DE19948684B4 - Computer-aided measurement method for determining the dielectric properties of floor layer structures and device for carrying out the method - Google Patents

Abstract

Computer-aided measurement method for determining the dielectric properties of soil layer structures in the at least axial region of a borehole, characterized in that the capacitance (C) in the interior or exterior of an insulation gap with n radial layers and with capacitor electrodes (E) are present between their boundary surfaces , built-up cylindrical capacitor (DEP) at a measuring point (M) in the radial layer n is measured capacitively with high precision at a measuring frequency in the alternating electromagnetic field, the length (L) of the cylindrical capacitor (DEP) being so great as determined by the angle Ψ Isolation gaps between the capacitor electrodes (E) are so small and the measurement frequency is dimensioned so low that their influence on the measurement is error-tolerable within the scope of the desired measurement accuracy, and that by forming the quotient of the measured capacitance (C) with that by air measurement, calibration measurement or Calculation known empty capacitance (C ₀ ^∞ ) of the cylindrical capacitor (DEP) an effective dielectric constant (ε ^* ) is calculated as a characteristic parameter for the real soil layer structure, from which then by mathematical inversion with knowledge of the ...

Description

The invention relates to a computer-aided Measuring method for determining the dielectric properties of Soil layer structures in the area of a borehole and on a device to carry out the procedure.

Findings on soil layer structures are of great importance in many different areas. Petrophysical properties are of interest to the oil industry, Science is interested in geological and seismic properties and research and the geophysical construction of ice areas of particular importance for polar research. Here are the measurements of the electrical properties to be regarded as basic measurements, since almost all of them are essential Properties of floor layer structures, such as their conductivity and density, can be derived. The following are the known methods for soil layer structure detection. The one in it mainly occurring reference to the so-called "borehole matrix" as a parameter grid the layers surrounding the borehole are also analogous the "core matrix" to acquire.

Known detection methods for soil layer structures are mainly based on inductive measurements - in addition to ultrasonic and thermal measurements - and accordingly use borehole probes that have an inductive magnetic effect. From the U.S. Patent 4,323,848 and from the U.S. Patent 4,502,010 So-called "magnetometers" are known with which the electrical conductivity in the ground can be measured. These are elongated or u-shaped coils in the measuring probe, which are excited via electrodes on the surface of the earth. The flux signal measured on the coil is then interpreted in relation to the surrounding soil conditions U.S. Patent 5,426,367 An overview of various inductive measurement methods - here for the inspection of drill rods - that use the electromagnetic, geophysical signals is given. On the one hand, magnetic direct current probes can be used. These are permanent or electro-magnetically polarized tubular rods with north-south orientation, in the middle of which a series of pick-up coils are arranged. Changes in the magnetic environment due to the lowering of the borehole in the borehole cause measurable changes in the magnetic flux in the sensor coils. Different reflected electrical pulses can also be detected inductively. Furthermore, high-frequency eddy current devices can be used in connection with permanent or direct current magnetic coil fields. Eddy currents are induced in the detector coils, which enable the detection of voids in the bottom layer structures. A third known method is based on a low-frequency phase shift in a frequency range of 60 Hz. An AC transmitter coil is arranged in the center of the borehole probe, and a receiver coil is also located in the borehole probe. When the borehole probe is lowered, the signal shift at the receiver coil is measured as a measure of the thickness of a layer of soil.

All inductive measurement methods is however, they have in common that they only have a relatively rough spatial resolution. This has led to that so far the measurement results in the field have only been "probably good" - "maybe bad "and" probably bad ". High spatial resolutions, especially in the range of relevant phase transitions, for example between rock and other phases with very similar conductivities, cannot be achieved with the known inductive measuring methods.

From the U.S. Patent 4,949,045 a borehole probe for the detection of soil layer formations is known, which is equipped with an electromagnetic transmitting and two interconnected receiving antennas. Here, too, the electromagnetic transmission signals are again preferably generated via coils. The measurements are made via an impedance matching between the receiving antennas. The conductivity at layer boundaries and an estimated dielectric constant are determined by measuring the phase shift of the attenuation of the transmitted signal. Such an arrangement is intended to reduce a serious disadvantage in known arrangements for measuring the electrical conductivity or the resistance in soil layer formations. Porous formations typically have high resistance, suggesting the presence of hydrocarbons, whereas low resistance porous formations are generally formed by water-saturated formations. However, drilling fluids or freely drilled drilling filtrates that surround the borehole probe have a different resistance than the soil layer formations to be measured. Measurements on a narrow radius around the borehole probe therefore do not relate to the real soil conditions and provide inaccurate results. There is no radial spatial resolution. With the in the U.S. Patent 4,949,045 The arrangement described should therefore be reached from the borehole probe at least two different radial depths. An attempt is made to make a reliable distinction with an error range of less than 11% between the individual detection areas.

The prior art, from which the invention is based on the method, is in the US-PS 4,319,191 disclosed. The method described here is also intended to determine dielectric constants of soil layer formations from measured phase shift values. To this end, an inductive transmitter-receiver system is used to carry out an inductive measurement process. This has different sensor coils that have a radial expansion and have different induction characteristics. The coils are set using an adjustable capacitor. To improve their signal behavior in the high-frequency radio frequency range, the coils are shielded in the form of a tube. With that in the U.S. Patent 4,319,191 Measuring methods disclosed should be achieved by a choice of the axial distance between transmitter and receiver coils measurement results that depend less than before on the borehole conditions. The electrical conductivities are determined from the calculated values for the phase shift and the damping with the aid of a diagram, which was created with computer support according to the Helmholtz equations and which assigns different dielectric constants and resistance values to the individual measured values. Radial assignment of the measurement results to the individual layers forming and surrounding the borehole probe is also not carried out with this measurement method.

For the present invention is therefore intended against the background of described methods to be a main aspect of the problem to be solved Procedure for determining the dielectric properties of soil layer formations indicate that a simple derivation of relevant soil parameters with a particularly high local resolution concentric in the axial direction, but also by including disturbing influences Allows layers in the radial direction. This is supposed to be for the derivatives Measurement parameters to be used have a particularly high local distinctive character exhibit. Furthermore, it is for one meaningful Assessment of the measurement results is important that these with a possible low Fehrler tolerance towards the real values of the soil layer structures to be measured are. Calculation-simplifying assumptions made with known measuring methods to a coarsening of the measurement results, are largely excluded. A suitable arrangement for carrying out the measurement process should be simple in their structure and thus in their handling. robustness and cost-effectiveness should also be aimed at.

To solve the problem described, it is therefore provided in the computer-assisted measurement method according to the invention that first the capacitance C in the interior or exterior of a cylindrical capacitor constructed with a number n radial layers is measured capacitively at the measurement location and then by forming the quotient of the measured capacitance with the through Air measurement, calibration measurement or calculation of known empty capacitance C ₀ ^{∞ of} the cylindrical capacitor, an effective dielectric constant ε ^{* is} calculated as a characteristic parameter for the real soil layer structure, from which mathematical inversion with knowledge of the geometric layer ratios (ρ ₁ , ..., ρ _n ) is then used. and the dielectric properties (ε ₁ , ..., ε _n ) of the layers concentrically filling the cylindrical capacitor up to the measurement location, the computationally store the dielectric properties ε _{i of} the bottom layer structures at the measurement location The error tolerance estimate of the numerical implementation takes into account the finally long extension of the cylindrical capacitor, minimized insulation gaps between the capacitor electrodes and electrostatic conditions as an approximation for low frequencies in the measurements.

For the first time in the development of prospection with the measuring method according to the invention Bottom layer structures detected purely capacitively and and on the Influence of additional, existing for technical reasons corrected radial layers, so that a radial spatial resolution is also possible. An investigation of the individual soil phases is therefore easy possible, since the relevant measurement parameter is no longer just the electrical one conductivity with its low distinctive character between different Phases of the bottom layer is. Rather, it is about the dielectric properties of the phases with a - also in smallest values - strong ones Material dependence. In particular, lets yourself about Mixing formulas in soil layers with high contrast in the dielectric Properties of the phases the proportional composition of the soil layer estimated. The measurement method provides both the dielectric constant and the conductivity of the material to be examined. Thus, in the area of a borehole, this means related to the core and the borehole environment, directly the dielectric Properties - also one inaccessible - rock layer can be easily determined provided the radii and dielectric properties the rest Layers are known. Due to the absolute nature of the measurements, the measuring method according to the invention hence well-defined material constants with minimal error can be reliably derived in the range of less than one percent.

The "effective dielectric constants" are scalar complex-valued quantities into which the dielectric constants, in the sense of the usual approach of relative dielectric constants in solid state physics (cf. for example Ibach and Lüth, ISBN 3-540-52193-3, Chapter 11, relation 11.10) , all in relation to the measuring con radial layers arranged. From the knowledge of the dielectric constant of all known layers and their geometric dimensions, in particular the thickness, the “absolute” dielectric constant of the material to be examined can be derived as a function of the radius. This is also a real material value as an absolute material constant that The absolute dielectric constant shows large, clearly distinguishable contrasts between the individual phases occurring in soil layer structures, for example for rocks in a range between 2 and 10, for water but above 80. The determination of the effective or absolute dielectric constants enables highly precise statements to be made about the type, structure and location of the real soil layer structures, which is why knowledge of these parameters enables ge in particular in the field of oil production accurate predictions of possible oil deposits, especially in inaccessible areas. The same naturally also applies to the extraction of other soil deposits.

The cylindrical adjustment of the measuring capacity enables one optimal adaptation to the borehole or the core. On the the prior art known in this regard will become apparent in the course of the description discussed in more detail. For a significant difference in the method of the invention however, this should already be discussed at this point. in the Contrary to the known methods, which assume for simplicity, that there are no gaps between the measuring electrodes and the material to be measured, In the present procedure, the real case is assumed. By the consideration of n different radial layers in the cylindrical capacitor can exactly deal with each existing layer structure, messwertverfälschende Simplifications are eliminated. In particular, empty or filled spaces between the measuring electrodes and the material to be measured, as in practice - straight in the borehole - always occur, included in the parameter determination or additional Layers, such as insulation or protective films or Liquid films, considered become. Especially when measuring soil layers with compared to the other radial layers very different dielectric properties is absolutely the Influence of the rest Correct radial layers. All different dielectrics that are either surrounded by the condenser half-shells (core) or surround it (borehole) so taken into account become. A multi-layer drill core sample can be prepared without additional sample preparation the dielectric properties are determined right down to the center of the core become.

By considering the individual Radial layers on the cylindrical Capacitor itself and on the measured material are also other applications than the soil prospection, which is the main area of application of the present Represents measuring method, quite possible. For example, should a possible one at this point Density detection via the measurement of the dielectric properties of liquid or gas flows in closed pipes, especially with a central axis guide. Enabled here too the stratification when measuring capacity an optimal approximation to the real case.

Because a total measuring capacity across from a measuring inductance with transmitters and receivers generally an essential one has a smaller size, are with the measuring method according to the invention also in the axial direction much higher local resolutions than previously available. Enivähnenswert is the influence of axially adjacent areas to the measurement site, which again has the axial resolution somewhat diminished. However, this can be treated with a simple estimate become. For small column, the influence is therefore relatively small, making it good is controllable. The high accuracy obtained with the measuring method according to the invention achievable measurement results but also by taking them into account further real measurement conditions. It is of a cylindrical shape Finite length capacitor and not - how often in theory - more infinite Length run out this means, there will be marginal influences included in the measurement results at the capacitor electrodes. Ultimately, however, a cylindrical capacitor can also be finite Length conscious be dimensioned so that it is like a capacitor for measurements infinite length works, which then simplifies the calculations accordingly, without to falsify them. Furthermore, gaps between the boundary surfaces of the Capacitor electrodes taken into account their size, however is set as low as possible to minimize influence. The isolating one However, the effect between the electrodes remains intact. The acceptance of electrostatic measurement conditions also means no distorting results Simplification for the measuring method according to the invention, there already for Measurements below 100 MHz the wavelength in air is large compared to that Capacitor diameter. This reduces the general electrodynamic question allowed on an electrostatic Problem. Clearly, the field then varies at low frequencies Measurements only negligible over the Linear expansion of the cylindrical Capacitor.

wobei sich die Koeffizienten mit i=(n-1),...,1 und m ϵ N₀ nach den Rekursionsformeln

The basic idea in the measuring method according to the invention is based on the implementation of purely capacitive measurements in the borehole area with radial layer resolution and under the boundary conditions already mentioned. The dielectric parameters that can be determined in this way are precise, easily differentiable and have a high spatial resolution. In their determination, they are subject to the general laws and algorithms for determining capacitive measured values and the numerical inversions applicable to them onsverfahren (see, for example, "Numerical Recipes in C", Press et al., Cambridge University Press, ISBN 0-521-43108-5, Chapter 9). This knowledge of the average specialist in the field of measurement technology is therefore sufficient for the use of a capacitive According to an embodiment of the measurement method according to the invention, it can also be particularly advantageous that for the mathematical derivation of the dielectric properties (ε ₁ , ..., ε _n ) of the bottom layer structures (ρ _i , ..., ρ _n ) the following general power series development - or a mathematically equivalent power series with analytically evaluated partial sums - is used:

where the coefficients with i = (n-1), ..., 1 and m ϵ N ₀ according to the recursion formulas

The curly brackets ({...}) used in the equations designate alternative sizes for the interior (</ drill core) or the exterior (> / borehole probe) of the cylindrical capacitor, which basically only affect the signs of the calculations and should be taken into account of the radius ratios that enter through a ¹ _m and b ¹ _m . S (∞) denotes the general power series, which is also mathematically unique because of the uniqueness of the solutions of the underlying differential equations. The trigonometric functions in the power series S (∞) in equation (1) relate to the potential distribution on the electrode surfaces. Any distribution is conceivable here, especially at the edge, the series development shown denotes a distribution that makes technical sense. Other series developments with a required arbitrariness from φ to the final totals in sin (2m + 1) φ or cos (2m + 1) φ are possible, but are not to be explained further here. Equations (5i) and (5a) result from the limitation of the solutions at ρ _n = 0 in the interior and ρ _n = ∞ in the exterior.

The relevant dielectric constant ε _i is calculated by means of numerical inversion, in particular according to another embodiment of the invention, preferably by solving the equation from the effective dielectric constant determined and its power series development according to the dielectric egg properties at the measurement location (e.g. Newton algorithm, regular falsi, interval nesting) of equation (1) for the effective dielectric constant ε ^* determined from the measured capacitance C and empty capacitance C ₀ ^∞ . It is initially assumed that all ε _{i are known} except for the one you are looking for. In the case of numerical inversion, a starting value is then selected for the ε _{i of} the slice of interest and it is determined iteratively from the variation of this input value. All of these calculations can be carried out quickly and easily using computer-implemented algorithms. The formula (1) given was obtained during its derivation by extracting the sum over a ¹ _m + b ¹ _m and the separate evaluation of the series for the empty capacity in an analytical expression for C ₀ ^∞ (cf. report on polar research 191 / '96, Relation 2.45) made clearer on the one hand, but also has important reasons for considering convergence on the other. The alternating row for C ₀ ^∞ with a known sum can be extracted and the remaining row geometrically majorized with the radius ratios. Taking into account the ρ _i growing outside and falling inside with index i and the different recursion starting points (5a, 5i) in recursion formulas (2) and (3) for inside and outside, you can see that all occurring radius products are less than one stay. The summands of the series S (∞) indexed with index m can therefore be estimated. The series S (φ) is geometrically majorized by definition. The residual term R (N) of the series S (∞) cannot be calculated directly, since the sum S of the series is not known. However, control by an absolutely convergent power series S * is possible. Due to their compact convergence, the remainder is arbitrarily small. This residual limb estimate can be transferred directly to programming. A current residual limb estimate is then obtained for each iterative loop run.

To the meaning and the basics To explain the above-mentioned equations in more detail, some are to follow versions on the theory of a protected cylindrical capacitor on which the equations are based be made with a concentrically layered dielectric. This is also based on the explanations in the report on polar research 191 / '96 "Conductivity and density measurement an Eisbohrkernern "by Frank Wilhelms, Alfred Wegener Institute for Polar and marine research, Bremerhaven. Taking the variation into account the dielectric constant of the medium in the direction of the cylinder axis, the potential distribution varies for a medium homogeneous in the plane perpendicular to the cylinder axis Not. First a variation of the dielectric constant along the cylinder axis contributes to the Capacity calculation at. The potential distribution is always the same and in the presence of a dielectric is reduced by the factor of the relative dielectric constant e more charge is influenced on the measuring electrode. For a concentric The potential distribution changes around the layered medium but along the cylinder axis with different dielectric constants, since these are included in the calculation of the potential distribution.

The coordinate names are the special description part, 5 for the electrode interior of a cylindrical capacitor. Cartesian coordinates (x, y) and polar coordinates (ρ, φ) are defined, there is no dependency in the z direction. Other angles are the 2 the special description section. The interior of the electrode is filled with a dielectric layered concentrically around the origin of the coordinate system. The layers of different relative dielectric constants ε ₁ , ε ₂ , ..., ε _n each begin at the electrode surface, beginning with radius ρ ₁ , and have the radii ρ ₁ , ρ ₂ , ..., ρ _n . For the exterior, the definition is not shown here, but is structured quite analogously. The radius ρ with index 1 begins on the electrode surface and the radius ρ for the nth layer is extended to ρ = ∞. The layer with the dielectric constant ε _i is located between the radii ρ _i and ρ _{i + 1} concentrically around the center of the electrode. In this general nomenclature, the electrode surface is designated by ρ ₁ corresponding to the outer boundary of the first dielectric layer. The problem for the outer area of the electrodes can be described analogously. Beginning on the surface of the electrode, the concentric layers of different dielectric constants are numbered, the nth layer extending to infinity. The scalar dielectric constants ε _i can generally be seen here as complex functions with which materials with ohmic charge carriers can be described.

A theoretical derivation of the potential function for any layer arrangements on the half-shell electrodes, from which further electrodynamic variables such as the electrical flux and the field strength distribution can be derived according to the physical laws, results in a separate solution for the angular and radial components from their linear combination recursive solution for the areas within the respective dielectrics. The naturally indicated coefficients a ¹ _m and b ¹ _m occurring therein depend exclusively on the dielectric constant ε _l and the radii ρ _{i of} the individual material layers. They can be calculated iteratively according to the recursion formulas (2) and (3) mentioned above together with the normalization condition (4). In the recursion formula, depending on the calculation required, one of the coefficients disappears in the exterior or interior during the initialization according to equation (5i, 5a). This means that the other coefficient starts with 1. The coefficients obtained are then normalized by division by their sum. The standardization condition according to equation (4) results from the potential distribution on the electrode surface by direct Comparison with a Fourier series development.

Metals are a special case for the algorithm according to equation (1). They behave like materials with an infinitely high dielectric constant, that is, through them the field lines enter and exit vertically. The inside of metals is field-free. The metal layer is the last layer from the cylinder electrode, since all information is shielded within a metal surface. In algorithm (1), this case is achieved by forming limit values by excluding the dielectric constant ε _n (with n as the highest index), shortening it when normalizing the coefficients, and then letting it strive towards infinity. This means that all fractions in which ε _n occurs are eliminated, so 1 ± ε _n / ε _{(n-1) must be} replaced by ± 1 / ε _(n-1) . According to an embodiment of the measuring method according to the invention, it is therefore advantageous if the measuring method is calibrated by forming the limit values of the algorithms, assuming an infinitely high dielectric constant for the last layer of the cylindrical capacitor. In this case, a metal tube as the last layer, seen from the electrode surface, can preferably be introduced into or pushed over the electrode surface to use the cylindrical capacitor as the calibration capacitance.

With a particularly suitable one Arrangement for carrying out the procedure the underlying apparatus is the so-called "DEP apparatus" (DiElectric Profiling), for example from the one already cited above Report on polar research 191 / '96, page 38 ff. Is known and exclusively for the capacitive measurement of electrical properties of ice cores is used at frequencies above the Debye relaxation. applications for unfrozen Materials or as a probe in a borehole are not provided. This report is the basic design concepts of a DEP apparatus can be seen (Chapter 2.2), on the one hand a "guarding concept" with a protected measuring electrode to reduce stray capacities and on the other hand a "blocking concept" with completely isolated electrodes (e.g. by anodizing) for reduction of polarization effects include. Furthermore, this report is a theoretical one Treatment of the DEP apparatus for carrying out conductivity measurements explained on ice cores (Chapter 2.3). However, this is a purely theoretical one Basic consideration, the - there she was first employed in such a specified manner - by one Set of significant simplifications and without error quantification emanates. On the one hand there is an infinitely long expansion of the capacitor to calculate the empty capacity and on the other - as a much more restrictive limitation - the complete absence of a layer between the capacitor electrodes and the ice core to be measured accepted. However, this assumption does not match the real situation, because it is a gapless enclosure of the drill core or system corresponds to the borehole. However, it is precisely in the borehole always another between the borehole probe and the borehole wall Medium, for example air, bean water, mud or granular drilling material, its disregarded Presence the measurement results, as already explained above, until falsify to uselessness can.

In the research report mentioned 191 / '96 are therefore the measuring principle and a suitable device illustrated on an ice core, a predictable application for real Cases, especially for the creation of a parametric borehole matrix for prospecting purposes, is not provided at this stage of the description. The conditions are strongly theorized and produce measurement results, their reliability no over the one mentioned at the beginning rough estimation strategy goes. However, the aim of the invention is to provide highly accurate information determinable parameters, the optimal statements about the existing soil layer structures allow. A summary of research report 191 / '96 is also the article “Precise dielectric profiling of ice cores a new device with improved guarding and its theon "by F. Wilhelms et al., Journal of Glaciology, Vol. 44, No. 146, 1998, pp. 171-174. Is in this essay however, only a theoretical formula for the empty capacity without consideration of insulating layers and the usual Basic structure of the electrodes described. It will be here again shown that there is a DEP apparatus with an appropriate choice of dimensions in approximation an error rate in the range of up to 15% like an infinitely long one cylindrical Condenser can behave without air gaps. The main contributor to the mistake limited by scatter admittances (in the cables and the measuring bridge) absolute accuracy of the measuring bridge at. However, the error can be caused by the calibration measurement described above be significantly reduced.

So far, capacitive-electric borehole probes are not known. Even the largest prospecting company "Schlumberger" on the market uses only magnetic-inductive probes with different transmitter-receiver arrangements using induction coils. The preferred device for carrying out the method according to the invention therefore provides a completely new prospecting probe with optimal handling for reliable implementation of capacitive measurements. According to an embodiment of this device with a dielectric profile apparatus with an electrically shielded and protected cylindrical DEP capacitor consisting of the measuring electrode, protective electrode and counter electrode, it is therefore provided that the length and the swept angular range of the measuring electrode in relation to the remaining marginal gaps and the length of the protective electrode is selected so that within the scope of the desired measuring accuracy, a simplifying, only variations in the plane theory taking into account perpendicular to the cylinder axis is used. The DEP apparatus can preferably be designed such that the length of the measuring electrode is in the range of 10 mm and that when the apparatus is used as a drill core detector, the length of the protective electrode is in the range of 300 mm or when the apparatus is used as a borehole probe Range from six to ten times thereof. With this configuration it can be clearly established that when the device is used as a borehole probe, a significantly larger dimensioning is carried out. In order to avoid repetitions in the justification, please refer to the special description section of the 6 and 7 directed.

Already in the receipt of the description was explained that as possible realistic Interpretation of the parameter calculation also the isolation gap between the electrode half-shells be, but with minimized dimensions. This can be kept well if, according to a next design the insulating gap between the measuring or protective electrode and the counter electrode is only as wide as it is from insulation or production technology establish is required. This can e.g. about the dielectric strength of the insulating material, the width of the saw blade for cutting one Trade tube in two half shells or manufacturing tolerances.

The measuring method according to the invention and a preferred one Order to carry it out are based on the schematic figures and diagrams explained in more detail. there shows

1 a flowchart of the measurement evaluation,

2 a device for performing the measurement method according to the invention in a spatial representation,

3 the device according to 2 in cross section,

4 the coordinate systems on the device according to 2 for the calculations,

5 the coordinates and designations in the concentrically layered dielectric,

6 1 shows a diagram of the dependence of the empty capacitance of a cylindrical capacitor for interior measurements on the length of the protective electrode,

7 a diagram of the dependence of the empty capacitance of a cylindrical capacitor for outside measurements on the protective electrode length and

8th a diagram of the dependence of the empty capacity of a cylindrical capacitor on air gaps at the edge.

The 1 shows the measurement evaluation after data acquisition as a data flow plan according to DIN 66001. During a measurement campaign, calibration measurements and repeated data acquisitions are carried out at the corresponding measurement positions. The subsequent measurement evaluation creates a calibration script using the calibration data record. After reading the input data into a central memory and converting them to the effective dielectric constants that characterize the soil layer to be measured, a routine "effdk", which implements the power series set out in the general description section in accordance with equation (1), and an iterative inversion algorithm is used to invert the measurement data sought value ε _{i of} the soil layer. The routine "effdk" comprises the recursion sequence set out in the general description part according to equations ( 2 ) ff.

In the 2 and 3 DEP apparatus (DiElectric Profiling) is shown as the preferred arrangement for carrying out the measurement method. It consists of two aluminum half-shells, one of which is connected to the Hi output of a self-balancing measuring bridge, not shown, for example HP 4284A or HP 4285A from Hewlett Packard, and forms a counter electrode Hi-E, to which an alternating frequency test signal is fed becomes. The other half-shell consists of a Guard-E protective electrode, into which a Lo-E Lo electrode connected to the Lo output of the measuring bridge is fitted as the measuring electrode. The insulation of the Guard electrode against the Guard-E protective electrode is carried out using thin adhesive tape (not shown). The Lo electrode covers a partial angle of 108 ° and has a length l of approx. 10 mm for the dynamic application of a borehole probe. For this application, the Guard-E protective electrode has a length L in the range of 1800 mm in order to ensure protection. In the case of stationary use for measuring drill cores, on the other hand, the Guard-E protective electrode only has to have a length L in the range of 300 mm. Also compare the comments on the 6 and 7 , The capacitance measurements are carried out via the self-balancing measuring bridges for small capacities, which are not shown in the figures, and which can be reduced in size if necessary.

However, since the protective electrode extension is still long compared to the extension of the Lo electrode, the electric field lines in the area of the Lo electrode run in a very good approximation in the plane perpendicular to the cylinder axis. This results in a reduction of the problem from three-dimensional coordinates to flat, two-dimensional polar coordinates. It should also be noted that on the outside - or on the inside - of the DEP apparatus there is an electrical potential drop of the same Size as on the inside - or on the outside - prevails. With a half-shell geometry without Guard-E protective electrodes on the side, this results in considerable stray capacitance. It turns out that the capacity is halved if you shield the outside - or the inside -. In the DEP apparatus, an electrical shield D _K made of aluminum is therefore attached to the outside - or D _B on the inside - in the area of the Lo electrode, which terminates with the Guard-E protective electrode. The shield is connected to earth potential so that the Guard-E protective electrode completely encloses the Lo electrode on the outside - or on the inside. When shading, the Guard-E protective electrode and Lo electrode are at the same potential as required by the protective electrode concept, since the Lo electrode is on virtual earth. The inserts in the previous text refer to the respective other application of the DEP apparatus. In the case of a borehole probe, a shield must be attached around the Lo electrode, since the capacities influenced are even larger than in the outside area. The insulation for the blocking electrode concept was achieved by anodizing the aluminum shells to form an aluminum oxide layer. Further constructive measures for the mechanical realization of a complete measuring station can be found in the previously mentioned research report 191 / '96.

The 4 the coordinate system for the individual calculations can be found. The origin of a Cartesian coordinate system (x, y, z) is chosen from the radius a in the center of the cylinder. The z axis lies along the axis of the cylinder formed from the two half shells. The other two axes are then arranged in one plane in the middle of the measuring electrode and perpendicular to the z axis. The x-axis forms the plane of symmetry between the two half-shells and the y-axis the orthogonal to it. In the 4 the definitions selected below are also shown. The posed problem of capacitance calculation according to the theory of the protected cylindrical capacitor is cylindrically symmetrical, therefore cylinder coordinates should be chosen instead of the Cartesian coordinates. Any location vector R is then represented in the cylinder coordinates (ρ, φ, Z). With the choice of the potential + V / 2 for the measuring and protective electrode or -V / 2 for the counter electrode, φ is a natural choice between -π and + π with 0 along the positive direction of the x-axis. The measuring electrode has a length of 1, so that its z coordinate runs between - 1/2 and + 1/2. It spans an angle Φ ₀ symmetrically about the y axis. The angular dimensions of the electrode, which run between ξ = (π -Φ ₀ ) / 2 and π - ξ, are required for the calculations. The protective and counter electrodes have the length L and have z coordinates between - L / 2 and + L / 2. A gap over the angle 2ψ to potential 0 at the edge can also be taken into account, that is, the protective electrode has angle coordinates from ψ to π - ψ and the counter electrode from - π + ψ to - ψ.

The 5 the coordinates and designations for the calculations in the concentrically layered dielectric are shown, as they are in particular the equations explained in more detail in the general description section ( 1 ) to (5i, a) are used. Cartesian coordinates (x, y) and polar coordinates (ρ, φ) are also defined here. The interior of the electrode is filled with a dielectric layered concentrically around the origin. The layers of different relative dielectric constants ε ₁ , ε ₂ , ..., ε _n each begin at the electrode surface and - starting at radius ρ ₁ - are continuously designated with ρ ₁ , ρ ₂ , ..., ρ _n , ie the layer with ε _i is between ρ _i and ρ _{i + 1} . The definition for the exterior is not shown here. However, this has a completely analog structure, begins with index 1 on the electrode surface and extends to the nth layer according to ρ = ∞.

In the 6 are calculation results for the interior in which 7 shown for the exterior of a real DEP capacitor without an insulating gap as a variation of the empty capacitance over the protective electrode length L. The calculations take into account a measuring electrode length l of 100 mm and a swept angle Φ ₀ of 108 °. This also covers the case of a 10 mm long measuring electrode Lo-E. The area highlighted in gray indicates the limits for the empty capacity of the cylindrical capacitor between the solution for an infinitely long cylinder C ₀ ^∞ and the finally long one with potential to zero at the limits of the cylinder C ₀ ^L. Accordingly, the value of the empty capacity is C ₀ ^∞ + C ₀ ^L / 2 with an error interval of C ₀ ^L / 2. For the dimensioning of a DEP apparatus, one chooses a length for which C ₀ ^L / 2 falls below the desired accuracy. A comparison of the 6 and 7 shows that the correction term for the interior case drops much faster than for the exterior case. While for the selected dimensions, the additional contribution of the correction term in the interior has already dropped to 1% with a protective electrode length of 20 cm, the protective electrode in the exterior must be more than six times (up to ten times) longer in order to reduce the additional contribution of the correction term to less than 1% to press. This shows that the step from using the interior of the arrangement as a measurement site (drill core) to using the exterior as a measurement site (borehole) requires far-reaching changes in dimensioning. The protective electrodes must be up to ten times longer. Having the interior of the DEP arrangement mathematically under control and using it with a relatively short arrangement does not mean that it can be used outdoors, which would not be possible with an inverted DEP apparatus with the same dimensions.

A clear interpretation of the results can be made based on the proportionality of Feldli niene-tight and influenced solution are developed. The longer the cylinder is, the more the field is compressed in the middle in the measuring electrode area and the field components in the direction of the cylinder axis become smaller. This makes it clear that the empty capacity of a finitely long cylinder is larger than that of an infinitely long one, since more charges can be accommodated on the surface of the field line sources for the additional space penetrated by the field. Since the interior is enclosed more effectively than an infinitely extended exterior, the field in the interior is compressed more than in the exterior. Furthermore, the results show that a borehole probe only has to be a few meters long in order to keep the error limit below 1%. However, such lengths are still easy to handle and, in this respect, the dimensions required here by theory do not represent any restrictions on the technical feasibility. The conservative choice of approximately 70 cm protective electrode length in known DEP apparatuses could even be approximately 30 in the future dimensioning of apparatus cm are reduced, since the uncertainty then remains the same with the length with the uncertainty of the air gaps remaining for technical reasons between the electrode edges.

The 8th finally shows the dependence of the empty capacitance on the insulating gaps between the electrode edges for the to 6

and 7 specified measuring electrode dimensions. When cutting an aluminum tube for a DEP capacitor, the circular saw blade cuts a 5 mm wide gap, which, for a tube with a diameter of 100 mm, creates an insulating or air gap with an angle ψ = 0.05 rad. Here too, the influence of the air gap in existing equipment is clearly below 1% and of the same order of magnitude as the influence of the finite length of the pipe.

DEP

Dielectric Profiling equipment

HP-LCR

power supply

Hi-E

counter electrode

Lo-E

measuring electrode

Guard-E

guard electrode

D _B

electrical Shielding for logging

D _K

electrical Shielding for core measurement

l

Length of measuring electrode

L

Length of Guard electrode

V

potential

a

Half shell radius

n

number of the radial layers

m

Summation Index

i

certain radial layer, measuring location

C

effective measuring capacitance

C ₀ ^∞

Empty capacity for one infinitely long cylinder

C ₀ ^L

Empty capacity for one Cylinder of length L

R

position vector

ε

effective permittivity

ε _i

relative permittivity layer i

x, y, z

Cartesian Koordiatensystem

ρ, φ, z

Cylindrical coordinate system

ρ, φ

Polar coordinate system

ξ, Φ ₀ , ψ

angle dimensions

Claims (8)

Computer-aided measurement method for determining the dielectric properties of soil layer structures in the at least axial region of a borehole, characterized in that the capacitance (C) in the interior or exterior of an insulation gap with n radial layers and with capacitor electrodes (E) are present between their boundary surfaces , built-up cylindrical capacitor (DEP) at a measuring point (M) in the radial layer n is measured capacitively with high precision at a measuring frequency in the alternating electromagnetic field, the length (L) of the cylindrical capacitor (DEP) being so great as determined by the angle Ψ Isolation gaps between the capacitor electrodes (E) are so small and the measurement frequency is dimensioned so low that their influence on the measurement is error-tolerable within the scope of the desired measurement accuracy, and that by forming the quotient of the measured capacitance (C) with that by air measurement, calibration measurement or Calculation known Lee rcapacity (C ₀ ^∞ ) of the cylindrical con an effective dielectric constant (ε ^* ) is calculated as a characteristic parameter for the real soil layer structure, from which the mathematical inversion with knowledge of the layer radii (ρ _i , ..., ρ _n ) and the relative dielectric constant (ε _i , ..., ε _n-1 ) of the cylindrical capacitor (DEP) concentrically to the measuring point (M) in the radial layer n space-filling layers 1 ... n-1 the relevant dielectric constant (ε _in ) in the radial layer n is calculated at the measurement location (M). Computer-aided measuring method according to claim 1, characterized in that for the calculation of the effective dielectric constant (ε ^* ) from the relative dielectric constant (ε ₁ , ..., ε _n ) and the layer radii (ρ ₁ , ..., ρ _n ) the following general Power series development - or a mathematically equivalent power series with analytically evaluated partial sums - is used

where the coefficients with i = (n-1), ..., 1 and m ϵ N ₀ according to the recursion formulas

Computer-aided measurement method according to claim 1 or 2, characterized in that the mathematical inversion takes place by solving the equation from the determined effective dielectric constant (ε ^* ) and its power series development according to the relevant dielectric constant (ε _n ) in the radial layer n at the measurement location (M) , Computer-aided measurement method according to at least one of claims 1 to 3, characterized in that a calibration of the measurement method by forming limit values of the algorithms ((1) ... (5)) assuming an infinitely high relevant dielectric constant (ε _n → ∞) for the respective last radial layer n is carried out at the measuring location (M) of the cylindrical capacitor (DEP). Device for carrying out the computer-aided measuring method for determining the dielectric properties of soil layer structures in the region of a borehole according to at least one of claims 1 to 4 with a dielectric profile apparatus with an electrically shielded and protected cylindrical DEP capacitor (DEP) made of a cylindrical measuring electrode (Lo-E ), Protective elec trode (Guard-E) and counter electrode (Hi-E) as measuring capacitance, characterized in that the length (l) and the width of the measuring electrode (Lo-E) determined by an angle Φ ₀ in relation to insulating gaps determined by an angle Y. between the measuring or protective electrode (Lo-E, Guard-E) and counter electrode (Hi-E) and the length (L) of the protective electrode (Guard-E) are selected so that the potential variation in the direction of the cylinder axis over the range of Measuring electrode (Lo-E) is within the scope of the desired measurement accuracy. Apparatus according to claim 5, characterized in that the Length (l) the measuring electrode (Lo-E) is in the range of 10 mm and that at use of the apparatus (DEP) as a core detector, the length (L) of Protective electrode (Guard-E) in the range of 300 mm or when used the apparatus (DEP) as a borehole probe in the range from six to Ten times that lies Device according to claim 5 or 6, characterized in that that the insulating gap determined by the angle Ψ between measuring or protective electrode (Lo-E, Guard-E) and counter electrode (Hi-E) are minimized. Device according to at least one of claims 5 to 7, characterized in that that use the cylindrical capacitor (DEP) as Eich capacity a metal tube as the last radial layer from the electrode surface seen inserted into it or pushed over it.