Geologic formations forming a reservoir for the accumulation of hydrocarbons in the subsurface of the earth contain a network of interconnected paths in which fluids are disposed that may ingress or egress from the reservoir. To determine the behavior of the fluids in the aforementioned network, knowledge of both the porosity and permeability of the geologic formations is desired. From this information, efficient development and management of hydrocarbon reservoirs may be achieved. For example, the resistivity of geologic formations is a function of both porosity and permeability. Considering that hydrocarbons are electrically insulative and most formation water contains salts, resistivity measurements are a valuable tool to determine the presence of hydrocarbon reservoirs in geologic formations and to monitor the changes in hydrocarbon content as production of the hydrocarbon proceeds.
To that end, there have been many prior art attempts to determine the electrical resistivity of geologic formations surrounding and between drill holes. In two articles, Crosshole electromagnetic tomography: A new technology for oil field characterization, The Leading Edge, March 1995, by Wilt et al. and Crosshole electromagnetic tomography: System design considerations and field results, Society of Exploration Geophysics, Vol. 60, No. 3, 1995 by Wilt et al., measurement of geologic formation resistivity is described employing a low frequency electromagnetic (em) system.
FIG. 1 shows the configuration of equipment used in the measurement of geologic formation resistivity between two drill holes. A transmitter, T, is located in one borehole and consists of a coil C.sub.T having multi-turn horizontal loop (vertical solenoid) of N.sub.T turns, having an effective cross section A.sub.T. The multi-turn horizontal loop carries an alternating current, I.sub.T, at a frequency of f.sub.0 Hz. In free space this multi-turn horizontal loop produces a time varying magnetic field, B.sub.0. The magnetic field, B.sub.0, is proportional to the magnetic moment of the transmitter, M.sub.T, and to a geometric factor, k.sub.1. The magnetic moment of the transmitter M.sub.T is defined as follows:
M.sub.T =N.sub.T I.sub.T A.sub.T (1)
The geometric factor, K.sub.1, is a function of a spatial location and orientation of a field component of the magnetic field, B.sub.0, measured by a receiver, R, with respect to the magnetic moment of the transmitter, M.sub.T. The receiver is located spaced-apart from the transmitter, T, and typically disposed in a borehole in the earth. In free space, therefore, the magnetic field, B.sub.0, is defined as follows: EQU B.sub.0 =k.sub.1 M.sub.T. (2)
The receiver, R, typically includes a multi-turn loop of wire, i.e., a coil, C.sub.R, having N.sub.R turns of wire, wound about a core of high permeability metal or ferrite. The changing magnetic field B.sub.R sensed by the receiver, R, with frequency f.sub.0, creates an induced voltage V.sub.R in the coil which is proportional to, B.sub.R; ; the frequency, f.sub.0 ; the number of turns of wire, N.sub.R ; the effective cross-sectional area of the coil, A.sub.R ; and the effective permeability, .mu..sub.R, of the coil C.sub.R. From the foregoing, it is shown that V.sub.R is defined as follows: EQU V.sub.R =f.sub.0 B.sub.R N.sub.R A.mu..sub.R (3)
Simplifying equation (3) above, V.sub.R may be written as follows: EQU V.sub.R =k.sub.R B.sub.R (4)
where k.sub.R =f.sub.0 N.sub.R A.sub.R.mu..sub.R. The product of A.sub.R.mu..sub.R is difficult to calculate. To accurately determine A.sub.R.mu..sub.R, CR is calibrated in a known field, at a known frequency to find an exact value for k.sub.R. Thereafter, the magnetic field, B.sub.R, sensed by the receiver, R, is related directly to the measured voltage V.sub.R by the following: EQU B.sub.R =V.sub.R /k.sub.R (5)
When this system is placed in a conducting geologic formation the time varying magnetic field, B.sub.0, produces an electromotive force in the geologic formation, which in turn drives currents therein, shown schematically as L.sub.1. The currents, L.sub.1, are proportional to the conductivity of the geologic formation and are concentric about the longitudinal axis of the borehole. The magnetic field proximate to the borehole is a result of the free space field, B.sub.0, called the primary magnetic field, and the field from the current L.sub.1, called the secondary magnetic field.
The current L.sub.1 is typically out of phase with respect to the transmitter current I.sub.T. At very low frequencies, where the inductive reactance of the surrounding formation is small, the induced current L.sub.1, is proportional to dB/dt and is consequently 90.degree. out of phase with respect to I.sub.T. As the frequency increases, the inductive reactance increases and the phase increases to be greater than 90.degree..
The secondary magnetic field at the receiver, R, is caused by the induced current and consequently also has a phase shift and so the total field is complex. The total measured field has a component, B.sub.R, in-phase with the transmitter current I.sub.T, (called the real component) and a component, B.sub.I, phase shifted by 90.degree. (called the imaginary or quadrature component). The values of the real, B.sub.R, and quadrature components, B.sub.I, of the magnetic field at a given frequency and geometrical configuration uniquely specify the electrical resistivity of a homogenous formation pierced by the drill holes. In an inhomogeneous geologic formation, the complex field is measured at a succession of points along the longitudinal axis of the receiver borehole for each of a succession of transmitter locations. The multiplicity of T-R locations suffices to determine the inhomogeneous resistivity between the holes as described in the papers above.
In general, the inhomogeneous distribution of electrical resistivity is determined through a process called inversion which is well described by Audio-frequency electromagnetic tomography in 2-D, Geophysics, Vol. 58, No. 4, 1993 by Zhou et al., Electromagnetic conductivity imaging with an iterative born inversion, IEEE Transactions on Geoscience and Remote Sensing, Vol. 31, No. 4, 1993 by Alumbaugh et al., An approach to nonlinear inversion with applications to cross-well EM tomography, 63rd Annual International Meeting, Society of Exploration Geophysics, Expanded Abstracts, 1993 by Torres-Verdin et al., and Crosswell electromagnetic inversion using integral and differential equations, Geophysics, Vol. 60, No. 3, 1995 by Newman. This process has been well demonstrated for the determination of resistivity in the vicinity of a single well or between spaced apart wells and is described in detail by Crosswell electromagnetic tomography: System design considerations and field results, Geophysics, Vol. 60, No. 3, 1995 by Wilt et al., Theoretical and practical considerations for crosswell electromagnetic tomography assuming a cylindrical geometry, Geophysics, Vol. 60, No. 3, by Alumbaugh and Wilt, and 3D EM imaging from a single borehole: a numerical feasibility study, 1998 by Alumbaugh and Wilt.
In brief, one embodiment of the inversion process consists in assigning resistivities to a multitude of cells or elements of the volume surrounding or between wells and systematically varying these resistivities until, in a least squares sense, the results from the cellular model of the formation match the observed data taken with the field transmitter receiver system described herein. In another embodiment a more specific model of the formation is assumed using geological, well log or other geophysical data and the parameters of this model (e.g. resistivity distribution, shape, layer thickness, etc.) are varied until, again in a least squares sense, the numerical results from the model match the field results. In another embodiment direct images of the distribution of resistivity may be obtained following the principles of diffusion tomography as described by Audio-frequency electromagnetic tomography in 2-D, Geophysics, Vol. 58, No. 4, 1993 by Zhou et al. In yet another method multifrequency em data is transformed to a mathematically defined wave field domain and the data are processed following the procedures of seismic tomography. These means of interpreting the em data are included here to illustrate the fact that em methods are of practical use in determining the resistivity of geological formations.
The measurements are typically made before extraction of hydrocarbons takes place and during the extraction process. To that end, the system of FIG. 1 is principally directed to detecting hydrocarbon reservoirs and to monitoring the changes in reservoir resistivity as hydrocarbon is withdrawn. The boreholes are typically cased with conductive liners (also called casings) in order to preserve the physical integrity of the borehole during subsequent hydrocarbon extraction. A problem exists, however, in that the conductive liners are electrically conductive and are themselves inhomogeneous and strongly attenuate the ac magnetic field introduced into the formation. They cannot be removed from the borehole once installed. As a result, the system shown above in FIG. 1 does not facilitate analysis of a hydrocarbon reservoir once conductive liners are installed and extraction of the hydrocarbons begins.
The problems presented by conductive liners are described by Augustin et al., in A Theoretical Study of Surface-To-Borehole Electromagnetic Logging in Cased Holes, Geophysics Vol. 54, No. 1 (1989); Uchida et al., in Effect of A Steel Casing on Crosshole EM Measurements, SEG Annual Meeting, Texas (1991); and Wu et al. in Influence of Steel Casing on Electromagnetic Sigals, Geophysics, Vol. 59, No. 3 (1994). From these papers, it is seen that the conductivity may be modeled as an additional shorted wire closely coupled to the transmitter T, shown schematically as L.sub.2 in FIG. 1.
The net or effective magnetic moment, M.sub.eff, of the transmitter, T, conductive liner combination is dictated by the inductive coupling therebetween. Physically, the resistivity of the conductive liner is very low and the inductance relatively high. This results in a current being induced in the conductive liner that is approximately 180.degree. out of phase of the transmitter current I.sub.T, i.e., the induced current is of opposite polarity to the transmitter current, I.sub.T, but almost of the same moment. In this manner, the magnetic field external to the conductive liner is greatly reduced. In effect, the conductive liner "shields" the transmitter, T, from the receiver, R, positioned outside of the conductive liner. The external field is produced by the difference in current, and hence moment, in the transmitter and conductive liner.
Since the induced moment in the liner is large, and nearly equal to the transmitter moment, small changes in the properties of the liner produce large fractional changes in the net of effective moment. In practice, liners are known to be inhomogeneous; there are variations in liner radius, thickness, permeability, and conductivity caused either by manufacturing/processing procedures or by corrosion/stress/temperature processes after installation. The central problems for the em methods described above for non cased, or open, well surveys is that the fields from the transmitter are severely attenuated in a cased well and that the net moment is highly variable as the transmitter traverses the length of the well. Without knowing the casing properties very precisely, it is difficult to distinguish between external field variations caused by the liner and the formation.
An analogous situation affects a magnetic field sensor within a cased borehole. The field to be detected induces currents concentric with the receiver coil whose sense is such as to reduce the field within the liner. The field to be detected is consequently highly attenuated and the measurement is highly influenced by the variations in attenuation caused by the variation in liner properties.
Various prior art has been developed to compensate for these liner effects. The fundamental problem is that the corrections, etc. have to be so accurate that a practical measurement system has yet been developed.
What is needed, therefore, is a measurement technique that provides accurate information concerning a geologic formation under analysis independent of the characteristics of a liner present.