Wellbore and Near-Surface Hydraulics of a Blown-Out Oil Well
Authors: Clark A.R. , Perkins T.K. 
Published: December 2007

Summary
A method is presented for calculating the critical flow velocity, pressure, and temperature at the exit of a blown-out oil well. The calculation depends on the wellbore geometry, the thermal properties of the wellbore and its surroundings, and an a priori knowledge or estimate of the well productivity index (PI) and gas/oil ratio (GOR). A procedure is also given for estimating the flow conditions at the end of the two-phase pressure transition region that forms above the well exit.

Introduction
Among the primary concerns associated with a blown-out oil well are the environmental effects of the expelled fluids. In addition to the obvious pollution hazards, there is the danger of gas/oil combustion. If the gas plume ignites, various additional problems are created. Heating effects of a burning well can damage nearby equipment and neighboring wellheads. To analyze and predict such effects, estimates of certain flow parameters at the discharge of the well are needed.The primary mechanism governing the hydraulics of a blown-out oil well is the rapid, near-surface liberation and subsequent expansion of large amounts of dissolved gas. As the accelerating fluids rise to the surface, their speed is limited by the available flowing pressure. For typical GOR'S, it has been found that the two-phase pressure drop limits the speed and, hence, the maximum rate of flow. As the speed of the fluids approaches the critical (sonic) speed of the mixture, the pressure drop increases dramatically. Corresponding to the two-phase sonic discharge velocity is the critical (minimum possible) discharge pressure. The critical flow state depends strongly on the relative volumes of oil and free gas present at the surface. As the critical pressure decreases, the volumetric fraction of free gas increases, causing an increase in the two-phase critical speed for typical GOR's.It is possible for a blowout flow rate to be less than critical because of partial blockage of the well exit. In such cases the surface pressure will stabilize at a value greater than the critical pressure. Whatever the nature of the well exit, however, there is a region of pressure transition between the underexpanded pipe flow and its associated two-phase atmospheric plume. The flow conditions at the end of this region are important for analyzing the subsequent interaction between the expelled wellbore fluids and the atmosphere.The analysis of the wellbore and discharge jet hydraulics has been coupled with the formation characteristics and the reservoir pressure. Knowledge of the well PI, bottomhole temperature, and GOR then fixes the critical flow conditions for a given well. A method has been developed for calculating the critical flow from an uncontrolled oil well. The discharge pressure, temperature, and speed are calculated interatively until the two-phase pressure drop limitation is established at the surface. Once the critical discharge conditions are determined, the next step is to calculate the flow at the end of the two-phase pressure transition region outside the wellbore. These calculations then serve to establish the starting point for analyzing the subsequent interaction between the expelled wellbore fluids and the atmosphere. Results obtained for the pressure transition region appear to be in good agreement with published predictions and photographs of supersonic underexpanded gas jets.
JPT
P. 2181^