicts the temperature profiles in the build sections connecting the laterals to each other or to a main wellbore, accounting for the changing well angle relative to the temperature profile in the earth. In addition, energy balance equations applied at each junction predict the effects of mixing on the temperature above each junction.
We applied the multilateral wellbore temperature model to a wide range of cases to determine the conditions for which intelligent completions are most useful. Parameters varied included fluid thermal properties, absolute values of temperature and pressure, geothermal gradient, flow rates from each lateral, and the trajectories of each build section. From this parametric study, guidelines for the optimal application of intelligent well completions are represented.
A model to predict the performance of multilateral wells was developed where production for each lateral, the overall production rate and the pressure in the well system are predicted by the multilateral deliverability model, which couples a reservoir inflow model with a wellbore flow model to calculate the production rate from each lateral. Pressure drop along the lateral was considered in the model.
The build section can be defined as a section of wellbore that is closed to the formation and that connects the productive lateral to the main wellbore or to another lateral. The temperature and pressure profiles of build sections are needed to relate the temperature and the pressure at the junction locations to the temperatures and pressures of the source laterals.
In order to develop a model to determine the temperature profile of build sections several works to predict this temperature profile in a flowing well were studied, such as Ramey, who presented approximate methods for predicting the temperature profile of either a single-phase incompressible liquid or a single-phase ideal gas flowing in injection and production wells. The solution assumed that heat transfer in the wellbore is steady state, while heat transfer to the earth will be unsteady radial conduction and neglected the effect of kinetic energy and friction. Sagar also introduced a simple model to predict temperature profiles in two-phase flowing wells, which was developed with measured temperature data from 392 wells, accounting for kinetic energy effects and Joule-Thomson expansion. Hasan and Kabir[4, 5] incorporated a new solution of the thermal diffusivity equation and the effect of both conductive and convective heat transport for the wellbore/formation system.
For the case of modeling the wellbore junctions, and having commingled fluids with different properties, the Mixing method was reviewed. In this method, an enthalpy balance applied to the mixing of two streams of fluid at different temperatures into one combined stream is used to determine the relative flow rates of streams.
We have formulated two models to describe the temperature profiles along the variable inclination build sections of multilateral wells, and to describe the resulting temperature when two fluid streams are mixed at a multilateral well junction. To model the temperature profile in a build section, we adapted Ramey's method to the variable inclination geometry of the build section, assuming a constant radius of curvature between the horizontal wellbore and the main wellbore. Other trajectories can be handled in a similar manner to that presented here. To determine the temperature of the mixed stream just above the junction, we apply an enthalpy balance to two streams combining at the junction.