Well integrity/control

Analytical Model Estimates Flow Rate and Total Discharge in Gas-Well Blowouts

Despite multitier safeguards, blowouts occur. When such accidents happen, rate estimation is an important and daunting task.

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Despite multitier safeguards, blowouts occur. When such accidents happen, rate estimation is an important and daunting task. This study presents an analytical model coupling the flow in a reservoir/wellbore system of a gas well. The model considers flow in the tubing, annulus, and riser and the attendant heat transfer. To gauge safety concerns, plume dispersion is modeled under various wind-speed scenarios when ignition sources are not present. In the event of ignition, the energy of the explosion is estimated with an empirical method.


The main purpose of this investigation is to assess the coupled nature of transient fluid flow in the reservoir and the combined fluid and heat flows in the wellbore. To that end, a coupled reservoir/wellbore analytical model was developed, which was then validated with field examples. In addition, this study attempts to address issues related to dispersion of the blowout plume and the explosion hazard that the gas poses.

Model Development

When a blowout happens, the formation fluid comes into the surroundings through the wellbore without any control and, in the meantime, the reservoir pressure declines because of depletion of the reservoir. To understand the blowout mechanism, the authors split the blowout model into three parts—reservoir, wellbore, and their interaction.

Reservoir Model. In the reservoir model, the material balance in the reservoir is considered to calculate the average reservoir pressure so that the average reservoir properties can be addressed properly.

Wellbore Model. During the blowout, a large amount of formation fluid flows from the reservoir to the bottom of the hole. Because of the high pressure deep in the wellbore, the velocities are relatively low. The upward movement of fluid will reduce the pressure, and the velocity of formation fluid will increase until it reaches sonic velocity because of the thermodynamics limitation. The existence of sonic velocity rarely occurs with a single-phase oilwell blowout because the large hydrostatic pressure gradient does not allow such high velocity. It generally does not happen with offshore wells, either, because the pressure difference between the wellhead and the bottom of the hole is not significant enough. However, with onshore gas wells and oil/gas wells, the sonic velocity becomes a critical factor that needs to be considered. It is important to calculate sonic velocities of different phases under various wellhead conditions.

In a blowout situation, various scenarios may play out given the unknown nature of formation conductivity, reservoir pressure, and fluid properties. For overpressured reservoirs, the diameter of the flow conduit will largely dictate the wellbore-pressure gradient. In small-volumetric reservoirs, the wellhead pressure may decrease gradually to a point at which the flow becomes marginal. In all situations, wellhead pressure controls the blowout behavior.

Reservoir/Wellbore Coupling. The phenomenon of a blowout is similar to high-rate production, except that the rate for the blowout keeps changing over time. As a result, it is possible to apply flow equations of a drawdown test to the blowout model by neglecting the superposition in time. The authors considered both the early-time transient and the late-time pseudosteady-state flow for a gas well in a bounded circular reservoir.

Applications of Model

The blowout rate declines with time as reservoir depletion occurs. To simplify the problem, the authors divided the blowout duration into small segments. They assumed that the blowout rate generally remains constant in each time segment. They first determine whether the sonic velocity could exist at each timestep. If the reservoir pressure is high enough to withstand the existence of sonic velocity, the velocity becomes a constraint at the wellhead. They used the sonic velocity of the fluid under standard conditions as an initial input. The new sonic velocity serves as a new input for the model. The iterative calculation procedure was continued until the solution convergence was attained within a specified tolerance at a given timestep. In addition, reservoir pressure can be obtained from the results at previous timesteps. This computation process continues until the wellhead pressure nears the ambient condition, indicating that the blowout is governed by the constant wellhead pressure. If the sonic velocity cannot exist, the wellhead pressure becomes the constraint at the wellhead and controls the blowout behavior.

Modeling Dispersion of Blowout Plume

During an onshore blowout, one of the following scenarios may play out:

  • Without an ignition source, the gas will disperse to the surroundings on the basis of wind speed. Therefore, the toxicity and dispersion of the plume, and the consequent hazard, need to be understood.
  • In the presence of an ignition source, the gas/air mixture may ignite and result in jet fire and explosion. To evaluate the fire and explosion hazards, the authors used the heat-flux intensity associated with a jet fire and the overpressure caused by an explosion.

The methodology presented in this study provides an opportunity to capture the evolution of blowout events under different operational conditions. The quantitative assessment of the risk related to a blowout can also help operational personnel make the right decisions at the right time.
In the absence of ignition, a plume will form because of the dispersion of the toxic/flammable gas. The shape of the plume depends on the wind speed and buoyancy effect.

The evolution of the plume under different wind speeds was analyzed with a commercial software package. The results illustrate the boundary of the plume. The top of the plume is higher for the low-wind-speed situation than it is for other situations because of the buoyancy effect. At higher wind speeds, the buoyancy effect is reduced and the plume begins to touch the ground. As a result, the health and safety of personnel and residents in the area will be in jeopardy. In addition, the mixing effect of released gas and air is enhanced with the increase of wind speed. Therefore, the plume affects a larger area in gentle wind speeds compared with situations with stronger winds.

When there is an ignition source near the wellbore, the gas/air mixture might be ignited, leading to explosion and fire. The explosion of gas leads to a reaction front moving away from the ignition source, accompanied by a shock wave. Even when the reaction material is exhausted, the movement of the shock wave does not stop. The pressure resulting from the shock wave over normal atmospheric pressure is called overpressure, and this is an important characterization of the consequence of the explosion.

When the effect of explosion is evaluated conservatively, the worst-case scenario is always considered. It indicates that the ignition source is present immediately after the initiation of blowout, when the plume of the released gas has the largest volume, leading to the largest area affected by explosion. Fig. 1 presents the worst-case scenario of an explosion when the ignition source is 5 ft from the well. The ovals indicate an overpressure of 0.3 psi (for a specified wind speed), which is considered a safety limitation for buildings and personnel. Any buildings and personnel inside the oval will be in danger if explosion occurred soon after the blowout. As Fig. 1 shows, a distance of 150 ft from the blowout source is covered by overpressure higher than 0.3 psi when the wind speed is 9.8 ft/sec. With an increase of wind speed, the unsafe area becomes smaller.

Fig. 1—Late explosion or the worst-case scenario caused by a blowout.


Jet fire is a flame with turbulent diffusion because of the combustion of continuously released hydrocarbon gas in a particular direction. Many jet fires are followed by explosions. The jet fires may occur immediately after a blowout in the presence of an ignition source. In that case, the radiation generated by the jet fire must be taken into account.


The blowout model presented here is applicable for onshore gas wells, and it also shows the potential application for offshore gas and oil wells. For offshore wells, because of the hydrostatic pressure at a given water depth, the flow is unlikely to be choked. Therefore, the blowout behavior will be governed by the constant wellhead pressure.

One difficulty with the proposed approach is that it is assumed that the blowout rate reaches maximum value immediately after the blowout. In fact, the blowout rate would increase from the normal production rate to the maximum value and then decline. Such an increase in the rate at the beginning of the blowout would take several minutes. This short time period can be neglected when the blowout lasts for days. However, for blowouts lasting a short period of time, such as several hours, the period in which the blowout rate increases will become significant for the prediction of production loss.

This study provides a useful approach to modeling blowouts under the assumption of a single tubing diameter in the absence of other wellhead restrictions. However, the model is capable of capturing phenomena that are more complicated during real blowout events.

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 170274, “Flow-Rate and Total-Discharge Estimations in Gas-Well Blowouts,” by R. Liu, A.R. Hasan, SPE, and S. Mannan, Texas A&M University, and C.S. Kabir, SPE, Hess, prepared for the 2014 SPE Deepwater Drilling and Completions Conference, Galveston, Texas, USA, 10–11 September. The paper has not been peer reviewed.