When a reservoir – any reservoir – is put under production, fluid compositions change; oil may be partially replaced by water or gas, gas may be expelled from oil, and so on. What is also significant is the fact that fluid pressures drop, changing the ‘internal stresses’ on the reservoir rock. Tempting as it may be, however, it is not possible to understand the (time-varying) geophysics of reservoir rocks by theorizing an isotropic pore space responding to fluid changes and changing ‘internal stress’. So we need to step back, look at some simple models, and understand what we know about how reservoirs actually perform.
We can start with a relatively simple idea. Porosity and permeability in a granular rock can be understood simplistically using a ‘billiard ball’ model of grains and porosity: beginning with a hexagonal crack distribution, increasing differential horizontal (external) stress progressively results in aligned crack/fracture sets. Once established, these aligned micro-cracks are sensitive to changes in internal stress caused by production.
What evidence is there that such preferred orientation of micro-cracks exists in nature, in particular in reservoir rocks? In fact, there is significant evidence, from observations of producing reservoirs, from shallow (ground water) reservoirs, and from seismic observations.
Observations of Producing Fields
Aligned cracks/fractures occur as differential horizontal stress increases. Source: After CrampinSeveral studies have shown that the hydraulic conductivities of faults and fractures in reservoirs can be influenced by geomechanical perturbations due to production operations and it is reasonable to anticipate that such dynamic permeabilities will be manifest as changes in flow-rates at production and injection wells. Heffer and co-workers (Edinburgh University) have shown that statistical correlations in flow-rate fluctuations between wells from fields in the North Sea appear to bear out this expectation. They are characterized by high correlations over very large separation distances between wells, and appear to be stress- and fault-related.
Note that typically, for a field with many injectors and producers, only a subset of wells are required in order to ‘explain’ the production at a subject well as required by the principle of parsimony; and that many of the correlated wells are at large distances from the subject well – not just nearest neighbors apparently influencing it.
Heffer has proposed that the most likely geomechanical mechanism to explain such orientational characteristics of correlations relative to stress state is dilatation or compaction of aligned compliant fractures in en echelon patterns and at critical densities, also previously proposed by others as active in the nucleation of shear failure.
Those characteristics are not consistent with the assumptions of most reservoir simulators; they are, however, characteristics to be expected in a system of coupled fluid flow and geomechanics near a critical point. Rather than just pure Darcy hydraulic flow between wells, there is probably a complex mixture of diffusive and wave propagation in a coupled system with long-range spatial and temporal correlations which incorporate the heterogeneities of pre-existing faults and fractures as well as being influenced by the modern day stress state.
This mechanism is also consistent with an independent empirical feature of production data: the observed frequencies of directionalities in flooding schemes. Beginning with evidence from fields under secondary recovery, it has been known for some time that the directions that injected fluids prefer to take through a reservoir from an injector well to breakthrough at a producing well tend to align on average with the local orientation of the maximum horizontal stress axis. For 37 field cases, taken from reservoirs which would not be conventionally considered as naturally fractured, the orientational distribution of the preferred directions shows this pattern. The interpretation is that the stress perturbations due to the flooding operations, those from fluid pressure changes and from temperature contrasts of the injected fluid from the in situ reservoir temperature, change the conductivities of the faults or smaller scale structure, with greater conductivity being induced on those fractures at small angles to the max horizontal stress. Numerical modeling of the geomechanics, coupled with fluid flow simulation with this concept as a guide, results in a very similar pattern in the rock deformation around a single injector. In summary, the orientation of well pattern relative to permeability axes can change recovery factors by 10’s of percentage points (Caudle et al., 1960).
These behaviors – directionalities in flooding schemes and coupled fluid flow and geomechanics near a critical point – are commercially profound, capable of major impact on recovery factors, but ones that conventional reservoir simulators are not able to handle.
Observations of Shallow Reservoirs
A model of a flood progressing through dilatant rock of medium permeability (after Heffer). For more information please refer to Kes Heffer’s papers on http://www.reservoir-dynamics.co.uk/publications.Less well known to the oil and gas industry are studies of the effects of fractures and micro-pores on aquifers and possible directionally-varying contamination of ground water by salinity or pollutants. Cook (2003) provides a comprehensive review and Chen et al. (2011) provide a recent example.
Quite modest geophysical experiments reveal these effects. For example, Nunn et al. (1983) used the then recently developed modifications of conventional seismic refraction and electrical resistivity techniques to measure in situ P-wave velocity and electrical resistivity anisotropy of chalk at sites in north Lincolnshire (the chalk being overlain by a thin covering of drift). All sites showed significant anisotropy with the directions of the maximum observed velocity and resistivity being consistent with direct fracture observations made at quarries in the study area; significantly, high fracture densities were implied. This work followed on earlier studies by Bamford and Nunn (1979) where similar P-wave anisotropy results had been obtained on the Carboniferous Limestone of north-west England, rooted in techniques developed by Bamford (1977) that demonstrated Pn velocity anisotropy in the continental upper mantle.
A New Geophysics
These observations of both deep and shallow reservoirs lead to the conclusion that time-lapse geophysics – any observations of any producing reservoirs over time – must be based on the understanding of the physics of fluid-filled, parallel, compliant, fractures/micro-cracks, dilating or compacting as the reservoir is produced. This ‘new geophysics’, documented over many years by Crampin, is based especially on understanding and observing the effects of closely-spaced stress-aligned fluid-saturated micro-cracks on seismic shear-wave splitting (SWS) in the crust and upper mantle. Whereas P-waves are in both theory and observation only weakly sensitive to such crack systems, SWS is wholly determined by parallel micro-cracks and can be measured with first-order accuracy. Thus SWS is a second-order quantity (small changes in shear-wave velocities) that can be read with first-order accuracy – leading to tremendous resolution.
Thus P-wave reflectivity, the basis of all our conventional reflection seismic technology, whether 2D, 3D or 4D, is not sensitive to rock anisotropy. P-wave velocity anisotropy and, most significantly, shear-wave splitting, are proffering a methodology for the new geophysical characterization of real rocks.
The Case for Permanent Reservoir Monitoring
Seismic consequences of dilatancy: P-wave reflectivity is relatively insensitive to systems of aligned cracks/fractures; S-waves are much more sensitive – in particular shear-wave splitting (also known as shear-wave bi-refringence) can be used to fully describe anisotropic, dilatant, rock bodies (after Crampin).The notion that reservoirs, having experienced a maximum horizontal stress over geological time scales, will contain micro-cracks that are both aligned and at a critical density – thus responding rapidly to quite small pressure changes induced by injection and production – has significant implications for geophysical, especially seismic, monitoring of reservoir dynamics.
Firstly, we can say that conventional 4D seismics only discern changes in P-wave reflectivity and thus offer at best an incomplete view of reservoir dynamics – one that is unquantifiable, allowing only empirical or ‘phenomenological’ comparisons. This answers my opening question but necessitates a follow-up statement.
And so, secondly, a complete, predictive, quantifiable, view of reservoir dynamics requires 3C seismic acquisition, with probable reservoir volatility strengthening the case for frequent measurement, i.e. permanent installations.
Finally, changes in stress can be monitored by changes in SWS so that stress-accumulation before fractures in reservoirs (and earthquakes and volcanic eruptions) can stress-forecast the time, magnitude, and estimated location of impending fractures (and earthquakes and eruptions). This is of course relevant to the practise of ‘fraccing’ and associated seismic activity.
References:
Stuart Crampin’s website: http://www.geos.ed.ac.uk/homes/scrampin/opinion/
Bamford, D., 1977: Pn velocity anisotropy in a continental upper mantle, Geophys. J.R.astr.Soc, Volume 49, pp.29–48.
Bamford, D. & Nunn, K., 1979: In situ measurements of crack anisotropy in the Carboniferous Limestone of Northwest England, Geophysical Prospecting, Volume 27, Issue 2, pp.322–338.
Caudle, B.H. & Lonaric, I.G., 1960: Oil Recovery in Five-Spot Pilot Floods, Trans AIME, Volume 219, pp.132–136 (results reproduced in ‘The Reservoir Engineering Aspects of Waterflooding’ ed. F.F. Craig, SPE Monograph vol. 3 (1971) Figs 5.14 & 5.15)
Chen, Z., Grasby, S.E., & Osadetz, K.G., 2011: Geological controls on regional transmissivity anisotropy, Geofluids, Volume 11, Issue 2, pp. 228–241.
Cook, P., 2003: A guide to regional groundwater flow in fractured rock aquifers, published by CSIRO, Australia, 115pp.
Nunn, K.R., Barker, R.D. & Bamford, D., 1983: In situ seismic and electrical measurements of fracture anisotropy in the Lincolnshire Chalk, Q.J.eng.Geol.London, Volume 16, pp.187–195.
