1136 EXPLORATION GEOPHYSICS 



PRODUCTIVITY DETERMINATIONS: WELLS 

 UNDER CASING-HEAD PRESSURE 



The producing characteristics of wells under pressure can best be 

 determined as follows: 



The bottom-hole pressure at some given datum point — usually the 

 average depth of the producing formation — is plotted as ordinate and the 

 production rate as abscissa. Methods of determining total pressures at a 

 given datum point have been described in connection with Figures 703 

 and 704. 



The productivity of the well may be determined by making a series 

 of measurements with varying casing-head pressures at a given pro- 

 duction rate to determine one of the pressure datum points. The rate 

 of production is now changed and after equilibrium is established a second 

 series of measurements is made to determine another pressure datum 

 point. Two or more of these pressure datum points are then plotted, and 

 the pressure-rate curve extrapolated to zero pressure (where no back- 

 pressure will be exerted against the producing formation) to determine 

 the theoretical maximum production rate for the well. 



Another procedure allows the productivity to be obtained with no 

 fluid above the pump. In this procedure, the pump is operated at a given 

 production rate and the casing-head pressure increased to a value such 

 that the well is pumped-oflF. Under this condition, the pressure at the 

 pump intake is equal to the casing-head pressure plus the weight of the 

 column of gas. The production rate is now changed by altering the speed 

 of the pump, and the procedure is repeated. A curve is then plotted 

 showing the total gas pressure versus production rate, and the curve is 

 extrapolated to zero pressure to give the theoretical potential of the well 

 at that particular depth setting of the pump. 



SOLUTION OF PUMPING PROBLEMS 



Dynamic Measurements. — It is possible to determine various im- 

 portant characteristics of a well, such as the maximum rate of production 

 and the reservoir pressure, etc., by dynamic measurements wherein the 

 bottom-hole pressure or the depth to the fluid level is determined as a 

 function of the time before equilibrium has been established, t The 

 theory of such measurements as applied to the determination of the 

 reservoir pressure will be illustrated for a case in which the following 

 assumptions are made. (1) The well is open to the atmosphere so that 

 the casing-head pressure pen is zero. (2) The weight of the gas column 

 pg is negligible. (3) The free area a of the open flow string is uniform. 

 (4) The fluid-pressure gradient c? is a constant, and the rate of produc- 



I 



t Morris Muskat, A.I.M.E. Petroleum Technology, 1937. 



