Mathematical Development of the Theory of Flowing Oil Wells

When a well strikes an oil-bearing layer, the oil has a pressure which isgenerally sufficient to enable it to rise to near the surface (sometimes abovethe surface). As soon as a well begins to produce, however, the liquid movesthrough the pores of the reservoir bed and the pressure in the well becomesmuch lower than the pressure originally prevailing there. At some distance fromthe well, however, the pressure in the reservoir bed remains unaltered; thusthe pressure of the oil has not only to lift the oil, but also to overcome thefriction resistance in the pores. The fact that so many oil wells are gushersis 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 latterpartly dissolved in the former) rises vertically from the oil-bearing layerthrough a cylindrical casing to the surface. In time conditions alter and thewell ceases to gush regularly, then the gushing can be further promoted byinserting a narrower tube in the well and connecting the top of the oil stringto the tubing. If the action in time becomes irregular, the gushing can be keptup for a further period by forcing gas between the two tubes. In the oil fieldsthe term" gas-lift" is used actually only where extraneous gas isapplied, as in the last of the stages mentioned. The action, however, is justthe same whether the gas exclusively originates from the formation, or ispartly applied artificially. Thus by gas-lift we simply mean a vertical tube inwhich the energy of gas under pressure, and of dissolved gas, is utilized forraising a liquid. In gushing oil wells the pressure is frequently very high and the absorptioncoefficient 0.4 (expressed in vol. ratio) of the coexisting gas is notparticularly high, so that in reality it should be assumed that a considerableportion of the gas, at any rate at the bottom of the gas-lift, is dissolved inthe oil. For water-producing wells this is not usually of such importance.