A New Approach for Accurate Prediction of Loading in Gas Wells Under Different Flowina Conditions

Abstract

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.

Liquid loading in gas wells: From core-scale transient measurements to coupled field-scale simulations

“…As presented in Table 1, several investigators have suggested different modified expressions derived from Turner model. Turner et al, 1969 Created the widely accepted Turner equation Coleman et al, 1991 Suggested not to use the 20% correction factor for low pressure gas wells Nosseir et al, 2000 Considered influences from different flow regimes Li et al, 2002 Involved the droplets' shape Veeken et al, 2003 Defined the concept of Turner ratio Guo et al, 2006 Took the minimum required kinetic energy of gas flow into account Belfroid et al, 2008 Concerned with the effects due to wellbore inclination Sutton et al, 2010 Used more realistic PVT properties Zhou and Yuan, 2010 Included the liquid droplet concentration in gas wells Veeken et al, 2010 Designed a specific expression for offshore gas wells Luan and He, 2012 Comprised droplets rollover in the gas rising process…”

Analytical Models for Liquid Loading in Multifractured Horizontal Gas Wells

“…Later, many researchers (Coleman et al 1991;Nosseir et al 2000;Liu et al 2006;Wang and Liu 2007;Peng 2010) proposed many new critical-flow-velocity-calculation models by modifying the Turner et al (1969) model. Coleman et al (1991) reported that the correction factor of 20% in that model is not enough for the gas wells with low reservoir pressure, and gave a new correction for the coefficient, which can obtain the desired results.…”

“…Li et al (2001) derived the critical-flow-velocity model with the coefficient of 2.5, assuming that the droplets would become ellipsoid in shape under the condition of high-speed gas-flow rate, and the drag coefficient of the ellipsoid is approximately unity. Nosseir et al (2000) and Liu et al (2006) noted that the drag coefficient is strongly related to the Reynolds number, and it is 0.2 when the Reynolds number is larger than 2 Â 10 5 , and the critical liquid-loading rate within the Reynolds number ranging from 3 Â 10 5 to 5 Â 10 6 was provided with the coefficient of the model of 6.65, which is larger than 5.46 in the Turner et al (1969) model and 6.6 in the modified Turner et al (1969) model. Wang and Liu (2007) argued that the shape of the droplet is a ball cap, according to the knowledge of fluid mechanics, and derived the formula of critical flow velocity with the coefficient of 1.8 and made a correction factor of 25% for the coefficient in the formula.…”

“…After liquid droplets are formed, some of them can be carried out of the horizontal wellbore by high-speed gas-flow rate. The critical liquid-loading gas-flow velocity can be calculated by the following expression (Pan and Hanratty 2002):…”

Using Dynamic Simulations to Optimize the Start-Up of Horizontal Wells and Evaluate Plunger Lift Capability: Horn River Shale Gas Trajectory-Based Case Study

“…They compared the results with field data and verified that it was necessary to apply an upward factor of 20% to insure a better match. After that, Coleman et al (1991) and Nosseir et al (2000) presented further research that suggested the factor should be higher or was not necessary. In addition, Belfroid et al (2008) improved Turner's equation so that this could consider the effects of inclination of the tubing.…”