Papers - Hydraulics of Flowing Wells - Mathematical Development of the Theory of Flowing Oil Wells (With Discussion)

When a well strikes an oil-bearing layer, the oil has a pressure which is generally sufficient to enable it to rise to near the surface (sometimes above the surface). As soon as a well begins to produce, however, the liquid moves through the pores of the reservoir bed and the pressure in the well becomes much lower than the pressure originally prevailing there. At some distance from the well, however, the pressure in the reservoir bed remains unaltered; thus the pressure of the oil has not only to lift the oil, but also to overcome the friction resistance in the pores. The fact that so many oil wells are gushers is a consequence of the energy accumulated in the gas. In gushing the well acts as a gas-lift. A mixture of liquid and gas (the latter partly dissolved in the former) rises vertically from the oil-bearing layer through a cylindrical casing to the surface. In time conditions alter and the well ceases to gush regularly, then the gushing can be further promoted by inserting a narrower tube in the well and connecting the top of the oil string to the tubing. If the action in time becomes irregular, the gushing can be kept up for a further period by forcing gas between the two tubes. In the oil fields the term "gas-lift" is used actually only where extraneous gas is applied, as in the last of the stages mentioned. The action, however, is just the same whether the gas exclusively originates from the formation, or is partly applied artificially. Thus by gas-lift we simply mean a vertical tube in which the energy of gas under pressure, and of dissolved gas, is utilized for raising a liquid. In gushing oil wells the pressure is frequently very high and the absorption coefficient 0.4 (expressed in vol. ratio) of the coexisting gas is not particularly high, so that in reality it should be assumed that a considerable portion of the gas, at any rate at the bottom of the gas-lift, is dissolved in the oil. For water-producing wells this is not usually of such importance. Where the volume of the flowing gas is much greater than that of the flowing liquid, the latter can be suspended in the former in the form of