**REVISED ****06-12-2007**

**© 2003 - 2007 WELLOG**

**All Rights Reserved**

**PART II, PAGE 2**

**ACOUSTIC TOOLS:**

**The interaction of acoustic waves in a
rock matrix affect velocity and attenuation of the acoustic signal. Rock
density, porosity, saturation
and fracturing have different affects that contribute to a very
complex acoustic signal which contains an abundance of information.**

**Acoustic tools are designed to generate an acoustic signal
(sound wave) having significant energy that will travel through the borehole
fluid, rock formation and back through the borehole fluid to an acoustic
receiver. Acoustic transmitters may be piezoelectric crystal or magnetostrictive.
Both types of transmitters convert electrical energy into mechanical
energy. The mechanical energy in the form of an acoustic wave travels into the
surrounding formation and is received by an acoustic receiver usually of the
piezoelectric type.**

**Acoustic waves traveling in an elastic media are subject to
stress and strain. Most of the interaction
of acoustic waves in a rock formation can be described mathematically using the
theory of elastic waves in an elastic media. In an elastic medium with small
strains, the strain is directly related to the stress that caused it. This relation is referred to as “Hooke’s
Law”. The total strain is the sum of the
strains produced by the individual stresses.**

**An acoustic waveform is subject to reflection and
refraction. Because the waveform moves in all directions and encounters varying
interactions, when waveforms rejoin, they may have constructive or destructive
interference with each-other. Among the
interactions, Plane waves referred to as “P waves” and shear waves referred to
as “S waves” a formed. These waves, called “head waves” are among the first to
arrive at the receiver. Various other waves are produced; conical waves,
pseudo-Rayleigh waves, and Stoneley
or tube waves.**

**It should be noted that P waves travel faster than S waves.**

**Example: Sandstone
(WY) having density of 2.28 gm/cc ;**

** Young’s modulus: Poisson’s ratio: Vp: Vs: Vp/Vs: Vs
as % of Vp:**

**0.014 0.060 7470 5130 1.46 68.42% **

**Matrix velocity – If a rock were truly elastic it would
have no porosity. But, rock contains
pore spaces, fractures and other discontinuities. The velocity of propagation in a rock matrix
is therefore affected by pressure, porosity, pore
fluid, fraction of the pore space containing a given fluid (saturation), fluid
type and temperature. Pressure has the effect of closing micro-fractures and
increasing velocity. Porosity has the effect of reducing velocity of S
waves. Temperature affects fluid
velocity and therefore has an effect on overall velocity.**

**Attenuation - Attenuation is greatly increased by
increasing porosity. Attenuation decreases with increasing pressure. **

**Attenuation of both P and S waves are minimum
in dry rock. Attenuation for both modes increases as partial saturation
occurs. P waves are attenuated twice as
much as S waves in partially saturated rock. As total saturation is reached, P wave
attenuation is REDUCED and S wave attenuation reaches MAXIMUM. **

**DELTA-T:**

**Velocity of an acoustic wave (Vp) is measured in terms of feet per second. The reciprocal (****D****t)**** is
measured in seconds per foot. In the case of rock matrices units are micro-seconds
(usec) per foot.
****D****t is also
referred to as “transit time”.**

**Typical transit times:**

**Shale 130 – 175 usec per ft. Example:
Shale (AZ) Vp = 6372 ft/sec., delta-t = 157 usec
per ft.**

**Sandstone 52.5**** – 55.5 usec per ft.**

**Limestone 47.5**** usec per ft. Example:
Limestone (PA) = Vp = 10899
ft. per sec., delta-t = 91.7**

**Dolomite 42.5 usec
per ft.**

**BOREHOLE COMPENSATION:**

**Acoustic logging tools use either one
transmitter and two receivers. Two transmitters and two receivers are
used to compensate for adverse borehole conditions and is
called Borehole Compensation (BHC). A
process of subtracting travel times from one transmitter to one receiver then
the other, has the effect of giving the resulting
formation travel time only. **

**Using the convention T12 = time from transmitter 1 to
receiver 2;**

**For change in hole diameter
(Dd):**

** T12
– T11 = l/v + ****D****d/vf ,
T21 – T22 = l/v + ****D****d/vf**

**Where:**

** l =
distance between receivers**

** vf = velocity of sound in fluid**

** ****D****d =
change in hole diameter**

**Averaging gives:**

** (T21
– T22 + T12 – T11)/2 =
l/v**

**If the tool is tilted:**

** (T21
– T22 + T12 – T11)/2 =
l cos(a)/v**

**Where: a = tilt
angle**

**Note: tilt angle can usually be ignored due to the length
of the tool and the small diameter of hole, cos(a) = 1.**

**In practice, acoustic logging must be performed in a fluid
filled well and the tool must be centralized in the hole.**

**Dry hole acoustic sondes are held stationary and pressed
against the side of the hole for each measurement.**

**POROSITY FROM ACOUSTIC TOOL:**

**Porosity (****f****) is calculated as follows:**

** ****f**** = (****D****t(****log) - ****D****t(ma)) / (****D****t(f) – ****D****(ma))**

**Where: ****D****t(****log) is delta-t obtained from the
log.**

** ****D****t(****ma) is
the delta-t of matrix rock having no porosity.**

** ****D****t(****f) is the
delta-t of the fluid contained in the pore space.**

**Typical ****D****t(****f) for water or mud is 188 to 200
microseconds (usec) per ft.**

**Note: vf
is less in mud.**

**CORRECTION FOR SHALE:**

**Correction for shale is performed when ****D****t(****sh****) exceeds 100 usec
per ft.**

**Multiply the calculated porosity by 100/**** D****t(sh)**

**CORRECTION FOR GAS:**

**When pore space contains gas, ****D****t(****fluid)
increases. The result is optimistic porosity calculations.**

**In many cases acoustic information is unreliable due to
cycle skipping caused by long ****D****t
intervals.**