|
Discussion |
Penparc, Cwmystwyth SY23 4AG, UK (e-mail: davidmd.james@ virgin.net) BP Exploration, Chertsey Road, Sunbury-on-Thames, Middlesex, TW16 7LN, UK (e-mail: jollr1@bp.com) Department of Earth Science & Engineering South Kensington Campus, Imperial College London, London SW7 2AZ, UK (e-mail: l.lonergan@ic.ac.uk)
D. M. D. James writes: I congratulate the authors on a very clear and comprehensive account of a widespread and complex phenomenon of increasing economic importance. However, presumably for didactic ease, they have made some simplifications that I feel are counterproductive for full physical understanding.
It is not entirely clear from the paper that sand intrusions require a concatenation of source/seal properties that on the face of it are very rare. These are that the source sand bed must have a negligible grain cohesion typical of burial at very low vertical effective stress (not shallow depth, necessarily) and that the seal must have effectively negligible permeability, typical of burial at very high vertical effective stress (and often associated with high cohesion). In most basins sands that can be fluidized are interbedded with ‘leaky‘ shales of high permeability (for shales) that do not sustain high overpressure during normal compaction. However, such high overpressure is vital because the intrusion is powered by a pressure decline at source that provides the mechanical energy to strain elastically the intrusion walls and to drive the ascent of the fluidized sand against frictional resistance. This cannot happen if fracture takes place when fluid pressure reaches a value merely equal to that of the horizontal stress (as illustrated by the authors in their figs 6 and 8) as this lies on the closure gradient of any fracture, not its inception gradient. How then can the requisite overpressure for fracture initiation and propagation be attained at the shallow depths normally associated with low vertical effective stress?
Of the obvious ways around this problem, the development of zero permeability diagenetic or clathrate seals seems unlikely to be a universal solution. More likely, and not mentioned in the paper, is that the source pressure builds up at such a high rate that the transient response of a seal with appreciable permeability appears to display negligible permeability on a pressure–depth plot. This high rate build-up will induce rapid deformation around the margins of the source body. As is well known, a normally ductile material will fail in brittle mode at high enough strain rate and the transient pressure could rise well above that required for fracture if source build-up rate exceeded its discharge rate. It could thus be adequate to power the intrusion even if the tensile strength of the seal was very low. (Clearly if this strength is negligible and pressure build up is very slow—such that it cannot rise further after fracture initiation—then fracture propagation, due to a pressure constrained to be only marginally higher than that appropriate to the fracture gradient, will cease on only minor pressure decline.) If correct, this requirement for a high strain-rate process of overpressure development strongly favours ‘catastrophic‘ control such as seismic shaking, instantaneous slump loading and slide excision, rather than compressional tectonic stress or progressive loading during basin subsidence. Rapid pressure rise in the source, due to the sudden establishment of a high permeability connection (e.g. via faults) with a deeper fluid source at higher pressure, is a common scenario and I concur with the authors that its importance in sand intrusion has been under-appreciated.
It is unfortunate that in their discussion of source-to-sill height (pp. 612–613) the authors neglect their earlier, and correct, formulation of the mechanical principles (p. 610). I hence consider that my Figure 1a more accurately represents the intrusion of a dyke/sill complex than do figures 6 and 8 of their paper. Upon adequate pressure build-up (a to b, or higher, not illustrated here), dyke propagation begins and continues concomitant with source pressure decline (b to c) until a sill is formed (d). With further pressure decline the sill will close (e), at which time the dyke must still be open. However, the volume of the sill and dyke will then grow no more (and will actually decrease a little due to partial elastic recovery in the walls); this will immediately induce back-pressure on the source and stop fluidisation, after which the injected slurry will become load bearing and its internal fluid pressure will decrease to lie on a hydrostatic gradient (e–f). The rate at which this happens seems worthy of research; clearly if slow then further intrusion governed by the density inversion associated with the still liquified slurry would seem likely. A speculative possibility is that a liquified but not a fluidized state could be maintained for a short period by shock waves generated by the abrupt loss of kinetic energy (a ‘water hammer‘ effect) as the intrusion ceases to propagate.
|
Editorial suggestions from Alex Maltman have considerably clarified this discussion.
5 November 2002
Richard Jolly & Lidia Lonergan reply: We thank James for his comments on our treatment of the mechanics of sand intrusion (Jolly & Lonergan 2002) and for highlighting areas in our original work that warrant further research and study. We acknowledge, as suggested by James, that significantly more geological complexity could be built into the simple model that we presented. However the aim of our original paper was to present a first-order quantitative formulation of how the geometry of a dyke–sill injection complex might be calculated as a function of the differential stresses operating during sand slurry intrusion. Because of the complexity of the natural phenomenon of sand injection within a consolidating layered sedimentary succession many of the parameters required for a fuller treatment of the problem are poorly understood. Thus we chose to formulate the problem as a first-order approximation.
For example, as James quite correctly points out, we did not include the vertical and horizontal and tensile strengths of the sediments in figures 6 and 8 and in the formulation of equations 9 and 10. We did this for a number of reasons. Firstly there is a paucity of reliable datasets that specify the magnitudes of the vertical and horizontal tensile strengths in unconsolidated sediments, making it very difficult to quantify this parameter. However indirect data such as borehole break out measurements and leak off tests in well bores (e.g. Gaarenstroom et al. 1993; Hillis 2001) show that lithified sedimentary rocks fail at values of around 0.8–0.9 times lithostatic stress, implying that these rocks have low tensile strengths relative to the magnitude of the lithostatic stress. It seems a reasonable first assumption to infer that at shallow burial depths the tensile strength of the unlithified sediments would be likewise low and significantly smaller than the vertical and horizontal stresses. Thus, to examine the first-order relationship between depth and scale of intrusion we felt it was an acceptable simplification to neglect the small tensile strengths of the sediment.
James also questions the validity of assuming that during upward injection in a sub-vertical dyke the sand slurry will follow a hydrostatic pressure gradient. The two factors that cause the intrusion gradient to deviate away from the hydrostatic gradient are a pressure decrease due to a volume change, and the dynamic pressure gradient of a flowing slurry. There is, however, very little documentation on the initial volumes of intrusion complex source beds and even less on the volumes of the intrusion complexes from which it might be possible to calculate a corresponding pressure drop. Also, little is known about the nature of intruding slurries, including values for the densities, viscosities and rates of flow—parameters required in any determination of the dynamic gradient. As such, the pressure decrease and dynamic gradient remain very significant uncertainties in our current understanding of intrusion processes. In light of these uncertainties the assumption of a hydrostatic pressure gradient does at least allow an end member case to be constrained, where the intrusion complex is volumetrically small compared to the source bed. In cases where there is a significant pressure drop and with a significantly higher dynamic pressure gradient the vertical dimensions of the intrusion complexes will indeed be greater than those calculated from the model presented in Jolly & Lonergan (2002). However this only addresses part of the possible complexity that could be added to our original simplified model. A poro-elastic model which includes a coupling of fluid pressure and local stress would also affect the scale of the intrusion complex. In this case then equation 9 would yield a maximum vertical estimate of vertical dimensions of the intrusion complex (as stated in the original paper), due to the decrease in effective differential stress with a corresponding increase in fluid pressure.
Of course we must strive to make such models more realistic, but this does not detract from the fact that useful insights can be obtained from a simple model, providing that the limitations and assumptions of the model are clearly understood.
12 January 2003
 |
References |
|---|
 TOP References |
|---|
Gaarenstroom, L., Tromp, R.A., de Jong, M.C. & Brandenburg, A.M. 1993. Overpressures in the Central North Sea: implications for trap integrity and drilling safety. In: Parker, J.R. (ed.) Petroleum Geology of Northwest Europe. Proceedings of the 4th Conference. The Geological Society, London, 1305–1313.
Hillis, R.R., 2001. Coupled changes in pore pressure and stress in oil fields and sedimentary basins. Petroleum Geoscience, 7, 419–425.[ISI][GeoRef]
Jolly, R.J.H. & Lonergan, L. 2002. Mechanisms and controls on the formation of sand intrusions. Journal of the Geological Society, London, 159, 605–617.
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
