Microwave electromagnetic logging with mudcake correction

The disclosure is directed to a technique used for determining the mudcake-corrected water-filled porosity of formations surrounding a borehole, and which can also be used for determining the thickness of the mudcake formed on the borehole. Microwave electromagnetic energy is transmitted into the formations. Near and far receiving antennas are employed for receiving microwave electromagnetic energy from the formations. Means responsive to the outputs of the receiving antennas are provided for obtaining a travel-time-dependent differential measurement. Further means, responsive to the output of one of the antennas, are provided for obtaining a travel-time-dependent direct measurement. Finally, means are provided for determining the mudcake-corrected water-filled porosity of the formations from the differential and direct measurements. The mudcake thickness may also be determined from the differential and direct measurements. In the preferred embodiment of the invention, the means for obtaining the travel-time-dependent differential measurement is operative to measure the phase difference between the electromagnetic energy received at the near and far receivers, and the means for obtaining the travel-time-dependent direct measurement is operative to measure the phase difference between a reference derived from the transmitted electromagnetic energy and the electromagnetic energy received at the far receiver.

BACKGROUND OF THE INVENTION 
Various techniques have been set forth for measuring the dielectric 
constant or electric permittivity of subsurface formations. Prior 
investigators have recognized that the relative dielectric constant of the 
different materials of earth formations vary widely (e.g. 2.2 for oil, 7.5 
for limestone, and 80 for water) and that the measurement of dielectric 
properties therefore holds promise of being a useful means of formation 
evaluation. Since hydrocarbons and fresh water can have similar 
resistivity, the contrast between the dielectric constant of hydrocarbons 
and water is especially meaningful in situations where low salinity is 
encountered. 
There has been recently developed a logging device which investigates earth 
formations surrounding a borehole by radiating microwave electromagnetic 
energy into the formations and then taking measurements which relate to 
the propagation of the energy in the formations. A form of this device, 
currently designated as an "electromagnetic propagation tool" (or "EPT") 
is disclosed in the U.S. Pat. No. 3,944,910. In operation of the EPT 
logging device, the relative phase of energy received at a spaced receiver 
pair is measured and used to obtain indications of the formation 
dielectric constant, typically in the so-called invaded zone of the 
formations which are nearest the borehole. (At a fixed frequency of 
operation, relative phase and travel time per unit distance are 
proportionally related, and travel time will be referred to in place of 
phase in this background discussion.) The wave attenuation may also be 
measured at the receivers and used to implement corrections to the EPT 
travel time measurements since the lossiness of the propagation medium can 
affect travel time therethrough. 
Since the dielectric constant of water is much higher than that of 
hydrocarbons or formation matrix material, the travel time will be largely 
dependent upon the fraction of water in the formations; i.e., the 
water-filled porosity of the formations, designated .phi..sub.w. In the 
above-referenced U.S. Pat. No. 3,944,910, and in U.S. Pat. No. 4,092,583, 
there are disclosed techniques for obtaining .phi..sub.w from travel time 
(and attenuation, where applicable) measurements taken with an EPT logging 
device. 
While the EPT has proved to be quite effective in obtaining measurements of 
properties of subsurface formations surrounding a borehole, viz. in the 
invaded zone thereof, it has been found that presence of a substantial 
mudcake can sometimes give rise to inaccuracies. The EPT has a relatively 
short spacing between transmitter and receivers and an attendant shallow 
depth of investigation. It therefore stands to reason that such a shallow 
investigation measurement device will necessarily be "looking" at mudcake 
to some extent. Techniques for determination of mudcake thickness and/or 
for correction of the effects of mudcake thickness have been set forth in 
the prior art in the context of certain logging devices, such as 
acoustical logging devices. For example, in the U.S. Pat. No. 3,608,373, 
there is disclosed an acoustic logging device which utilizes the 
difference between direct and differential pulsed acoustic travel times to 
obtain mudcake thickness. The use of a difference follows directly from a 
difference in travel paths of the acoustic wave; i.e., one path (the 
differential) having travel time through the mudcake cancel out, whereas 
the other path (direct) includes travel time through the mudcake. This 
simplified plane-wave type of model is not sufficient, however, when 
considering the effects of mudcake on an EPT device wherein continuous 
wave electromagnetic energy, rather than acoustic energy, is measured at 
the receivers in the relatively "near field" of the wave energy. The 
spacings of the EPT device necessitate a "near field" phenomenon analysis 
which takes into account electrical properties of both the mudcake and the 
formations that will affect the field measured at the receivers. In 
particular, both the conductivity and the dielectric constant of the 
mudcake and the formations, as well as the mudcake thickness, will affect 
the field detected at the receivers of the logging device. Accordingly, 
simple relationships between travel times will not yield a meaningful 
mudcake correction for the EPT. 
It is one of the objects of the present invention to provide an apparatus 
and method for determining mudcake-corrected EPT-determined measurements 
of formations surrounding a borehole. 
SUMMARY OF THE INVENTION 
The present invention is directed to an apparatus and method for 
determining the mudcake-corrected water-filled porosity of formations 
surrounding a borehole, and can also be used to determine the thickness of 
the mudcake formed on said borehole. In accordance with an embodiment of 
the invented apparatus, there is provided a source of microwave 
electromagnetic energy. A transmitting antenna is used for transmitting 
the microwave electromagnetic energy into the formations. Near and far 
receiving antennas are employed for receiving microwave electromagnetic 
energy from the formations. Means responsive to the outputs of the 
receiving antennas are provided for obtaining a travel-time-dependent 
differential measurement. Further means, responsive to the output of one 
of the antennas, are provided for obtaining a travel-time-dependent direct 
measurement. Finally, means are provided for determining the 
mudcake-corrected water-filled porosity of the formations from the 
differential and direct mesurements. The mudcake thickness may also be 
determined from the differential and direct measurements. 
In the preferred embodiment of the invention, the means for obtaining a 
travel-time-dependent direct measurement is responsive to the output of 
the far receiver, and the means for obtaining both travel-time-dependent 
measurements are each operative to measure the phase velocity of the 
electromagnetic energy. More particularly, the means for obtaining the 
travel-time-dependent differential measurement is operative to measure the 
phase difference between the electromagnetic energy received at the near 
and far receivers, and the means for obtaining the travel-time-dependent 
direct measurement is operative to measure the phase difference between a 
reference derived from the transmitted electromagnetic energy and the 
electromagnetic energy received at the far receiver. 
Further features and advantages of the invention will become more readily 
apparent from the following detailed description when taken in conjunction 
with the accompanying drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring to FIG. 1, there is shown a representative embodiment of an 
apparatus 30 in accordance with the present invention, and which can be 
used for practicing the method of the invention, for investigating 
subsurface formations 31 traversed by a borehole 32. The borehole 32 is 
typically filled with a drilling fluid or mud which contains finely 
divided solids in suspension. Generally, the fluid pressure in the 
formations traversed by the borehole is less than the hydrostatic pressure 
of the column of mud in the borehole, so that the mud and mud filtrate 
flow somewhat into the formations. As is well known, the formations tend 
to screen the small particles suspended in the mud so that a mudcake is 
formed on the walls of the borehole. The thickness of the mudcake varies 
with formation parameters such as permeability, but at least a very thin 
mudcake is usually present on the borehole wall. In FIG. 1, the mudcake is 
indicated by reference numeral 40. 
The investigating apparatus or logging device 30 is suspended in the 
borehole 32 on an armored cable 33, the length of which substantially 
determines the relative depth of the device 30. The cable length is 
controlled by suitable means at the surface such as a drum and winch 
mechanism (not shown). The logging device 30 includes an elongated 
cylindrical support member 34, the interior portion of which has a 
fluid-tight housing containing the bulk of the downhole electronics. 
Mounted on one side of support member 34 is a pad 37 which contains, inter 
alia, transmitting antenna T and vertically spaced receiving antennas 
R.sub.1 and R.sub.2. On the other side of support member 34 is mounted a 
backup arm 38 which may be hydraulically controlled to maintain the pad 37 
in contact with the borehole wall. The backup arm 38 can also be used to 
provide a caliper reading. Electronic signals indicative of the 
information obtained by the logging device are transmitted through the 
cable 32 to a computing module 85 and a recorder 95, located at the 
surface of the earth. The particular means shown in FIG. 1 for maintaining 
the antennas in engagement with the borehole wall is illustrative, and it 
will be appreciated that other known suitable means for accomplishing this 
objective can be utilized. 
The downhole electronics contained within member 34 are shown, for 
convenience of illustration, at the side of the borehole. Solid-state 
oscillator 45 provides output energy in the microwave region of the 
spectrum. The microwave region is defined herein as including the range of 
frequencies between about 300 MHz. and 300 GHz. In the present embodiment, 
the oscillator operates at a frequency of 1.1 GHz; i.e., 
1.1.times.10.sup.9 cycles per second. The output of oscillator 45 is 
coupled through an isolator 46 and a directional coupler 58 to the 
transmitting antenna T. Microwave energy is transmitted into the 
surrounding formations establishing an energy field. The energy received 
at antennas R.sub.1 and R.sub.2 is respectively coupled to input terminals 
of the mixers 47 and 48. The signals which arrive from R1 and R2 are out 
of phase with each other by an amount which depends on the properties on 
the media surrounding these receivers. Secondary input terminals of the 
mixers 47 and 48 are supplied with microwave energy at a frequency that is 
separated from the transmitter frequency by some relatively low frequency 
which is typically in the radio frequency range. In the illustrated 
embodiment, a solidstate oscillator 49 supplies microwave energy to mixers 
47 and 48 at a frequency of 1.1001 GHz, or 100 KHz above the transmitter 
frequency. The outputs of the mixers 47 and 48 therefore contain the 
difference frequency of 100 KHz. In accordance with well known principals, 
the mixer outputs maintain the phase relationship of the signals from 
R.sub.1 and R.sub.2, but the task of phase detection is facilitated at the 
lower frequency of the mixed signals. To insure that the difference 
frequency between the outputs of the oscillators 45 and 49 remains at 100 
KHz, the oscillator outputs are sampled and fed to a mixer 50. The output 
of the mixer is received by a frequency stabilization circuit 51 which 
detects drifts from the 100 KHz standard and generates a correction signal 
51A which controls oscillator 49 in the manner of a conventional 
phase-locked loop. 
The outputs of mixers 47 and 48 are applied to a phase detector circuit 53, 
whose output is a signal level which is proportional to the phase 
difference between the signals received at R.sub.1 and R.sub.2, this phase 
difference being designated as .theta..sub.diff. Phase detection may be, 
for example, of the type disclosed in the U.S. Pat. No. 3,849,721, wherein 
zero-crossings of the mixer outputs are detected and then utilized to turn 
a flip-flop on and off to obtain pulses whose duration represent the 
desired phase difference. The pulses can be integrated to obtain a signal 
level representative of .theta..sub.diff. At a fixed frequency of 
operation, travel time is proportional to phase, and the travel time 
output of detector 53 is designated as t.sub.pl. 
The directional coupler 58 receives a portion of the energy from 
transmitter T reflected directly back from the formations, and this energy 
is coupled to a mixer 59 which receives as its other input the 1.1001 GHz 
signal from oscillator 49. The output of mixer 59 therefore has a 
reference phase related to the phase to the transmitted microwave energy, 
although it will be understood that there are alternative ways in which a 
reference phase can be established. The output of mixer 59 and the output 
of mixer 48 are coupled to a phase detector 54 whose output, designated 
.theta..sub.f, is the phase difference between a reference phase derived 
from the transmitter and the phase of the signal received at the far 
receiver, R.sub.2. This phase is a function of the properties of the media 
surrounding the region between the transmitter and the far receiver of the 
logging device 30. The travel time proportional to .theta..sub.f is 
designated as t.sub.plf. 
The outputs of phase detector circuits, 53 and 54 are transmitted to the 
surface of the earth through the armored cable 33. At the surface of the 
earth, these signals are applied to a computing module 85 which is 
operative to determine a mudcake-corrected water-filled porosity, 
.phi..sub.wcor, and to determine mudcake thickness, h.sub.mc, in 
accordance with principles of the invention. The signals representative of 
these determined quantities are recorded versus borehole depth by a 
recorder 95 that is conventionally driven by a rotating wheel 96. The 
wheel 96 is coupled to the cable 33 and rotates in synchronism with the 
motion of the cable so as to move as a function of borehole depth. The 
signals representative of t.sub.pl and t.sub.plf can also be recorded as a 
function of borehole depth, as indicated by the dashed lines coupling 
these signals to the recorder 95. 
Referring to FIG. 2, there is shown cross-plot graph of t.sub.plf versus 
t.sub.pl for various values of .phi..sub.wcor and h.sub.mc. When values of 
t.sub.pl and t.sub.plf are received uphole from phase detectors 53 and 54, 
the computing module 85 is operative to determine .phi..sub.wcor and/or 
h.sub.mc in accordance with the relationships represented in this graph 
(or, for particular conditions, relationships representable by other 
graphs, as will be described), such as by employing a table look-up 
routine or curve matching. For example, measurements of a differential 
travel-time of about 12 nanoseconds per meter and a direct travel time of 
about 14 nanoseconds per meter would indicate a corrected water-filled 
porosity, .phi..sub.wcor, of about 10 percent and a mudcake thickness, 
h.sub.mc, of about 1/4 inch (point Q of FIG. 2). It is readily seen that 
for a given value of t.sub.pl, increasing values of t.sub.plf would 
indicate a thicker mudcake. Conversely, for increasing values of t.sub.plf 
(again, for a given fixed value of t.sub.pl ), the corrected value 
.phi..sub.wcor will be smaller than would have been indicated by t .sub.p1 
alone. This stands to reason since the t.sub.pl measurement actually 
"looks" to some degree at the mudcake which has a high water content and 
whose influence (absent correction) would result in a higher-than-actual 
indication of water-filled porosity. 
The manner in which the graph of FIG. 2 can be obtained (and, preferably, 
the information thereof entered in a look-up table of computing module 85 
of FIG. 1) will now be described. Consider the model of FIG. 3 which 
includes a formation 301, a mudcake 302 and a metal region 303 
representative of the pad 37 of the logging device 30 (FIG. 1) in which 
the antennas are housed. The mudcake has a thickness designated h.sub.mc 
and conductivity and dielectric constant designated .sigma..sub.mc and 
.epsilon..sub.mc, respectively. The formation has conductivity and 
dielectric constant designated .sigma..sub.t and .epsilon..sub.t, 
respectively. When logging with an EPT type of logging device, the antenna 
spacings are generally such that the depth of investigation is shallow and 
the measurements indicate properties of the formation invaded zone. For 
generality, however, the zone 301 has subscripts t to indicate formation 
parameters. The formation has a water-filled porosity (i.e., the pore 
fraction thereof containing water) designated .phi..sub.w, and the 
conductivity of the water therein is designated .sigma..sub.w. In the 
model of FIG. 3, the magnetic field generated at the transmitting antenna 
T is approximated by a magnetic line source perpendicular to the plane of 
the paper. 
Before setting forth the specifics of how the curves of FIG. 2 are obtained 
from the model of FIG. 3, the general approach will be briefly explained. 
The magnetic field at a distance x from the source can be expressed as a 
function 
EQU H(x)=f(x, h.sub.mc, .sigma..sub.mc, .epsilon..sub.mc, .sigma..sub.t, 
.epsilon..sub.t)=H.sub.x e.sup.j.theta..sbsp.x (1) 
where the quantities in the parenthesis are those of the FIG. 3 model and 
H.sub.x and .theta..sub.x are respectively the magnitude and phase of the 
field at x. The mudcake parameters .sigma..sub.mc and .epsilon..sub.mc are 
assumed (for example .sigma..sub.mc =1.275 mhos per meter, .sigma..sub.w 
=0.001 mhos per meter, and .epsilon..sub.mc =20 for the FIG. 3 model and 
FIG. 2 curves). To obtain a single point of the FIG. 2 curves, values of 
h.sub.mc and .phi..sub.w are selected. The selected value of .phi..sub.w 
is used to obtain .sigma..sub.t and .epsilon..sub.t using the assumed 
.sigma..sub.w value, as will be described. Then, the relationship (1) can 
be employed for the cases x=x.sub.1 (the distance to the near receiver 
R.sub.1) and x=x.sub.2 (the distance to the far receiver R.sub.2) to 
obtain phase angles .theta..sub.diff. and .theta..sub.f ; i.e., 
respectively, the relative phase difference as between x.sub.2 and x.sub.1 
and the relative phase at x.sub.2 (with respect to a phase reference near 
the transmitter). The differential travel time, t.sub. pl, is proportional 
to .theta..sub.diff. and the direct travel time t.sub.plf is proportional 
to .theta..sub.f. Therefore, the location of the particular point 
(h.sub.mc, 5/8.sub.w) is established on the t.sub.pl vs. t.sub.plf plot. 
Further points on the plot (or, stored in the look-up table) are then 
determined in the same way. The values of .phi..sub.w in the FIG. 2 plot 
take into account the effects of the mudcake, and are thus designated 
.phi..sub.wcor. 
Turning now to the actual expression for the magnetic field at x, we have 
##EQU1## 
where M is magnetic moment per unit length of the source, and the 
"reflection coefficient", .GAMMA., is 
##EQU2## 
The longitudinal propagation constants, .gamma., are 
##EQU3## 
where .xi. is the integration variable and the propagation constants, k, 
are given by 
##EQU4## 
and: k.sub.o is the free space number, 
.epsilon..sub.o is the free space dielectric constant, 
.omega. is the angular frequency of the source 
(=2.pi..times.1.1.times.10.sup.9 in this case). 
H(x) is a complex quantity which can be set forth at the points R.sub.1 and 
R.sub.2, i.e., at distances x.sub.1 and x.sub.2, as 
EQU H(x.sub.n)=H.sub.xl e.sup.j.theta..sbsp.1 (8) 
EQU H(x.sub.f)=H.sub.x2 e.sup.j.theta..sbsp.2 (9) 
where H.sub.x1 and H.sub.x2 are magnitudes and .theta..sub.1 and 
.theta..sub.2 are phases. Taking the natural log of the ratio of (8) and 
(9) yields 
##EQU5## 
Equating imaginary parts then gives 
##EQU6## 
To obtain .theta..sub.f (i.e., the relative phase at x.sub.2 with respect 
to a fixed phase reference at or near the transmitter) substitute 
x.sub.ref, a short reference distance, for x.sub.n to obtain 
##EQU7## 
Now, relationship, (2) can be substituted into (11) and (12) to solve for 
.theta..sub.diff and .theta..sub.f. In equation (7), .sigma..sub.t and 
.epsilon..sub.t are respectively obtained, using the assumed .sigma..sub.w 
and the selected .phi..sub.w, from the Archie relationship for the EPT and 
the time-averaged dielectric permittivity relationship (see e.g. U.S. Pat. 
Nos. 3,944,910, 4,092,583, and copending U.S. Application Ser. No. 
806,983, assigned to the same assignee as the present application), with a 
matrix .epsilon..sub.m of 7.5 (e.g. limestone). As above-stated, 
.theta..sub.diff and .theta..sub.f are respectively proportional to 
t.sub.pl and t.sub.plf. For the EPT frequency and spacings, we have: 
EQU t.sub.pl =0.0631.multidot.(.theta..sub.diff) nsec/meter (13) 
EQU t.sub.plf =0.0631.multidot.(.theta..sub.f) nsec/meter (14) 
Having obtained t.sub.pl and t.sub.plf for selected values of h.sub.mc and 
.phi..sub.w, h.sub.mc is then successively incremented and the same 
procedure is followed. The value of .phi..sub.w is then incremented 
successively (each time going through the full range of h.sub.mc) to 
successively obtain the complete cross-plot information. 
Various techniques, well known in the art, can be employed to obtain and 
record .phi..sub.wcor and h.sub.mc consistent with the relationships set 
forth, either at the well logging site or at a remote location. It is 
preferred that a general purpose digital computer be loaded with a table 
of values of .phi..sub.wcor and h.sub.mc corresponding to particular 
values of t.sub.pl and t.sub.plf. This can be done in the same manner as 
that just described for obtaining the curves of FIG. 2. Later, once the 
values have been stored and during operation, as values of t.sub.pl and 
t.sub.plf are obtained from phase detectors 53 and 54, the computer 
automatically looks up corresponding values of .phi..sub.wcor and h.sub.mc 
in the stored table, and these values are recorded on recorder 95. 
An alternative to the table look-up technique would be a curve matching 
technique using, for example, a least-squares process. Another alternative 
is to obtain solutions to equations (11) and (12) iteratively by selecting 
"guess" values and then incrementing them successively to converge to 
solutions. A still further possible approach is to provide a special 
purpose analogue or digital computer which provides output functions that 
simulate the family of curves of FIG. 2. It will also be recognized that 
by using the described logging device in a test pit borehole, appropriate 
stored values could be obtained empirically. 
FIG. 4 is a plot of porosity vs. mudcake thickness, with the solid line 
curves representing the mudcake corrected water-filled porosity, 
.phi..sub.wcor, corrected using the curves of FIG. 2, and the dashed line 
curves representing the uncorrected (apparent) water-filled porosity, 
.phi..sub.wa that would be expected to be obtained without the corrections 
hereof. The curves of FIG. 4 assume .sigma..sub.mc =0.87 mhos per meter, 
.epsilon..sub.mc =20 and .sigma..sub.w =.sigma..sub.mf =1 mho per meter; 
i.e., conditions which do not necessarily correspond to the conditions 
used when formulating the curves of FIG. 2. (Indeed, an unlikely degree of 
mismatch between the conditions assumed when formulating correction 
factors and actual conditions helps to demonstrate that precise knowledge 
of actual conditions is not required for the useful corrections hereof.) 
It is seen that the solid line curves yield a substantially consistent 
indication of water-filled porosity over the range of mudcake thicknesses. 
In contrast, the dashed line curves illustrate the effect mudcake can have 
(if not corrected for) on determinations of apparent water-filled 
porosity. The dashed line curves of FIG. 4 are obtained as follows An 
initial "true" (actual) value of porosity is selected (e.g. 5% for the 
bottom curve of FIG. 4) along with an initial selected value of h.sub.mc 
(e.g. h.sub.mc =1/8" for the leftmost point, excepting h.sub.mc =0, of the 
bottom curve of FIG. 4). These values and the assumed conditions (noted 
above and listed on FIG. 4) are used to obtain the differential phase 
.theta..sub.diff consistent with the relationship (11) set forth above. 
From .theta..sub.diff (which is proportional to the differential travel 
time in accordance with (13)) a water-filled porosity .phi..sub.wa 
("apparent" or uncorrected) is obtained from 
##EQU8## 
where t.sub.p.sigma.l is the travel time through water having a lossiness 
consistent with .sigma..sub.w and t.sub.pm is the travel time through the 
formation matrix. The resultant value of .phi..sub.wa is then plotted as 
the point P.sub.1 of FIG. 4. The same procedure is then successively used 
with h.sub.mc =1/4" and h.sub.mc .times.3/8" obtain the points P.sub.2 and 
P.sub.3 of FIG. 4. The next value of true porosity (10% in FIG. 4) is then 
used in conjunction with successive mudcake thicknesses to obtain the next 
higher dashed line curve, and so on. 
To obtain the solid line curves of FIG. 4, .phi..sub.w (true) and h.sub.mc 
are again selected and .theta..sub.diff is computed, as before. In this 
case, however, .theta..sub.f is also computed in accordance with 
relationship (12). The differential travel time, t.sub.pl, and the direct 
travel time to the far receiver, t.sub.plf are then obtained from 
.theta..sub.diff and .theta..sub.f, respectively (relationships (13) and 
(14)), and the curves of FIG. 2 (or the look-up table of computing module 
85) are then entered to read a corrected .phi..sub.wcor which is plotted 
in FIG. 4 (e.g., point N.sub.1). The next points N.sub.2 and N.sub.3 are 
obtained by incrementing h.sub.mc to 1/4" and 5/8", and repeating the 
procedure. The selected value of .phi..sub.w (true) can then be 
successively incremented to obtain the other solid line curves of FIG. 4. 
It can be noted that the minor deviations of the solid line curves from 
the actual .phi..sub.w at h.sub.mc =0 are due to the difference in the 
assumed .sigma. and .epsilon. conditions as between FIGS. 2 and 4. The 
graph of FIG. 2 can be utilized with reasonable accuracy for other 
mudcakes and formation water resistivities. 
For highly lossy mudcakes, it is preferred that a different cross-plot be 
utilized for porosity correction and/or mudcake thickness determination 
(again, the information contained in the cross-plot being entered in the 
table look-up of computing module 85). FIG. 5 illustrates the cross-plot 
obtained for the conditions .sigma..sub.mc =10.275 mhos per meter, 
.epsilon..sub.mc =20, and formation water resistivity, R.sub.w =R.sub.mf 
=1000 ohm-meter. In order to know which cross-plot information should be 
utilized, it is desirable to have an approximate knowledge of the mudcake 
conductivity, this parameter generally being measurable uphole. FIG. 6 is 
a plot, like that of FIG. 4, of porosity versus mudcake thickness, but 
where the solid line curves representing the mudcake corrected 
water-filled porosity, .phi..sub.wcor, corrected using the curves of FIG. 
5, and the dashed line curves again representing the uncorrected 
water-filled porosity, .phi..sub.wa, that would be expected to be obtained 
without the corrections hereof. It is seen that a higher conductivity 
mudcake requires less correction than in the previous case. This stands to 
reason since a higher conductivity mudcake will result in a stronger field 
in the lower loss formation media. 
Although mudcake conductivity can be measured uphole, this is generally not 
true for the dielectric constant of the mudcake. However, mudcake 
dielectric constant is believed to generally be in the range of about 
20-25. While it is advantageous to have as accurate of value for mudcake 
dielectric constant as possible in obtaining the illustrated cross-plots, 
relatively accurate determinations of mudcake-corrected water-filled 
porosity and/or mudcake thickness can be made within the expected range of 
inaccuracy of assumed mudcake dielectric constant. 
The invention has been described with reference to a particular embodiment, 
but variations within the spirit and scope of the invention will occur to 
those skilled in the art. For example, the use of borehole compensation 
and temperature correction techniques, as is well known, can be readily 
employed, but is omitted from the present description for ease of 
explanation.