Theoretical Stability Analysis of Flowing Oil Wells and Gas Lift Wells

Abstract

Some naturally flowing wells and some gas lift wells will experience flow instabilities characterized by regular or irregular cyclic variations in tubing pressure and flow rate. The unsteady equations of motion for flow out of the reservoir, flow out of the annulus and flow up the tubing are derived and then solved by the LaPlace Transform method. This analysis produces a characteristic equation whose coefficients allow one to determine if a particular well is stable or unstable. In addition, the characteristic equation coefficients can sometimes provide useful information on what well parameters can be changed to make an unstable well stable. Introduction Many oil wells, natural flowing or otherwise, reach a stage in their flowing life when liquid rates are low. Such wells may be candidates for flow instabilities, commonly called heading. Marshall defined heading as a flow regime characterized by regular and perhaps irregular cyclic changes in pressure at any point in the tubing string. Numerous studies of heading have been reported since the pioneering work of Donahue in 1930. Among them the first comprehensive discussion of the phenomenon of heading was the one given by Gilbert in his pioneering paper. Gilbert identified three types of heading: formation, tubing and annulus. Annulus heading, Gilbert explained, occurs when bubbles of free gas at the bottom of the hole are big enough to escape entrainment with the liquid entering the tubing (that is, big gas bubbles go up the annulus), and the gas liquid ratio in the tubing is smaller than the gas-lift optimum for the average producing rate of the well. This flowing condition occurs when there is no packer in the well. Tubing heading, whose effect Gilbert said is minimal, is due to the segregation of free gas from liquid in the rising fluid column in the tubing. He attributed the occurrence of formation heading to the case where a well is tapping a fissured or cavernous reservoir. Grupping etal analyzed formation heading and showed that it could be caused by two formations with different gas-liquid ratios producing together through one tubing string. Some of the first experimental field work was done by Fancher et al, and in that work, pressure traverses were recorded during a heading cycle. They found that there was no correlation between heading, flow rate, and gas-liquid ratio; however, in their particular experiment, no heading occurred when the liquid rate was above 192bpd. Ros and later Duns and Ros also mentioned the heading phenomenon as occurring in the transition zone between various flow patterns and prepared a correlation to predict pressure loss in this flow region. They found that heading was more severe in smaller pipes for lower liquid velocities. Zarrinal et al accumulated some data on the flow regime that exists just before a well heads up and dies. A recent work by Torre et al on annulus or casing heading concludes that heading only occurs when the slope of pressure loss as a function of gas flow rate is negative. On the particular case of heading in continuous-flow gas-lift wells, Simmons suggested the problem can be corrected by over-injection of gas. DeMoss et al offered an example in which gas-lift wells are stabilized by installing orifices in the lowermost gas-lift mandrel. P. 335^

Predicting instabilities in gas-lifted wells simulation

“…When used for the casing-heading simulation (see section III-A) the parameters are pointed out by (3) . Values signalled by (2) are used for the simulation of section II-B.5.…”

“…Then, differential equations are used to derive criterion taking the form of a set of inequalities. A more dynamical system oriented approach can be found in [3]. The analysis relies on Routh's criterion and a detailed study of the root locations of a third order transfer function when physical parameters of interest vary.…”

“…The analysis relies on Routh's criterion and a detailed study of the root locations of a third order transfer function when physical parameters of interest vary. In [1], a unified criteria based on previous studies of [3] and [2] is proposed. In all these works the oil column is considered homogenous, which implicitly neglects the propagation phenomenon in the tubing.…”

Parameter Sensitivity Analysis of Gas-Lift Well Unloading Processes

“…Asheim's model was aimed at the situation of an oilfield, which is more consistent with practical situations. Existing studies for instability of casing heading have mainly focused on its characterization and on researching the stability criteria [5][6][7][8][9]. Hu B.…”

Distributed delay model for density wave dynamics in gas lifted wells

“…Preventing instabilities through closed loop control has been an active field of research (see [10], [8] and [1]). These instabilities are defined as a flow regime characterized by regular and perhaps irregular cyclic changes in pressure at any point in the tubing string D (see [2]). Among these, one finds the "casing-heading" and the density-wave instability.…”