In this work, current formulations used to calculate the heat losses and the pressure drop in steam injection wells are compared using a modular simulator which allows a great flexibility in the physical and mathematical modeling.
For the fluid, this investigation focuses on the one-dimensional model using a two-phase flow patterns map. For the surrounding formation, both RAMEY's analytical approach and FAROUQ-ALI's numerical one, are considered.
A parametric sensitivity study showed the importance of friction and flow regimes specially for deep wells. Consequently, seven expressions for the two-phase friction factor as well as four flow patterns maps recommended in the literature are tested.
Other aspects of the problem such as the influence of the acceleration term and of the fluid enthalpies evaluation accuracy, are also investigated. The errors arising from the formulation itself (assuming exact input data) are compared with those coming from the finite accuracy to be expected in any real data. The study is performed using three representative data sets.
During the design of steam injection projects, well models can provide very useful information. The bottom-hole pressure and steam quality, the casing temperature profile or the fraction of the injected heat lost into the formation, are examples of important parameters that can be determined by such models.
Several steam-water flow models for steam injection [1,2] or for geothermal applications [3,4] have been published. In general, the two phase flow is simulated using a steady-state one dimensional model with local slip between phases. With this formulation, and assuming thermo-dynamical equilibrium, four independent variables are needed to characterize the state of the fluid (quality, pressure and velocities for instance). In almost all the cases, three differential conservation equations are used and completed by a correlation giving the value of a particular velocity (slip velocity, bubble velocity,...).
In spite of this apparent homogeneity, the results produced by those models disagree when the flow cannot be considered as being homogeneous [5]. The selection of a regimes map and of a group of correlations is difficult and rather subjective because of the lack of definitive arguments on behalf of a choice or another. Moreover, approximations and correlations are often used to simplify the differential equations and to estimate some complex terms (friction gradient, heat losses,...) even outside of their range of validity.
The use of field measurements may provide a selection criteria but they are not complete enough because of the difficulty to evaluate some parameters. The recent development of special test facilities [6,7] might soon eliminate this problem.
The well model presented in the appendix has a modular structure allowing to easily change the physical and mathematical modeling. It's standard version [5] is based on recent publications of Farouq-Ali [2] and Chierici [3]. In this work, it is used as reference the tests on the different formulations of a particular term were performed using the standard version with only the studied term modified.
For comparison purposes, three data sets are considered (Table 1).
