Correcting Surface Pressures To Reflect Downhole Pressure Changes Measured With a Fluid-Filled Capillary Tube
Authors: Miller Constance W. , Zerzan J. Michael 
Published: December 2007

Introduction
One method of monitoring the downhole pressure during a well test, when the fluid in a well is two phase and when the high temperature and salinity of phase and when the high temperature and salinity of the fluid eliminates the use of a pressure transducer downhole, is with a fluid-filled capillary tube attached to a pressure transducer at the wellhead. The system originally was designed to measure the pressure profile in a well under steady-state pressure profile in a well under steady-state conditions. When the downhole pressure is not a function of time, the wellhead pressure in the capillary tube is related to the downhole pressure only by the static head of the fluid in the tube. However, when the instrument is used to measure pressure transients, the fluid transmission line will pressure transients, the fluid transmission line will distort and delay the downhole pressure signal. To use the system under these conditions, one must either correct the measured pressures for the effect of the instrument or design the system so that the error in the recorded signal will be negligible.

Modeling Signal Propagation
Equations were developed previously for modeling of a pressure signal through a fluid transmission line. It was assumed that the temperature of the tubing was at the temperature of the surrounding fluid. When the fluid used is a liquid, it was found that the propagation of the signal is controlled by a propagation of the signal is controlled by a diffusion-like equation:
(1)
with a diffusion coefficient of r i/8 mu c f. The second term on the right side is the pressure pulse generated by a temperature change in time. When a gas is used, compressibility effects become more important, and a wave-like equation with damping results:
(2)
when d = rho c f dp + rho Beta dT and delta rho/delta rho t = - delta(rho u)/delta x. The second term on the right side is the damping term.The equations were checked by a simple experiment for the isothermal case. Capillary tubing 8,000 ft (2438 m) in length with an inner radius of 0.054 in. (0.137 cm) was filled with 10-cs silicone oil to test Eq. 1 and then with nitrogen to test Eq. 2. At one end, the tubing was connected to a nitrogen-filled bottle at 2,000 psi (13.7 MPa). At this end, a Sperry-Sun Model PN283354 pressure monitor was connected to the capillary tubing by a tee to measure static pressures. At the second end, the tubing was closed off and connected directly to the Hewlett-Packard Model 2811A quartz pressure gauge. The fluid in the tubing was allowed to equilibrate at some initial pressure. Then a valve was opened between the tubing and nitrogen-filled bottle to increase the pressure by Delta p at this end. The pressure change with pressure by Delta p at this end. The pressure change with time was recorded at the second end. The tubing was at room temperature, so it was assumed that during the test delta T/delta t =0. Fig. 1 shows the comparison between the experiment and the numerical solution of Eq. 1 and 2. A step change k input at one end of the tubing, and then measured and calculated pressures at the second end are compared. Note that pressures at the second end are compared. Note that there is excellent agreement.Conclusions about the system design can be made from the above equations. The maximum tubing diameter possible should be used as the diffusion coefficient in Eq. 2 depends on r i.
JPT
P. 2020