Summary Several authors have introduced various mathematical equations to calculate the critical flow rate necessary to keep gas wells unloaded. The most widely used equation is that of Turner et al.1 However, Turner's equation required empirical adjustment with different ranges of data which made the application rather questionable. In this paper we present a new approach for calculating the critical flow rate necessary to keep gas wells unloaded. This approach still adopts Turner's basic concepts, but considers different flow conditions that result in different flow regimes. Hence it explains the previous discrepancies of Turner's equation (the droplet model) with different data ranges, and presents a new set of equations that eliminates the need for empirical adjustment and better matches actual data records. Introduction The gas well loading phenomenon is one of the most serious problems that reduces, and eventually cuts, production in gas wells. This phenomenon occurs as a result of liquid accumulation: either water and/or condensate in the well bore. Over time, these liquids cause additional hydrostatic backpressure on the reservoir which results in a continual reduction of the available transport energy. The well therefore starts slugging which gives an even larger chance of liquid accumulation that completely overcomes the reservoir pressure and causes the well to die. Fig. 1 illustrates the development of the loading phenomenon in a gas well. Typical solutions were to unload the well artificially, either mechanically (using pumps) or with gas lift (kicking with nitrogen through coiled tubing). However, in addition to the expense and loss of production, artificial lift solutions remain temporary and the well is subject to reloading again. Therefore, thought was directed toward developing some solutions that enable the well to continuously unload itself without the aid of external help (unloading operations). Numerous theories have offered methods by which to predict and control the onset of loadup. Turner et al.'s method for predicting when gas well loadup will occur is most widely used. Turner et al. developed two physical models for transporting fluids up vertical conduits: the liquid droplet and the liquid film models. A comparison of these two models with field data led to the conclusion that the onset of loadup could be predicted adequately with the droplet model, but that a 20% adjustment of the equation upward was necessary. This upward adjustment improved the match and was empirically recognized by other researchers working on the same subject. Lescarboura,2 adopting the same empirical adjustment, presented a computerized version of the droplet model to predict critical gas flow rates for continuous liquid removal from the wellbore. Later, Coleman3et al. stated they obtained a good match with their actual field records using the droplet model without any adjustment. They found that, in practice the critical flow rate required to keep low pressure gas wells unloaded can be predicted adequately with the liquid droplet model without the 20% upward adjustment. This in turn raises questions of the droplet model limitations and when to apply an adjustment. And how much? In this paper we focus on changes in flow regimes and their impact on gas well loading. Hence it presents a better explanation of the loading phenomenon under different flowing conditions. Analytical Approach: Concepts and Development The analytical approach dealing with the gas well loading phenomenon is mainly based on the force balance concept. There are two major forces acting upon a droplet of liquid falling in a gas stream: gravitional force pulling the droplet downward and gas stream force tending to drag the droplet upward. Fig. 2 shows a schematic of the forces acting on a liquid droplet.1 Analytical Equations For Different Flow Conditions (Historical Review) Laminar Flow Regime. In 1851 Stokes introduced his equation for calculating the critical terminal velocity when the relative motion between the particle and fluid is laminar, i.e., for values of NRe<1. For the same laminar flow region, Hadamard5 and Rybczynski6 in 1911 and 1912, respectively, developed independently the same type of equation. However, their equation can be considered a modification of Stokes' law. Stokes assumed smooth, hard, spherical particles which cannot be exactly the case with gas bubbles or liquid droplets. This is because circulation within a fluid drop lessens the velocity adjacent the drop, decreases the energy dissipation, and results in a higher fall or rise velocity for a fluid drop compared to a solid particle.4 That is why the Hadamard and Rybczynski equation is initially Stokes' law multiplied by a factor that is always greater than unity (3?+3?p)/(2?+3?p). In 1962, Levich7 and others working on the same subject compared the above two equations of Stokes and Hadamard and found by experimental data that Stokes' law applies better to small impure fluid particles (which is probably the case in gas wells) while for larger particle sizes, or small particles of exceptionally pure fluid, the Hadamard and Rybczynski equation applies better. Levich explained this by the fact that, in ordinary systems, trace impurities may have some surfactant properties that inhibit internal circulation within the particle, and cause it to behave essentially as a solid particle, i.e., in accordance with Stokes' law. Larger particles, on the other hand, are not so greatly affected, and even when surfactants are present the behavior is close to that given by the Hadamard and Rybczynski equation.4 Transition Flow Regime. The transition, or gradually developing turbulence region, was described by Allen8 in 1900. He introduced an equation for the range of 1<NRe<1,000.

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