faulting, fracturing and in situ stress prediction in the...

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Tectonophysics 320 (2000) 311–329www.elsevier.com/locate/tecto

Faulting, fracturing and in situ stress prediction in the AhnetBasin, Algeria — a finite element approach

Fred Beekman a,*, Madjid Badsi b,1, Jan-Diederik van Wees aa Tectonics/Structural Geology Group, Vrije Universiteit, De Boelelaan 1085, 1081 HV Amsterdam, Netherlands

b Institut Francais du Petrole, B.P. 311, 92506 Rueil-Malmaison, France

Abstract

Many low-efficiency hydrocarbon reservoirs are productive largely because effective reservoir permeability iscontrolled by faults and natural fractures. Accurate and low-cost information on basic fault and fracture properties,orientation in particular, is critical in reducing well costs and increasing well recoveries. This paper describes how weused an advanced numerical modelling technique, the finite element method (FEM ), to compute site-specific in situstresses and rock deformation and to predict fracture attributes as a function of material properties, structural positionand tectonic stress. Presented are the numerical results of two-dimensional, plane-strain end-member FEM models ofa hydrocarbon-bearing fault-propagation-fold structure. Interpretation of the modelling results remains qualitativebecause of the intrinsic limitations of numerical modelling; however, it still allows comparisons with (the littleavailable) geological and geophysical data.

In all models, the weak mechanical strength and flow properties of a thick shale layer (the main seal ) leads to adecoupling of the structural deformation of the shallower sediments from the underlying sediments and basement,and results in flexural slip across the shale layer. All models predict rock fracturing to initiate at the surface and toexpand with depth under increasing horizontal tectonic compression. The stress regime for the formation of newfractures changes from compressional to shear with depth. If pre-existing fractures exist, only (sub)horizontal fracturesare predicted to open, thus defining the principal orientation of effective reservoir permeability. In models that donot include a blind thrust fault in the basement, flexural amplification of the initial fold structure generates additionalfracturing in the crest of the anticline controlled by the material properties of the rocks. The folding-induced fracturingexpands laterally along the stratigraphic boundaries under enhanced tectonic loading. Models incorporating a blindthrust fault correctly predict the formation of secondary syn- and anti-thetic mesoscale faults in the basement andsediments of the hanging wall. Some of these faults cut reservoir and/or seal layers, and thus may influence effectivereservoir permeability and affect seal integrity. The predicted faults divide the sediments across the anticline in severalcompartments with different stress levels and different rock failure (and proximity to failure). These numerical modeloutcomes can assist classic interpretation of seismic and well bore data in search of fractured and overpressuredhydrocarbon reservoirs. © 2000 Elsevier Science B.V. All rights reserved.

Keywords: Ahnet basin; fracture modelling; hydrocarbon reservoir; stress prediction

* Corresponding author. Fax: +31-20-6462457; http://www.geo.vu.nl/~beef.E-mail address: [email protected] (F. Beekman)1 Now at Sonatrach, Algeria.

0040-1951/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.PII: S0040-1951 ( 00 ) 00037-8

312 F. Beekman et al. / Tectonophysics 320 (2000) 311–329

1. Introduction by scanned cathodoluminescence imaging(Laubach, 1997) can be a cost-effective and highlyreliable method of determining the presence ofNatural fracture systems are important contrib-

utors to reservoir permeability, and sometimes fractures in the subsurface and, more importantly,the orientation of fractures that control reservoirporosity, in many hydrocarbon reservoirs. Low-

efficiency hydrocarbon reservoirs that have very permeability. Unfortunately, the portion of thereservoir sampled by boreholes usually is extremelylow matrix permeabilities are productive largely

because delivery of fluids to well bores is controlled small, and a reservoir can be significantly fracturedeven if there is no evidence for these fractures inby natural fractures. In addition to the enhance-

ment of flow and storage of fluids in low-perme- borehole data.The orientation of natural fractures that controlability and low-porosity rocks, fractures and faults

may be necessary to allow primary migration of reservoir permeability is governed by the regionalstress field. Borehole breakouts, earthquake focalhydrocarbons from source rocks and to rupture

seals in pressure cells (Hunt, 1990). mechanism solutions and stress measurements cangive the direction of the maximum principal hori-Faults play an important role in creating hydro-

carbon traps and in the formation of sealed com- zontal stress (Zoback, 1992). Fractures and faultsparallel to the regional maximum horizontal com-partments in hydrocarbon reservoirs. When a fault

cuts a reservoir sequence it is desirable to predict pressive stress will be more permeable than frac-tures perpendicular to this stress. The parallelthe likely sealing behaviour of the fault system

(Knipe, 1997; Yielding et al., 1997). Evaluating fractures will tend to be open and will define theprincipal orientation of effective reservoir perme-fault seals (e.g. juxtaposition, clay smear,

cataclasis, cementation) forms an important aspect ability. Fractures with other orientations will tendto be squeezed shut by horizontal compressiveof hydrocarbon exploration and production. Fault-

seal assessment requires knowledge of the distribu- stress and, therefore, will contribute less to reser-voir permeability. Moreover, induced fractures cre-tion and the origin of sealing properties along

individual faults, as well as an understanding of ated during drilling will tend to propagate parallelto the orientation of maximum compressive stressthe geometry of the faults under evaluation.

A known pattern of hydrocarbon distribution (e.g. Major and Holtz, 1997).Basic fracture information, including reliableand the orientation of effective fracture permeabil-

ity may suggest strategies for maximising recovery. data on fracture strike, is often exceedingly sparse,hindering efficient development through optimisedBoreholes parallel to the trend of maximum hydro-

carbon volume and perpendicular to the strike of well placement or directional drilling. As explora-tion and development move into increasingly chal-effective fractures will maximise primary recovery

(Major and Holtz, 1997). For low-productivity lenging and deeper reservoirs where naturalfractures are key to successful completion, accuratereservoirs, in which reservoir permeability is con-

trolled by faults and natural fractures, it is impor- and low-cost information on fracture orientationand other fracture attributes will be critical totant, therefore, to know (1) the spatial distribution

of faults and fractures (if present), (2) their orien- reducing well costs and increasing well recoveries.Modern, advanced numerical modelling techniquestation and (3) how permeable they are.

Although there are some geophysical methods may provide such information. In this paper weinvestigate the potential of the finite elementof identifying subsurface fractures [e.g. cross-hole

tomography (Saito and Ohtomo, 1989) and seismic method in the calculation of site-specific stressesand fracture attributes and in the prediction ofreflection analysis of shear waves (Mueller, 1992)],

these are generally quite expensive and commonly faulting and related formation of differently pres-sured compartments in hydrocarbon reservoirs.are not economically justifiable in mature, rela-

tively low-production reservoirs. However, frac- This study also intends to demonstrate the useful-ness of mechanical modelling to test hypothesesture detection using borehole-imaging logs (Major

and Holtz, 1997) and mapping of microfractures on the geometry of structural traps, and to under-

313F. Beekman et al. / Tectonophysics 320 (2000) 311–329

stand better the fault mechanics and the mechan- reflection line (Fig. 2) traverses the northern partof the reservoir structure, running perpendicularical properties of reservoir rocks.

The reservoir structure investigated, located in to most of the mesoscale reverse faults observedin the structure (Badsi, 1992). A small map (Fig. 2,the Ahnet Basin, Algeria, is approached from a

larger-scale point of view, applying geomechanical inset) of the top of the main reservoir sandstonegives an impression of the spatial structure andmodelling methodologies from finite element mod-

elling (FEM) analyses of tectonic problems on the dimensions of this gas-bearing reservoir.The anticline reservoir structure comprises fivebasin-, crust- and lithosphere-scale (e.g. Van Wees

and Stephenson, 1995; Beekman et al., 1996, 1997; stratigraphic units of Palaeozoic age (Beicip-Sonatrach, 1970; Badsi, 1992), lying on top of aVan Wees et al., 1996). The modelling remains

qualitative because of the intrinsic limitations of Precambrian sandstone basement and covered byMesozoic carbonates. The Palaeozoic units com-large-scale modelling (in space and time); however,

it still allows comparisons with geological and prise, from bottom to top: (5) a Cambro-Ordovician layer of predominantly sandstones; (4)geophysical data. This will allow us to constrain

the principal parameters, to gain more insight into a thick layer of Silurian shales; followed by (3) aLower and Middle Devonian layer with alternatingthe causes and effects of rock deformation pro-

cesses, and to predict fracture attributes as a sandstones and shales, and a distinct unit of con-densed carbonates at the top; this is overlaid byfunction of structural position and tectonic stress.(2), a thick layer of predominantly UpperDevonian Frasnian sandstone; and finally (1), thealternating sequences of sandstones and shales2. Case study: hydrocarbon reservoir in the Ahnet

Basin (Algeria) from the Upper Devonian Famennian series.The source rocks of the reservoir are mainly

the marine shales in the Silurian and FrasnianIn order to test the predictive potential of finiteelement analyses of hydrocarbon reservoir related units (Tissot et al., 1972; Klemme and Ulmishek,

1991). Secondary sources may exist in the middlestructural problems, an anticlinal reservoir struc-ture located in the Ahnet Basin (Algeria) in the sections of the Silurian and in the Cambro-

Ordovician (Badsi, 1992). The reservoir rocks arenorthern part of the African continent (Fig. 1) hasbeen selected as a case study. The structure is of mainly constituted by the sandstones of the

Cambro-Ordovician (Macgregor, 1996).Variscan age and most likely formed as a faultpropagation fold ( Klitsch, 1970; Beuf et al., 1971; The material properties of the sedimentary

layers and basement incorporated in the numericalBoudjema, 1987). An east–west-running seismicmodels are listed in Table 1. All properties, exceptthe cohesion, have been measured directly fromborehole rock samples. No data are available forthe cohesion of the sediments and basement. Foreach unit two rock cohesion values are adoptedwhich differ by one order of magnitude and serveas representative end-member values(Carmichael, 1989).

The present-day intraplate stress field in thenorthern part of the African plate is generated byactive plate boundary processes connected withthe on-going inter-plate N–S convergence betweenthe African and European plates (Zoback, 1992).As a result, the intraplate stress field in northernAfrica is uniformly oriented over wide areas withFig. 1. Map of northern Africa, showing the location of the

Ahnet Basin, Algeria. a predominant NNW–SSE direction of the maxi-


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Table 1Material properties (see Fig. 3)

Stratigraphic Lithology Density Young’s modulus Poisson’s Cohesion Friction angleunit (kg m−3) (GPa) ratio (MPa) (deg)

1. Famennian shales/sandstone 2500 27.5 0.20 2/20 312. Frasnian sandstone 2480 27.5 0.25 3/30 333. Lower/Middle Devonian sandstone/shales 2500 27.5 0.20 2/20 314. Silurian shales 2530 27.0 0.15 1/10 105. Cambro-Ordovician sandstone 2480 28.0 0.25 3/30 306. Precambrian basement sandstone 2480 28.0 0.25 5/50 50

mum horizontal compression. Consequently, the sion (Chiarelli, 1978)], a horizontal shortening upto a total of 500 m is applied in incremental stepsanticline structure has been, and still is, subjected

to horizontal compression (Chiarelli, 1978). of 5 m, equally divided over the two vertical edges.Please note that, since there are only rate-indepen-dent rock deformation processes, the rate at whichthe shortening is applied (the loading velocity) is3. Finite element modelunimportant. However, the shortening still mustbe applied in small incremental steps to trackPrimarily based on the seismic cross-section

(Fig. 2), but also incorporating surface geology closely the load-history-dependent plastic strainsand to gain a better convergence behaviour in thefield data and correlating the little available bore-

hole data, a two-dimensional finite element model non-linear models. The total applied shortening isequivalent to a bulk horizontal shortening of caof the anticline has been constructed (Fig. 3). Tests

with meshes of different size showed that a model 0.5%. This satisfies the implicit demand that thereservoir structure is not allowed to deviate toowith spatial dimensions of at least 100 km length

by 40 km depth is required to avoid interference much from its initial geometry, because the modelis constructed on the base of the final (present-with numerical problems typically occurring at the

edges. To reduce the number of elements, and thus day) geometry.At time zero, all models are prestressed withthe computation time, the size of the elements is

increased away from the region of interest (the their own gravitational stress field computed in anearlier run but without any pre-existing faultsreservoir). This has led to a total of almost 30 000

elements and 15 000 nodes. The elements used are included (Fig. 4a).The vertical displacements caused by thethree-node, isoparametric triangles, with linear

shape functions and thus constant strain and stress. prestressing (‘the model subsides under its ownweight’, Fig. 4b) are being corrected by force bal-The finite element code used for the elasto-plastic

calculations is Tecton (Melosh and Raefsky, 1980). ancing (Fig. 4c).Modified versions of Tecton allow the implementa-tion of pre-existing faults in models [slippery nodeapproach (Melosh and Williams, 1987)], if neces- 4. Modelling resultssary with friction on the fault plane (Beekmanet al., 1996). Modelling results will be presented and dis-

cussed for two end-member cases of a series ofIn all models the upper surface is free to deformhorizontally and vertically. The lower boundary is models that comprise a blind thrust fault which

dips to the east and becomes horizontal at a depthrestricted to move vertically but allowed to deformhorizontally. In order to subject the anticline of ca 12 km. The free parameter in this series is

the static friction along the thrust fault. The twohydrocarbon trap structure to a horizontal com-pressional stress field [mimicking Alpine compres- end-members represent models with infinitely high


Fig. 3. Two-dimensional finite element model of the reservoir structure. Top panel shows full model geometry. Lower panel shows aclose-up of the material distribution in the anticlinal reservoir structure (box in top panel ).

friction (implying no thrust fault present at all ) 4.1. Structural deformation(Fig. 5a) and zero friction (Fig. 6a) along the blindthrust fault. The material properties adopted are The two end-member models respond in dra-

matically different ways to the applied horizontallisted in Table 1 (results are shown for the lowcohesion values). In both end-member models the shortening. The infinite friction model (hereafter

referred to as the ‘non-fault model’) essentiallyreservoir section (boxed area) is subjected to anincreasing horizontal compressive stress, mimick- responds by flexural amplification of the initially

present, anticline structure (Fig. 5b and c). Uplifting Alpine compression, as described in Section 3.Figs. 5–10 show the spatial distribution of several of the surface across the anticline typically is

several tens of metres. In contrast, the internalstrain-, stress-, fracture- and fault-related modelparameters, described hereafter. Most modelling deformation of the anticline structure within the

zero friction model (the ‘fault model’) is governedresults are presented after 200 m of applied short-ening, although for some parameters a different to a high degree by slip along the blind thrust

fault in the underlying basement (Fig. 6b and c).amount of shortening (500 m) is selected in orderto best demonstrate the potential of the finite Close examination of the horizontal displacements

reveals that the dipping basement fault becomeselement method in calculating structural deforma-tion and in situ stresses, and in predicting site- somewhat steeper under the applied horizontal

compression. This leads to some gravitationallyspecific fracture attributes and stress-induced fault-ing in hydrocarbon reservoirs. induced downwards sliding of the hanging wall.


Fig. 4. Model response due to initial gravitationally derived body force loading. (a) Applied boundary conditions. (b) Verticaldisplacements in the top central part (the reservoir) of the model. It demonstrates the self-compaction of the model under its ownweight. Surface displacements exceed 500 m. (c) Vertical displacements after correction for gravitational compaction.

At the surface this is evidenced by several metres folds in west Virginia (Dunne, 1986). Decouplingis more pronounced in the non-fault modelof subsidence of the area overlying the tip of the(Fig. 5c), where the flexural amplification pro-thrust fault (Fig. 6b).duces a flexural slip of some tens of metres on theA deformational feature that both end-memberwestern flank of the anticline.models have in common is a mechanical decou-

pling of the stratigraphic sediments above theSilurian shale layer from the units and the base- 4.2. In situ stressesment underlying the shale. In both models thisleads to flexural slip over the mechanically weak The weak mechanical properties of the shaleshale layer across the entire anticline. Similar inter- layer are also expressed by the low differentiallayer slip over a strong layer-parallel anisotropy stress s1−s3 this layer sustains in both end-produced by the presence of interbedded, weak member models, especially when compared with

the immediately under- and over-lying sandstonecherts has been observed, for instance, in detached


Fig. 5. Modelling results for the end-member model with infinitely high friction along a blind basement thrust fault, which, therefore,is effectively not present (the ‘non-fault model’). Selected results are presented after 200 or 500 m of applied horizontal shortening(on top of initial gravitational loading). (a) Boundary and loading conditions. (b) Cumulative vertical displacements. (c) Cumulativehorizontal displacements.

units (Figs. 7a and 8a; please note different con- stress increases roughly linearly with depth due tothe increase of lithostatic pressure with depth. Thistouring range). Jumps in differential stress magni-

tude at both the top and bottom interfaces of the increase with depth is more or less homogeneousin the non-fault model (Fig. 7a), only being per-Silurian shale unit vary laterally and may reach

maximum values of several tens of megapascals. turbed by the shale layer (although differentialstress increases with depth even within this layer).In fact, both models show that abrupt changes in

stress magnitude also occur at every other strati- This is also true for the fault model (Fig. 8a), buthere the differential stress distribution is also moregraphic interface, although substantially less large.

This, obviously, is the result of differences in the intensely perturbed in the anticline, evidently asthe result of slip along the thrust fault in thematerial properties between the layers, in particu-

lar the density and the elastic properties. underlying basement. There is a complex patternof alternating areas with lower and higherIn both end-member models the differential


Fig. 6. As Fig. 5, but results are displayed for the end-member model with zero friction along the blind basement thrust fault (the‘fault model’).

differential stress magnitudes in the shallow units bring it back to the yield limit (‘stick-slip’-likebehaviour). The proximity to failure parameteracross the anticline, particularly in the western

flank. may help to identify which parts of a model arefar away from yielding and thus can be consideredto be mechanically strong and stable. More interes-4.3. Proximity to rock failuretingly, the proximity to failure also reveals whichparts of a reservoir are close to failure or areThe proximity to failure is defined as the local

ratio between the effective stress and the failure already failing, for instance by generating newfractures or by opening existing fractures.stress (yield stress). Where this ratio is one, the

effective stress has reached the yield limit and rock After 200 m of applied shortening, in both end-member models the uppermost sandstone/shalefailure occurs. Owing to local strain redistribution

( like fault slip), the stress may relax and descend layer of Fammenian age and the Silurian shaleunit are failing over the entire width of the modelbelow the yield limit (ratio less than one), thus

bringing the rock out of failure. On-going model (Figs. 7b and 8b). The other Devoniansandstone/shale (unit 3) is by now also prone toloading will increase the effective stress again and


Fig. 7. Modelling results for the ‘non-fault model’ (Fig. 5a). (a) Principal stress difference s1−s3. Where the stress exceeds the uppercontouring limit, elements are coloured light grey. (b) The proximity to failure, defined by the ratio between effective stress andfailure stress. When the ratio is one ( light-grey coloured elements), rocks are failing.

Fig. 8. As Fig. 7, but results are displayed for the ‘fault model’ (Fig. 6a).


fail, whereas the two sandstone layers and the tion and fracture mode [extension fractures ( joints,veins), shear fractures (small faults), pressure solu-basement sandstones still remain far away from

yielding. This clearly illustrates the weakening tion (stylolites)]. Other fracture attributes, likefracture length and fracture density (or intensity),effect that the presence of shales has on the

mechanical deformation of individual stratigraphic cannot be assessed because the FEM does notallow modelling of individual fractures.layers within the models, expressed, for instance,

in the sometimes slightly lower values for the In the numerical calculations, all deformationdirectly related with failure of rocks is simulatedfriction angles of the rocks of each unit (Table 1).

There are also some clear differences in the by plastic flow because it is technically impossibleto create new discrete fracture and fault planesfailure proximity distributions of both models. In

the non-fault model (Fig. 7b), the stress-induced numerically during a model run. However, usingavailable geological knowledge of the deformationflexural uplift of the anticline leads to some addi-

tional rock failure in the crest of the anticline, processes involved with failure of different typesof rock, the calculated plastic deformation in themost likely caused by flexural bending stresses.

The effective stress is obviously increased suffi- models can be interpreted geologically as eitherbrittle failure or as viscous flow. For instance,ciently to reach the yield limit, even in parts of the

Frasnian sandstone. Failure proximity ratios, natu- from a geological and geomechanical point of viewit is more likely that the Silurian shales will deformrally, can also vary within a unit, as is demon-

strated on the flanks of the anticline, where in by some viscous flow process than that they willyield in a brittle manner, whereas the opposite isboth the Frasnian sandstone and the Devonian

sandstone/shale the lower parts of each layer are true for the more competent sandstone units inthe models. The calculated spatial distribution ofout of (although close to) failure and the upper

parts are in failure (Fig. 7b). If, in these parts of yielding also needs to be interpreted geologically.Calculated plastic strain can occur in either intensethe model, failure implies fracturing, this predicted

inter- and intra-layer spatial variation of fracturing and highly localised bands, which can be interpre-ted as faults, or in less intense and more diffusealong stratigraphic interfaces has direct conse-

quences for vertical and horizontal connectivity of bands, in which case it can be interpreted asnatural fracturing.permeable, fracture-controlled parts of hydro-

carbon reservoirs. This is also true for the fault In both end-member models (and all othermodels investigated for that matter) the Silurianmodel (Fig. 8b), where slip along the basement

thrust fault and related changes in the stress field shale layer already yields completely by gravita-tional loading only, thus even without any shorten-have led to a laterally alternating series of failing

(fractured) and not-failing (not-fractured) com- ing applied yet. Associated deformation isinterpreted as non-brittle flow (which can be plasticpartments within the upper three units on the

western flank of the anticline. and/or viscous), with effective strains in the orderof 1% and more after some 200 m of applied modelshortening (Figs. 9a and 10a).4.4. Rock failure: faulting, fracturing and plastic

deformation In the non-fault model (Fig. 9a), the low inten-sity and diffuse fracture mode seems to be the onlybrittle deformation mechanism active in the shal-The failure proximity plots essentially show

where, inside the anticline structure, the rocks are low, sandstone-dominated units in yielding.Fracturing starts at the surface of the model overfailing and where not under the applied gravita-

tional and compressional loading. The three panels the whole width and expands downwards underincreased compressional loading. Additional frac-in Figs. 9 and 10 concentrate on the rocks in

failure, and attempt to unravel the way in which turing develops in the crest of the anticline, obvi-ously due to stress-induced flexural uplift andthe rocks are failing (by either plastic or ductile

flow, localised faulting, fracturing) and try to amplified folding of the anticline structure. Thisfracturing slowly propagates in a lateral, as wellextract fracture attributes such as fracture orienta-


Fig. 9. Modelling results for the non-fault model (Fig. 5a). The grey shade contours are plotted on a black background for the model(not to be mistaken as a contour value). (a) Cumulative effective plastic strain. Black elements have not yielded (yet). In light greyelements the plastic strain has exceeded the upper contouring limit. (b) Dip angle of s1. (c) The three major types of fracturing(extensional, shear, compressional ).

as a vertical, direction under enhanced horizontal lie in the plane of the model. By subsequentlycomparing the out-of-plane principal stress withloading.

Having interpreted that the main mode of rock the two in-plane principal stresses and assumingAndersonian stress conditions (Anderson, 1951) itfailure in the non-fault model is fracturing, the

next step is to determine the orientation and mode is possible to determine the actual state of stress,i.e. compressive, strike-slip, or normal stressof the fractures, both controlled by direction and

relative magnitude of the principal stresses. system, dependent on whether the vertical principalstress is the smallest, intermediate or largest princi-Because all our numerical models are two-dimen-

sional plane-strain, the out-of-plane stress is always pal stress respectively.When discussing the relationship between frac-a principal stress and perpendicular to the model,

and the other two principal stresses must therefore tures and principal stresses, two distinct cases must


Fig. 10. As Fig. 9, but results are displayed for the ‘fault model’ (Fig. 6a). The continuous and dotted thick white lines in panel (a)are secondary mesoscale faults (planar bands of highly localised, intense plastic rock failure) predicted by the numerical model.

be recognised: (1) reactivation of pre-existing frac- Coulomb failure criterion also to be the criterionfor critical fracture stress, the location and orienta-tures or (2) formation of new fractures. In the

first case the fractures were formed during previous tion of open fractures can be deduced immediatelyfrom Fig. 9b, which displays the dip angle of thephases of deformation of the area of interest, and

may have any orientation. In this case only those maximum compressive stress in areas with criti-cally stressed fractures. Open fractures will befractures that are critically stressed and that strike

subparallel to the direction of maximum compres- subvertical everywhere (s1 is subhorizontal ) whererock failure occurs, and will be oriented east–west,sive stress will tend to be open and will define the

principal orientation of effective reservoir perme- parallel to the section and to s1 (the maximumcompressive principal stress).ability. Fractures with other orientations will tend

to be squeezed shut by maximum compressive The orientation and mode of new fractures canbe determined by using Anderson’s theory on thestress and, therefore, will contribute less to reser-

voir permeability. When assuming the Mohr– mechanics of faulting (Anderson, 1951). By apply-


ing the condition that near the free surface one of gates through the overlying Palaeozoic sedimentsup to the surface (Fig. 10a). This secondary faultthe principal stresses is (sub)vertical, Anderson

(1951) showed that the three major classes of new develops an antithetic branch at the top of theSilurian shale unit, which is also observed on thefractures and faults (extensional, shear and com-

pressional ) result from the three principal classes seismic section (Fig. 2). More secondary faults,somewhat smaller and oriented synthetic as wellof inequality that may exist between the principal

stresses. This concept can be grasped readily by as antithetic, are predicted at shallow levels in thecrest of the anticline. The modelling also predictsexamining a section through the Coulomb failure

surface in principal stress space (as shown in the initiation of a second, large antithetic faulteast of the crest and which propagates downwardsFig. 11a) at some arbitrary value of sv. A six-sided

figure, symmetrical about the line sH=sh is through the basement and eastwards towards themain thrust.obtained (Fig. 11b) that completely describes the

fracture criterion at this value of sv (see Scholz, Orientations and other attributes of both pre-existing and new fractures are more or less similar1990). Sides I and II of the figure are the loci of

failure for the conditions where sv is the largest in both end-member models. Except, in the faultmodel, the model-wide pattern of fracturing isprincipal stress, therefore producing normal faults

and/or extensional fractures ( joints, veins) that perturbed by a lateral series of compartments withno fracturing, located in the stratigraphic unitsstrike parallel to the largest horizontal principal

stress and that dip Q=p/4+w/2 (Fig. 11c) [Q#60° above the Silurian shale and present only in thewestern flank of the anticline (Fig. 10b). Also, infor the materials considered here, having friction

angles w#30° (Table 1)]. For sides III and IV, sv the vicinity of some of the new mesoscale faults, afault-induced perturbation of the local stress fieldis the intermediate principal stress, thus defining

conditions for strike-slip faulting and/or shear has led to a rotation of the maximal principalstress from subhorizontal to subvertical and, there-fracturing on vertical conjugate planes. The dihe-

dral angles of conjugate shear fractures are bisected fore, also to a change in the mode of fracturingfrom shear or compressional fracturing to exten-by the maximum horizontal principal stress direc-

tion (Fig. 11c) and the angle magnitude is given sional fracturing (Fig. 10c).by h=p/4−w/2 (about 30°). Sides V and VI definecompressional faulting for the condition of sv thesmallest principal stress, producing fractures (sty-lolites) perpendicular to the maximum horizontal 5. Discussioncompression and dipping h=p/4−w/2 (about 30°).

Fig. 9c displays the spatial distribution of the In the geomechanical analysis presented, themethodology used in numerical modelling recog-three major fracture classes in the non-fault model.

Under the current state of stress (after 200 m of nises that field data (such as in situ stresses,material properties and geological features) willapplied shortening), new fractures that are formed

in the competent rocks of the anticline will be never be known completely. The models remainsimple, with assumed data that are consistent withmainly shear fractures and some stylolites in the

crest. The modelling results indicate that no open known field data and hydrocarbon-engineeringjudgement. It is futile to expect the models tofractures, which control fracture permeability, will

be formed in the non-fault model. provide hydrocarbon production data, such asdiscriminating distinct fractures, when there isA similar analysis can be carried out for the

thrust fault model (Fig. 10). Here, besides distrib- large uncertainty in the input data. However, anumerical model is still useful in providing auted rock failure (fracturing), intense rock failure

also occurs that is localised in several planar bands, picture of the mechanisms that may occur withinparticular hydrocarbon systems. More insight intowhich are interpreted as secondary mesoscale

faults. A large, antithetic fault cuts the basement these mechanisms may help to improve strategiesfor maximising hydrocarbon recovery, for instanceof the hanging wall of the main thrust and propa-


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by optimising well placement or directional constraining factors (e.g. the system must be inequilibrium). In our models, the initial in situdrilling.

The model simplifications, e.g. constant density vertical stresses are equal to the lithostatic weightof the overburden: s

zz=rgz, where g is gravita-with depth (no porosity or thermal effects), no

fluid flow and pore pressure effects, and prescribed tional acceleration, r is the mass density of thematerial, and z is the depth below the surface. Thedisplacements as boundary conditions, are accept-

able within this concept. Because of these assump- in situ horizontal stresses are given by the naturalratio between horizontal and vertical stress:tions, and because of the little data available to

test the model results against, the model outcomes sxx/szz=n/(1−n), where n is Poisson’s ratio. This

formula is derived from the assumption that grav-must be interpreted qualitatively. Nevertheless,comparisons with available geological and geo- ity is suddenly applied to an elastic mass of mate-

rial in which lateral movement is prevented. Thisphysical data are still allowed. Unfortunately, forour case study no industrial data were released on condition hardly ever applies in practice, owing to

repeated tectonic movements, material failure,in situ stress magnitudes, on the presence of frac-tures, nor on the orientations and other attributes overburden removal, sedimentation and locked-in

stresses due to faulting. Of course, if we hadof possible fractures. Consequently, the modeloutcomes for these parameters remain predictions enough knowledge of the geologic history of a

structure, we might simulate the whole processthat hopefully can be tested in the future whenfracture data become available. Our modelling at numerically, so as to arrive at the initial state of

stress for our models. This approach usually is notleast demonstrates that the finite element methodcan be used to predict several fracture attributes feasible. A compromise is made by installing a set

of stresses in the model, and run the model untilby computing stresses and strains, and by applyingwell-established rock fracture laws. Moreover, pre- an equilibrium state is obtained that serves as the

initial in situ state of stress.dicted fracturing patterns and attributes are sup-ported by other modelling results. For instance, All finite element models are constructed on the

basis of seismic sections, borehole data and surfacethe blind thrust fault model with zero frictionpredicts mesoscale faults to form only in the geology, which are representative only for the

present-day geometry of the reservoir. For thewestern half of the anticline, which is confirmedby the seismic data. Several faults are computed modelling results to remain valid, the models are

not allowed to deform to such an extent that theirat their correct locations, and, for one mesoscalefault, branching is predicted to occur at the upper final geometry substantially deviates from the ini-

tial geometry. The amount of shortening appliedinterface of a shale layer, which conforms withobservations. Despite the fit between model predic- to the models, therefore, remains small: less than

0.5%. As explained in the previous paragraph, ittions and observations, more and better qualitydata are required of the case study reservoir (or usually is not feasible to model the entire geological

deformation history of a specific structure. In ourany reservoir, for that matter) to better assess thepotential and quality of the finite element method case study, the first-order geometry of the struc-

tural trap is the result of a fault propagation foldas a numerical tool for the prediction of naturalfracturing of hydrocarbon reservoirs. of Variscan origin. Such a structure can be geomet-

rically restored to its prefolding geometry.In all geologic situations, there is an in situstate of stress in the ground before a geologic Restored sections can be used to construct new

finite element models that can simulate at leastconstruction is deformed. This initial state mustbe included in the models because it can influence part of the geologic history of a structure and,

therefore, can produce more reliable predictionsthe subsequent behaviour of the model. Ideally,information about the initial state comes from on the present-day stress, strain and rock failure

patterns within a hydrocarbon reservoir.field measurements, but, when these are not avail-able, an attempt can be made to reproduce this in The two end-member models represent limiting

cases of a series of models in which the frictionsitu state for a range of possible conditions and


along the blind thrust fault in the basement varies. friction coefficient of 0.3 in Fig. 12, which displaysincrements in fault slip along the listric segmentAnalyses of similar models with friction on the

listric segment of the basement fault to ensure of the thrust fault (horizontal axis) and underincreased tectonic loading (vertical axis).thrust behaviour, indicate only fault activity to

occur for friction coefficients of less than 0.4 Fluid flow and pore pressures, not included inthe numerical models, play an important role in(equivalent to an angle of internal friction of 20°).

For friction coefficients of 0.4 and more the listric the evolution of hydrocarbon reservoirs (e.g.Miller, 1995; Osborne and Swarbrick, 1997).part of the thrust fault remains locked, at least

during the first 500 m of applied horizontal model Restricted fluid flow resulting in too much porefluid in too little space causes overpressures, andshortening, because naturally the fault, or parts of

the fault, can still become active under enhanced because changes in pore pressure also change insitu total stresses, and vice versa, high pore pres-horizontal compression. When fault activity occurs

it varies in space and under increased tectonic sures (overpressures) can cause natural hydraulicfractures and keep them open for extended timeloading (through ‘time’). This is illustrated for a

Fig. 12. Fault activity diagram. Every wiggle trace shows slip increment (by wiggle amplitude) as a function of increasing compressionalloading (vertical axis). Each trace represents a discrete point (solid dots in Fig. 3) of the listric segment of the blind thrust fault.Trace 1 is for the fault tip; trace 72 is where the thrust fault becomes horizontal. A (static) friction coefficient of 0.3 has been assignedto the listric part of the thrust fault; the horizontal segment remains frictionless to ensure thrust behaviour.


periods. Such fractures may occur in tectonically method, besides computing in situ stresses andpredicting fracture attributes, is also able to predictextensional, neutral, or compressional settings.

Because the pore pressure and the in situ total the position and orientation of faults that cutreservoir layers and affect the integrity of reservoirstresses do not vary independently, then whether

fractures form, their orientation, and the pore- seals. Therefore, it may also be used to identifypotentially overpressured compartments in hydro-pressure magnitudes causing the fractures depend

on the geological processes that cause overpressure carbon reservoirs rapidly.and on the rocks’ mechanical properties.

There are two fundamentally different ways thatgeologic processes cause overpressures (Miller, Acknowledgements1995): one is pore volume decrease by mechanicalloading, and the other is pore-fluid volume L’Institut Francais du Petrole and Beicip-decrease that can occur independently of burial Sonatrach are gratefully acknowledged for supply-depth changes. Compaction disequilibrium and ing the data of the case study. We kindly thanktectonic loading are examples of the first mecha- A. Schindler and A. Poliakov for their constructivenism; Darcy-type inflow and diagenetic reactions reviews. This is Netherlands Research School forare examples of the second mechanism. Other Sedimentary Geology publication number 990808.mechanisms, such as aquathermal expansion andporosity reduction via diagenetic cements, arehybrid overpressure source mechanisms. As a Referencesrock’s burial depth changes, these mechanisms actsimultaneously to change in situ stresses. However, Anderson, E.M., 1951. The Dynamics of Faulting, second ed.

Oliver & Boyd, Edinburgh.different mechanisms can affect in situ stressesBadsi, M., 1992. Failles et fractures dans le bassin de l’Ahnet.differently, and the total change in the stresses

Apport du retraitement sismique. Memoire DEA Geosci-ultimately depends on the relative strength of eachences ENSPM.

mechanism. In our numerical models the only Beekman, F., Bull, J.M., Cloetingh, S., Scrutton, R.A., 1996.overpressure source mechanism present is tectoni- Crustal fault reactivation facilitating lithospheric folding/

buckling in the central Indian Ocean. In: Buchanan, P.G.,cally induced lateral compression of the hydro-Nieuwland, D.A. (Eds.), Modern Developments in Struc-carbon trap. Pore pressure increase in tectonicallytural Interpretation, Validation and Modelling. Geologicalcompressive settings enhances the change of hori-Society Special Publication 99., 251–263.

zontal fracturing. Beekman, F., Stephenson, R.A., Korsch, R.D., 1997. Mechan-A good knowledge of the tectonic history and ical stability of the Redbank Thrust Zone, central Australia:

dynamic and rheological implications. Australian Journalstructural framework of sedimentary basins thatof Earth Sciences 44, 215–226.contain hydrocarbon reservoirs is essential when

Beicip-Sonatrach, 1970. Synthese du Cambro-Ordovicien dupredicting tectonic overpressures in such basins.Sahara Algerien. Rapport interne.

Fractures that open in response to pore pressures Beuf, S., Biju-Duval, B., De Charpal, D., Rognon, R., Benna-that are changing on a geological time scale are cef, A., 1971. Les gres du Paleozoique inferieur au Sahare.

Sedimentation et discontinuites: evolution structurale d’unstable and will remain open as long as there arecraton. Publications Institut Francais du Petrole College Sci-no large changes in the geological processes thatence et Technologie du Petrole 18. Technip, Paris.led to their formation. The effects of tectonic

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Carmichael, R.S., 1989. Practical Handbook of Physical Prop-due to local tectonic processes can be very rapid,erties of Rocks and Minerals. CRC Press, Boca Raton, FL,and decrease of pressure can be similarly rapid if741 pp.large volumes of fluid driven by seismic valving or

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