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Summary. A computer simulator of the flow and pressure behaviors in wellbores and diverters (large horizontal flowlines from the wellhead) was developed to predict performance during shallow gas blowouts. The model is based on the solution of the unsteady-state mechanical energy-balance equation for pipe flow. Four main regions are considered: the reservoir, the two-phase gas/liquid region in the wellbore, the liquid being displaced ahead of the two-phase region, and the diverter. For the reservoir, equations for transient radial gas flow are used. In the two-phase region, Aziz et al.'s two-phase flow model is used to calculate liquid holdup and frictional pressure drop. For liquid ahead of the gas, pressure losses caused by the acceleration of the liquid column are pressure losses caused by the acceleration of the liquid column are considered. Flow in the diverter allows for two-phase critical flow at the diverter exit. At each timestep, the model calculates the pressure, fraction of each phase present, and velocity throughout the well and the diverter by use of an iterative procedure. The model has shown that the pressure and velocity behaviors depend strongly on the initial difference pressure and velocity behaviors depend strongly on the initial difference between bottomhole pressure (BHP) and reservoir pressure and on the wellbore and diverter diameters.

Introduction

A major concern during shallow offshore drilling operations is the detection and control of a sudden gas influx that can occur when drilling penetrates an overpressured gas-bearing formation. Although most kicks are handled effectively, blowouts occur and result in loss of lives, injuries, and millions of dollars in damages.

To assist in the analyses of kick phenomena, computer models have been developed to simulate the conditions present during a kick. The objective of a kick simulator is to calculate the pressure and velocity distributions in the wellbore and surface pressure and velocity distributions in the wellbore and surface fittings as a function of time.

The computer model presented here differs from existing models because it is fully transient and uses a two-phase flow correlation, resulting in a more realistic gas distribution in the wellbore. In addition, the model incorporates a diverter to aid in well control analysis. The simulator begins with the start of gas influx at the bottom of the hole. The model tracks the movement of gas up the wellbore and out the diverter, calculating the pressure and velocity distributions in the system as a function of time.

Theoretical Approach

Fig. 1 illustrates the conceptual approach used to model the areas of interest in this system. The drilling fluid referred to as the liquid phase is introduced through the bit at the hole bottom. After drilling phase is introduced through the bit at the hole bottom. After drilling penetrates an overpressured gas sand, the gas enters the wellbore penetrates an overpressured gas sand, the gas enters the wellbore at this location (Region 1). As the gas flows into the wellbore annulus, a two-phase region is created (Region 2). An interface marks the boundary between the uncontaminated drilling fluid (Region 3) and the two-phase mixture below. The annular fluids circulate up the hole and exit through the diverter (Region 4).

Region 1-Reservoir/Gas Influx. The actual dynamic conditions present when the drill bit encounters and continues to drill through present when the drill bit encounters and continues to drill through an overpressured gas sand are extremely complex. A realistic approach, based on emphasizing the transient behavior of the process, was taken to model the gas influx. The formation properties, specified by the user, determine the rate of gas influx. The transient radial gas-flow equation used for an infinite reservoir with constant reservoir pressure is

1,000KH (PR2-P2) qg = .................................(1) (50,300)(86,400)PDugp

where the dimensionless variables are pD = 0. 5 [ln(tD) + 0.81] and tD=

Eq. 1 calculates the rate of gas influx introduced into the annulus at the bottom of the hole (Region 1). The major factor controlling the rate of gas influx is the reservoir pressure of the gas sand. In application, several initial pressure drops (pR -p) were assumed such that the reservoir pressure was calculated from the initial single-phase flowing BHP (BHFP).

Region 2-Two-Phase Gas/Liquid Region in the Wellbore. The gas influx at the bottom of the hole creates a region consisting of gas and drilling liquid. This two-phase region moves upward, displacing uncontaminated drilling fluid still in the wellbore.

With the gas solubility in a water-based drilling fluid neglected, seven variables are necessary to describe this two-phase (vertical) system completely: temperature, pressure, gas and liquid velocities, gas and liquid densities, and liquid volume fraction (holdup). The temperature profile of the wellbore is user-specified and assumed constant throughout the simulation. The liquid density is also assumed to be constant throughout the simulation. This assumption is valid for water-based muds given the shallow well depth and the previous assumption of gas insolubility in the liquid. Gas density is calculated with a z factor. The remaining four variables are calculated with unsteady-state gas and liquid mass balances, a mixture-momentum equation, and a two-phase holdup correlation. The equations used for ID vertical flow are

/ t(pg(1.0-yL)+ / D(pgVg(1.0-yL))=0,..................... (2)

/ t(PLYL+ / D(PLVLYL)=0,................................. (3) / t(PLVLYL+pgvg(1.0-yL))

+ /D(PLYLV2L+pg(1.0-YL)vL2)=0............................. (4)

and YL=f(qL,qg,p,t,d)...................................... (5)

Eqs. 2 and 3 are single-phase mass balances for gas and liquid (mud). Eq. 4 is the mixture-momentum equation for the two-phase system. Eq. 5 represents a two-phase holdup correlation used to calculate liquid holdup, L. These equations must be solved simultaneously to determine the pressure, gas and liquid velocities, and liquid holdup.

The mixture-momentum equation combined with the holdup correlation is a form of the "drift flux" model. Eqs. 4 and 5 are used instead of single-phase momentum balances because of the unknown nature of the interaction between the phases.

The Aziz et al. two-phase vertical-holdup correlation was used to determine the liquid holdup and the two-phase frictional pressure drop. This correlation considers slip, the difference in the in-situ gas and liquid velocities, and flow regimes. Liquid holdup is defined as the ratio of the volume of a pipe segment occupied by liquid to the total volume of the pipe segment. The holdup and friction-factor correlations are dependent on the flow regime present in the pipe section considered. The flow regimes considered in this correlation are bubble, slug, transition, and mist flow.

Region 3-Uncontaminated Single-Phase Wellbore Liquid. In the single-phase liquid region, the important parameters are pressure drop and liquid velocity.

SPEDE

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