Fluxes in reservoir simulation models are calcuated as a function of transmissibilities between the centres of grid-blocks

PUNQ COMPLEX MODEL - STRUCTURE

Basic Structure

The structure of the PUNQ complex model is fairly typical of North Sea fault-bounded trap reservoirs (Figs 1 & 2). The reservoir is therefore bounded by a large reservoir-bounding normal fault, with a maximum fault throw of ca 450m, and is dominated by a related footwall high, which together with the main bounding fault provides structural closure. A population of intra-reservoir normal faults (n=41) comprises faults which have downthrow directions which are both synthetic and antithetic to those of the main bounding fault. Individual faults show displacement variations along their length and often tip-out, or die out, within the reservoir map area.

Figure 1: 3-D surface model showing the structure of the PUNQ complex model. The horizons shown are Top reservoir (i.e. Top Tarbet), Top Ness (pink), Top Mid Ness Shale (cream), Top Rannoch (green), Top Etive (light brown), Base Etive (dark brown). The Mid Ness Shale therefore appears as a dark green layer.

Figure 2: 3-D surface model showing the structure of the PUNQ complex model. The horizons shown are Top reservoir (i.e. Top Tarbet), Top Ness (pink), Top Mid Ness Shale (cream), Top Rannoch (green), Top Etive (light brown), Base Etive (dark brown). The Mid Ness Shale therefore appears as a dark green layer.

The structure of the area is based loosely on that of a North Sea field, but with the faults verticalised for the purposes of cellular model construction (i.e. Eclipse). The top reservoir fault and structure contour map was therefore taken as the uppermost surface from which the entire reservoir sequence hangs. Given the pre-faulting nature of the reservoir sequence, although the faults show lateral displacement variations, they do not show any upwards or downwards displacement changes. Fault maps are therefore the same for all horizons, which is a reasonable approximation given the lengths of the fault traces (usually greater than a few hundred metres) and the thickness of the reservoir (ca 200m). Structure contour maps for different horizons only differ in respect of what approximates a bulk shift in depth, with slight differences in structure contour patterns reflecting the rather subdued changes in isopach thickness from one reservoir unit to another. The resulting structure is one in which structural closure provides an oil column, with an oil-water contact which closes at both ends of the field (i.e. shown as black line on Figs 1 & 2). Again for the purposes of cellular model building individual faults are discretised in plan view, at the scale of the plan view orthogonal grid block geometry (Fig. 3).

Figure 3: Cellular model of coarse version of PUNQ complex model (20x60x20) – similar perspective as in Figure 1.

Figure 4: Maximum displacement vs Fault trace length for faults within the PUNQ complex model – field shown in red. Also shown is the field for selected faults from the published literature (Yielding et al. 1992, Watterson et al. 1996).

Quantitative systematics of intra-reservoir faults

A maximum fault throw (D) vs fault trace length (L) plot shows a positive correlation and throw/length ratios, which are consistent with data from natural fault systems (Fig. 4; Yielding et al. 1992, Watterson et al. 1996); fault throw is the vertical component of displacement on a fault. Fault size population curves, for both maximum throw and for fault trace length, show the power-law characteristics which are diagnostic of many natural datasets (Fig. 5). Power-law populations are described by the following expression

N a S^-E where N is the number of faults of size greater than or equal to S and E is the power-law exponent. When this function is plotted on log-log axes, a straight line results with a slope of -E. Fault systems are generally analysed from either line samples (1-D) or maps (2-D). 2-D fault populations for typical North sea offshore datasets, such as those presented below for the PUNQ Complex model, represent either the maximum throw (D) or the trace length (L) of individual fault traces intersecting a given horizon (often the top reservoir horizon) with approximate straight line curves down to the effective limit of seismic resolution. Following a recently developed methodology the population of seismically imaged faults provides a basis for prediction of sub-seismic fault populations, by extrapolation of the population curve for seismically imaged faults down to sub-seismic fault displacements. Extrapolation for the PUNQ Complex model fault population predicts a reletively small numbers of sub-seismic faults (the reservoir is characterised by a low fault population slope) and relevant flow modelling suggests that the effects of sub-seismic faults on flow within the reservoir will be minor to insignificant. The effects of sub-seismic faults on the effective properties of the reservoir have not therefore been included.

Figure 5: Maximum throw and fault trace length populations for PUNQ complex model (red), for reservoir datasets from the North Viking Graben (green) and from the Southern Central Graben (blue) and for a high quality coalmine dataset from UK (pink).

Cellular model

The top reservoir fault and structure contour map are combined with the sedimentological property model to provide reservoir flow simulation models in corner point geometry format, at user defined grid block resolutions: this process can be performed reletively routinely. Our method also generates varying fault transmissibility multipliers over entire fault surfaces from fault displacements and vshale of the faulted sequence using the method of Manzocchi et al. (1999),described in detail below. These fault properties are generated from three variables which represent the principal inversion parameters of the model. Other parameters such as fault displacement, horizon elevation etc. are fixed for the purposes of the PUNQ project.

Figure 6: Coarse PUNQ Complex Model (20x60x20) showing net:gross values of reservoir sequence. (a) with fault surfaces shown and (b) with net:gross values shown on fault surfaces.

Fault Properties

Introduction

Faults influence flow in a reservoir simulation model in two ways (Manzocchi et al. 1999). Firstly, they alter the connectivity of sedimentological flow units. Displacements across faults can cause partial or total juxtaposition of different flow units, possibly connecting stratigraphically disconnected high permeability units as well as juxtaposing high against low permeability units. For faults incorporated discretely in flow simulation models, these effects are captured as a function of the relative depths of the corners of the grid-blocks separated by a fault. Faults generally increase the overall vertical connectivity of a reservoir and decrease the overall horizontal connectivity, but the precise influence of fault displacements on reservoir connectivity is complex, as seismic data cannot resolve details of fault structure: what appears to be a single fault on seismic often comprises multiple fault strands which can have a significantly different effect on flow unit connectivity than a single strand. These relatively large scale connectivity effects which can be analysed with Allan diagrams, with sequence / throw juxtaposition diagrams or with aggregate connectivity plots.
        The second influence of faults on flow arises from the petrophysical properties of the fault-rock, usually included by using transmissibility multipliers. Below we outline and discuss a new, geologically driven method for determining fault transmissibility multipliers as a function of known properties of the reservoir model. The method aims to predict fault zone properties and to capture the influence of unresolved fault zone structure in sandstone/shale sequences using a simple algorithm. Inevitably the method requires assumptions and approximations, and few quantitative data exist to condition the resultant model. The model therefore needs calibration against dynamic reservoir data but considerable uncertainty will always be associated with the fault transmissibility determinations due to the natural unpredictability of fault zone structure and content.
        Fault permeability and thickness are physically observable properties of fault zones, whilst transmissibility multipliers are numerical devices used in lieu of these properties. As the permeability and thickness of sub-surface faults can be estimated, albeit imprecisely, it seems sensible that these estimates be used to determine the transmissibility multipliers for faults in reservoirs for which no dynamic data are available. The use of dynamic data in conditioning faulted simulation models is beyond the scope of this contribution, which aims only to present a method for determining transmissibility multipliers based on a static geological prediction. Dynamic information, where available, provides the only firm indication of the behaviour of any particular fault in a reservoir and must therefore be the prime data conditioning the overall transmissibility assigned to the fault. Nonetheless, an appreciation of the dependencies contained within fault transmissibility multipliers is necessary if the dynamic information is used to construct models, which not only match the production and pressure history, but are also geologically palatable.
        Faults in reservoirs are sampled either at low resolution by seismic or at a high resolution by wells. Seismic interpretation provides information about the locations and displacements of large faults, but cannot resolve the small scale structure within the fault zone. Wells sample faults at a particular point in a reservoir, and cored faults provide direct samples from which fault zone properties can be measured. Fault zones are complex heterogeneous and anisotropic volumes of varying composition and thickness, and a well samples only a single line through a zone. Predicting flow through a fault requires a model of fault zone structure at a resolution which cannot be obtained from either data-source. The conceptual model we consider for the determination of fault transmissibility multipliers is shown on Figure 7: see Manzocchi et al. (1999) for further details.

Figure 7. Conceptual up-scaling hierarchy. a) At the sub-metre scale, the fault-rock permeability is a function of its shale content. b) At the sub-grid-block scale, the fault zones are considered heterogeneous in permeability and thickness. c) At the grid-block scale each grid-block connection is assigned a uniform transmissibility.

At the smallest scale, the fault is conceptualised as a volume of a particular thickness and shale content (Fig. 7a), and the proportion of shale in the volume is assumed to be the main control on the fault permeability. The shale content of the fault zone is calculated as a function of the faulted sequence using the Shale Gouge Ratio method (described in the following section). The displacement of a fault is assumed to be the main control on fault zone thickness, and a secondary control on fault zone permeability. At an intermediate scale (Fig. 7b), thickness and permeability are assumed to be log-normally distributed with 75% of the values covering two orders of magnitude around the median value. The correlation-lengths of this heterogeneity are assumed to be substantially smaller than the simulation grid-block size. At the simulation grid-block scale (Fig. 7c), the transmissibility multiplier assigned to each grid-block fault-face is an appropriately up-scaled representation of this heterogeneous fault zone. We do not attempt to capture effects of cement seals, which are the least predictable fault seal type.

Fault zone permeability

Over recent years a methodology has emerged for the analysis of the seal capacity of faults in sandstone / shale sequences. These methods do not try to resolve precise details of the structure of fault zones, but instead use proxy-properties to make inferences about the behaviour of a fault, through empirical correlations with other faults of known behaviour in the same hydrocarbon province. The most versatile proxy-property is the Shale Gouge Ratio (SGR). SGR is the proportion of phyllosilicate which has been displaced past any particular point on a fault (e.g. Yielding et al. 1997). The minimum SGR on the fault surface is assumed to have the lowest capillary entry pressure, and databases comparing pressure difference supported across faults, with SGR mapped onto the fault surface, are used to assess the integrity of unproven fault traps. These studies suggest that an SGR greater than about 15-20 % results in a membrane seal capable of separating fluids of different phases. This cut-off is supported by outcrop characterisation which shows that faults with SGRs in excess of this value have at least one shale layer within the fault zone which is continuous over the outcrop (e.g. Lindsay et al. 1993; Foxford et al. in press). Cut-off values also appear to be transferable between different hydrocarbon provinces (Yielding et al. 1997).
        We make the assumption suggested by Yielding et al. (1997), that SGR is equivalent to the shale content (Vshale) of the fault gouge. This assumption is useful as although it is possible to calculate the SGR for a sub-surface fault zone, the precise shale content of the zone cannot be predicted directly. Available plug permeability data, on the other hand, are recorded as a function of the volumetric shale fraction of the core plugs which are taken as representative of the fault zone.
        Figure 8 shows plug and probe permeability data for various reservoir and out-crop fault-rock samples (Antonellini and Aydin 1994; Knai 1996; Gibson 1998, Ottesen Ellevset et al. in press). The data show a general decrease in fault zone permeability with increasing shale content, and large variations in permeability at a particular shale content. At very low shale content there is an apparently bimodal distribution governed by fault displacement, demonstrated by the data from Antonellini and Aydin (1994). These data are probe permeameter measurements from samples of the Moab (Vshale = 0) and Slickrock (Average Vshale = 0.09) members of the Entrada Sandstone formation. The clean Moab Sandstone shows a clear distinction between the permeability of deformation bands (displacements in the range 1 mm to a few centimetres and average fault-rock permeabilities of about 10 mD) and slip surfaces (displacements greater than about 1m, and average permeabilities of less than 0.01 mD). In the more shaley Slickrock member, the permeabilities of deformation bands and slip surfaces are similar to each other, with average values around 0.8 mD. A decrease in the influence of displacement on fault permeability with increasing shale content is caused by these differences in deformation style. In pure sandstone, cataclastic intensity increases with displacement, ultimately resulting in highly polished, intensely cataclastic slip surfaces with exceptionally low permeabilities. Deformation bands in more shaley sandstone are less cataclastic, as displacement is accommodated by small-scale smearing of the phyllosilicates (e.g. Antonellini et al. 1994), and the main control on fault permeability is the shale content of the fault.
        The curves on Figure 8 show an empirical prediction of fault zone permeability as a function of shale content and displacement. The curves are given by the equation:

(1) where k_f is fault permeability (in mD) and D is fault displacement (in metres). We assume that the value of k_f obtained is the median value of a log-normal permeability distribution covering about two orders of magnitude. Therefore, for D=20m, SGR = 0.2, predicted k_f lies in the range 0.012 mD < k_f < 1.2 mD, and the median value is 0.12 mD. The influence of displacement on fault zone permeability in this relationship is not as great at very low shale content as the data on Figure 8 suggest. Therefore Equation 1 does not provide a reliable estimate of permeability as SGR approaches 0.

Figure 8. Log permeability (mD) vs. volumetric shale fraction for fault-rock. Large data-points are plug permeability measurements from core and outcrop samples from a variety of locations (Gibson 1998). Filled circles: cataclastic deformation bands. Open circles: solution deformation bands. Filled squares: clay gouge. Small data-points are probe-permeability measurements of deformation bands (open circles) and slip surfaces (crosses) from sandstones in SE Utah (Antonellini and Aydin 1994). Boxes are summaries of data from the Sleipner Field (Ottesen Ellevset et al. in press). (i) Cataclastic deformation bands. (ii) Framework phyllosilicate fault rocks. (iii) Shale smears. The line labelled "K" represents average values, based on core samples from the Heidrun Field, used in a full-field flow simulation (Knai 1996). The curves (Equation 1) represent the relationship used in this work for permeability as a function of SGR (assumed equivalent to the fault-rock volumetric shale fraction) and displacement. Curves are given for D=1 mm (dashed line), D=10 cm, D=1m, D=10 m and D=1 km (heavy line).

Fault zone thickness

Fault zones comprise portions where two or more slip surfaces bound volumes of more or less deformed rock; and portions where the entire displacement is accommodated on single slip surfaces (lacunae). The thickness of the fault zone is defined as either the separation between the outermost slip surfaces (where more than one are present) minus the thickness of undeformed lenses, or the thickness of the slip-surface itself in a lacuna. Compilations of fault outcrop data demonstrate an approximately linear relationship between fault zone displacement and fault rock thickness (t_f ) over several decades of scale-range with thickness values distributed over about two orders of magnitude for a particular displacement.
Figure 9 summarises the data compiled by Hull (1988), and data from faults in mixed sandstone / shale sequences in Sinai (Knott et al. 1996), SE Utah (Foxford et al. in press) and Lancashire, UK (Walsh et al. 1998). Also plotted for several displacements are synthetic thickness values generated using the relationship:

t_f = D/66, (2) to define a median thickness value, and a standard deviation for log t_f of 0.9 to define a log-normal thickness distribution. The data populate closely the envelopes defined by the outcrop studies for displacements over about 1 m. Equation 2 tends to under-predict the thickness of smaller faults, but as fault displacements less than 1 m are seldom incorporated in production flow simulation models, there is no need to predict accurately their thickness for this application.

Figure 9. Log thickness vs. log displacement (both in meters). Summaries of out-crop measurements are given as envelopes containing measurements from a variety of sources (Hull 1988), from faults in Nubian Sandstone in Western Sinai (Knott et al. 1996), from the Moab fault in SE Utah (Foxford et al. in press) and from faults in a Westphalian sandstone/shale sequence from Lancahsire, UK (Walsh et al. 1998). 200 log-normally-distributed thickness data (small diamonds) have been generated at various displacements with median value following the relationship t_f= D/66 . The harmonic averages of these data (large circles) follow the relationship t_f= D/170.

Fault zone properies at the grid-block scale
        Fault zone properties are variable and unpredictable over short distances. Foxford et al. (in press) characterised the well-exposed Moab Fault in S.E. Utah over short sections at various locations along it’s 40 km trace and concluded that it is impossible to extrapolate predictions of the structure of the fault zone over distances greater than about 10 m. Similar fault zone thickness variability has been observed either in samples of different faults from the same sequence (e.g. Knott et al. 1996) or samples at different positions on the same fault trace (e.g. Blenkinsop 1989). The limited evidence available suggests that fault zone permeability is at least as heterogeneous as thickness (e.g. Figure 8, Antonellini and Aydin 1994; Fowles and Burley 1994).
        There are modelling advantages to fault zone structure being unpredictable over extremely small distances. The representative elementary volume (REV) of a correlated random field is about four times larger than the range of the semivariogram defining the field. If the correlation length of fault zones is assumed to be in the order of 10 - 20m, then the REV is in the order of 40-80 m. A typical reservoir simulation grid-block is about 100 m wide, and therefore contains a representative portion of a fault if the correlation length is as small as qualitative estimates suggest. Correlation lengths of fault zones are extremely speculative, as the data necessary to address the issues fully do not exist. This is an area requiring further research, and for the purposes of this report we assume an REV for fault zones exists, and that it is smaller than a reservoir grid-block. Many aspects of fault zones, such as relay ramps, are likely to have correlation-lengths much larger than a grid-block, however we make this assumption because it is convenient to do so, as the representative fault permeability and thickness are the area-weighted arithmetic and harmonic averages, respectively.
        We assume that both thickness and permeability vary over the area of a grid-block according to a log-normal distribution. The median value of a log-normal distribution is the mean of the normal distribution of the log-variable. For a log-normal distribution with a log-variable mean

and standard deviation

, the arithmetic average of the distribution is

, and the harmonic average is

. For any particular SGR and displacement, we assume that the median permeability and thickness values are given by Equations 1 and 2, in each case with

=0.9. This standard deviation is equivalent to about 75% of the values lying within

one order of magnitude of the median, and 90% lying within

1.5 orders of magnitude (Figure 3). For thickness,

=0.9 gives the harmonic average thickness as a function of displacement:

. (3) For permeability,

and

=0.9 gives the arithmetic average permeability as a function of SGR and displacement:

. (4) Equations 3 and 4 give the fault zone thickness and permeability averages appropriate for incorporation in a reservoir flow simulator based on the assumptions about fault zone structure and properties which have been described above.

Fault zone properties in the simulator
Fluxes in reservoir simulation models are calculated as a function of transmissibilities between pairs of grid-blocks, and fault properties are represented as multipliers which operate on transmissibility. Transmissibilities are obtained by dividing the equivalent permeability of the blocks by the distance separating their centres (this assumes an intersection area of 1 and ignores grid-block dips - the precise details of calculating transmissibility differs between simulators). Figure 10 illustrates the transmissibility, Trans_ij, between two blocks separated by a transmissibility multiplier and a discrete thickness of fault-rock.
Equating these gives the transmissibility multiplier as a function of the dimensions and permeability of the grid-blocks and the thickness and permeability of the fault:

(5) For the special case where

and

becomes:

, (6) which is equivalent to the transmissibility factor defined by Walsh et al. (1998). For a case where

, Equation 6 can be used as a multiplier on the permeability of one of the grid-blocks adjacent to the fault, effectively assigning the entire thickness of fault-rock to this cell. This provides the same transmissibility across the fault as applying Equation 6 to the interface between the two grid-blocks, but also modifies the transmissibility on the other side of the grid-block to which the permeability multiplier has been assigned. Therefore the transmissibility multiplier provides a numerically more robust representation of the fault than the permeability multiplier.

a) , b)
Figure 10. The transmissibility between two grid-blocks separated by (a) a transmissibility multiplier and (b) a discrete thickness of fault-rock.

Application to the punq complex model

Figure 11 illustrates the method applied to the coarse (20 x 60 x 20 grid-blocks) version of the complex Punq model, shown in aerial view in Figure 11a and in cross-section for the highlighted fault in Figure 11b. The thickness of the fault is calculated as a function of the displacement at each cell centre (Fig. 11c). The fault properties are calculated as a function of the shale content of the grid-block to provide an SGR map (Fig. 11d) which is combined with fault displacement to obtain a fault permeability map (Fig. 11e). Fault permeability multipliers acting on the hangingwall grid-block permeabilities are shown on Figure 11f, and fault transmissibility multipliers acting on block to block transmissibilites are shown on Figure 11g. The transmissibility multiplier requires greater definition than the permeability multiplier, as a value must be calculated for each connection. The 24,000 block model illustrated contains 96,000 vertical grid-block faces, of which over 14,000 are faulted. As the resolution of the model changes, so does the fraction of faces occupied by faults (Table 1). Hence the permeability multiplier, which is much simpler to implement, may be adequate for high resolution models which have only a small percentage of faulted faces, but not for low resolution models which require transmissibility multipliers.

Table 1. The proportion of faulted faces in the Punq complex model as a function of discretisation.

Aerial discretisation	vertical faces (per layer)	faulted faces (per layer)	faulted faces (%)
12 x 44	2112	470	22.3
20 x 60	4800	730	15.2
30 x 110	13200	1292	9.8
60 x 220	52800	2620	5.0

        Heterogeneity in the value of either multiplier reflects both the smooth variation in fault zone properties and the rapid variation in grid-block permeabilities. The first influence provides the overall trends in the multiplier. For instance in the area of the fault surface between the hangingwall and footwall cut-offs of the Mid-Ness shale, SGR is high, fault permeability is low and the multipliers are generally low. More rapid variation in grid-block permeabilities locally overprints the relatively smooth variation caused by the fault zone properties, for instance in the area with high transmissibility multipliers two grid-blocks above the hangingwall cut-off of the Mid-Ness shale. Fault permeability is low in this area, but the value of the multiplier is responding to a locally low permeability in the hangingwall section of Upper-Ness.
        The method provides fault multiplier models of much higher resolution than is usual. This high resolution is necessary as the permeability of the grid-blocks is more heterogeneous than the predicted fault properties, and both determine the values of the multiplier. The method is based on a geological model of the faults, and the factors which most influence fault zone content are fault displacement and details of the faulted sedimentary succession, both of which change rapidly at the resolution of a simulation model. As fault zone content depends on the sedimentology, any stochastic realisation of the reservoir sedimentology requires a new generation of the fault permeabilities, but more importantly requires a new set of multipliers, as these depend additionally on the grid-block permeabilities.
        The exercise described above is automatically performed for all faults in the PUNQ Complex Model. Figure 12 provides a suite of 3-D images of the coarse version of the PUNQ Complex Model (20x60x20), showing a range of fault properties mapped over individual surfaces.

Inversion parameters
The simplest fault property inversion parameter is the fault transmissibility multiplier, however owing to the dependency of grid-block permeability on this parameter, use of the multiplier without consideration of the underlying physical fault properties may result in geologically implausible models. For this reason, inversion of the underlying geological property field (Vshale), combined with global relationships linking SGR and fault displacement (which is known) to permeability and thickness, allows the fault transmissibility multipliers to be determined at each step within the inversion loop while retaining the close geological association between sedimentological and fault properties The preferred routine for including fault properties in the inversion workflow is as follows. (i) Determine a Vshale distribution as a function of the sedimentological model.
ii) Determine SGR for each faulted connection. iii) Determine fault thickness and permeability, for each connection, as a function of the relationships and respectively, where a, b and c are constants defined by priors (Table 2). iv) Determine the transmissibility multipliers for the next flow simulation model. The structural element of the inversion loop is now automated in a computer program which is soon to be provided to project partners.

Table 2. Prior definition of the global relationship linking fault SGR and displacement to fault permeability and thickness.

	Distribution type	mean	standard deviation
constant a	log normal	170	0.55
constant b	normal	0.4	0.625
constant c	log normal	0.25	0.24

Figure 11. Fault transmissibility and permeability multipliers for a fault in the 20 x 60 x 20 version of the Punq complex model. a) Aerial model, with the illustrated fault highlighted. b) Summary of the fault surface. All hangingwall cut-offs and some footwall cutt-offs are shown. The shaded area represents the region over which the active grid-cells are juxtaposed. b) Fault thickness (solid line) is calculated at grid-block centres from the fault displacement (dashed line) c) Fault surface SGR calculated for the hangingwall grid-blocks (fraction). d) Fault permeability calculated for the hangingwall grid-blocks (mD, log scale). e) Fault permeability multiplier calculated for the hangingwall grid-blocks (linear scale). f) Fault transmissibility multiplier (linear scale).

Figure 12: Coarse version of PUNQ Complex model (20x60x20), showing net:gross and effective vshale (top left and right respectively), and showing SGR and Transmissibility Multiplier fault surface properties (bottom left and right respectively).

References
ANTONELLINI, A. & AYDIN A. 1994. Effect of faulting on fluid flow in porous sandstones: petrophysical properties. American Association of Petroleum Geologists Bulletin, 78, 181-201.

ANTONELLINI, A., AYDIN A. & POLLARD, D. D. 1994. Microstructure of deformation bands in porous sandstones at Arches National Park, Utah. Journal of Structural Geology, 16, 941-959.

BLENKINSOP, T. G. 1989. Thickness-displacement relationships for deformation zones: Discussion. Journal of structural geology,11, 1051-1054.

FOWLES, J. & BURLEY, S. 1994. Textural and permeability characteristics of faulted, high porosity sandstones. Marine and Petroleum Geology 11, 608-623.

FOXFORD, K. A., WALSH, J. J., WATTERSON, J., GARDEN, I. R., GUSCOTT, S. C. & BURLEY, S. D. in press. Structure and content of the Moab Fault zone, Utah, U. S. A. In: Knipe R. J et al. (eds.): Faulting, fault sealing and fluid flow in hydrocarbon reservoirs. Special Issue of the Geological Society, London.

GIBSON, R. G. 1994, 1998. Physical character and fluid-flow properties of sandstone derived fault gouge. In: Coward, M. P., Johnson, H. and Daltaban, T. (eds.): Structural geology in reservoir characterisation. Special issue of the Geological Society, London, 127,

HULL, J. 1988. Thickness-displacement relationships for deformation zones. Journal of Structural Geology 10, 431-435.

KNAI, T. A. 1996. Faults impact on fluid flow in the Heidrun Field. In: Faulting, Fault Sealing and Fluid Flow in Hydrocarbon Reservoirs, Leeds, 75. (Abstract)

KNOTT, S. D., BEACH. A., BROCKBANK, P. J., BROWN, J. L., MCCALLUM, J. E. & WELDON, A. I. 1996. Spatial and mechanical controls on normal fault populations. Journal of Structural Geology 18, 359-372.

LINDSAY, N. G., MURPHY, F. C., WALSH, J. J. & WATTERSON, J. 1993. Outcrop studies of shale smears on fault surfaces. In: Flint, S. & Bryant, A. D. (eds.) The geological modelling of hydrocarbon reservoirs and outcrop. International Association of Sedimentology, 15, 113-123.

MANZOCCHI, T., WALSH, J.J., NELL, P.A.R. & YIELDING, G. 1999. Fault transmissibility multipliers for flow simulation models. Petroleum Geoscience 5, 53-63.

OTTESEN ELLEVSET, S., KNIPE, R. J., OLSEN, T. S., FISHER, Q. T. & JONES, G. in press. Fault controlled communication in the Sleipner Vest Field, Norwegian continental shelf: detailed quantitative input for reservoir simulation and well planning. In: Knipe R. J et al. (eds.): Faulting, fault sealing and fluid flow in hydrocarbon reservoirs. Special issue of the Geological Society, London.

WALSH, J. J., WATTERSON, J., HEATH, A. E. & CHILDS, C. 1998 Representation and scaling of faults in fluid flow models. Petroleum Geoscience 4, 241-251.

WATTERSON, J., WALSH, J. J., GILLESPIE, P. A. & EASTON, S 1996. Scaling systematics of fault sizes on a large scale range fault map. Journal of Structural Geology 18, 199-214.

YIELDING, G., WALSH, J. J. & WATTERSON, J. 1992. The prediction of small-scale faulting in reservoirs. First Break 10, 449-460.

YIELDING, G., FREEMAN, B. & NEEDHAM, D. T. 1997. Quantitative fault seal prediction. American Association of Petroleum Geologist.81, 897-917.