NO783345L - PROCEDURE AND DEVICE FOR DETERMINING CHARACTERISTICS OF UNDERGROUND FORMATIONS - Google Patents

Description

The present invention relates to a process

method and apparatus for the investigation of underground formations,

and more particularly, a method and apparatus for determining a composite parameter of the formation water in formations surrounding a borehole, such as the composite conductivity of the formation water. By using the composite parameter, other useful information can be provided, for example a determination of the water saturation, even in shale-free formations.

The amount of oil or gas in a unit volume of a subsurface reservoir is a product of its porosity and its

hydrocarbon saturation. The total porosity of a formation, denoted 4»^., is the fraction of a unit volume of the formation that is occupied by pore space. Hydrocarbon saturation, denoted , is the fraction of the pore volume that is filled with hydrocarbons. In addition to porosity and hydrocarbon saturation, two other factors are necessary to determine whether a reservoir is commercially mineable, namely the extent of the reservoir and its producibility. By

assessment of producibility, it is important to know how easily fluid can flow through the pore system. This depends on the way the pores are interconnected and is a property known as permeability.

In order to determine the amount of producible hydrocarbons in a formation, it is useful to obtain a measure of the mass-volume fraction of hydrocarbons displaced by mud invasion during the drilling operation. During drilling, the mud in the borehole is usually composed so that the hydrostatic pressure of the mud column is greater than the pressure in the formations. The differential pressure forces mud filtrate into the permeable or permeable formations. Very close to the borehole, practically all the formation water and some of the formation's hydrocarbons, if present, are washed away by the mud filtrate. This area is known as the "rinsed zone". The volume fraction of hydrocarbons

which is displaced by invasion of the flushed zone, is an indication of the amount of "mobile" hydrocarbons in the particular

part of the formations. This volume fraction of hydrocarbons displaced by invasion can be expressed as <|>t (S^- ), where is the remaining hydrocarbon saturation in the flushed zone

(ie the saturation of hydrocarbons that were not washed away by the sludge filtrate and are usually considered immobile). The saturation of the sludge filtrate, denoted as S xo, can be represented as

The hydrocarbon saturation in the uninvaded formations, denoted , can be expressed as where S is the water saturation of the formations; i.e. the proportion of the pore spaces which are filled with water. From equations (1) and (2) it can be seen that the previously stated expression for the volume fraction of oil displaced by invasion, <|>t (S^~'Shr) ' can be expressed as

Generally, relatively accurate determinations of

<t>^using known logging techniques, so accurate be-

moods of S and are very useful, among other things to be-xo w

vote the volume share of hydrocarbons displaced by invasion, and therefore the share of producible hydrocarbons for particular formations such as. surrounds the borehole.

There are classical previously known techniques for determining water saturation and/or related parameters. It has been established that the specific resistance of a pure formation

(ie a formation that does not contain any significant amount

clay) completely saturated with water, is proportional to the water's specific resistance. The proportionality constant, denoted F, is called f ormas j.onsf the actor. We therefore have

where R is the specific resistance of the formation 100% saturated with

o

water with specific conductivity R . The formation factor is a function of the porosity, and can be expressed as

where a and m can usually be assumed to be 1 and 2 respectively. Using these values, the real specific resistance,

denoted R^_ , for a pure formation is expressed as

where n, the saturation exponent, can usually be assumed to be 2. By \ using the specified classical equation, a value, denoted R' , which is a calculated "wet" specific resistance value, is calculated according to a prior art technique. it is assumed that the formation is completely saturated with water, i.e. S =1. From equation (6) it can be seen that In this calculation, cb^ can be obtained from log information, for example from neutron and/or density log readings, and R can be obtained from local knowledge of the specific conductivity of the formation water, or for example from a pure water-bearing section of a resistivity log. The calculated value R^ is compared with a measured value of specific resistance, denoted R^, for example obtained from a deep survey's resistance or induction log. In zones that have no hydrocarbons, R^ will follow Rfc, but when R^ is less than Rfc, it is an indication of the presence of hydrocarbons. Thus, by comparing the calculated specific wet resistance (R^) and the measured specific resistance (R^.)<, potential hydrocarbon-bearing zones can be identified. From equations (6) and (7) it can be seen that another way of using this information is to obtain a calculated value of apparent water saturation, denoted , from the relationship

When significantly different from 1, this also indicates potential hydrocarbon-bearing zones.

The types of techniques described are effective in relatively clean formations, but in shaly-free formations the shales contribute to the conductivity, and the usual ratios between specific resistances indicated do not apply. Consequently, and for example, the previously described comparison of R^ and R^ can lead to incorrect conclusions in a shale-free area of the formations, and the comparisons in these areas (as well as the determination of the water saturation in them) must normally necessarily be overlooked. In addition to the results being less useful than they could be, this can tend to file to

weaken the credibility of the entire calculated log comparison, which is a disadvantage when trying to exploit the resulting information commercially. Accurate determination of S^ can also be difficult in ski-free areas. Of course, these are only limited examples of how shale freedom can interfere with the interpretation of measurements, but similar problems with shale freedom arise in other cases, such as when characteristics (such as S ) of invaded zones are to be determined or when

xo

interpretation of log readings of thermal attenuation in lined boreholes.

A number of techniques of varying complexity exist to aid in the interpretation of results obtained in schist-free formations. The way shale freedom affects log readings depends on the proportion of shale and its physical properties. It can also depend on how the slates are distributed in the formations. It is usually assumed that the shale material is distributed in shale-free sands in three possible ways; there are "laminar shale" where the shale is found in the form of thin layers between which there are layers of sand, "structural shale" where the shale is found as grains or nodules in the formation groundmass, and "dispersed shale" where the shale material is finely distributed in the sand that partially fills the spaces between the grains. Shale sand assessments are usually made by assuming a special type of shale distribution model and including in the model information indicating the volume of shale or similar. For example, in a simplified laminar sand/shale model, an equation of the same form as equation (6) is presented, but which includes a second expression which is a function of the mass volume fraction of shale in the thin layers. The same is the case for another known model where an expression is provided which depends on the volume fraction of shale as determined from a total clay indicator. In a simplified model for dispersed shales, values are provided for a "groundmass porosity" that includes all spaces occupied by fluids and distributed shales, and another value is provided that represents the proportion of this porosity occupied by the shales. A further method relates to the conductivity distribution of the shale in relation to its cation exchange capacity, as this capacity can be determined on the basis of the clay volume, among other things.

They described prior art techniques that require

either a determination of the volume of shale or clay, or similar information, has been satisfactory in some applications. In addition to the difficulties in obtaining accurate information regarding the volume and composition of shale or clay and its conductivity, there is a further problem with the simplified models according to prior art, and that is that different forms of shale can appear simultaneously in the same formation.<p>reliable techniques, some of which use extensive statistical processing of data, exist and usually give good results, but they tend to be relatively complicated and may require either large computing capacity and/or considerable processing time.

It is an object of the present invention to provide a solution to these suggested problems and to present techniques which are effective even in schist-free formations,

but which are not unduly complicated or difficult to perform.

The inventor has discovered that determining a "composite" parameter for the formation water in formations surrounding a borehole, such as the composite conductivity of the formation water, allows a relatively accurate determination of formation characteristics, such as water saturation, as they

certain -values have meaning even in schist-free areas of the formations. Unlike previous experiments that tried to determine the volume

of shale or clay in the formations and then introducing suitable factors which often involve a lot of guesswork, the invention determines a composite water parameter, for example a composite water conductivity, which represents the conductivity of the water mass in the formations, including both free water and bound water. Bound water that is captured in the slates is included in this determination, so unlike previously known techniques, the slates can be considered porous. After determining the composite water conductivity, the water saturation can be obtained directly using relatively simple conditions that do not require estimates of the volume of shale in the formations. The effects of shale are taken into account in the present invention by the different conductivities (or other parameters such as capture cross section) for the formation water components (free and bound) that make up the total amount of water. "Free water" is used here for water that

can move relatively freely under normal reservoir dynamics, while "bound water" is used for water that is not sufficiently free to move under the influence of normal reservoir dynamics.

According to one embodiment of the invention, there is provided an apparatus for determining a composite parameter (such as the composite conductivity or the composite capture cross-section) for the formation water in formations surrounding a borehole. Means are provided for deriving a first quantity which is representative of the parameter which can be attributed to the free water in the formations.

Means have also been provided for discharge of another size which is representative of the proportion of bound water in the formations.

(As will be seen, the second size can alternatively be obtained indirectly from the proportion of free water). Additional means are provided for the derivation of a third quantity which is representative of the parameter attributable to the bound water in the formations. The composite parameter is then determined as a function of the first, second and third magnitudes.

According to an embodiment of the invention, a fourth size is derived as the difference between the third and the first size. The composite parameter is then determined as the sum of the first quantity and the product of the second and fourth quantities. In one embodiment of the present invention, the composite water conductivity, denoted cr'wc / is expressed by the following ratio:

where C _ is the conductivity of the free water in the formations, <X ,

wf ^ J wb is the conductivity'due to the bound water in the formations, S is the water saturation of the formations (which is equal to ^— w), and is the saturation of the bound water in the formations (which is equal to

*wb

^— ). The expression (9) divides the composite water conductivity between the conductivity of the free water (the above-mentioned first quantity) and the conductivity in a differential term expressing the difference between the conductivity of the bound water and the free water (the above-mentioned fourth quantity). Mathematical manipulations show that another for the expression (9) is

In this form, the composite water conductivity can be seen as the sum of a first expression, representing the proportion of free water multiplied by the conductivity of the free water, plus a second expression representing the proportion of bound water multiplied by the conductivity of the bound water. As can be seen from the above, the proportion of free water, S -./S (which is wi w complimentary to the proportion of bound water, since the total water volume consists of the volume of free water plus the volume of bound water) could alternatively be used in the expressions (9) or (10). "For example, the expression (10) would then take the form

which one can see is equivalent to (10) since S w S w f _ + S wb, .

Therefore, when the expression "the proportion of bound water" or the like is used here, it will be understood that its compliment (the proportion of free water) can alternatively be applied in the appropriate form.

In another embodiment of the invention, the composite parameter for the formation water is the composite capture cross-section, denoted • As is known, the capture cross-section is a measure of the proportion of thermal neutrons that are absorbed per time unit, and is usually measured using a logging device that measures neutron thermal decay time (NDT), for example as described in US Patent No. RE 28,477. The composite neutron entry cross section, E-'wc', is here expressed as

which is similar to expression (9), but where £ ^ is the capture cross-section for the free water in the formations and £^ is the capture cross-section for the bound water in the formations.

According to a further feature of the invention, a value for the water saturation is produced which provides meaningful information even in areas free of ice. This avoids the previously known estimate for a suitable "cementation exponent" for shale-free formations.

According to further other features of the invention, conditions similar to (9) or (10) can be produced expressed with a generalized parameter, "P", and which are used to obtain a free, a bound or a composite water parameter, depending on which, information you want and a-v which information can be measured or derived. In particular, if it is desired to obtain a parameter for the free water, the following generalized relationship can be presented, which has the same form as relationship (9) above

where P wc is a composite water parameter, P w, b is a bound water parameter and P ' ^ is the free water parameter to be determined. In one embodiment of the invention, the free water parameter to be determined in the form of a variable iT > w a wr c is defined as the signal attenuation that can be attributed to the formations when it is assumed that all the water in them is free water. Means are provided for deriving a function of the parameter (the attenuation in this case) in at least one region of the formations (usually a clean sand region) where substantially all of the water present is free water. Means are also provided for deriving a quantity that is representative of the water content in the formations at a particular depth level in the borehole. This quantity can be t^, the propagation time of electromagnetic microwave energy in the formations, which is dependent on the water content. The free water parameter (in the form of the variable 6w a ^ in this case) at the particular depth level is then determined from the derived function and the quantity representing the water content. Measurements of attenuation and propagation time are usually obtained using an "EMP" logging device that uses electromagnetic microwave propagation. Expressed in terms of the attenuation, a, the relationship (9a) can be expressed as

where 'Oirøk is the bound water counterpart of , and a^ c is a "composite" attenuation for the relevant formation water.

As described in more detail below, the "distribution" of the attenuation between the free and the bound water implied by expression (9b) can lead to your technique for determining the proportion of bound water, once the values of a, a~ and are determined.

In particular, S . /S is determined from

cwb w

which follows directly from relation (9b).

Further features and advantages of the present invention will be apparent from the following detailed description taken in conjunction with the attached drawings. Figure 1 is a simplified block core of an apparatus in accordance with an embodiment of the invention. Figure 2 is a block diagram of the computing unit 60 of Figure 1. Figure 3 is a block diagram of the computing unit 70 of Figure 1. Figure 4 is a block diagram of the computing unit 80 of Figure 1. Figure 5 is a frequency diagram useful for obtaining values of subsurface characteristics which can be used according to the present invention. Figure 6 is a log of values, including calculated values, in relation to depth, which shows how the invention can be utilized. Figure 7 is a block diagram of circuits useful in obtaining a signal representative of apparent composite capture cross-sections of subsurface formations.

Figure 8 is a block diagram of a circuit for achieving

of values of apparent water catchment cross section. for underground formations.

Figure 9 is. a block diagram of a circuit for obtaining signals representative of a "wet" trap cross-section which can be compared with measured values of trap cross-section. Figure 10 is a block diagram of a circuit for obtaining values of the water saturation in the invaded zone. Figure 11 is a block diagram of a circuit for obtaining an alternative value for bound water saturation. Figure 12 is a block diagram of a circuit for obtaining a signal that is representative of the proportion of bound water. Figure 13 is a frequency diagram for obtaining values of subsoil characteristics that can be used in the present invention. Figure 14 is a block diagram of a circuit for obtaining signals representative of free water attenuation, free mass water attenuation, and EMP-derived conductivity.

Figure 1 shows a representative embodiment

of an apparatus in accordance with the present invention for the investigation of underground formations 31 which are penetrated by

a borehole 32. The borehole 32 is usually filled with a drilling fluid or mud containing dissolved finely divided solids

substances. The examination device or logging device 40 hangs

i, the borehole 32 of an armored cable 33, the length of which essentially determines the relative depth of the device 40. The cable length is controlled by suitable means on the surface such as a drum and winch mechanism (not shown). . The circuit 51 is shown at the surface, although parts of it may usually be downhole, and it represents the total processing circuits for the various logging units in the apparatus 40.

The survey apparatus 40 comprises a suitable device for determining specific resistance such as an induction log device 41. As is known, the specific resistance or conductivity of a formation is indicated by induction log readings, the measured conductivity being measured being denoted <r^_. The examination apparatus downhole comprises an epithermal neutron examination device 42 on the side wall with a source and a detector mounted on a sliding body 42A. A device of this type is described, for example, in US patent no. 2,769,918. Each count registered in the epithermal neutron detector is received by a processing circuit in the overall circuit .51 which comprises a function shaper which works in a well-known manner so that it forms a signal 4>N representing the formation porosity as determined by the neutron logger. The survey apparatus 40 further comprises a survey device 43 for surveying the formation density for producing borehole log measurements which can be used to calculate the mass density of the adjacent formations in a known manner. For this purpose, a sliding body 43A accommodates a source and two detectors (not shown) separated at different distances from the source. This arrangement of source and detectors produces signals corresponding to the mass density of the ground formations, for example as described in US Patent No. 3,321,625. The circuit 51 comprises 'conventional circuits which convert the signals derived from the detector at short and long distance from the source into a calculated mass density. If desired, a passer signal can also be used to determine the mass density as known in the area. The resulting density is fed to the unit for calculating the porosity in the block 51 which calculates the porosity, derived from the mass density in a well-known manner. The derived porosity is denoted as 4>D. The examination apparatus further comprises a device 44 which is a gamma ray logging device for measuring the natural radioactivity of the formations. As is known in the field, the device 44 can comprise a detector, for example a scintillation counter, which measures the gamma radiation in the formations in the vicinity of the detector. An output from circuit 51 is a signal designated "GR" representing the gamma ray log reading. Additional devices may be provided as needed in accordance with variants of the invention as described below. For example, a device 45 is available for obtaining measurements of the spontaneous potential ("SP") of the formations. This device can be of the type described in US patent no. 3,453,530, as this patent also describes devices for determining deep and shallow specific resistances. An electromagnetic propagation apparatus ("EMP") 46 is also available, and comprises a slider 46A with transmitter and receiver antennas. Electromagnetic microwave energy is transmitted through the formations (usually the invaded zone) and formation characteristics are determined by measuring the attenuation and/or phase (or velocity) of the received microwave energy. This type of logging device is described in US Patent No. 3,944,910. Measurements indicating attenuation, denoted a, and travel time or propagation time (which depends on the speed), denoted t , are available from this device. US Patent Applications Nos. 806,983 and 788,393 also describe techniques for obtaining an "EMP"-derived conductivity measurement, denoted ^T^p' and for obtaining a. measurement of the water filling porosity for bound water, denoted 4> ^. Signals representative of these measured values ■ are illustrated as available outputs from circuit 51. An NDT device (neutron detection tool) 47, for example of the type described in US Patent No. RE 28,477, is also available and results in an output value for capture cross-section, t , from processing circuit 51.

To keep the survey apparatus 40 centrally in the borehole, extendable members 42B, 43B and 46B may be provided which can be brought into contact with the borehole walls on opposite sides of the members 42A, 43A and 46A. For centering the upper part of the examination apparatus, centering means 49 can also be arranged. As noted, a borehole fitter can be combined with the arms that carry the sliding bodies and generate a signal representative of the borehole diameter of the circuit 51.

While all the measurements to be used in the practice of the invention are for convenience. illustrated as being derived from a single survey device, it will be understood that these measurements can typically be derived from multiple survey devices being passed through the borehole at different times. In such cases, data from each run can be stored, for example on magnetic tape, for later processing according to the present invention. Data can also be derived from a remote location by, for example, transmission.

One or more signal outputs from the blpck 51 are shown in Figure 1 as available to the calculation circuits 60, 70, 80 and 510. In the embodiment of Figure 1, the calculation circuit 60 produces a signal representative of an apparent composite water conductivity, denoted ,^"'wco' in accordance with the relationship

(9). Computing circuit 70 responds to the signal representative of <T'wco and to the signals from block 51 (especially the porosity indicating signal), to produce a "wet" conductivity signal, G~'0- Computing circuit 80 produces a calculated value of the water saturation,. S , in accordance with an equation to be stated below. The calculation circuit 510 is used to generate attenuation values for free and bound water and a signal that is representative of the proportion of bound water. These

the signals together with some or all of the outputs from the circuit 51 are recorded as a function of depth on the recording device 90.

Reference is now made to Figures 2 and 3, where embodiments of the calculation circuits 60 and 70 in Figure 1 are shown. First, all the structural components of the circuits will be described. The source of various signals along with further rationale will then be explained. A pair of difference circuits 601 and C602 are provided. The positive input terminal of circuit 601 receives the signal GR, i.e. a signal representative of the output of the gamma ray logging device 44. The positive input terminal of circuit 602 receives a signal denoted GR^/ which is a signal level representative of a gamma ray logging level for the bound water in the formations under investigation. The negative input terminals of both differential circuits 601 and 602 receive a signal level designated GRw^, which is a gamma ray log level of the free water in the formations under investigation. The outputs from circuits 601 and 602, which are representative of GR - GR c and GR , - GR c respectively, are connected to a ratio circuit 603 which produces a signal proportional to the ratio of the output from circuit 601 divided by the output from circuit 602 The output from ratio circuit 603 is a signal representative of , i.e., the saturation for bound water in the formations in accordance with the ratio

The output from the ratio circuit 603 is connected via the limiter 604 to an input on a multiplier circuit 605. The other input to the multiplier circuit 605 is the output from a difference circuit 606. The circuit 606 receives on its positive input sk clamp a signal level that is representative of < i.e. the conductivity for the bound water in the formations under investigation. The negative input terminal of the differential circuit 606 receives a signal level representative of ^£W»ie. the conductivity of the formations' free water. This last signal is also an input to a summing circuit 607 whose second input is the output of the multiplying circuit 605. The output of the summing circuit 607 is a signal representative of apparent composite water conductivity in the formations under investigation, i.e.

This expression can be seen to be the same as expression (9) above

for composite water conductivity,<r , except that S is

3" toilet w

assumed to be 1, meaning the result is an "apparent" composite water conductivity.

Figure 3 shows an embodiment of the calculation circuit 70 of Figure 1 which is used to generate a signal representative of (T , i.e. the calculated "wet" conductivity of the investigated formations. The circuit 51 (Figure 1) is a porosity calculation circuit 511 which responds to the signals representative of d> N and D. The circuit 511 uses this information in a well-known manner to provide a signal commonly known as <J>ND, which includes information from both the neutron and density log readings to obtain an indication of the total porosity of the formation, denoted 4>t. Techniques for obtaining cj>ND are well known in the art, and a suitable neutron density porosity calculator is described, for example, in US Patent No. 3,590,228. However, it will be understood that any suitable alternative technique for obtaining cj>t may be used, including, for example, techniques using other logging information, such as from a sonic log.The output of circuit 511 is coupled to a k wader circuit 701 whose output is consequently proportional to 4>^2 _. This signal is then coupled to an input terminal of a multiplier circuit 702, the second input of which is <S"'wco", i.e., the apparent composite water conductivity as determined in the calculation circuit 60 (Figure 1, Figure 2). Accordingly, the output of the multiplier circuit 702 (as also, the output of the calculation circuit 70 — figure 1) is a signal proportional to wcomulti.<p>lized by é 2, and this therefore indicates the calculated "wet11 conductivity of the formations, ^'0/ in accordance with a relationship analogous to (7) above, namely:

It will now be described how the inputs to the calculation circuit 60 can be obtained. In particular, one technique for obtaining values of Swb, C"wl5 and 0"wf is as follows: Log values of o"t, GR and <t>t are first provided over a depth range of interest. Using the measured specific resistance, (j- (which is preferably a deep resistance measurement) at each depth level above the area of interest you can calculate a value denoted as v

wow

This has the same form as relation (7) above, and one sees that

<X^a is a simple calculated apparent water conductivity (which must not be confused with the apparent composite water conductivity , o"' , developed in accordance with equation (13)), the

wco

that is to say, it is the calculated value of the water conductivity that one would expect for the achieved resistance measurement (crt) to be a result of the achieved total porosity-

the measurement when it is assumed that the total porosity is filled with water (that is, when it is assumed that S =1). In other words: a formation. with porosity $ -which is filled with water of conductivity <S w' a would result in the conductivity of the measured form

tsr^- If desired, a calculation circuit of the type used can

in figure 3 (which uses an analogous equation to develop CT^ from v rvw' co ), is used to obtain <$' wa in accordance with equation (1.5)

by substituting s-^ as the conductivity input to the multiplier circuit 702. Having obtained C"^ at each depth level over the area in question, the inverses of these values can now be used in conjunction with the gamma ray log (GR) readings taken over the same depth range, to to produce a frequency diagram of the type shown in Figure 3. Frequency diagrams are commonly used in borehole logging (see, for example, Schlumberger "Log Interpretation-Volume II", 1974 Edition). At each depth level, the values l/cr' result waog GR at a point in the diagram. Once all the points are plotted, the number of points falling within each small elementary region (of a chosen size) in the diagram is summed and presented numerically. The resulting diagram is as shown in Figure 5, with the numbers representative of the frequency of occurrence of points at each particular elemental area of the diagram In the example shown, the area designated 501 contained the highest concentration of points ion (i.e. more than five points at each elemental range), and the frequency of occurrence within that range is omitted for ease of illustration. The position on the GR axis denoted GR ^ is indicated by the line of lowest gamma ray readings in the diagram, as shown by the dashed line. The position on the GR axis denoted as GR^ >' is indicated by the GR value at which increasing GR no longer results in increasing values of

1/ is' • This means that at GR , mainly all the water is in

qwa '2wb 3

the formations bound (by the shale freedom that exists). Anyone

additional shale freedom would mean an increase in GR, but would not increase the proportion of bound water since essentially all the water present was indicated as bound at the GR^ line. The fractional part of bound water is then determined by interpolation between the reference lines GR and GR , , i.e. as

J wf 3 wb

That line on the l/o-' -axis at which l/ty<*>not wa wa

longer varies particularly with GR (beyond GR , ) , indicates 1/ cr , ,

WD WD

since as previously mentioned, essentially all the formation water at this point on the curve is bound. Consequently, c , derived from the dashed line, is labeled with this designation. The inventor has found that c ^ is essentially constant and has a value of about 7 mho/m at 75 C. However, it is not assumed that this is a universal constant, and that it may vary somewhat in different areas. In all cases it can be determined, for example from the diagram in figure 5. The value of the conductivity & f to free water can be obtained, for example, from the dotted line for free water in figure 5. As is known,6"f can alternatively be obtained from an area with clean sand on the basis of a resistivity log or local knowledge It is understood that at least some of the values mentioned here can be obtained by other techniques.

When values for GRwf, GR^, crwf and crw^ have been determined for the relevant depth range, corresponding signal levels can be inputs to the calculation circuit 60 (figure 2). Now log values of GR (as a function of depth) can be input to circuit 60 and cr'wco can be output and recorded dynamically. At the same time, the calculation circuit 70 (figure 3) produces (5-' as an output to the recording device 90. This signal can now be superimposed with <jr , which is a great advantage for being able to identify potential hydrocarbon-bearing zones.

Figure 6 shows the nature of the signals that can be registered by the recording device 90 in the embodiment of Figure 1. The vertical axis represents the depth. The middle trace shows the inverse value of (the broken line) and^^(solid line); that is, the calculated wet specific resistance and the measured deep specific resistance. The divergent regions of these curves, such as the regions labeled 2 and 3, indicate that the measured deep resistivity is significantly greater than the calculated "wet" resistivity (or conversely that the measured deep conductivity is significantly less than the calculated "wet" conductivity), thereby indicating that they are potential hydrocarbon-bearing zones. The left trace indicates the output of a log of spontaneous potential (SP) over the same depth range. The relatively high value of SP in, for example, the areas designated 4 and 5, is at the shale line and characterizes shale-free areas. It can be seen that the curves for specific resistance generally follow each other even in the schist-free zones, which should be the case for water-bearing schist-free areas. This continuous tracking of the measured and the calculated specific resistance signals is an important advantage of the present invention, since comparable prior art techniques are usually unreliable in skid-free areas, as discussed in the introduction.

The determination of a calculated value for the water saturation, S W, will now be considered. Equation (9) above indicated that the composite water conductivity, cr / is expressed as: From equation (6) we can write

where (r is the (unknown) real conductivity of the formation water. By replacing the expression for composite water conductivity ) with <5" in (17) one gets:

toilet w

The apparent water conductivity <v' (as described in connection with figure 5) is equal to <X^/ <t>^. Insertion in (18) gear

which can be rewritten as:

. [ «r Æ]s2 + [s , ( cr v.V-. cr -<j'=o (20) . wf w wbv wb uwf w J wa v.

This quadratic equation can be solved with respect to S to obtain:

From the relationship (21) it can be seen that a value for the water saturation, obtained by applying the composite (free and bound) water technique according to the invention, can provide meaningful information even in shale-free areas, since the effects of the shale when binding one part of the formation water, is taken into account in the ratio - Consequently, as in prior art, one avoids estimating a suitable "cementation" exponent for shale-free areas.

Figure 4 shows an embodiment of the calculation circuit 80 used to produce a signal which is representative of calculated water saturation, denoted S, according to equation (21). The signal that is representative of. "true" or measured specific resistance, <y (Figure 1), is an input to a ratio circuit 811. The other input to the ratio circuit is the output of a squaring circuit 812 whose input is a signal representative of <J>.. Accordingly, the output of the ratio circuit 811 proportional to cf^/ é^, which is equal to the apparent conductivity of the formation, cfW' ci.. This signal is again coupled to an input of a multiplying circuit 805 whose second input is a signal representative for (J"wf • The output of the multiplier circuit 805 is coupled, with an eri weighting factor of 4, to an input of a summing circuit 804. The signal cf^ is also coupled to the negative input terminal of a difference circuit 801 whose positive input terminal receives a signal representative of O^k* The output from the difference circuit 801 is an input to a multiplier circuit 802. The other input to the multiplier circuit 802 is a signal representative of S^, which can for example be derived from the output of the limiter 604 in Figure 2. Accordingly, the output of the multiplier circuit 802 is a signal representative of S^ (cVWD.-' ,0'wf) • This signal is coupled to a squaring circuit 803 and to the positive input terminal of the difference circuit 807 .. The output from the squaring circuit 803 is connected to the second input terminal of the summing circuit 804 whose output in turn is connected to a square root circuit 806. The output from the square root circuit 806 is connected to the negative input terminal of the difference circuit 807. The output of the difference circuit 807 is coupled to an input of a ratio circuit 808, the second input of which receives the signal representative of <s'w^, this signal being assigned a weighting factor of 2. The output of the ratio circuit 808 is the desired signal which is representative for S^, in accordance with equation (21). The right track in figure 6 illu-

plots the recorded values of the calculated water saturation,

w

The determination of a composite conductivity and the determination of water saturation in accordance with the principle of the invention apply equally well in the invaded zone of the formations. In, for example, conditions (9) and (18), the quantity cr .p would be replaced by

cf pp. (ie the conductivity of the invading mud f iltrate) and

wmf

the water saturation S would be replaced by the invaded zone metninc Sxq. The EMP lpgge device referred to above measures characteristics of the invaded zone. In the above-mentioned US Patent Application No. 788,393, a technique for measuring $wb by using an EMP ldgge device is described. This technique can be used here as an alternative to find S^ from S^ = ' 1

in another above-mentioned US patent application No. 806,983, it is stated that conductivity measured using an EMP device, and denoted °EMP', depends on the conductivity of the formation ion water, crw, and is a linear function of the water filling porosity, <i> W, i.e. :

Since S = <f> /<$. and 6 = <*>.,_ S , the relationship (22) can be expressed as: w w t ^ w t wa By inserting the composite water conductivity from the expression (9) for crw in (22), one gets:

By substituting c ^ for C and Sv^ for STI and solving with respect to

,tmr wi xo w

S , you get

xo

Reference is now made to Figure 10 where there is shown a block diagram of a calculation circuit 80' suitable for obtaining a signal representing the calculated water saturation for the

in

invaded the zone, S , in accordance with equation (25). A ratio circuit 111 receives as an input a signal representative of C™., and as its second input a signal representative-ijJYLir

tively for <f>t. The signal ff"E^p can be derived from the EMP device 46 (Figure 1) using the processing circuit 51 as described

in the above-mentioned US Patent Application No. 806,983. Another ratio circuit 112 receives as an input a signal representative of

for <fc £, and as its second input the signal representative of the total porosity, <t>^. As noted just above can be derived from the measurements taken with an EMP logger, and in this example is used in conjunction with <J>t, to obtain

Swb (the output of the relationship circuit 112). However, it will be understood from S^ can be achieved using other techniques, such as those described here'. A differential circuit 113 receives as its input the signals representative of (which can be obtained as indicated above and is typically, but not necessarily, about a multiplier circuit 114 whose output is therefore S^ (C^ - & m£) The output of the difference circuit 115 then represents the counter in the expression (25). This output, and the signal representative of (j-' , are the inputs to another ratio circuit 116, whose exit

months in

is representative of S , according to the expression (25). This signal can then be registered in the manner illustrated in Figure 5.

The measurements of the spontaneous potential (from the SP device 45 (Figure 1) can also be used, for example as an alternative technique for obtaining the Sw^. The SP measurement can be expressed as

where K is a constant dependent on absolute temperature and cr' mf^ is a composite conductivity of the sludge filtrate in the invaded zone, having the same form as 6"w, c as expressed by relation (9). Using the relation (9) as a basis, we have:

By putting (27) and (28.) into (26) and arranging, you get:

In a water-bearing area of the formations where S = S

xo w reduces (29) to:

Therefore, relation (30) can be utilized as an alternative technique for obtaining S ^ (where SP is taken from an aquifer). Figure 11 shows circuits that can be used to obtain a signal representative of S ^ according to condition (30). The combination of ratio circuit 121, antilogarithm circuit 122, difference circuit 124, and multiplier circuit 126 is used to obtain the numerator, while ratio circuit 123, antilogarithm circuit 122, and difference circuit 125 are used to obtain the denominator of . The ratio circuit 127 then gives v' and the summing circuit 128 and the inverting circuit 129 are used to obtain a signal representative of S wb, .

In the previously described embodiments, the determined composite parameter of the formations has been the composite conductivity (or resistivity). Another composite parameter that can be determined is the composite capture cross-section, which is obtained using an NDT log plus inputs similar to those indicated above. As is known, the NDT log is particularly useful in lined holes where resistance logs cannot be used. In such cases, the expression (11) given above is:

An apparently composite capture cross-section, denoted

5"' , can be obtained in the same way as 6""' was provided above-** wcocc cwco

for, and by using the calculation circuit 60' illustrated in Figure 7. In Figure 7, the multiplication circuit 705, the difference circuit 706, and the summation circuit 707 work in the same way as the corresponding en-

names 605, 606, and 607 in Figure 2. Appropriate values for I

*wb °^ ^wb can °PPnas vec^ plotting £ in relation to GR in the manner described in connection with figure 5. The only difference is that instead of using relation (15) to obtain a calculated• apparent water conductivity, an apparent water interception cross-section, £<*>wa' to be plotted as a function of GR, is obtained from the known relationship

where £ma is the bedrock capture cross-section for the particular lithology involved. The circuit in Figure 8, comprising the difference circuit 881, the ratio circuit 882 and the summation circuit 883, can be used to obtain 5-' wa in accordance with the ratio (31). After plotting E wa as a function of GR, £<w>f°9EWD can be determined, for example as suggested in connection with Figure 5. S ^ can be obtained using the arrangement of circuits 601, 602, 603 and 604 of Figure 2 , and as described in connection with this. After deciding, one can now

wco

calculate a "wet" capture cross section (analogous to that obtained using relation (14) above) from:

The circuits of Figure 9, including the difference circuit 901, the multiplier circuits 902 and 903 and the summing circuit 904, can be used to produce a signal representative of <^'0- This signal can then overlap the measured log value, L , on

the way illustrated by the middle track in figure 5,

to uncover potential hydrocarbon-bearing zones.

An additional composite parameter that can be expressed

by the generalized relation (9a), the attenuation oi, i.e. the relative attenuation (usually corrected for temperature and scattering loss) is measured by means of the apparatus for propagation of electromagnetic microwave energy ("MP"-46 in Figure 1). The relationship for this parameter is stated above (9b), and will be considered at a glance. Assume first, as stated in US Patent No. 4,092,583, that the measured attenuation in the formation (denoted a) can be expressed as

where a is the attenuation attributable to the formation water (it

that is, its composite water, according to the principle) and «m is the attenuation attributable to the formation groundmass. Since

a is very small compared to a. , one can write

m w

This ratio expresses that the formation attenuation is volumetrically "adjusted" by a factor ^> to take into account that losses mainly only occur in the part of the formation occupied by the water. Reference is now made to relation (9b) there

where a ^ is the attenuation attributable to the free water (i.e. the attenuation that could be measured with the EMP logger in a theoretical environment consisting exclusively of the formation's free water), and a. ^ is the attenuation attributable to the bound water (i.e. the attenuation that one would measure with the EMP logger in a theoretical environment consisting exclusively of the formation's bound water), and a is the attenuation due to the composite water (i.e. the attenuation that one would measure with an EMP -logging device in a theoretical environment consisting exclusively of the formation water in question).

Solving equation (9b) for the bound water fraction'^wb^w'gives f°rno-'-the (9c) previously indicated above: According to the present invention, a^^og°wb (el" ler these, parameters multiplied by the water-filled porosity, <J>w to obtain "total variables" Qa^ £ °9 ^^ b^ determined by using attenuation and travel time measurements (or velocity) made with a logging device for measuring electromagnetic propagation such as "EMP" 46 in Figure 1. The conductivity (usually of the invaded zone of the formation) obtained using the "EMP" device, denoted ^"EMp > can be expressed as

where K is a constant, t ^ is the measured propagation time through the formations, and a is the total attenuation determined from the

measured attenuation corrected for scattering loss and temperature, where

a = <t> a (relation (34) above) . While the ratio (35) for

w wc conductivity is expected to remain largely independent of the salinity of the formation water, it has been observed that G"Etøp often exceeds the conductivity measured using other devices. An explanation for the observed for-

the difference in conductivity is that not all the losses represented by the mass attenuation measurements a are due to the conductivity or the salinity of the formation water. Extraordinary losses are assumed to occur in the presence of bound water, the nature of these losses being more dielectric than conductive. The inventor has discovered that by treating bound water losses separately from the ordi-

near expected losses from free water, the problem is solved and more realistic values' of &„ tMT> are provided According to

EMP.

a feature of the invention that will be described, it will be

voted an attenuation representative of variables such as is more appropriate for use in obtaining 0"EMp- 1 example below is this attenuation representing variable the variable for free water <f>^ a^ f The particular variable is also useful in connection with other techniques where attenuation is. used as a entry or a correction.

Reference is now made to Figure 12 where an embodiment of the calculation circuit 510 in Figure 1 is shown which is used to generate a signal which is representative of the bound water proportion, /S^/S^. A pair of difference circuits 501 and 502 are provided. The positive input terminal of circuit 501 receives a signal representative of the magnitude «wc and the negative input terminal of circuit 501 receives a signal representative of the magnitude . The positive input terminal of circuit 502 receives a signal representative of the magnitude awb'0( 3 ^an9ative input terminal of circuit 502 receives the signal representative of the magnitude . The outputs of the difference circuits 501 and 502 are each coupled to a ratio circuit 503 which produces a signal that is proportional

. with the ratio between the output from circuit 501 and the output from

circuit 502. The output from ratio circuit 503 is therefore a signal representative of . the proportion of bound water, S^/S^,

according to relation (9c). In reality, and as explained later, the inputs to the calculation circuit 510 may each have a common multiplier, d>.

w

It will now be described how the inputs to the calculation circuit 510 can be provided. A preferred technique for deriving the values of ar^ and (or of related mass variables 0<3 ^^ wb^ is SOm ^0-Mjer: The log values of a

(attenuation) and t^ (duration time) are first obtained over a range of depth levels of interest (eg, using the EMP device 46 of Figure 1 - where these outputs are indicated to be available from the processing circuit 51). The obtained values of ot and t ^ are plotted as a function of each other, as shown on the frequency diagram at. figure 13. The values for a can first be corrected for temperature and for scattering loss. The diagram in figure 13 can be understood by recognizing that higher porosity generally results in higher values for both damping and running time (at least when this porosity contains water ). This is because the water causes a much greater loss than the rock base mass (therefore greater damping) and the speed is too electromagnetic

energy through water is lower than through the ground mass (therefore greater duration). Consequently, increasing values of t ^ and a on the diagram usually correspond to increasing values of the porosity. It can be noted that a can alternatively be plotted in relation to other non-conductivity-dependent measurements that reflect the total porosity, <i>t, such as <J>ND, which has been previously described.

The point labeled t on the t^-axis represents the running time through the formation base mass. Two trend lines, designated the "free water trend line" and the "bound water trend line" are constructed by starting at point ;t and drawing lines through the approximate bottom and top edges of the main collection of points in the diagram. These trend lines can be understood in the following way: In the parts of the formations that contain mainly only free water, both t ^ and a will increase with the porosity, the increase of the running time being dependent on the water volume dg the increase in the damping being dependent on both the water volume and.its conductivity. Consequently, the slope of the free water trend line will depend on the conductivity or losses attributable to the free water. The same will generally be the case for those parts of the formations where mainly all the water is bound water. In this case, however, the attenuation will be a function not only of the volume of water and its conductivity, but also of the higher losses, including dipole losses, attributable to the bound water. Consequently, the trend line for bound water has a significantly greater slope than the trend line for free water. It will be understood that these trend lines representing the relationships between attenuation and duration in an area of predominantly free water (such as clean sand) and an area of bound water (such as

such as shale), can first be determined on the basis of logs

taken in such formation areas. It will also be understood that these conditions are functions that can be determined and that do not necessarily need to be linear, but are illustrated as if they were linear in figure 13.

Once the free water and bound water trend lines (or functions) have been determined, at each depth range of interest, a free water attenuation quantity representative of the attenuation attributable to the formations (surrounding the depth level in question) can be obtained if mainly all the water in the formations was free water. Likewise, one can derive an attenuation value for bound water that is representative of the attenuation in the formations (surrounding the depth level of interest) if essentially all the water in the formations was bound water. By using these quantities in conjunction with the measured attenuation at the considered depth level, one can then determine the proportion of bound water in the formations surrounding the particular depth level. With reference to Figure 13, one can consider the single point shown {a, tp^) 0<3 the vertical line drawn through it. At the particular measured value of t^, the intercept with the free water trendline indicates the attenuation value that would be measured if the water in the pore spaces of this particular formation contained exclusively free water (i.e.

<t> , a ,.) / while the intersection with the bound water trend line indicates the attenuation that would have been measured if the pore spaces of this formation contained exclusively bound water (i.e.

a , ) . In reality, the measured attenuation is ia - <f> a )

w wbcw wc

an attenuation that has a value between these two extreme values, and the total water in the pore spaces can be considered as composite water with attenuation «wc • Consequently, it is seen that the ratio (9C) and the output from the calculation circuit 510 represent a linear division between the two extreme values and gives the proportion of bound water, S^/ S^.

(Note that the multiplier ø in front of each term will be canceled in the output of the arithmetic circuit 510 if <f> a . 6 a~

■ 3 3 w wc w wf

and <t>^are used as input sizes) .

In addition to the use of ©a ~ and 6 a , to obtain w wr w wb

of the fraction of free water, the mass formation attenuation if all the water were free water (ie cj>w • useful as noted above, in determining cr„,,_, since attenuation due to

EMP

bound water present will not result in an unreasonably high value of rf. In particular, C „„_ can be determined from

^rj. \jEMPcEMP

which is a modified form of relation (35) where the mass damping for free water (<t> w a wf_) is substituted for the mass damping for

compound water (<J> a which is the equivalent for the measured a in v^w wc

according to (34) above).

An alternative technique for achieving the mass damping

for free water, d> w a _, is to use the apparatus in figure 14. One

w wfcjr c

ratio circuit 431 receives at its inputs signals representative of a and 0^, both as determined from measurements

taken with an EMP device 46 (Figure 1) in a purely non-hydrocarbon bearing area of the formations where substantially all the water present is free water. (The signal representing (f>w can, for example, be obtained using a technique according to US Patent No. 4,092,583). The ratio a/é in this range will be representative of a wf_ in accordance with the conditions (34) and (9b), where Swb=0 for this case.In particular, is

so that a wf = a/ é w when S wb. =0. After obtaining the para-

the meter a r- for the formations, the variable å> a ... (i.e.

wf J ^w wf v the mass attenuation in free water) is now determined at a particular depth level of interest by multiplying the output of ratio circuit 431 by a signal representative of <f> at that depth level, which is performed by means of multiplier circuit 432. A further multiplying circuit 433 can then be used to obtain a signal representative of ^EMP

in accordance with relation (36). It will be understood that analog circuits can be used to obtain a corresponding parameter for bound water, G!Wk» from information in a shaly area, and then the mass attenuation for bound water at particular depth levels of interest can

is achieved by using a multiplier circuit to produce a signal representative of w aWD* The signals representative of ø w a wf _ and 3 <S EMP can also be recorded if desired, using the recording device 90 of Figure 1.

It can be noted in connection with obtaining values associated with either bound or free water, that non-linear interpolation can be used if desired (e.g. in figure 13). Since ^p]_ can further be affected by residual hydrocarbons in the near-wellbore formation, the indicated attenuation attributed to free or bound water may be slightly inaccurate. However, since both t^ and a will decrease due to hydrocarbon effects, there is some compensation in the indirect saturations

for bound and free water. When a ' c or d> a c is determined,

• wf wf . the hydrocarbon effects will lower corresponding values of t and will produce slightly lower values of , and therefore, used in conductivity measurements, lower values for C^p* Use of a (J>t measurement (relatively independent of hydrocarbon effects)

instead of using the method shown in figure 13, can be recommended in some cases.

The present invention has been described with reference to particular embodiments, but variants within the scope of the invention will be apparent to those skilled in the field. For example, while the circuits have been described to provide analog signals representative of the desired quantities, it will be understood that a digital general purpose computer can easily be programmed to implement the techniques presented here. While conductivity values have been used to illustrate the invention, one will easily realize that the inverse of the values used here can be used in connection with the inverse of the conductivity, i.e. the specific resistance.

Claims (56)

1. Procedure for determining a composite parameter for the formation water in formations surrounding a borehole, where a first quantity representative of is derived mentioned parameter and which can be attributed to the four waters in the formations, characterized by the fact that a second quantity which is representative of the proportion of bound water in the formations', that a third quantity is derived which is representative of the said parameter and can be attributed to the bound water in the formations, and in that the said composite parameter is derived as a function of the said first, second and third sizes. . 2. Method according to claim 1, characterized in that a fourth size is derived which is representative of the difference between said third and first size. 3. Method according to claim 2, characterized in that said parameter is determined as the sum of said first size and the product of said second and fourth size. 4. Method according to claim 1, 2 or 3, characterized in that the parameter is the capture cross section.• 5. Procedure according to claim 1, 2 or 3, characterized in that the parameter is the conductivity. 6. Method according to claim 5, characterized in that a fifth quantity is derived which is representative of the proportion of free water in said formations, and where said composite water conductivity is determined as the sum of first and second products, the first product being said fifth size times said first size and the second product is the second size times the third size. 7. Method according to claim 5, characterized in that the compound. the conductivity, rf'- , becomes wc determined as d-erC*wf is the conductivity of the free water in the formations, .tfWD is the conductivity of the bound water in the formations, S ■ , is the bound ^water saturation in the formations and Sw is the water saturation in the formations. 8. Method according to claim 5, characterized in that the composite conductivity is an apparent/composite water conductivity, C frøCO" and is determined as where 0'w£ is the conductivity of the free water in the formations, tf ^ is the conductivity of the bound water in the formations, and S ^ is the bound water saturation in the formations. 9. Method according to claim 8, characterized in that a calculated "wet" conductivity is determined for the formations, C*, which o where <J>t is the total porosity of the formations. 10. Apparatus for determining a composite parameter for the formation water in formations surrounding a borehole, comprising means for deriving a first quantity representative of said parameter and attributable to the free water in the formations, characterized by means for deriving a second quantity which is representative of the proportion of bound water in the formations, means for deriving a third quantity which is representative of the parameter and which can be attributed to the bound water in the formations, as well as means for determining said composite parameter as a function of said first, second and third quantity. 11. Apparatus according to claim 10, characterized by . means for deriving a fourth quantity which is representative of the difference between said third and first quantity. 12. Apparatus according to claim 11, characterized in that said parameter is determined as the sum of said first size and the product of said second and fourth size. 13. Apparatus according to claim 10, 11 or 12, characterized in that the parameter is the capture cross-section. 14. Apparatus according to claims 10, 11 or 12, characterized in that the parameter is the conductivity. 15. Apparatus according to claim 14, characterized by means for deriving a fifth magnitude such as . is representative of the proportion of free water in the formations, and where said composite water conductivity is determined as the sum of the first and second products, the first product being the fifth size times the first size and the second product being the second size times the third size. 16. Apparatus according to claim 14, characterized in that composite conductivity, tf', is determined wc as where C is the conductivity of the free water in the formations, cT is the conductivity of the bound water in the formations, is the bound water saturation in the formations, and SW is the water saturation in the formations. 17. Apparatus according to claim 14, characterized in that said composite conductivity is an apparent composite water conductivity, ( fW' CO, and is determined as where <SW£ is the conductivity of the free water in the formations, is the conductivity of the bound water in the formations, and S is the bound water saturation in the formations. 18. Apparatus according to claim 17, characterized by means for determining a calculated "wet" conductivity for the formations, Cq»' which where <J>^ is the total porosity of the formations. 19. Method for determining the water saturation for formations surrounding a borehole, where a first quantity is derived that is representative of the conductivity of the free water in the formations, characterized in that a second quantity is derived that is representative of the proportion of bound water in the formations , that a third quantity representative of the conductivity of the bound water in the formations is derived, that a quantity representative of the measured conductivity of the formations is derived, and that the water saturation of the formations is determined as a function of the aforementioned first, second and third size and said size representing the measured conductivity. . 20. Method according to claim 19, characterized in that a quantity representative of the porosity of the formations is derived, and where the determination of the water ning is also a function of said size which represents the porosity. 21. Method according to claim 20, characterized in that the determination of the water saturation comprises the derivation of a quantity that is representative of the apparent conductivity for water in the formations in dependence on the measured quantity that represents the conductivity and the represents the porosity, as the determination of the water saturation then becomes a function of said first, second and third size and the size that represents said apparent water conductivity. 22. Method according to claim 21, characterized in that the water saturation is determined as where •6'W£ is the conductivity of the free water in said formations, <5 rwk is the conductivity of the bound water in the formations, is the bound water saturation in the formations, and «j'wa is the apparent conductivity of the water in the formations. 23. Method according to claim 19, characterized in that the determined water saturation is the water saturation for.the invaded zone of the formations. 24. Method according to claim 23, characterized in that the first size is representative of . the conductivity of the mud filtrate in the invaded zone of the formations. 25. Method according to claim 24, characterized in that said quantity representing measured conductivity is a conductivity derived from an EPT logging device. 26. Method according to claim 25, characterized in that said saturation of the formations' invaded zone, S', is determined as xo where cr* mv f is the conductivity of the mud filtrate invading the formations, is the conductivity of the bound water in the formations, S is the saturation of the bound water in the formations, <J>t is the total porosity of the formations, and° ~EM p is the conductivity of the invaded formation as determined by one EMP logging device. 27. Apparatus for determining the water saturation of formations surrounding a borehole, comprising means for discharging one first quantity which is representative of the conductivity of the free water in the formations, characterized by means of deriving a second quantity which is representative for the proportion of bound water in the formations, means for deriving a third quantity that is representative of the conductivity of the bound water in the formations, means for deriving a quantity that is representative of the measured conductivity of the formations, and means for determining the water saturation of the formations as a function of said first, second and third size and said size representing the measured conductivity. 28. Apparatus according to claim 27, characterized by means for deriving a quantity that is representative of the porosity of the formations, and where the determination of in the water saturation is also a function of said size which represents the porosity. 29. Apparatus according to claim 28, characterized in that the means for determining the water saturation comprise means that react to the size representing the measured conductivity and the size representing the porosity, for deriving a size that is representative of the apparent water conductivity of the formations, the determination of the water saturation then becomes a function of said first, second and third quantities and the quantity representing the apparent water conductivity. 30. Apparatus according to claim 29, characterized in that the water saturation is determined as where C^ is the conductivity of the free water in the formations, C f^ is the conductivity of the bound water in the formations, S^-^ is the bound water saturation in the formations, and C wa is the apparent conductivity of water in the formations. 31. Apparatus according to claim 27, characterized in that the determined water saturation is the water saturation in the invaded zone of the formations. 32. Apparatus according to claim 32, characterized in that said first size is representative of the conductivity of the sludge filtrate in the invaded zone. 33. Apparatus according to claim 32, characterized in that the quantity which is representative of measured conductivity is a conductivity measured by means of an EPT logging device. 34. Apparatus according to claim 33, characterized in that the saturation of the invaded zone in the formation, S , is determined as xo 35. Procedure for determining a variable for free water in the formations surrounding a borehole, characterized in that a function is derived that is representative of the parameter in at least one area of the formations where mainly all the water present is free water, that a quantity is derived which is representative of the water content in the formations, and by the fact that the variable for free water be voted on the basis of said function and said size. 36. Method according to claim 35, characterized in that said size representing water the content, is derived from at least one measurement in the formations surrounding a particular depth level in the borehole. 37. Method according to claim 36, characterized in that the variable for free water is the attenuation of electromagnetic energy due to the formations that surround . the particular depth level if essentially all the water in said surrounding formations were free water, and where said function is derived from attenuation measurements. 38. Method according to claim 35, 36 or 37, characterized in that the size representing the water content is derived from at least one duration measurement. 39. Method according to claim 37, characterized in that said attenuation measurements are measurements taken with a logging device for propagation of electromagnetic microwave energy.. 40. Method according to claim 38, characterized in that the duration measurements are measurements taken with a logging device for the propagation of electromagnetic microwave energy. 41. Apparatus for determining a variable for free water in formations surrounding a borehole, characterized by means for deriving a function representative of the parameter in at least one area of the formations where essentially all the water present is free water, means for deriving a size that is representative for the water content in the formations, and means for determining the variable for free water based on the function and said size. 42. Apparatus according to claim 41, characterized in that said quantity, which is representative of the water content, is derived from at least one measurement in the formations surrounding a particular depth level in the borehole. 43. Apparatus according to claim 42, characterized in that the variable for free water is the attenuation of electromagnetic energy that can be attributed to the surrounding formations at that particular depth level if essentially all the water in the formations was free water, and where the function is derived from attenuation measurements. 44. Apparatus according to claim 41, 42 or 43, characterized in that said quantity representing the water content is derived from at least one duration measurement. 45. Apparatus according to claim 4, characterized in that said attenuation measurements are measurements taken with a logging device that uses propagation of electromagnetic microwave energy. 46. Apparatus according to claim 44, characterized in that the attenuation and duration measurements are measurements taken with a logging device that uses propagation of electromagnetic microwave energy* 47. Method for determining the proportion of bound water in formations surrounding a borehole, characterized in that a first quantity is derived which is representative of the attenuation of electromagnetic energy that can be attributed to the formations if mainly all the water in the formations was free water, that a second quantity is derived that is representative of the attenuation of electromagnetic energy that can be attributed to the formations if essentially all the water in the formations was bound water, that a third quantity is derived depending on the measured attenuation of electromagnetic energy in the formations, and that the proportion of bound water is determined from the first, second and third size. 48. The method according to claim 47, characterized in that the third size depends on an attenuation measurement taken with a logging device that uses propagation of electromagnetic microwave energy. 49. Method according to claim 47 or 48, characterized in that the proportion of bound water is determined as the difference between the third and the first size divided by the difference between the second and the first size. 50. Method according to claim 47, 48 or 49, characterized in that the derivation of the first quantity comprises: derivation of a first function which is representative of the attenuation. in at least one area of the formations where essentially all the water present is free water, deriving a quantity representative of the water content, and determining the first quantity from the first function and the quantity representative of the water content. 51. Method according to claim 50, characterized in that the derivation of the second quantity includes: derivation of a second function which is representative of the damping in at least one area of the formations where mainly all the water present is bound water, and determination of the the second size on the basis of said second function and the size representing the water content. 52.. Apparatus for determining the proportion of bound water in formations surrounding a borehole, characterized by means for outputting a first quantity representative of the attenuation of electromagnetic energy attributable to the formations if substantially all the water therein was free water, means for the derivation of a second quantity representative of the attenuation of electromagnetic energy attributable to the formations if substantially all the water therein was bound water, means of derivation of a third quantity which is dependent on the measured attenuation of electromagnetic energy in said formations, and means for determining the proportion of bound water from said first, second and third size. 53. Apparatus according to claim 52, characterized in that the third size depends on an attenuation measurement taken with a logging device that uses propagation of electromagnetic microwave energy. 54. Apparatus according to claim 52 or 53, characterized in that the proportion of bound water is determined as the difference between the third and first size divided by the difference between the second and first size. 55. Apparatus according to claim 52, 53 or 54, characterized in that the means for deriving the first quantity comprise: means for deriving a first function which is representative of the attenuation attributable to at least one area of the formations where essentially all the water present is free water, means for deriving a quantity representative of water content, and means for determining the first quantity from said first function and the quantity representing water content. 56. Apparatus according to claim 55, characterized in that the means for deriving the second quantity comprise: means for deriving a second function which is representative of the attenuation attributable to at least one area of the formations where essentially all the water present is bound. water, and means for determining the second quantity from the second function and the quantity representative of the water content.