Un simulateur de production de puits exploité en gas-lift. Deuxième partie : domaines de fonctionnement A Production Simulator for Gas-Lift Wells. Part Two: Working Conditions

Abstract

Après une description des conditions d'accès aux domaines de fonctionnement étudiés, les différents types de fonctionnement du système non-linéaire sont présentés pour les trois couples de paramètres retenus. Des oscillations amorties sont mises en évidence au voisinage de la limite du fonctionnement stationnaire stable. L'influence non négligeable de la désorption gazeuse est observée. Les formes envisageables de la notion de rendement sont évoquées et pour un couple de paramètres, un espace de fonctionnement optimal est indiqué. The production simulator of a gas-lift well has already been described [1]. It should be noted that the physical modeling of the process requires 43 variables, 3 partial differential equations, 17 algebraic equations, 19 constants and 4 correlations. This entire set is used to describe the parts of the model, i. e. the annular space, the reservoir, the tubing (separated into two portions by the injection orifice) all making up the complete model formed by the gathering of the elements in the light of the boundary exchange conditions. The numerical solving of this system of equations requires first-order spatio-temporal discretizing, which leads to a set of recurring equations in space (well depth) and in time (time of simulation). The identification of possible types of operating, searching for their domains of existance, and the effect of different possible approximations are part of the understanding of this complex nonlinear system, which has a variety of industrial uses. Among the set of parameters making up the model, the present study is concerned with three that are directly involved in the gas-lift phenomenon, i. e. the gas flow rate upon entering the annular space QATg, the pressure at the tubing head Ptt, and the diameter of the injection orifice Do. The first two are inputs for the gas-lift black box in the sense of automation, and the third is the major physical parameter governing the characteristics of the two-phase gas/oil mixture. In this three-dimensional space, plane by plane the domain of existance is located for stable stationary operating (I), stable alternative operating (II), and the numerical stoppage zone of simulations (III), where the conditions for pocket-slug flow no longer exist. We also find an oscillation zone at the boundary of the stationary space (curve (C), Figs. 1, 9 and 10). The boundaries of the domains investigated are linked to physical conditions, i. e. diameter, flow rate, pressure and flow regime. Specific developments are shown in Figs. 2 to 5. Fig. 2a shows stable stationary development. Fig. 2b shows stable alternative development. Figs. 3a and 3b analyze the alternative behavior with Do variable. Figs. 4a and 4b show oscillating developments. Fig. 5 shows the development of the period of dampened oscillations. Fig. 6 analyzes the approach of an oscillating situation. Conventional nonlinearity can be seen in Fig. 7. The introduction of the thermal behavior of the well (thermodynamic effect) is revealed by Fig. 8. Whereas the saving of this contribution makes for a gain of a factor of three in computing time, it is absolutely not justified by the importance of its effect. The concept of efficiency is indispensible for a so-called productionsystem, but what could be defined as efficiency for the gas-lift process? Several definitions are considered. Whereas the types of operation of the gas-lift process can be listed by a structured simulation set, the concept of efficiency in one or another of the uses considered would require these simulations to be performed systematically in a fairly close mesh in the three preceding spaces. There is nothing to oppose this type of computing, unless it is the tedius nature of the operation. However, the results obtained in space (QATg, Do) (Figs. 1, 6 and 7) serve to situate a quasi-constant zone 6f maximum efficiency over an interval having the value Do. The coherence of this simulator is reinforced by all the results obtained. These are only simulations, and we regret not being able to compare the results of an experiment in which any opeation is performed.