Mud Acoustics in Modern Drilling - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 281

especially because the mathematics and modeling issues bear strong similarities
to our work in axial and torsional vibrations, swab-surge analysis and dissipation
modeling. As we have already developed all of our modeling concepts for
vibrations and swab-surge problems, we will discuss only the nuances of MWD
acoustic telemetry with brevity, and especially because its readership audience is
likely to be limited and highly specialized.
5.5.3 Mud pulse telemetry - the acoustic source.
We begin our discussions on mud pulse telemetry with a description of the
acoustic sources in commercial use. Mud pulse signal generation is achieved
using three different types of modulators, pulsers, valves or signal generators.
These so-called positive pressure, negative pressure and mud siren pulsers
produce (unfortunately) low data rate signals associated with long acoustic
waves that propagate up and down the mud column within the drillpipe.
Wavelengths are typically hundreds of feet long, much larger than the physical
dimensions of signal modulators, which are typically measured in inches. On
this scale, the MWD modulator is an acoustic source: like sources in seismics,
ultrasonics and nondestructive testing, they must be accurately characterized if
their transmitted signals are to be properly deconvolved at the surface receiver.
5.5.3.1 Positive pressure poppet valves.
When the poppet valve shown in the schematic of Figure 5.4 closes against
a fixed seat, a positive pressure wave (that is, an over-pressure relative to the
ambient hydrostatic levels) is created ahead of the valve that travels uphole.
This over-pressure results because a significant volume of oncoming nearby
drilling fluid is quickly brought to rest. At the same time, the mud at the
downstream side of the valve pulls away, thereby creating an opposite under-
pressure, or negative pressure wave. The net effect is a differential pressure
acting through or across the valve, or a “delta-p.” This delta-p, denoted p, is
created and appears internally within the drill collar waveguide, by virtue of
mechanical valve action; it is, in all respects, the forcing function excitation
introduced in Chapter 1. The p across the valve consists of two parts. Even if
the poppet valve is stationary, a pressure drop that is constant with time will
exist, due to pure viscous losses. If the poppet valve moves slowly with respect
to the valve seat, a quasi-steady hydraulic pressure drop varies slowly with time,
and can be detected uphole as a quasi-steady change in simple hydraulic
pressure. If the valve moves quickly, e.g., as the diaphragm in a telephone
transmitter does, an additional contribution due to the fluid compressibility of
the mud arises. For example, a thin disk or diaphragm that completely blocks a
duct will create a water-hammer delta-p equal to 2 vc when it is suddenly jerked
with a speed v (see Example 5.2). Thus, delta-p' s comprise of hydraulic (DC)
and acoustic (or, AC sound) flow components.