M.I. Epov

Evolution of geomechanical and electro-hydrodynamic fields in deep well drilling in rocks

The authors have developed and numerically implemented 3D model of evolution of geomechanical and hydrodynamic fields during deep well drilling. The modeling exercises showed low-permeable zones of irreversible deformations that appear under definitely interrelated rock strength properties, drilling mud pressure and in situ horizontal stresses in the borehole environment. These low-permeable irreversible-deformation zones give rise to angular anisotropy of distribution of water content and drilling mud resistivity in the invaded zone, which greatly affects geophysical logging data and must be taken into account in the logging data inversion.

Interaction of seismic waves with zones of concentration of initial stresses

402 The three dimensional nonuniform structure of the Earth and the continuous tectonic and geody namic processes generate zones of anomalous (both increased and decreased) concentrations of stresses, which can influence the propagation of seismic waves. Many publications starting from the basic papers [1–3] have been dedicated to investigation of wave processes in prestressed media, and interest in this field of study has not decreased. Recently, primary attention has been focused on research into localization of the con centration regions of preliminary stresses and recon struction of the distribution of their values (see, for example, [4, 5]). In this paper, we present a mathematical model and a complex of algorithms and programming codes developed on its basis, which is intended to investigate the manifestations of the prestressed state in the seis mic wave fields on the scales characteristic of the solu tions of some practical problems of the internal struc ture of the Earth. With this in mind, we formulated the determining equations of the propagation of small amplitude waves in elastic media with initial stresses. They became the basis of a complex of algorithms and programming codes oriented to application of modern high accuracy numerical methods and use of compu tational systems with parallel architecture. These equations belong to the hyperbolic system of differen tial equations of the first order, in which the velocity vector, stress tensor, and the rotation vector of the medium element are unknown functions. We solved numerically the problems that clearly demonstrate a significant influence of the initial stresses on the char acter of wave propagation.

Logging interpretation taking into account hydrodynamical and geomechanical processes in an invaded zone

The problem of interpretation of geophysical data taking into account hydrodynamical and geo-mechanical processes in oil-drilling wells is considered. The effects emerging due to change of porosity and permeability are studied, and the influence of such effects on the geophysical measurements in a borehole is analyzed on the basis of characteristic parameters of the Kogalym oilfield reservoirs.

Acoustic method for defining the stress state of a rock massif based on solution of the seismic inverse problem

A method for estimating the stress–strain state of a rock massif in the vicinity of underground facilities is substantiated. This method is based on solution of the boundary inverse problem of defining the components of an external stress field from the acoustic sounding data. The acoustic sounding data used are the arrival times of diving head longitudinal waves, recorded in a long mine shaft. Numerical experiments have revealed the optimal arrangement of the recording network and the limited relative error in the input data, which, taken together, provide for solvability of the inverse problem.

Numerical homogenization of electric characteristics of media with contrast small-scale inclusions

In geoelectric science, including ground electric survey, marine electric survey, and drillhole studies to interpret data, a generalized characteristic called the average electric resistivity is used. The average resistivity is the volume average value of a heterogeneous medium, i.e., the ground, and electric resistivity is an inner feature of the micro scopic structure of a material. Consequently, the arith metical average which does not take into account the inner microstructure of the arbittrary object can lead to erroneous identification of electric properties (resistivity) according to the data of electric survey, as the resistivity of an object composed of different scales and contrasting inclusions in physical properties can considerably differ from the resistivity of its compo nents. Comparative analyses of the results of mathe matical simulation and laboratory tests on samples of multiscale and contrasting structure allowed us to determine the homogenization procedure for electric resistivity of this object. At present to study the physical properties of heter ogeneous mediums, multiscale methods and hetero geneous multiple scale finite element methods are used [1–4]. A material composed of solid media and multiple scale inclusions with various geometries and contrasting electrical properties is considered as a het erogeneous medium. Laboratory and in situ tests showed that a heterogeneous medium in volumes larger than the volume of one inclusion has stable physical characteristics, e.g., thermal conductivity and electric conductivity (value inverse to electric resistivity), which are in general different from the characteristics of individual components. These char acteristics of media [2, 3, 5] are called effective, and to determine them the theory of homogenization is used. It is based on special asymptotical methods of averag ing differential operators for periodical and almost periodical solutions [1, 6, 7] and multiscale methods [3–5, 8, 9] decomposing the solution space into the sum of two subspaces including “coarse” ones that describe the effective properties of the medium and “fine” ones that allow one to take into consideration the properties of inclusions with sufficient precision.

Streaming potential in a deformed porous medium and geophysical applications

189 The method of the streaming potential (SP) was applied as one of the first methods for determining the structure of fluid saturated terrigenous collectors, dis tinguishing the clay and sand sublayers and also for estimating their porosity during logging. It was also used for determining the location of water–oil contact [1]. It follows from the theory of electric osmosis that an external electric field is caused by the excess of the formation pressure over the pressure in the borehole. The mud filtrate flows in the borehole induce currents of ion conductivity; the vector of the induced electric field is directed normal to the borehole axis and the electric potential at its wall depends strongly on the location of the water–oil contact.

Evolution of streaming potential near the borehole during drilling

The theoretical approach to the description of dynamics of an electric field near the borehole result� ing from penetration of drilling mud filtrate into the collector under the influence of excessive pressure during drilling is developed. Water based drilling mud containing a solid clay fraction, the most abundant in drilling procedures, is considered. The evolution of hydrophysical properties and electric conductivity of the nearborehole zone during borehole drilling is well studied for vertical (1, 2) and less for horizontal (3) boreholes. Realistic mathematical models have been developed, and the evolution of streaming potential in connection with filtration of drilling mud in per� meable rocks has been considered for the widely applied method of the streaming potential. The streaming potential appears as a result of electroki� netic effects in the nearborehole zone and changes in time with the depth of filtrate penetration and growth of the mudcake on the wall of the borehole. Calculations performed on the basis of the suggested mathematical model particularly demonstrate that, under definite drilling regimes, change in permeable zone depth by several tens of centimeters results in such variations of the potential on the wall of the borehole which may be registered by probes with a standard resolution (several mV). MATHEMATICAL MODEL The excess of pressure in the borehole over the for� mation pressure during drilling and other operations in the borehole results in penetration of fluid different from that in the rock that influences the evolution of electrophysical properties of the nearborehole zone. Information about the depth of the permeable zone is important for interpretation of the data of electromag� netic well logging, as well as for subsequent exploita� tion. The question about the possibility of estimation of the depth of the permeable zone by measurement of the streaming potential on the wall of the borehole may be reduced to study of the electric field near the borehole depending on the position of the penetration front at which parameters such as electric conductiv� ity, hydraulic permeability, and others have jumps.

Streaming potential near a hydrofracture

We suggest a mathematical model for the dynamics of the streaming potential near a hydrofracture of a seam after termination of water pumping into the fracture.

Focusing and Spatial Resolution of Electromagnetic Three-Coil Sounders

Distribution density functions for the sensitivity of a three-coil sounder are constructed as the weighted mean rock volume between the in-phase surfaces of running electromagnetic waves, which propagate from the emitting coil to the close measuring coils. The wave propagation velocity vector can be decomposed into two components; therefore, the focusing (the point of maximum sensitivity) and the resolution (the domain of sensitivity) of the three-coil sounder in the radial and vertical directions are different. The comparison of the apparent resistance obtained using the method of probabilistic convolution and the method of convolution with the radial volume distribution density between the in-phase surfaces of the emitting dipole is performed for the example of penetration into the oil stratum.