Laboratory measurements of the relative permeability of cataclastic fault rocks: An important consideration for production simulation modelling

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Marine and Petroleum Geology 25 (2008) 473–485 www.elsevier.com/locate/marpetgeo

Laboratory measurements of the relative permeability of cataclastic fault rocks: An important consideration for production simulation modelling Suleiman Al-Hinaia,, Quentin J. Fishera, Bader Al-Busafib, Phillip Guisec, Carlos A. Grattonic a School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK Petroleum Development of Oman, MAF, Sultanate of Oman, P.O. Box 81, PC: 113, Muscat c Rock Deformation Research Limited, School of Earth and Environment, University of Leeds, Leeds LS2 9JT, UK b

Received 5 February 2007; received in revised form 5 July 2007; accepted 7 July 2007

Abstract It is becoming increasingly common practice to model the impact of faults on fluid flow within petroleum reservoirs by applying transmissibility multipliers, calculated from the single-phase permeability of fault rocks, to the grid-blocks adjacent to faults in production simulations. The multi-phase flow properties (e.g. relative permeability and capillary pressure) of fault rocks are not considered because special core analysis has never previously been conducted on fault rock samples. Here, we partially fill this knowledge gap by presenting data from the first experiments that have measured the gas relative permeability (krg) of cataclastic fault rocks. The cataclastic faults were collected from an outcrop of Permo-Triassic sandstone in the Moray Firth, Scotland; the fault rocks are similar to those found within Rotliegend gas reservoirs in the UK southern North Sea. The relative permeability measurements were made using a gas pulse-decay technique on samples whose water saturation was varied using vapour chambers. The measurements indicate that if the same fault rocks were present in gas reservoirs from the southern Permian Basin they would have krg values of o0.02. Failure to take into account relative permeability effects could therefore lead to an overestimation of the transmissibility of faults within gas reservoirs by several orders of magnitude. Incorporation of these new results into a simplified production simulation model can explain the pressure evolution from a compartmentalised Rotliegend gas reservoir from the southern North Sea, offshore Netherlands, which could not easily be explained using only single-phase permeability data from fault rocks. r 2007 Elsevier Ltd. All rights reserved. Keywords: Relative permeability; Fault seal; Reservoir simulation; Fault rocks; Rotliegend

1. Introduction It is well known that faults can severely compartmentalise reservoirs resulting in reduced petroleum recovery (Corrigan, 1993). It is therefore likely that an ability to accurately model the impact of sealing and partially sealing faults on fluid flow could lead to more accurate predictions of future reservoir performance and may even improve development decisions. Historically, the impact of faults on fluid flow within petroleum reservoirs has been modelled by Corresponding author. Tel.: +44 113 343 1930; fax: +44 113 245 6233.

E-mail address: [email protected] (S. Al-Hinai). 0264-8172/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.marpetgeo.2007.07.005

altering the transmissibility multipliers (TMs) on the gridblocks adjacent to faults by trial-and-error until a history match of the production data has been achieved. A problem with such an approach is that history matches are invariably non-unique and so there is a danger that fault TMs are used to compensate for problems with the simulation model that are not actually related to the presence of faults. Thus, although a convincing history match is achieved, the simulation model may not be particularly useful for predicting future production behaviour (Dake, 2001). Far more data has recently been collected on the structure of faults (Harris et al., 2003) and the single-phase

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permeability of fault rocks (Fisher and Knipe, 1998; 2001). Such information allows a more sophisticated, geologically reasonable, treatment of faults in production simulation models such as described by Manzocchi et al. (1999). In the method of Manzocchi et al. (1999) TMs, are calculated from input such as fault permeability, fault thickness, gridblock size and undeformed reservoir permeability and applied to the grid-blocks on either side of the fault to take into account the impact of faults on fluid flow. A key problem with calculating TMs based on such data is that no account is taken of the relative permeability of the fault rocks. This is not surprising as there are no published data on the relative permeability of fault rocks. In this paper, we attempt to fill this knowledge gap by presenting results of what we believe to be the first measurements ever published on the relative permeability of fault rocks. We then go on to show how incorporation of these new results into a production simulation model can explain production data from a North Sea gas reservoir that cannot easily be modelled based only on the absolute permeability of the fault rocks. These new results may mean that we are now in a far better position to predict future production from gas reservoirs, which may lead to better day-to-day decision making. We begin by describing the experimental methodology and the specimens used to obtain the multi-phase flow properties of cataclastic fault rock samples. The results from these experiments are then presented. Finally, we describe how the results have been incorporated into a simplified production simulation model for a North Sea gas reservoir.

NJ16157021). This subsidiary fault (hereinafter referred to as the Clashach fault) trends E/W to WSW/ENE and dips to the south. The fault displacement at the Clashach Quarry is uncertain but the mismatch of aeolian units across the fault suggest a minimum displacement of 20 m. The fault is composed of a 25 cm wide core comprising a dense zone of deformation bands that have experienced significant cataclasis. Localisation of faulting at the edge of the fault core has produced a polished fault surface slikensides whose orientation is consistent with a dip-slip displacement. A 100 m wide damage zone is present around the core of the fault containing a lower density of small displacement faults with offsets of o1 mm to a few 10’s of centimetres. These small-scale faults have also experienced significant cataclasis. The main phase of faulting probably occurred during the Late Jurassic development of the Inner Moray Firth rift; Underhill (1991) provides a review of the regional basin development. The Hopeman Sandstone is a clean, high-porosity, yellow-brown, sandstone of predominantly aeolian origin, which lies unconformably on Devonian sediments of the Orcadian Basin. It is approximately 70 m thick in this area, and in general dips at a shallow angle to north. A 15 cm  15 cm  30 cm block from the core of the fault as well as a 10 cm  10 cm  10 cm block of undeformed Hopeman sandstone were obtained for microstructural and petrophysical property analysis. In total seven 2.0 in (5.08 cm) long, 1.0 in (2.54 cm) diameter cores were drilled perpendicular to the strike of the fault for the flow experiments reported here. 3. Experimental methodology

2. Sample location A subsidiary fault to the extensional Lossiemouth fault zone (Fig. 1), which lies on the southern margin of the Moray Firth, cuts through the Late Permian/Early Triassic Hopeman sandstone in the Clashach Quarry near Burghead in Northeast Scotland, (N571420 5100 ; W31240 2700 ;

The samples were scanned using an X-ray computed tomography (CT) system and their microstructure was analysed using a scanning electron microscope. All samples were cleaned by Soxhlet extraction and dried before being tested. Porosity was measured using a helium expansion porosimeter. Absolute (i.e. single-phase) gas and water permeability measurements were made using a variety of techniques described below. In all the experiments, the flow direction is perpendicular to the deformation bands. The air-water capillary pressure was measured using an ultracentrifuge. Gas relative permeability measurements were made on samples whose saturation was varied using vapour chambers. The methods are described in more detail below. 3.1. Microstructural analysis

Fig. 1. Photograph of the fault zone from which samples were collected in the Clashach Quarry, near Burghead, Scotland.

Resin impregnated polished blocks of the fault rock and the adjacent undeformed Hopeman sandstone were examined using a CAMSCAN CS44 electron microscope equipped with a secondary electron detector, a highresolution solid-state four quadrant back-scattered electron (BSE) detector, a cathodoluminescence (CL) detector and an EDAX energy dispersive X-ray spectrometer (EDS).

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The images were saved in 8-bit (256 grey-levels) digital form, and then imported into an image analysis package. The BSE signal is proportional to the mean atomic number of individual minerals. The composition and porosity of the samples could therefore be established by carefully thresholding the images and using the image analysis package to calculate the area occupied by each mineral phase as well as porosity. 3.2. X-ray tomography The samples were examined using a Picker PQ2000 dual energy CT scanner to ensure those selected for analysis did not contain open, high permeability, fractures formed during uplift or sample collection that are unlikely to be present in many gas reservoirs for which these rocks are being used as analogues (e.g. Rotliegend gas reservoirs of the southern North Sea, UK). 3.3. Absolute permeability determination The single-phase permeability of the fault rock was determined using both the steady-state (gas and brine) and the unsteady state (gas pulse-decay) methods. 3.3.1. Steady-state liquid permeameter Brine permeability measurements were made using a custom-designed flow-pump permeameter (Olson and Daniel, 1981; Olsen et al., 1991). This computerised permeameter, which uses an accurate constant-rate flow pump and a linear differential pressure transducer, is capable of accurately measuring permeabilities in the range of 10 D to 0.001 mD. Permeability measurements were made on 1 in diameter plugs oriented perpendicular to the fault plane. To saturate the samples with water prior to permeability analysis they were firstly placed in a saturator under vacuum and left overnight. The saturator was then flushed with CO2, left for an hour and evacuated again to remove the CO2. Deionised water was then allowed to drain into the chamber and the pressure was then increased to 2000 psi. The specimens were left to saturate at 2000 psi for 12 h. The sleeved samples were placed in a secondary rubber or neoprene membrane and confined in a triaxial cell at a pressure of around 115 psi to prevent leakage of permanent down the sides of the sample. A back pressure of around 38 psi was used during testing. 3.3.2. Steady-state gas permeability Steady-state gas permeability measurements were made by flowing nitrogen gas across samples that were confined at a pressure of 1500 psi within a Hassler cell. The gas permeability was calculated, when steady-state flow was reached, based on the pressure drop across the sample, the flow rate, the gas viscosity, as well as the sample dimensions. Measurements were taken at different pore pressures to obtain the Klinkenberg corrected gas permeability. The Klinkenberg corrected permeability is obtained

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by plotting the reciprocal of the pressure versus the permeability measured at each pressure. The corrected permeability value is taken where the pressure is infinity. 3.4. Pulse-decay permeametry Measuring the permeability of tight rocks presents several problems, since standard measuring techniques are generally impractical and difficult to apply. Usual methods of measuring permeabilities in the laboratory have utilised steady-state flow. If the permeability is low, long periods of time are required to establish steady-state flow, thus, these procedures are impractical. Brace et al. (1968) introduced a transient flow method to measure permeability of Westerly Granite. Their experimental arrangement consists of a cylindrical sample, which is connected to two fluid reservoirs. At the start of the experiment, the fluid pressure in the upstream reservoir is suddenly increased. As this pressure decays, fluid flows from the upstream reservoir, across the sample to the downstream reservoir. In their procedure, the permeability of the sample is calculated from the observed pressure decay in the upstream reservoir. The mathematical analysis adopted by Brace et al. (1968) for transient pulse test assumes that there is no compressive storage in the rock sample. This assumption is invalid for rocks that have significant porosity, although it was reasonable for the work they did since they dealt with low porosity crystalline rocks. Several mathematical models have been suggested for the transient pulse test (e.g. Lin, 1977; Hsieh et al., 1981a, b). Jones (1997) proposed a new technique that was able to reduce the analytical time required for traditional pulse-decay permeameters by only investigating a portion of the pulsedecay curve after a smooth pressure gradient has been established. This has resulted in a significant decrease in analytical time-albeit at the expense of pore volume determination, which must be determined independently. In this study, pulse-decay measurements were made using a Core Laboratories PDP-200 pulse-decay permeameter, which is built based on the design of Jones (1997). The PDP-200 has software that calculates the permeability of the sample based on the pressure decay curve; it calculates the gas viscosity based on the type of gas used in the experiment and the pressure. Helium gas was used in the tests. The system is ideal for direct measurement of tight gas sands, fault rocks and other low permeability porous media with permeability below 0.1 mD. 3.5. Capillary pressure determination using centrifuge Air-water drainage capillary pressure curves were obtained from five samples of the Clashach fault using an Optima L-100 XP ultracentrifuge. The ultracentrifuge was operated during our experiments at up to 15,000 rpm, which is equivalent to a capillary pressure of 1250 psi. Following saturation, the samples were placed in the

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centrifuge and their drainage air-water capillary pressures were determined by gradually increasing the speed of the centrifuge and measuring the amount of water expelled from the specimens as a function of time for each speed. The length of time required for the water saturation to reach equilibrium varied from sample to sample for each time-step. Samples (HP2U and HP2V) were left in the centrifuge for almost a month and run to a speed of 15,000 rpm. Other experiments were carried out over a 10–15-day period. The data were then analysed using the PORCAP software (D&B Ruth Enterprises). 3.6. Vapour-pressure methods for changing saturation Thompson (1870) showed that the vapour pressure above a liquid surface is a function of its curvature. As the capillary pressure is a function of the liquid surface curvature it is possible to obtain capillary pressure curves by measuring the change in saturation of a sample as a function of vapour pressure (e.g. Melrose, 1987, 1990; Morrow et al., 1984; Ward and Morrow, 1985). In particular, capillary pressure can be calculated using the modified Kelvin equation:   p RT Pc ¼ ln v1 , (1) pv2 V m where Pc is the capillary pressure, pv1 the partial pressure for brine within pores, pv2 the partial pressure for equilibrating salt solution, R the universal gas constant, T the absolute temperature and Vm the molar volume for water. The technique is especially suited for pore systems characterised by abnormally high capillary pressures. However, this method is unable to measure the capillary pressures at high water saturation. This is because the technique reduces its sensitivity at high relative humidity (i.e. 495%), which limits the capillary pressure to a lower value of 1000 psi (Newsham et al., 2004). The lower limit of 1000 psi means that the technique is ideally suited for use in conjunction with the ultracentrifuge, which measures the capillary pressure up to 1250 psi. In the present study, we placed the samples in chamber in which the vapour pressure was altered by using different saturated salt solutions (ISO 483, 1988). 3.7. Relative permeability measurement No previous attempts have been made to measure the gas relative permeability of cataclastic faults. Numerical modelling suggested it would be far too time-consuming to undertake steady-state relative permeability measurements on such rocks. Therefore, it was decided to conduct gas pulse-decay permeametry on samples whose saturation was altered using the ultracentrifuge or vapour chambers (e.g. Melrose, 1987; Collins, 1976; Calhoun et al., 1949). The saturation of three cores of fault rock was varied using the ultracentrifuge. After the equilibration at a given

speed (i.e. capillary pressure), the samples were placed in the pulse-decay permeameter and attempts were made to measure their relative permeability to gas. To obtain gas relative permeability measurements at higher capillary pressures (i.e. lower water saturations), the three cores of the fault rock were placed in desiccators whose humidity was varied as described above. The samples were weighed every 24 h until equilibrium was achieved, e.g. constant weight. The weight difference between the sample after equilibration in the vapour chamber and its dry weight was used to calculate the water saturations. The effective gas permeability was then determined in the pulse-decay permeameter. The samples were then placed in a desiccator containing a different salt solution (relative humidity) and the process of equilibration and gas permeability determination was repeated. 4. Experimental results 4.1. Microstructural results The undeformed Hopeman sandstone, is well sorted with a fine to medium grain-size and composed of 83% quartz, 6% K-feldspar, 1% clay with a porosity of around 10% (Fig. 2). The main diagenetic process to affect the sample was the precipitation of mesocrystalline quartz cement, which makes up around 21% of the rock volume. It has been suggested that the silica maybe hydrothermal in origin as the Lossiemouth fault is a major basin bounding fault (Stuart Haszledine, pers. com. 2006). The fault rock (Fig. 3) clearly has a porosity down to around 3%, which is far less than the host sandstone. It should be noted that the 3% value is lower than for the samples tested that are quoted in Table 1 because the latter are composed of alternating bands of fault rock and undeformed sandstone. The reduction in porosity within the fault rock occurred as a result of two processes. First, during deformation, the fault rock experienced considerable grain-fracturing, which reduced grain-size and grain-sorting, increased grain angularity, allowing the grain-fragments to be packed more effectively than the undeformed grains in the surrounding sandstone. Second, following faulting, the fault rock experienced enhanced quartz cementation. The fresh fracture surfaces were probably ideal nucleation sites for quartz cement. The resulting fault rock obtained is extremely well lithified making it easy to obtain undamaged cores. Fig. 4 shows the CT images obtained from fault cores. Each pixel of a CT image represents the normalised X-ray attenuation of that piece of material. The attenuation coefficient is function of both the electron density (bulk density) and atomic number. In rocks, the CT number is a function of the rock density and the fluids contained within the pore space. So the images in Fig. 4 show that the cores are highly heterogeneous and composed of alternating parallel bands of low porosity cataclastic fault rock separated by lenses of relatively undeformed sandstone.

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Fig. 2. BSE (left) and CL (right) micrographs showing the undeformed Hopeman sandstone near to the fault within the Clashach fault.

Fig. 3. BSE (left) and CL (right) micrographs showing the fault rock present along Clashach fault.

Table 1 Single-phase permeability results from the seven cores of the Hopeman fault rock analysed during this study Sample

Length (cm)

Diameter (cm)

Pore volume (cm3)

Porosity (%)

Pulse decay (mD)

Klinkenberg permeability (mD)

Water permeability (mD)

HP3b HP3a HP2U HP2V HP2X HP2Y HP2Z

5.08 4.89 4.94 4.75 4.79 4.77 4.84

2.49 2.47 2.49 2.49 2.5 2.5 2.5

2.23 1.88 1.45 1.39 1.53 1.27 1.54

9.02 8.02 6.03 6.01 6.49 5.41 6.47

0.003 0.001 0.006 0.003 0.005 0.002 0.004

0.004 0.002 0.006 – – – –

0.003 0.003 – – – – –

4.2. Absolute permeability results

4.3. Capillary pressure results

Pulse-decay permeametry results (Table 1) show that the gas permeability of the core samples varied between 0.001 and 0.006 mD. The variation in permeability between samples is to be expected considering the heterogeneous nature of the fault core. The pulse-decay measurements are within 0.001 mD of the Klinkenberg corrected gas permeability values, which we believe is good considering the low permeability of these samples. The steady-state water permeability results are within the same order of magnitude of the pulse-decay permeametry and Klinkenberg corrected values. Again these results are surprisingly consistent considering that the steady-state water permeability measurements were made at lower confining pressures and the use of water as the permeant could have lead to the swelling of the small amount of clay present.

The capillary pressure results processed using the Forbes second method algorithms within the PORCAP software are shown in Fig. 5. Most samples appear to reach a minimum water saturation (Sw) of around 0.4–0.5 at a capillary pressure of around 100–350 psi. The only exception to this was sample HP2V, whose water saturation continued to decrease steadily reaching an Sw of around 0.2 at a capillary pressure of 1250 psi. 4.4. Relative permeability measurements Pulse-decay gas permeability measurements could not always be obtained from samples desaturated with the ultracentrifuge. This is because at low centrifugal speed, most of the pore throats are filled with water and the gas network does not span across the whole sample. The gas

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Fig. 4. X-ray tomography of two cataclastic fault rocks. Note the heterogeneity variation along the length of the sample, which is clearly shown in the right-hand plot.

relative permeability results reported here are from samples whose saturation had been varied using the vapour chambers; the results are shown in Fig. 6. It should be noted that we did not use flow simulations to history match the experimental results because the method used for changing water saturations and making gas relative permeability measurements is not affected by capillary end effects. The results show that the effective gas permeability at the minimum water saturation that was achieved by centrifuge (i.e. Sw ¼ 0.40 at capillary pressure of 1250 psi) is o0.02 of the absolute permeability values. This permeability was used to generate a Corey representation of the gas relative permeability. The capillary pressure measurement of 1250 psi needs to be adjusted to reservoir to take into account differences in the interfacial tension between air and water in the laboratory experiments and between gas and water in the laboratory. Firoozabadi and Ramey (1988) suggest the gas–water interfacial tension at room temperature and pressure is around 72 mN/m, which reduces to around 45 mN/m at 100 1C and 3000 psi. In which case, the 1250 psi value measured in the centrifuge is equivalent to a capillary pressure of around 780 psi under conditions that representative of gas reservoirs in the

southern North Sea. Even large gas columns such as the 400 m found within the Indefatigable field (McCrone et al., 2003) only generate a capillary pressure of around 540 psi. Therefore, if these fault rocks were present within southern North Sea gas reservoirs they would be expected to have a relative permeability to gas of o0.02. 5. Incorporation of results into a production simulation model The Rotliegend play in the southern North Sea consists of high net-to-gross aeolian sandstones of Late Permian age deposited on the southern edge of the Southern Permian Basin. The Rotliegend reservoir sandstones directly overly the prolific Carboniferous source rocks, and are generally sealed by a thick sequence of Zechstein evaporites. compartmentalisation of the Rotliegend reservoirs is one of the key issues affecting gas production. For example, van der Molen et al. (2003) showed that a 250 bars (3627 psi) pressure difference built up across a fault during production from a Rotliegend reservoir from offshore Netherlands. In this case, the fault clearly juxtaposed Rotliegend against Rotliegend suggesting that

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1

600 Pc(psi)

Production (cc)

FAB

500 400 300 200 100

0.8 0.6 0.4

Exp Prod Sim prod

0.2 0

0 0

0.2

0.4

0.6

0.8

1

0

Sw

Pc(psi)

Production (cc)

FAB

500 400 300 200 100 0

0.8 0.6 0.4

Exp Prod Sim prod

0.2

0.2

0.4

0.6

0.8

1

0

Sw 600

5000 10000 speed (rpm)

15000

1 Production (cc)

FAB

500 Pc(psi)

15000

0

0

400 300 200 100

0.8 0.6 0.4

Exp Prod Sim prod

0.2 0

0 0

0.2

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Sw 1200

5000 10000 speed (rpm)

15000

1 Production (cc)

FAB

1000 Pc(psi)

5000 10000 speed (rpm)

1

600

800 600 400 200

0.8 0.6 0.4

Exp Prod Sim prod

0.2 0

0 0

0.2

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800 600 400 200

0.8 0.6 0.4

Exp Prod Sim prod

0.2 0

0 0

0.2

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5000 10000 speed (rpm)

15000

Fig. 5. Air-water capillary pressure drainage curves for five samples of the Clashach fault. Maximum centrifuge speed was 10,000 rpm for HP2X (a), HP2Y (b), HP2Z (c) and a maximum speed of 15,000 rpm for HP2U (d) and HP2 V (e).

the presence of the fault rock itself was responsible for the compartmentalisation. In the following section, we present some results from a simplified production simulation model, which show how the relative permeability and

capillary pressure results presented above can help explain the cross-fault pressure differences described by van der Molen et al. (2003). We begin by describing the production simulation model and then compare the results from

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Fig. 7. 3D view showing the initial gas saturation in the reservoir. Production is from compartment 1.

TM

tf

k1

L1

kf

k2

k1

k2

L2

L1

L2

Fig. 8. The representation of a fault straddling two grid blocks as a ‘‘multipliers’’ to the interblock transmissibility. (b) The modelled fault of thickness tf physically occupies a thickness of tf/2 of each neighbouring grid block.

Fig. 6. Experimental gas relative permeability (krg) results for three samples of the Clashach fault.

simulations in which the multi-phase flow properties of the fault rocks are used compared with traditional methods used to model the impact of faults on petroleum production based on their single-phase permeabilities. 5.1. Model description A simplified production simulation model (Fig. 7) was created using EclipseTM 100 black oil simulator, with similar compartment sizes to those in the reservoir described by van der Molen et al. (2003). In particular, the basic model is 3000 m long, 4000 m wide and 300 m thick. A fault was included within the model to create two compartments. The model was constructed so that the area of Rotligend:Rotliegend juxtaposed by the fault was similar to that in the reservoir described by van der Molen et al. (2003). Two gas producers were placed in compartment one that were around 270 and 1100 m from the fault. Production rates in the producers were controlled by setting the bottom hole pressure to 50 bars (725 psi). Gas producers were not placed in compartment two. Two distinct models were created (Fig. 8). In the first, TMs were calculated to take into account the presence of

the fault using the methodology described by Manzocchi et al. (1999) in which no account is taken of the relative permeability or capillary pressure of the fault rocks. In the second, the local grid refinement (LGR) capabilities of EclipseTM were used to include the fault discretely so that it could be given its own capillary pressure and relative permeability curves based on the results presented in this study. The LGR was used to reduce any numerical dispersion and instability due to the different properties between the undeformed and deformed rocks. For both types of models, base case examples were run in which the fault was given the same properties as the undeformed reservoir. We did not have access to host rock permeability data from the reservoir described by van der Molen et al. (2003) so we have run each model with reservoir permeabilities of 10, 100 and 1000 mD (Cases 1, 2 and 3, respectively). These permeability values are in the range that we have encountered in our work on other Rotliegend reservoirs from the southern North Sea (Fisher and Knipe, 2001). 5.1.1. Modelling the impact of faults using TMs The impact of faults on fluid flow in production simulation models is usually taken into account by applying TMs to the faces of grid-blocks within reservoir simulators to account for the fact that they contain a certain portion of faulted material. Following Manzocchi et al. (1999), TMs can be estimated if the permeability and

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thickness of the fault rock, the average permeabilities of the undeformed sediment in the grid-blocks juxtaposed by the fault as well as the grid-block dimensions are known. In particular, the transmissibility, Tranij, between two gridblocks, i and j, separated by a fault of constant thickness is calculated using   2 Tranij ¼ , (2) ðLi =ki Þ þ ðLj =kj Þ where Li and Lj are the cell lengths, ki and kj are the permeabilities of the undeformed cells. If fault rock of constant thickness is present between the two grid-blocks (i.e. Fig. 8), i and j, the transmissibility between the gridblocks across the fault, Tran Fij, i and j, separated by a fault of constant thickness is calculated using   2 Tran F ij ¼ , ððLi  tf Þ=ki Þ þ ð2tf =kf Þ þ ððLj  tf Þ=kj Þ (3) where tf is the fault rock thickness, and kf the fault rock permeability. In the main production simulation packages it is possible to take into account the presence of fault rock by applying a TM to the face of grid-blocks adjacent to the fault; the TM is calculated using TM ¼

Tran F ij . Tranij

(4)

For the present study, TM values were calculated from an average of the single-phase fault rock permeability values (i.e. 0.004 mD) presented above and assuming a fault rock thickness of 0.5 m. This fault rock thickness is consistent with the correlations between fault throw and fault thickness presented by Hull (1988). It is also consistent with field observations of fault rock thickness made during our visit to the Clashach Quarry. 5.1.2. Modelling the impact of faults using a LGR It is clear that the method of calculating TMs described above does not involve any information of the capillary pressure or relative permeability behaviour of fault rocks. We therefore constructed a series of models in which the fault was represented as discrete cells using a LGR. Around 80 LGR cells are added in such a way to produce a gradual transition in the cell pore volumes from the fault cells to the host cells, with fault size of 0.5 m. The cells representing the fault were given the same absolute permeability as used to calculate the TMs described above. These cells were given their own relative permeability and capillary pressure curves based on the data presented above (Fig. 9). We did not have any information on the water relative permeability of the cataclastic faults therefore we used a Corey representation for the water relative permeability and assumed that the Corey exponent for water-wet reservoir rocks are valid in this case (Fig. 9). However, the lack of significant water production in most Rotliegend reservoirs indicates that the undeformed reservoir is at irreducible water saturation so we do not

Fig. 9. (a) Relative permeability and (b) capillary pressure data from the fault rock used in the production simulation models in which the fault was represented as a discrete cell. Corey functions have been used to fit the relative permeability data so that it could be extrapolated to Sw values that were too high to allow gas relative permeability measurements to be made.

expect significant movement of water between the fault rock and the reservoir during production. In addition, we conducted a sensitivity analysis, which suggested the simulation model results were insensitive to the shape of the water relative permeability curve for the fault rocks. We also ran some sensitivity studies to investigate the impact of the shape of the fault rock gas relative permeability curve on the simulation model results; these are discussed below. Other than the inclusion of the fault as a discrete plane, the models run were identical to those as described for the TM representation of fault rocks described above. A large number of models were also run to ensure that the results presented were not artefacts resulting from the gridding used. In particular, thickness of the cells used for the LGR was tested by simulating well tests close to partially sealing faults for which analytical solutions were available (see Al-Busafi et al., 2005). A model was also run in which the cells representing the fault were given the same capillary pressure and relative permeability curves as for the host sediment; these gave the same results as for the models in which TMs, calculated based on the single-phase fault rock permeability results, were used. Berg and Øian

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(2007) performed a grid refinement study to investigate whether is the chosen grid resolution was sufficient of resolving the effect of capillary forces. The fact that we are assuming the fault to be a single plane, compared to the complex fault zone modelled by Berg and Øian (2007) means that we did not need to perform such an investigation for the present study. 5.2. Production simulation modelling results Plots of the average pressure of each compartment, as well as the pressure different between the two compartments as a function of time are presented in Figs. 10–12. As would be expected, gas pressures in both compartments are virtually identical in the models in which fault rock properties are ignored (i.e. TM ¼ 1 in Fig. 10 and LGR no fault in Fig. 11). The results are also virtually identical

Fig. 11. Results from simulation models in which fault rocks were not included (LGR no fault) and those in which the faults was included discretely and given its own relative permeability and capillary pressure curve (LGR with fault): (a) Pressure in compartment 1. (b) Pressure in compartment 2. (c) The pressure difference between compartments 1 and 2. Cases 1, 2 and 3 are for reservoir permeabilities of 10, 100 and 1000 mD, respectively.

Fig. 10. Results from simulation models in which fault rocks were not included (TM ¼ 1) and those in which faults rock properties were incorporated using transmissibility multipliers (TM ¼ calculated): (a) Pressure in compartment 1. (b) Pressure in compartment 2. (c) The pressure difference between compartments 1 and 2. Cases 1, 2 and 3 are for reservoir permeabilities of 10, 100 and 1000 mD, respectively.

to those from the model with a reservoir permeability of 10 mD in which fault rock properties were included using TM values calculated from the absolute permeability measurements and estimates of fault rock thickness (i.e. Case 1 in Fig. 10). In the models with reservoir permeabilities of 100 and 1000 mD, in which fault properties were incorporated using TMs (i.e. Cases 2 and 3 in Fig. 10), pressure differentials can be seen to develop between compartments 1 and 2. However, these models could not reproduce the 250 bar (3627 psi) cross-fault production-induced pressure difference reported by van der Molen et al. (2003).

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models, we assumed that the minimum krg values were equal to the lowest measured in the laboratory (i.e. minimum krg ¼ 0.001). In this case, the large pressure differentials between the compartments that have been observed in the field could not be reproduced. A model was also run in which it was assumed that the fault rock entered a ‘‘permeability jail’’ (i.e. krg ¼ 0) at water saturations above 0.4. In this case, we could reproduce the 250 bar pressure difference observed within the field. These sensitivity studies indicate that the extrapolated krg curves used in the models (e.g. Fig. 9) are consistent with crossfault pressure differences that have been reported from Rotleigend reservoirs. 6. Discussion The similarity of the results from the production simulation model of the reservoir with 10 mD permeability in which fault properties were not included and those from equivalent models in which fault properties were included using TM values calculated from single-phase permeability values may seem somewhat surprising. However, Yaxley (1987), showed that well bore pressures during interferences tests conducted across partially sealing faults are controlled by the specific transmissibility ratio, a, defined as a¼

Fig. 12. Comparison of results from simulation models in which fault rock properties were included using transmissibility multipliers (TM calculated) with and those in which the faults was included discretely and given its own relative permeability and capillary pressure curve (LGR with fault): (a) Pressure in compartment 1. (b) Pressure in compartment 2. (c) The pressure difference between compartments 1 and 2. Cases 1, 2 and 3 are for reservoir permeabilities of 10, 100 and 1000 mD, respectively.

In contrast, when the fault was included discretely and given its own relative permeability and capillary pressure curves, consistent with the experimental results described here (i.e. LGR with fault in Fig. 11), the fault acted almost as a total barrier to gas production and was able to reproduce the 250 bar (3627 psi) pressure difference reported by van der Molen et al. (2003). Clearly, the fault rock krg curves used in Fig. 9 were extrapolated to krg values that were several orders of magnitude lower than those measured in the laboratory. We ran several models to determine the extent to which our results were dependent upon the krg values used. In the first

kf d , tf k r

(5)

where d is the distance between two wells, and kr the permeability of the undeformed reservoir. Faults have minimal impact on interference tests conducted between wells where values of a are greater than 1. If a is less than 0.001, the faults behave like total seals during the test. Calculation of a for the different models described above provides a guide as to the impact of faults on fluid flow. To calculate a we have assumed that d is equivalent to the average distance between the centres of the compartments i.e. 2000 m. In the model in which the reservoir has a permeability 10 mD and the fault properties are included using a TM, a equals 1.6. On the other hand, a is equal to 0.016 for the model in which the reservoir has a permeability 1000 mD and fault properties have been included using a TM based on the single-phase fault rock permeability. These simple calculations help explain why the simulation model results for the unfaulted reservoir with a 10 mD permeability are similar to those from the faulted 10 mD reservoir in which fault rock properties have been included using a TM calculated from the absolute fault rock permeabilities. The a of 0.016 also explains why the fault in the model with a reservoir permeability of 1000 mD, where fault rock properties have incorporated using a TM, is acting as a partial, but not complete barrier to fluid flow. Including the relative permeability and capillary pressure of the fault in the simulation models was able to reproduce the production data because it effectively reduced the fault

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rock permeability, and hence a, by more than two orders of magnitude and hence made the faults, particularly in the high permeability reservoirs, behave like absolute seals to gas on a production time-scale. The findings that the relative permeability and capillary pressure data help explain the large cross-fault pressure differences resulting from production from some Rotliegend reservoirs. It also highlights the potential importance of incorporating the multi-phase flow properties of faults into production simulation models. Indeed, the modelling conducted during this study actually explains why Rotliegend reservoirs become so compartmentalised. In the simple example represented in this paper, we were able to include relative permeability and capillary pressure data from the fault rock by including the fault as a discrete plane using a LGR. It is not practical to include faults as discrete planes in more structurally complex reservoirs due to limitations on the number of grid-blocks that can be including in full-field simulation models. For such cases, it has been suggested that pseudo-functions (i.e. pseudorelative permeability and pseudo-capillary pressure curves) could be constructed to take into account the multi-phase flow behaviour of faults (Fisher and Knipe, 2001; Manzocchi et al., 2002). Work is currently being undertaken to identify reliable methods for this to be achieved during routine production simulation models. 7. Conclusions The first gas relative permeability data from cataclastic faults rocks has been presented. The results suggest that for if these were present within gas reservoirs in the southern North Sea they would have krg values of o0.02. These results explain the high level of compartmentalisation observed within some Rotliegend gas reservoirs, in the southern North Sea offshore UK and Netherlands, that is not easily modelled when only the absolute values of fault rocks are considered. In effect, methods that attempt to model the impact of faults on gas flow based only on absolute permeability values could be overestimating crossfault transmissibility by over several orders of magnitude. Further work is required to collect relative permeability data from different types of fault rock and for different wetting conditions. Further work is also required to develop methods that will be adopted by Industry to routinely incorporate the multi-phase flow properties of fault rocks into full field production simulation models. Acknowledgements The first author would like to thank the Petroleum Development Oman (PDO) for funding this Ph.D. research. BP, Chevron, ConocoPhilips, Corpro, Encana, Petrobras, Total and Shell are thanked for providing the funding, which allowed us to conduct a pilot study to investigate relative permeability of fault rocks. Schlumberger are also thanked for providing us with licenses for the

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