1124 EXPLORATION GEOPHYSICS 



By combining Equations 1 and 2 the rate of production may be 

 expressed as follows : 



Q = c{Pr-hd-pg-pcn) (3) 



Equations 2 and 3 are the basic theoretical equations relating the rate 

 of production Q with the bottom-hole pressure pT,n and with the fluid level 

 h. Because pr is assumed to be a constant, it follows from Equation 2 that 

 a graph of the values of bottom-hole pressure pi,n as ordinate and rates of 

 production Q as abscissa is approximately a straight line. Also, it is evident 

 from Equation 3 that a graph of the values of the fluid level h versus Q is 

 approximately a straight line. Extrapolation of this line to the Q inter- 

 cept {h = 0) yields the theoretical maximum rate of production, because 

 h = corresponds to a minimum back pressure of the fluid in the hole.* 

 Thus, from Equation 2 



Qui!ix = C(pr- pg- pch) (4) 



As will be illustrated later, this theoretical rate is ordinarily not achieved in 

 practice, because a definite hydrostatic flow head is necessary to force the 

 oil to flow into the pump. 



The production characteristics of a well may be determined by measur- 

 ing or calculating the factors in Equations 2 or 3. Equation 2 is employed 

 when using bottom hole pressure gauges, while Equation 3 utilizes the 

 data obtained from fluid-level measurements. 



BOTTOM-HOLE PRESSURE GAUGES 



The bottom-hole pressure gauges in use at the present time are usually 

 of a self-contained, continuous recording design.t The gauges are enclosed 

 in a suitable case and consist essentially of two parts: (a) pressure ele- 

 ment to record the hydrostatic pressure and (b) a clock, pressure or 

 thermal-drive chart drum. A stylus attached to the free end of the pressure 

 element records its movement on sensitized paper or metal affixed to the 

 chart drum. The clock-drive comprises a small spring clock mechanism 

 capable of driving the chart for periods of 24 to 72 hours. The pressure- 

 drive depends upon a decrease in recorded pressure to rotate the chart. 

 The thermal-drive comprises a bimetallic temperature-actuated system 

 which produces a small angular rotation of the chart. The operation of 

 the latter system depends on the increase of temperature with depth. 



In flowing or gas-lift wells, depth pressure measurements may conveniently be 

 made by running the bottom-hole pressure gauge into the tubing on a wire line, without 

 greatly interfering with the well's production. In some wells it may not be possible to 



* For thick sands and fluid level below the top of the sand a mean pressure should 

 be used. 



t C. V. Millikan and C. V. Sidwell, loc. cit. 

 E. K. Parks and C. W. Gibbs, "Instruments and Equipment for Recording Subsurface 

 Pressures," A.I.M.E. Petroleum Technology, 1934, pp. 42-52. 



Paul G. Exline, "A Precision Gage for Subsurface Pressure Measurements," A. P. I., Drill- 

 ing and Production Practice, 1936, p. 116. 



