Production Engineering - Use of Data on the Build-up of Bottom-hole Pressures

In preparing a well for pumping, observations are often made of the fluid level in the well bore or bottom-hole pressures at various times before equilibrium has set in. From a qualitative point of view one may immediately infer that if the rise in the bottom-hole pressure or fluid level is rapid the permeability of the sand about the well bore is large, and converse conclusions may be drawn if the rise is slow. However, a more quantitative estimate will give additional information of value, as will be shown in this paper. To derive such an estimate we may proceed as follows. Let h be the fluid height, above the sand face, at time t, and let yo be the average density of the fluid that enters the bore. The bottom-hole pressure, for a fluid height h will therefore be p = rogh, neglecting, of course, the friction drop in the well bore, while the fluid is rising, as may be justifiably done for most pumping wells. If a is the free area of the open-flow string—assumed to be uniform— the rate of production from the sand during the rise of fluid will be: where the last part of the equation merely indicates that, in general, the production rate Q must be considered as a function of the back pressure, and is determined by it alone. In fact, equation 1 shows that if the rate of rise of the pressure or fluid level is determined as a function of the height of rise, or p, for a number of values of the latter, this functional relation between Q and p will be immediately given. Conversely, if we know this functional relation, the rate of increase of p or h may be predicted, or, by observing the rate of rise of p or h some of the constants of the sand may be determined. Thus we may approximate the production from a well in a pumping state by that of a dead