Understanding Gas-Well Load-Up Behavior

Abstract

Summary This paper describes the hydraulics of wellbore load-up for gas wells. Atheoretical model of transient load-up hydraulics is presented and comparedwith field test data. Application of this technology allows predictivetechniques to be used in predictive techniques to be used in analyzing gas-wellload-up. It also establishes an understanding of loadup behavior, which isvaluable in analyses of production problems and evaluations of productionalternatives for low-pressure gas wells. Introduction Part 1 of this series outlined data that Part 1 of this series outlined datathat validated the theory for predicting the critical rate, qc, forlow-pressure gas wells. This second part outlines and validates the theory forpredicting the behavior of a low-pressure gas well after qc is reached, whenthe well is in an unsteady-state load-up condition. Doing so will offer abetter definition of gaswell load-up behavior and a better understanding of howto cope with the problem. To understand the transient load-up condition, it is helpful to construct apicture of a gas well in load-up (Fig. 1). Fig. 1a represents a well flowingabove its critical rate; i.e., qg >qc. In this state, at t=O, all fluidproduced with the gas is carried out of the produced with the gas is carriedout of the wellbore conduit and the wellbore exhibits a relatively predictable, steady-state behavior. The drive energy available that causes gas to flow from this well is boundedby the average reservoir pressure in the well's drainage area, PR and thesystem pressure, Ps' The flowing sandface pressure, Psf' is Ps' The flowingsandface pressure, Psf' is dictated by the reservoir performance. The flowingwellhead pressure, psf, is controlled by the performance of any surfaceequipment or pipeline. At the onset of load-up where qg less than qc and t=1, liquid is no longercarried out of the wellbore; instead, it is held up in the wellbore in the formof an aerated column (Fig. 1b). The same boundary conditions exist for thedrive energy; however, psf and p, qr converge toward their pressure p, qrconverge toward their pressure boundaries as the produced fluid accumulates andincreases the hydrostatic pressure of the flowing gas column. The sandfacepressure, psf gradually increases until it is equal to psf gradually increasesuntil it is equal to the average reservoir pressure, PR This increase in psfwith time causes a comparable decline in gas flow rate and During this load-up period, the pressure loss in the well flowline (Pwf-ps), the gas column in the wellbore (Pli-Pwf) and the reservoir drawdown (Pe-Psf)all decrease because these pressure losses are primarily frictional anddecrease with decreasing flow rates. However, the pressure caused by thebuilding of a hydrostatic liquid column in the wellbore (Psf-Pli) increases. This hydrostatic column continues to build until such time as the hydrostaticconditions of the wellbore, combined with pwf balance the reservoir drivingforces and cause the well to die (Fig. 1c). Now, at t=2, the well is completelyloaded and qg=0. Once this occurs, PR continues to increase until it either equalizes withthe reservoir pressure at the well's drainage radius boundary, Pe at t=3 orovercomes the load-up-induced hydrostatic head and begins to unload thewell. The well's ability to unload itself depends on such variables as reservoirtransient flow performance, remaining amount of load performance, remainingamount of load fluid, changes in the system pressure boundary and wellboreconfiguration and depth. When a well can no longer complete the unloading cyclenaturally, it has reached its "blowdown limit which is covered in Part 3 ofthis series. Theory This description of gas-well load-up can be modeled predictively withconventional quantitative analysis techniques. First. because gas-well load-upis driven by the time history of the liquid column height, it is necessary todefine a liquid control volume, as shown in Fig. 2. The primary differentialequation to be solved for the liquid balance is With the definition of the liquid holdup fraction,3 YL, Then, To solve Eq. 3, an expression for the rate of liquid in and liquid out, QLinand QLout must be determined. JPT P. 334

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