Florian K Lehner
University of Salzburg, Geography and Geology, Department Member
Research Interests:
A gas blowout may be brougbt under control by injecting water into the formation through relief wells. By avoiding direct contact between relief well and blowout well, this technique reduces the inflow of gas by creating sufficient... more
A gas blowout may be brougbt under control by
injecting water into the formation through relief
wells. By avoiding direct contact between relief
well and blowout well, this technique reduces the
inflow of gas by creating sufficient backpressure
in tbe /ormation itself. [t guarantees a /easible,
successful reliej-well injection rate, no matter bow
large tbe li{ting capacity of the blowout well may
be. A constraint condition on relie[-we[l injection
pressures is found that ensures killing o~ the
blowout. The minimum number of relief wells then
follows from injection-pressure limitations. The
positions of the relief wells are kept arbitrary in
the analysis, but the results indicate that their
lanalng points should be close to tbe blowout well
and that direct communication with the latter (e. g.,
by formation fracturing) should be avoided. Tbe
analysis yields no information as to .shuto/f times
or cumulative injection requirements. These must
be found from a separate study, wbicb could be
guided by the results presented in this paper.
injecting water into the formation through relief
wells. By avoiding direct contact between relief
well and blowout well, this technique reduces the
inflow of gas by creating sufficient backpressure
in tbe /ormation itself. [t guarantees a /easible,
successful reliej-well injection rate, no matter bow
large tbe li{ting capacity of the blowout well may
be. A constraint condition on relie[-we[l injection
pressures is found that ensures killing o~ the
blowout. The minimum number of relief wells then
follows from injection-pressure limitations. The
positions of the relief wells are kept arbitrary in
the analysis, but the results indicate that their
lanalng points should be close to tbe blowout well
and that direct communication with the latter (e. g.,
by formation fracturing) should be avoided. Tbe
analysis yields no information as to .shuto/f times
or cumulative injection requirements. These must
be found from a separate study, wbicb could be
guided by the results presented in this paper.
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An analysis is made of viscoelastic lithosphere/asthenosphere coupling in the time-dependent redistribution of stress along plate boundaries or other seismic lineaments following great earthquakes. The study is based on a generalization... more
An analysis is made of viscoelastic lithosphere/asthenosphere coupling in the time-dependent redistribution of stress along plate boundaries or other seismic lineaments following great earthquakes. The study is based on a generalization by Rice of Elsasser's model of stress-diffusion, in which general elastic plane stress deformations are allowed in lithospheric plates which are coupled in an elementary way to a (Maxwellian) viscoelastic asthenosphere. Solutions are developed which describe the large-scale quasistatic distribution of thickness-averaged stresses in the lithosphere at or near stationary or travelling rupture zones, modeled here by either crack-like zones of fixed stress drop or dislocation-type slip zones. Sudden ruptures shed load onto the asthenosphere which is gradually transferred back to the lithosphere by a slow relaxation process. The spatial and temporal characteristics of the predicted stress alterations suggest a significant role of lithosphere/asthenosphere coupling effects in triggering interactions of great earthquakes, patterns of prolonged aftershock activity, and the breaking of barriers or gaps by time-dependent stressing.
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The large-scale response of an elastic lithosphere, riding on a ‘thin’ viscoelastic asthenosphere, to periodically occurring ruptures at a transform or subduction-type plate boundary is described approximately by appropriate limit cycle... more
The large-scale response of an elastic lithosphere, riding on a ‘thin’ viscoelastic asthenosphere, to periodically occurring ruptures at a transform or subduction-type plate boundary is described approximately by appropriate limit cycle solutions for a plate/foundation model introduced previously by Rice. The cyclic behaviour of thickness-averaged displacements, strains and strain rates, their decay away from the plate boundary, and a resolution into coseismic and post-seismic alterations are obtained and their dependence on repeat time and a characteristic relaxation time investigated. A comparison is made with existing periodic solutions for the surface deformations in a Nur-Mavko half-space model. This suggests important effects due to viscosity stratification on post-seismic rebound when earthquake repeat times exceed relevant relaxation times by at least one order of magnitude.
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It is shown that in diffusionless coherent first-order phase transformations in stressed solids an energy-momentum tensor appears in the role of a chemical potential. A thermodynamic equilibrium condition is derived in terms of this... more
It is shown that in diffusionless coherent first-order phase transformations in stressed solids an energy-momentum tensor appears in the role of a chemical potential. A thermodynamic equilibrium condition is derived in terms of this tensor from balance relations and a dissipation inequality, and its use in formulating linear phenomenological relations for irreversible phase transformations in nonhydrostatic systems is pointed out.
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The note shows the connection between Dahlen's analysis and so-called Rankine states of plastic equilibrium in a sloping half-space. This leads to an alternative, graphical as well as analytical solution of the critical wedge problem,... more
The note shows the connection between Dahlen's analysis and so-called Rankine states of plastic equilibrium in a sloping half-space. This leads to an alternative, graphical as well as analytical solution of the critical wedge problem, which allows one to gain a rapid understanding of the exact geometry and mechanics of the eight possible wedges, corresponding to four "passive" (compressional) and four "active" (extensional) limit equilibrium states.
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A method of constructing plane potential flows past doubly periodic arrays of cylindrical obstacles is described. It is based on Rankine’s well-known technique of determining by simple superposition the shape of an oval-shaped obstacle... more
A method of constructing plane potential flows past doubly periodic arrays of cylindrical obstacles is described. It is based on Rankine’s well-known technique of determining by simple superposition the shape of an oval-shaped obstacle simultaneously with the flow round the obstacle. This paper deals with the use of such potentials in calculating effective medium conductivities for a class of doubly periodic two-phase materials which contain either non-conducting or perfectly conducting cylindrical inclusions embedded within a conducting matrix phase.
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The onset of interfacial instability in two coherent semi-infinite layers of different properties and the corresponding critical wavelength are found by solving a static bifurcation problem in finite plane strain. Subsequently, the... more
The onset of interfacial instability in two coherent semi-infinite layers of different properties and the corresponding critical wavelength are found by solving a static bifurcation problem in finite plane strain. Subsequently, the stability of perturbations of any wavelength is determined from the appropriate linearized equations of motion. For gravitationally stable or unstable density stratifications, the critical stress at which the interface is destabilized is shown to depend on the wavelength of a perturbation; it is also determined in a complex manner by initial stress gradients perpendicular to the layer interface and by layer stiffness, as is illustrated here in detail for the examples of a hyperelastic solid and an elastoplastic solid, both resting on an inviscid fluid of different density. The very large wavelength that is predicted for the gravitational instability of a semi-infinite elastic solid on a buoyant fluid substratum brings forward the essential role of pre-stress and associated stiffness reduction as well as that of a finite layer thickness in destabilizing geological and geophysical two-layer systems.
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Lubricating squeeze flow of a ductile substratum under varying overburden is a characteristic element of the tectonics of salt basins and many deltas. Large-scale mass movements of salt or overpressured shales can occur in this manner,... more
Lubricating squeeze flow of a ductile substratum under varying overburden is a characteristic element of the tectonics of salt basins and many deltas. Large-scale mass movements of salt or overpressured shales can occur in this manner, accompanied by deformation of a sedi-mentary overburden. The theory outlined in this paper deals with large-scale extrusive flow in mobile substrata that is driven by differential loads and buoyancy forces. The theory assumes slowly varying overburden and substratum thicknesses. It treats the salt (or shale) substratum as a viscous 'lubricating layer' and the overburden as a dead load that offers no significant resistance to shear along vertical planes, but will support horizontal stresses within the limits of 'active' and 'passive' Coulomb plastic states. For a prescribed sea floor (sedimentation boundary) and basement topography, the theory yields a single differential equation in the layer thickness h of the salt (or shale) layer. When buoyancy effects are negligible, squeeze flow in a substratum of varying thickness will propagate substratum isopachs as 'kinematic waves' with a speed proportional to (tan α) n h n+1 , where tan α is the overburden slope and n the power law exponent governing the creep response of the substratum. Buoyancy introduces nonlinear unstable ('backward') diffusion effects leading to localized flow reversal and suggesting a mechanism for the generation of 'pinch-and-swell' structures that may subsequently evolve into salt domes. Buoyancy also enters as the principal driving force for the large-scale updip extrusion of salt in areas affected by differential subsidence. The theory sheds light on a frequently observed form of gravity-induced slope failure, which is characterized by the simultaneous occurrence of extensional and compressive faulting in distinct sections of the slope.
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The problem of predicting the land subsidence caused by the depletion of underground hydrocarbon reservoirs is of considerable concern to the petroleum industry in many parts of the world and has been dealt with in numerous studies over... more
The problem of predicting the land subsidence caused by the depletion of underground hydrocarbon reservoirs is of considerable concern to the petroleum industry in many parts of the world and has been dealt with in numerous studies over the last 40 years. When treated as a poroelastic inclusion problem, an integral representation, known as Maysel’s formula from formally analogous thermoelastic problems can provide an attractive method of solution. Maysel’s method suggests an economic approach to solving general, nonhomogeneous problems of compaction-induced stressing and surface subsidence numerically. We illustrate its use for a disk-shaped reservoir in a horizontally stratified half-space.