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, first published January 27, 2014; doi 10.1144/petgeo2013-014Petroleum Geoscience P. J. R. Fitch, M. D. Jackson, G. J. Hampson and C. M. John strategyin carbonate ramp reservoirs: impact of fluid properties and production Interaction of stratigraphic and sedimentological heterogeneities with flow

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Petroleum Geosciencehttp://dx.doi.org/10.1144/petgeo2013-014Published Online First

© 2014 EAGE/The Geological Society of London

IntroductIon

Carbonate reservoirs remain a major challenge for development and production. Poor prediction of production behaviour in car-bonate reservoirs is related to typical hydrocarbon recovery fac-tors below 35% (Montaron 2008; Meddaugh et al. 2011). Geological heterogeneities attributed to stratigraphic, sedimento-logical and diagenetic features exist over a range of length-scales, and are inferred to control reservoir architecture and the petrophysical properties of carbonate rocks (e.g. Sibley et al. 1997; Jennings et al. 2000; Lawrence et al. 2002; Pranter et al. 2006; Adams et al. 2011; Hollis et al. 2011). Numerous field development programs have clearly highlighted the need for a better understanding of the impact of heterogeneity on flow in carbonate reservoirs, especially in relation to rock and fluid properties, and development strategy (e.g. Jennings et al. 2000; Vaughan et al. 2004; Pranter et al. 2006; Agar et al. 2010; Hollis et al. 2011; Meddaugh et al. 2011). Integrated geological characterization and flow modelling studies of carbonate reser-voirs have been widely discussed (e.g. Bard et al. 1995; O’Hanlon et al. 1996; Abbaszadeh et al. 2000). However, previ-ously published examples have typically focused on the behav-iour of a subset of geological heterogeneities specific to the carbonate reservoir of interest (e.g. Stiles & Magruder 1992;

O’Hanlon et al. 1996; Sibley et al. 1997; Abbaszadeh et al. 2000; Lawrence et al. 2002; Pavlas 2002; Stenger et al. 2009). An integrated study of carbonate reservoirs, capturing all types and scales of heterogeneities documented in outcrop and subsur-face examples, coupled with production simulation experiments, is required to provide a framework for the identification of those key heterogeneities that should be incorporated into reservoir models, and to illustrate how individual heterogeneities impact on flow.

Numerous studies have attempted to systematically investi-gate and identify key heterogeneities that impact flow in silici-clastic reservoirs deposited in a range of environments (Weber 1986; Kjønsvik et al. 1994; Jones et al. 1995; Jackson et al. 2005, 2009; Howell et al. 2008; Manzocchi et al. 2008; Choi et al. 2011). However, equivalent generic studies in carbonate reservoirs are lacking. The continuum of carbonate depositional systems and associated stratigraphic architectures between end-members of carbonate ramps and carbonate platforms has been investigated in a number of recent publications, using outcrop case studies and forward modelling experiments (e.g. Pomar 2001; Burgess & Wright 2003; Bosence 2005; Dorobek 2008; Williams et al. 2011), and Jung & Aigner (2012) provided a comprehensive classification of carbonate geobodies within the context of broad classes of platform type and environments of

Interaction of stratigraphic and sedimentological heterogeneities with flow in carbonate ramp reservoirs: impact of fluid properties and

production strategy

P. J. r. Fitch*, M. d. Jackson, G. J. Hampson and c. M. JohnDepartment of Earth Science and Engineering, Imperial College London, South Kensington Campus,

London SW7 2AZ, UK*Corresponding author (e-mail: [email protected])

AbstrAct: It is well known that heterogeneities in carbonate reservoirs impact fluid flow during production. However, few studies have examined the impact of the same heterogeneities on flow behaviour with different fluid properties and production scenarios. We use integrated flow simulation and experimental design techniques to investigate the relative, first-order impact of stratigraphic and sedimentological heterogeneities on simulated recovery in carbonate ramp reservoirs. Two production strategies are compared, which pro-mote dominance of either horizontal or vertical flow.

We find that the modelled geology is more important than the simulated fluid properties and production scenarios over the ranges tested. Of the het-erogeneities modelled here, rock properties and stratigraphic heterogeneities that control reservoir architecture and the spatial distribution of environment of deposition (EOD) belts are important controls on recovery regardless of the production strategy. The presence of cemented hardground surfaces becomes the key control on oil recovery in displacements dominated by vertical flow. Permeability anisotropy is of low importance for all production strategies. The impacts of stratigraphic heterogeneities on recovery factor and water break-through are more strongly influenced by fluid properties and well spacing in displacements dominated by vertical flow. These results help to streamline the reservoir modelling process, by identifying key heterogeneities, and to optimize production strategies.

2013-014research-articlethematic set: [Fundamental controls on Flow in carbonates]XXX10.1144/petgeo2013-014P. J. R. FitchInteraction of carbonate heterogeneities with flow2014

at Imperial College London on February 24, 2014http://pg.lyellcollection.org/Downloaded from



P. J. R. Fitch et al.2

deposition (EODs). While providing insight into the range in stratigraphic architectures, EOD types and geobody heterogenei-ties present in carbonate ramps and platforms, these studies do not identify the relative impact of these heterogeneities on flow during hydrocarbon recovery.

We use a hierarchical classification scheme for heterogenei-ties in carbonate ramp reservoirs to identify and constrain con-ceptual end-member settings for a selection of first-order stratigraphic and sedimentological controls on fluid flow. The hierarchy is based on a comprehensive review of published out-crop analogues and subsurface examples, including the homocli-nal ramps of Spain (Badenas et al. 2010), Germany (Koehrer et al. 2010; Palermo et al. 2010) and Morocco (Pierre et al. 2010; Amour et al. 2011, 2013), and the distally steepened ramps of Italy (Mutti et al. 1996), Menorca, Spain (Pomar et al. 2002) and Oman (Cozzi et al. 2010). The scheme details the architecture, geometry and spatial distribution of stratigraphic and sedimentological heterogeneities in carbonate ramp reser-voirs. Levels 1–3 of the hierarchy (Fig. 1a–c) record strati-graphic heterogeneities, with a focus on the architecture and spatial distribution of EOD belts, at decreasing length-scales. The distribution and arrangement of geobodies and depositional facies within EOD belts are documented at level 4 (Fig. 1d), whilst level 5 focuses on bed-scale features (Fig. 1e). Heterogeneity at centimetre–micrometre scales (e.g. sedimentary structures, grain shapes and pore networks) are recorded at lev-els 6 and 7 of the hierarchy. We have investigated first-order stratigraphic and sedimentological heterogeneities that are rele-vant to hydrocarbon production from carbonate ramp reservoirs that are unkarsted, and which are unfractured or contain frac-tures that do not significantly impact flow (e.g. because the frac-tures are poorly connected). We recognize that structural and

diagenetic heterogeneities are important controls on hydrocarbon production in many carbonate reservoirs (e.g. Belayneh et al. 2006; Matthäi et al. 2007; Shedid 2009; Agar et al. 2010; Hollis et al. 2011), but these are not the focus of this paper.

Fitch et al. (2012) report an initial application of the hierar-chy to assess the impact of stratigraphic heterogeneities at levels 1–3 (Fig. 1a–c) on flow behaviour of carbonate ramp reservoirs, using simulated hydrocarbon production via waterflooding, with vertical injection and production wells completed over the entire reservoir interval. In these simulation experiments, the most important factors controlling production were the rock properties representing a particular EOD belt, and stratigraphic architecture, which controls the volume, geometry and spatial distribution of the EOD belts. Flow in these models was primarily horizontal, because: (1) the chosen well type and completion strategy pro-moted horizontal flow; and (2) the relatively large pressure gradi-ents induced between injection and production wells suppressed gravity forces, largely preventing the higher density water from flowing below the lower density oil to form a ‘gravity tongue’. Fitch et al. (2012) postulate that the low ranking of heterogenei-ties controlling vertical flow, such as permeability anisotropy within EOD belts and the presence of laterally extensive cemented barriers along stratigraphic surfaces, arose because flow was predominantly horizontal. Their hypothesis is supported by reservoir-specific studies of production mechanisms that pro-mote vertical flow (e.g. primary recovery through gravity drain-age), in which the heterogeneities controlling vertical flow were of key importance (e.g. Abbaszadeh et al. 2000; Ates et al. 2005; Hollis et al. 2011). However, there has been no systematic inves-tigation of the interaction between stratigraphic and sedimento-logical heterogeneity and production mechanism in carbonate reservoirs using the same suite of models.

c.10 m

c. 10 kmInner ramp EOD

MidrampEOD

Outer ramp EOD

c. 10 km

c. 10 m

paleoseaward

paleoseaward

c. 10 mc. 10 km

c. 10 km

paleoseaward(A) Level 1

(B) Level 2

(C) Level 3

(D) Level 4

c. 1 m

c. 10 m

(E) Level 5

Terrestrial

PelagicsOuter rampMid rampInner ramp

Key to Environments of deposition(EODs) (Fig. 1A-C)

Oncoidal wackestone

Microbial floatstone-rudstonePeloidal packstone-grainstoneOoidal grainstone

Mudstone-wackestone with

Key to depositional facies (Fig. 1D-E)

in-situ corals

Skeletal wackestone-packstone

FirmgroundHardground

MarlInterbedded wackestone and mudstone

Stratigraphic Surfaces

Pelagic EOD

c. 100 m

palaeolandward

palaeolandward

palaeolandward

palaeolandward

Fig. 1. Generic hierarchy of heterogeneities within carbonate ramp reservoirs across a range of length-scales. (a) Level 1: large-scale stratigraphic cycle. (b) Level 2: medium-scale stratigraphic cycle. (c) Level 3: small-scale stratigraphic cycle or parasequence. (d) Level 4: depositional facies architecture within a single parasequence. (e) Level 5: package of beds within a depositional facies body or belt. Note that levels 6 and 7, which describe intra-bed architecture and pore networks, respectively, are not shown here.




Interaction of carbonate heterogeneities with flow 3

The aim of this paper is to investigate how the impact of stratigraphic and sedimentological heterogeneities on recovery from carbonate ramp reservoirs changes for waterflood produc-tion strategies that promote horizontal and vertical flow. Our modelling experiments are not designed to replicate specific res-ervoir case studies via the accumulation of geological and flow-related detail, but, instead, to distil the essence of complex rock–fluid systems to serve as a benchmark for comparison with real reservoir data (cf. the first stage of the ‘top down’ modelling approach described by Williams et al. 2004). This paper comple-ments the work of Agada et al. (2014) and Shekhar et al. (2014). Shekhar et al. (2014) document the impact of geological hetero-geneity on simulated production from reservoir models that are based on an outcrop analogue of a Middle Jurassic carbonate ramp (the ‘Island’ outcrop, High Atlas Mountains, Morocco) that can readily be placed into the stratigraphic framework(s) investi-gated in our generic study. Agada et al. (2014) perform a series of detailed and systematic flow simulations on the same outcrop model to explore optimization solutions to enhance hydrocarbon recovery. Rock and fluid properties, and simulated production constraints, are consistent between the three articles, allowing comparison of the findings from the individual studies.

stratigraphic and sedimentological heterogeneities

Six generic stratigraphic and sedimentological heterogeneities, from levels 1–3 of the hierarchical classification scheme (Fig. 1a–c), were chosen for investigation as key first-order controls on reservoir geometry, architecture and the spatial distribution of rock properties. Two end-members, termed setting (i) and (ii), were chosen to represent the range of values for each heteroge-neity (Fig. 2). The choice of heterogeneity settings is summa-rized briefly below. EOD belts that form the focus of this study are the inner, mid and outer ramp. The boundaries between inner- and mid-ramp EODs, and between mid- and outer-ramp EODs, represent the position of fair-weather wave base and storm wave base, respectively (Burchette & Wright 1992; Bosence & Wilson 2003). Each of the six studied heterogenei-ties is described in turn below.

EOD-belt interfingering length. The length over which EOD-belt boundaries interfinger represents the maximum, dip-oriented,

extent of EOD-belt boundaries between two sequence bounda-ries (Fig. 2). Migration of EOD belts is controlled by the rates of sea-level rise or fall, sediment production and basinal sedi-ment transport, and by pre-existing bathymetry (Sarg 1988; Bur-chette & Wright 1992; James 1997; Bosence & Wilson 2003; Schlager 2005; Immenhauser 2009; Williams et al. 2011). Set-ting (i) represents low rates of sediment production, moderate–high rates of sea-level rise, inefficient basinal sediment transport and/or steeply dipping antecedent bathymetry that result in a ‘short’ interfingering length of 8 km (Fig. 2). This corresponds to a lower limit in interfingering length, evident in published out-crop and subsurface transects (e.g. Borgomano et al. 2002; Ven-nin et al. 2003; Cozzi et al. 2010; Pierre et al. 2010). Setting (ii) corresponds to high rates of sediment production, sea-level fall or slow sea-level rise, efficient basinal sediment transport and/or gently dipping antecedent bathymetry that cause EOD belts to migrate further into the basin, resulting in a ‘long’ inter-fingering length of 24 km (Fig. 2). This represents an upper limit of interfingering length for documented case studies (e.g. Pomar et al. 2002; van Buchem et al. 2002; Wynn & Read 2008; Pierre et al. 2010). Our choice of EOD-belt interfingering length is not prescribed to a specific order or frequency of stratigraphic cycle because the documented examples that we use from the litera-ture occur over a wide range of interpreted sequence orders and cycle frequencies.

EOD-belt geometry. EOD-belt geometry defines a progradational or retrogradational–progradational architecture, depending on, for example, the relationship between the rates of sea-level rise and sediment production in a sequence. Setting (i) describes the case where only progradation is recorded between two sequence boundaries, using a simple linear EOD-belt boundary (Fig. 2). Here, retrogradational deposits are absent and the maximum flooding surface coincides with the underlying sequence bound-ary (e.g. Jacquin et al. 1991; Spalletti et al. 2000; van Buchem et al. 2002). Setting (ii) consists of a more complex geometry for EOD-belt boundaries, including both retrogradation and sub-sequent progradation (e.g. Wright & Burchette 1996; Carminati et al. 2007; Koehrer et al. 2010; Pierre et al. 2010; Williams et al. 2011). The transgressive–regressive architecture of setting (ii) is captured by incorporating a maximum flooding surface between the base and top sequence boundaries. Backstepping of the EOD belts is represented by a landwards shift of the bound-ary by 25% of the total interfingering length (Fig. 2).

EOD-belt rock properties. The EOD-belt rock properties reflect depositional facies characteristics and proportions described in an outcrop study of the Jurassic Assoul Formation, Amellago Can-yon, Morocco (Amour et al. 2011, 2013; Agada et al. 2014; Shekhar et al. 2014). The rock properties for each depositional facies type were obtained from a proprietary dataset of Mesozoic carbonate reservoirs from the Middle East, which provides a series of summary statistics from a catalogue of core plug meas-urements that define porosity–permeability relationships based on specific facies descriptors (see Benson et al. 2014; Shekhar et al. 2014). An average value of porosity and permeability for each depositional facies type present in a specific EOD was assigned to that EOD belt, weighted by the proportions of different depo-sitional facies in each EOD belt reported by Amour et al. (2011) (Table 1). Rock properties of individual EOD belts are uniform within a given EOD. We recognize that rock properties vary within EOD belts, and also within constituent depositional facies, because heterogeneities at smaller length-scales are present; moreover, these heterogeneities at level 4 and above in the hier-archy may influence flow (e.g. Fig. 1d, e). However, here we focus on the impact of larger-scale stratigraphic features that

Fig. 2. Summary of the six stratigraphic and sedimentological heterogeneities selected for investigation in the reservoir models. EOD-belt petrophysical properties (heterogeneities 3 and 4) are provided in Table 1. Conceptual sketches are shown for illustrative purposes, with no scale implied.





control the volume and distribution of EOD belts. This approach is justified in the first step of a ‘top-down’ study (Williams et al. 2004) because the EOD belts defined in Table 1 are associated with major, order-of-magnitude contrasts in petrophysical proper-ties. Attempting to model the variation in petrophysical properties associated with smaller-scale heterogeneity is not merited without capturing its spatial organization. EOD-belt rock property setting (i) represents a grain-dominated ramp, with high porosity and permeability values, while setting (ii) represents a mud-domi-nated ramp, with low porosity and permeability values (Fig. 2, Table 1).

Anisotropy of EOD-belt permeability. Permeability anisotropy, as used here, describes the difference between horizontal and verti-cal permeability at the scale of a reservoir model grid-block (see the next section). Setting (i) corresponds to isotropic behaviour, in which horizontal and vertical permeability are equal (kh=kv: Fig. 2, Table 1), and are given by the arithmetic average, derived from the summary statistics for depositional facies present in an EOD belt, weighted by their proportions within the EOD belt. Isotropic permeability provides the largest possible upper end-member for comparison. Setting (ii) accounts for the intercala-tion of thin, bodies of mud- and grain-dominated depositional facies that are laterally continuous at the grid-block scale, litho-logical variability between beds within depositional facies types, and textural variations within beds associated with sedimentary structures and bioturbation (e.g. Sahin et al. 1998). In this set-ting, the arithmetic average permeability used in setting (i) is assigned as the horizontal permeability (kh), but the vertical per-meability (kv) is given by the harmonic average of values for depositional facies from the proprietary dataset. The resulting kv/kh ratios range from 0.1 to 0.45 for the different EOD belts (Fig. 2, Table 1).

Character of EOD-belt boundaries. The transition between two laterally adjacent EOD belts is represented by the character of the EOD-belt boundaries. Setting (i) records a sharp, distinct change between EOD belts (Fig. 2). Setting (ii) represents a gra-dational boundary between EOD belts, consisting of three transi-tional zones, each of 100 m extent down depositional dip, where the middle zone is centred at the original EOD-belt boundary (Fig. 2). This simple approach provides a first-order approxima-tion of transects from published outcrop studies that document interfingering of depositional facies at EOD-belt boundaries over lengths of 100–500 m (e.g. Castel et al. 2007; Koehrer et al. 2010; Pierre et al. 2010; Elrick 2011). Rock properties are weight averaged according to their proximity to the neighbour-ing belts; the middle zone reflects average porosity and permea-bility of neighbouring EOD belts, while outer transition zones are assigned properties that reflect 75 and 25 % of the closest and furthest neighbouring EOD belts, respectively.

Sequence boundary rock properties. In our surface-based geo-logical models, sequence boundaries can act as simple frame-work features, with no associated modification of petrophysical properties (setting (i): Fig. 2). However, bioturbation and cemen-tation associated with early diagenesis can result in a decrease in porosity and permeability in a hardground or firmground mark-ing the sequence boundary (e.g. Bachmann & Kuss 1998; Pomar et al. 2002; Christ et al. 2012a; Amour et al. 2013). Setting (ii) is an upper end-member setting characterized by a laterally extensive, 10 cm-thick zone of decreased porosity and permea-bility below each sequence boundary (10% of the porosity and permeability assigned to the underlying EOD belt: Christ et al. 2012a), and the application of a zero transmissibility multiplier to the sequence boundaries, so that no vertical flow can occur

across them. We note that karstification at sequence boundaries is also common, and can result in locally enhanced permeability (e.g. Mazzullo & Chilingarian 1992; Djatmiko & Hansamuit 2010; Rahimpour-Bonab et al. 2012). However, for consistency with the Jurassic ‘Island’ outcrop analogue, where karst is not observed (Amour et al. 2011; Christ et al. 2012a), we do not investigate karsted sequence boundaries here.

MetHod

We used a suite of reservoir-scale models, sampled from larger models of the entire ramp, that capture generic styles of gross stratigraphic architecture in carbonate ramp systems. Each model has an areal extent of 4×4 km and a vertical thickness of approxi-mately 66 m. The areal extent was chosen to represent a sector model that captures several injection and production well pairs at spacings that are typical for Middle Eastern carbonate reservoirs (e.g. Sibley et al. 1997). Vertical thickness is representative of a medium-scale stratigraphic cycle and its constituent stratigraphic elements (Fig. 1b–c); it corresponds to several stacked reservoir zones in Middle Eastern carbonate reservoirs (e.g. Sibley et al. 1997), and is consistent with the thickness of the modelled inter-val of the ‘Island’ outcrop analogue studied by Amour et al. (2011, 2013). The models were constructed using surfaces that represent stratigraphic surfaces and EOD-belt boundaries, and gridded using corner-point grids that capture the surface geome-tries in an accurate and computationally efficient manner (White et al. 2004; Jackson et al. 2005; Sech et al. 2009). Grid cells are 66.6×66.6 m in area and vary in thickness, up to a maximum of 1 m. Grid layers build up from the underlying surface, and pinch out against overlying surfaces to ensure that the grid conforms to the surface-based geological framework. Inactive cells were bridged by non-neighbour connections so that they do not act as barriers to flow. The number of grid cells that were active for flow simulation ranged from 242 000 to 385 000, depending on the complexity of the stratigraphic framework and EOD-belt geometries in a particular model.

We used ReliaSoft’s DOE++ experimental design software to efficiently explore the parameter space defined by the heteroge-neities investigated in the suite of reservoir models. Specifically, we used a 26–3 fractional factorial experimental design, which allows the main effects of each heterogeneity to be estimated independently of other heterogeneities, assuming that higher-order interactions between heterogeneities are insignificant (Box et al. 1987; Wu & Hamada 2000; White & Royer 2003). This experimental design required two end-member settings to be specified for each of the six stratigraphic and sedimentological heterogeneities under investigation, and established a rank order of heterogeneities based on their simulated reservoir perfor-mance. A total of eight models were constructed, combining het-erogeneity settings as required by the experimental design, and flow simulation of this suite of models was carried out for each production scheme under investigation. The characteristics of the investigated stratigraphic and sedimentological heterogeneities were summarized in the previous section, and the simulated pro-duction schemes are outlined below.

resulting stratigraphic architectures

Three subtly different classes of reservoir architecture are observed, depending on the combination of end-member settings of the mod-elled stratigraphic heterogeneities (Fig. 3, Table 2): (1) models β, δ, η and θ display a layer-cake geometry with limited lateral thick-ness variation and no pinchouts in EOD belts; (2) models α and ε display a layer-cake geometry with pronounced lateral thickness variations, but no pinchouts, in EOD belts; and (3) models γ and ζ





show a nearly layer-cake geometry with pronounced lateral thick-ness variations and some pinchouts of EOD belts (Fig. 3).

rock and fluid properties

Relative permeability and capillary pressure are controlled by depositional and diagenetic fabric, fluid properties and wetting behaviour (Tiab & Donaldson 1996; Lucia 2007). Despite the broad range of pore-scale topologies and variable wettability observed for carbonate rocks (e.g. Okasha et al. 2003; Esfahani & Haghighi 2004; Sola et al. 2007; Meissner et al. 2009), and recognition that the approach to modelling relative permeability and capillary pressure can have a significant effect on predicted production behaviour (e.g. Hollis et al. 2011), many simulation models use a single set of relative permeability and capillary pressure curves. In our study, we used two approaches to model these data: (1) a single set of relative permeability and capillary pressure curves applied to the whole reservoir model (Fig. 4b, e); and (2) multiple sets of relative permeability and capillary pressure curves applied to three permeability classes of <10 mD, 10–100 mD and >100 mD (Fig. 4c, f). This approach enabled us to determine whether the simulated impact of heterogeneities on flow was dependent upon the approach used to model relative permeability and capillary pressure data. For simplicity, the same primary water–oil drainage curves were used in all models to establish the initial water saturation (Fig. 4a, b) because our focus here is on the impact of relative permeability and capillary pressure data on waterflood recovery factor, rather than on oil initially in place (OIIP). We recognize that variations in the ini-tial water saturation, related to variations in drainage capillary pressure curves associated with rock quality, are observed in many reservoirs. The relative permeability and capillary pressure curves used here represent proprietary data from an intermedi-ate-wet carbonate reservoir.

Another parameter that may have a significant impact on recovery during waterflood simulations is the end-point mobility ratio of the displacing phase (water) to the displaced phase (oil) (e.g. Friedmann et al. 2003; Larue & Friedmann 2005; Choi et al. 2011). We examine the effect of varying the end-point mobility ratio on the relative ranking of stratigraphic and sedi-mentological heterogeneities using values of 0.94 (favourable displacement) and 7.22 (unfavourable displacement), correspond-ing to oil viscosities of 0.52 and 4.0 cP, respectively. Additional fluid properties are summarized in Table 3.

Production strategy

Oil recovery was simulated in the models over 20 years with a waterflood using: (1) a single line drive with 4 km well spacing; (2) a repeat line drive with 1 km well spacing; and (3) a five-spot pattern with 500 m well spacing for injection and production wells (Fig. 5, Table 4). Bottom hole pressure (BHP) limits for the injection and production wells were used to maintain the water injection rate to yield a pressure gradient of 0.5 (favourable displacement) to 2.0 (unfavourable displacement) psi/ft between the wells. BHP limits are provided in Table 4; a lower limit on production wells was defined by an oil bubble point pressure of 2200 psi. These pressure constraints were chosen to represent waterflood production strategies for Middle Eastern carbonate reservoirs, consistent with other manuscripts in this thematic set (Agada et al. 2014; Shekar et al. 2014). No other constraints were placed on the wells. The 4 km line drive (Fig. 5a) was included in this study to represent the simplest boundary condi-tions for flow through the model domain. However, this scenario required unrealistically high injection well BHP to maintain the target pressure gradient. All three simulated production schemes used vertical wells, and a 10 m-thick aquifer was incorporated into the lower part of each model. Two completion strategies were investigated. In the first, injection and production wells were completed over the whole reservoir interval; this strategy is termed ‘dominated by horizontal flow’ in Figure 5. In the sec-ond, injection wells were completed over a 5 m interval below the initial oil–water contact, and production wells were com-pleted over a 16 m-thick interval from the top of the oil zone; this strategy promotes vertical flow and is termed ‘dominated by vertical flow’ in Figure 5 (cf. Willhite 1986).

results

Production simulation results

The eight models show a wide range of production behaviours, as described below and discussed in a later section. Results for the ‘vertical flow’ strategy, in which injection wells are com-pleted at the base and production wells are completed at the top of the reservoir, are summarized in Figure 6a, b for the 4 km line drive well placement. Results for the ‘horizontal flow’ strategy, where wells are completed over the entire reser-voir interval, are summarized in Figure 6c for comparison. The

table 1. Rock properties used in flow simulation models. Ø, porosity (pu=porosity units), kh , horizontal permeability (and isotropic permeability, kv=k h ), and kv , vertical permeability. High and low values of rock properties are used as settings (i) and (ii) of heterogeneity 3 (Fig. 2). A uniform rock compressibility of 5 microsip is used in all models (1 microsip=10–6/psi)

Environment of deposition (EOD)

Rock properties

High (grain dominated) Low (mud dominated)

Name Lithology and sedimentary structure (after Amour et al. 2011) Ø (pu) kh (mD) kv (mD) Ø (pu) kh (mD) kv (mD)

Inner ramp (Semi-restricted ramp)

Bioclastic wackestone, packstone and framestones; low–medium bioturbation intensity; presence of micritization and microencrustation

0.21 320 47 0.02 170 24

Mid ramp (High-energy ramp)

Packstone, grainstone and floatstone–rudstone; ooids, peloids and bioclastic components; medium–high bioturbation intensity; cross-bedding, encrustation and spary cements dominate

0.38 4200 2000 0.18 840 390

Outer ramp (Marly open ramp)

Marl, carbonate mudstone and wackestone; localized boundstone; bioclastic and peloidal grain components; low–medium bioturbation intensity; episodic terrigenous sediment input

0.17 2.4 0.21 0.001 0.58 0.05

Pelagics Marl and shale dominated 0.11 0.15 0.02 0.001 0.01 0.001





average recovery factor for the ensemble of models is 41%. The lowest recovery factors of 0.4–0.5 % are obtained for mod-els α, γ, η and θ using the ‘vertical flow’ strategy, where the pressure in the upper part of the reservoir rapidly falls to the minimum permitted producer BHP, and the wells are shut in after 2–4 years of production (Fig. 6b). Furthermore, water breakthrough, which is taken to correspond to a watercut of 1%, occurs after 3–7 years in models β, δ, ε and ζ, but does not occur during the 20 year production life in models α, γ, η and θ (Fig. 6a). Recovery using the ‘vertical flow’ strategy is consistently lower than for the ‘horizontal flow’ strategy. The comparatively high recovery factor of 70–72% observed in models ε–θ, using the ‘horizontal flow’ strategy, reflects the high matrix porosity and permeability in these models, the low residual oil saturation defined by the relative permeability curves, and the lack of a connected fracture network. Early water breakthrough occurs in all cases under the ‘horizontal flow’ strategy, with total water cut >90% after only 5 years of production.

In general, the variation in oil produced is larger than the var-iation in recovery factor; as we show in the next section, this is because the combination of heterogeneities impacts the volume of OIIP more significantly than the volume produced after 20 years. Both oil produced and recovery factor are typically higher when flow is predominantly horizontal, particularly in models α, γ, η and θ in which sequence boundaries are associ-ated with laterally extensive barriers to flow; recovery is essen-tially zero in these models when flow is predominantly vertical (recovery factor of c. 0.5%). Moreover, recovery for a favourable

mobility ratio is always higher than for an unfavourable mobility ratio (Fig. 7a, b). However, the approach to modelling relative permeability and capillary pressure generally has little impact on recovery (Fig. 7c, ds). When flow is predominantly horizontal, the highest recoveries are always observed for the 1 km repeat line drive well placing (Fig. 7f). The 1 km repeat line drive also results in highest recoveries for models α, γ, ε, η and θ when flow is predominantly vertical, but the highest recoveries are observed for the 4 km line drive for models β, δ and ζ (Fig. 7f). Clearly, oil recovery varies significantly depending on the combi-nation of heterogeneities in each model, the end-point mobility ratio, well spacing and on whether the completion strategy yields predominantly horizontal or vertical flow. In the next section, we investigate which heterogeneities have the most significant impact on oil volumes in place and recovery during production.

relative impact of different stratigraphic and sedimentological heterogeneities on oIIP

Our experimental design allows the relative influence of the individual stratigraphic and sedimentological heterogeneities on production performance criteria to be ranked relative to the aver-age behaviour of the eight models, based on the impact of changing a given heterogeneity from setting (i) to setting (ii) (Fig. 2). Below we describe the relative impacts of the investi-gated heterogeneities on OIIP, before describing in the next sec-tion their relative impacts on the volume of oil produced and recovery factor after 20 years, and the time to water break-through. We find that EOD-belt rock properties (heterogeneity 3

66 mInner rampMid rampOuter rampPelagic

Environment ofdeposition (EOD):

Stratigraphic surface barriersTransitional EOD boundaries

4 km

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table 2. Heterogeneity setting incorporated into the geological models, following our experimental design. Heterogeneity settings (i) and (ii) are illustrated schematically in Figure 2: (1i) short or (1ii) long interfingering length of EOD belts; (2i) prograding or (2ii) retrograding-prograding EOD-belt geometry; (3i) grain-dominated or (3ii) mud-dominated EOD-belt rock properties; (4i) isotropic or (4ii) anisotropic EOD-belt permeability; (5i) sharp or (5ii) transitional EOD-belt boundaries; and sequence boundaries with (6i) no petrophysical properties or (6ii) barriers to vertical flow

Heterogeneity

Geological model

α β γ δ ε ζ η θ

1. Interfingering length of EOD belts 1(i) 1(ii) 1(i) 1(ii) 1(i) 1(i) 1(ii) 1(ii)2. Geometry of EOD belts 2(i) 2(i) 2(ii) 2(ii) 2(i) 2(ii) 2(i) 2(ii)3. Rock properties of EOD belts 3(i) 3(i) 3(i) 3(i) 3(ii) 3(ii) 3(ii) 3(ii)4. Anisotropy of EOD-belt permeability 4(i) 4(ii) 4(ii) 4(i) 4(ii) 4(i) 4(i) 4(ii)5. Character of EOD-belt boundaries 5(ii) 5(i) 5(i) 5(ii) 5(ii) 5(i) 5(i) 5(ii)6. Sequence boundary rock properties 6(ii) 6(i) 6(ii) 6(i) 6(i) 6(i) 6(ii) 6(ii)

Fig. 3. Depositional dip sections through the eight reservoir models (α–θ; Table 2), illustrating the geometry and spatial arrangement of EOD belts (heterogeneities 1 and 2; Fig. 2), character of EOD-belt boundaries (heterogeneity 5; Fig. 2) and character of sequence boundaries (heterogeneity 6; Fig. 2). All models have the same areal extent of 4×4 km, and a vertical thickness of 66 m.





in Fig. 2) is the key control on OIIP (Fig. 8); note that a response >100% means only that the average effect of changing the heterogeneity setting is greater than the average value of the given performance measure over the eight models. Switching from high, grain-dominated porosities to low, mud-dominated porosities for the EOD belts significantly decreases OIIP and, in order of decreasing impact, the other heterogeneities influencing OIIP are the EOD-belt interfingering length, EOD-belt geometry (heterogeneities 1 and 2, decreasing OIIP by 37 and 23%, respectively), character of the EOD-belt boundaries and sequence boundary rock properties (heterogeneities 5 and 6, respectively, both of which change OIIP by c. 5 %). Anisotropy of EOD-belt permeability (heterogeneity 4 in Fig. 2) has no impact on OIIP. Note that the impact of heterogeneity on OIIP is the same regardless of the mobility ratio, relative permeability and (imbi-bition) capillary pressure, well spacing, and completion strategy, as these have no effect on OIIP. Note also that the low ranking of heterogeneities 4 (permeability anisotropy) and 6 (sequence boundary rock properties) is expected as these features have lit-tle or no effect on OIIP. However, these two heterogeneity types may have a significant effect on flow and, therefore, recovery, as we show in the next subsection.

relative impact of different stratigraphic and sedimentological heterogeneities on recovery for predominantly vertical flow

For predominantly vertical flow, in which injection and pro-duction wells are completed near the base and top of the reser-voir (Fig. 5), the heterogeneity with the greatest impact on production is the rock properties assigned to sequence bounda-ries (heterogeneity 6 in Fig. 2). Modelling these surfaces as impermeable barriers significantly decreases oil production and recovery factor, and inhibits water breakthrough (Fig. 9). The high ranking of this heterogeneity is independent of the end-point mobility ratio, relative permeability and capillary pres-sure curves (Fig. 9), and of well spacing (Fig. 10). The rank order of the other heterogeneities is largely the same for oil produced, although the rank order for recovery factor and time to water breakthrough depends on the end-point mobility ratio (Fig. 9b, c) and on well spacing (Fig. 10). Note that these het-erogeneities have a much smaller impact on recovery factor and time to breakthrough than on the volume of oil produced (typically <10%: Fig. 9).

The second-ranked heterogeneity for oil produced, recovery factor (for an unfavourable mobility ratio) and breakthrough time (for a favourable mobility ratio) is the EOD-belt rock properties (heterogeneity 3 in Fig. 2, Table 1); switching from high, grain-dominated permeabilities and porosities to low, mud-dominated permeabilities and porosities for the EOD belts decreases the vol-ume of oil produced and delays water breakthrough (for a favour-able mobility ratio: Fig. 9a, c), but increases the recovery factor (Fig. 9b). This response is observed because switching to the low EOD-belt rock properties has a larger negative impact on OIIP than on recovery. EOD-belt rock properties have a much smaller impact on recovery factor for a favourable mobility ratio, and breakthrough time for an unfavourable mobility ratio, but have a more significant impact at smaller well spacing (Fig. 10). The

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Pc (<10mD) Pc (10-100mD)Pc (>100mD)

Fig. 4. Relative permeability (a–c) and capillary pressure curves (d–f) used in simulation experiments: primary water–oil drainage curves (a, d); single set of water–oil imbibition curves (b, e); and multiple water–oil imbibition curves (c, f). The same set of relative permeability and capillary pressure curves is applied to displacements with favourable and unfavourable end-point mobility ratios in each of our experiments.

table 3. Fluid properties used in the simulation experiments

Property Oil Water

Black oil with no gas cap

Density (g cm–3) 0.85 (34.9º API) 0.95Viscosity (cP) 0.52 or 4.0 0.36Formation volume factor (m3/Sm3) 1 1Compressibility (1/bar) 1×10–4 3×10–5

Bubble point pressure (psia) 2200 Initial reservoir pressure (psia) 3000





Water injector well Oil producer well

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(A) 4 km Line (B) 1 km Repeat Line (C) 5 Spot Pattern

Up depositional dip Up depositional dip Up depositional dip

Map view

FWL FWL FWL

66 m

Depositional dip section (displacement dominated by vertical flow)

66 m

Depositional dip section (displacement dominated by horizontal flow)

Fig. 5. Line drawing showing model dimensions and well placements in the simulation models for three waterflood production schemes: (a) 4 km line drive; (b) 1 km repeat line drive; and (c) 500 m five-spot pattern.

table 4. Injection and production well spacing, and BHP limits for the simulated production scenarios, using two end-point mobility ratios

Waterflood production scheme Well spacing(km)

Injection well BHP (psi)

Production well BHP(psi)

Mobility ratio 0.94 (Favourable)

Mobility ratio 7.22 (Unfavourable)

(A) Line drive 4 9030 28 500 2200(B) Repeat line drive 1 3910 8770 2200(C) Five-spot pattern 0.5 3400 6800 2200





EOD-belt interfingering length (heterogeneity 1 in Fig. 2) is the third-ranked heterogeneity influencing oil produced, recovery fac-tor (for an unfavourable mobility ratio) and time to water break-through (for a favourable mobility ratio: Fig. 9a, c); switching from the short to long interfingering length increases oil recovery and recovery factor (Fig. 9a, b), but decreases time to water break-through (Fig. 9c). EOD-belt interfingering length also has a much smaller impact on recovery factor for a favourable mobility ratio, and breakthrough time for an unfavourable mobility ratio, and a more significant impact at smaller well spacing (Fig. 10). EOD-belt geometry (heterogeneity 2 in Fig. 2) is the fourth-ranked het-erogeneity for oil produced (Fig. 9); incorporating a retrogradational component into the EOD-belt geometry decreases oil recovery (both volume and recovery factor: Fig. 9a, b), but delays water breakthrough (Fig. 9c). EOD-belt permeability anisotropy (hetero-geneity 4 in Fig. 2) is ranked fifth for oil produced, but higher for recovery factor and breakthrough time for a favourable mobility ratio; the introduction of permeability anisotropy decreases the vol-ume of oil produced and recovery factor (Fig. 9a, b), and increases the time to water breakthrough (Fig. 9c). The character of the EOD-belt boundaries (heterogeneity 5 in Fig. 2) has the lowest

ranking for oil production, but is higher ranked for recovery factor and breakthrough time, depending upon the end-point mobility ratio (Fig. 9b). Switching from sharp to transitional EOD-belt boundaries decreases oil recovery factor, and may delay or acceler-ate water breakthrough depending up the end-point mobility ratio.

The rank order of heterogeneities is the same for oil produc-tion regardless of the end-point mobility ratio, the approach to modelling relative permeability and capillary pressure, or the chosen well spacing (Figs 9a & 10a). However, as discussed above, varying these parameters does change the magnitude and rank order of heterogeneities impacting on recovery factor and breakthrough time (Figs 9b, c & 10b, c). In particular, an unfa-vourable mobility ratio increases the impact on recovery factor of EOD-belt interfingering length, and EOD-belt rock properties (Fig. 9b), but decreases the effect of these parameters on break-through time (Fig. 9c). Changing the well spacing does not sig-nificantly modify the magnitude or rank order of the impact of each heterogeneity setting on oil produced (Fig. 10a), but there are some more significant changes for recovery factor (Fig. 10b) and time to water breakthrough (Fig. 10c); in particular, EOD-belt rock properties and EOD-belt interfingering length have a

Fig. 6. Volume of oil produced over 20 years for models α–θ (Table 2, Fig. 2) using a single set of relative permeability and capillary pressure curves (Fig. 4b, e), favourable end-point mobility ratio, and the 4 km line drive well placement (Fig. 5a); the data are shown on separate plots for clarity. Models lacking barriers to vertical flow along sequence boundaries (a) are associated with significantly larger volumes of oil produced than models containing such barriers (b) and are plotted separately for clarity. Production results for the predominantly vertical displacements (a, b) are compared to those obtained for a predominantly horizontal displacement (c).





Fig. 7. The impact of (a, b) end-point mobility ratio, (c, d) modelling of relative permeability and capillary pressure, and (e, f) production strategy on total oil production (a, c, e) and recovery factor (b, d, f) after 20 years of simulated production. On each plot, data points show the average of all simulations of a particular model. Filled symbols show results obtained from simulations in which vertical flow is dominant; open symbols show results obtained from simulations in which horizontal flow is dominant.





larger impact on recovery factor for the repeat line drive and five-spot well patterns, in which the well spacing is much smaller than in the 4 km line drive. We return to these issues in the Discussion section.

comparison of the impact of stratigraphic and sedimentological heterogeneities on oil recovery for predominantly horizontal and vertical flow

Figure 11 compares the impact of the studied stratigraphic and sedimentological heterogeneities, and their rank order, on oil recovery for production schemes that promote predominantly hori-zontal flow and predominantly vertical flow (Fig. 5). The volume of oil produced and recovery factor after 20 years are used as the measures for comparison.

The most striking difference between the rank order of het-erogeneities for the two flow directions is the approximately 10-fold increase in the impact of sequence boundary rock prop-erties (heterogeneity 6 in Fig. 2) on oil recovery for predomi-nantly vertical flow (compare black and grey bars in Fig. 11), regardless of the end-point mobility ratio, approach to modelling relative permeability and capillary pressure, and chosen well spacing (Fig. 5). The presence of flow barriers along sequence boundaries significantly reduces recovery when flow is predomi-nantly vertical, but yields slightly higher recovery when flow is predominantly horizontal.

EOD-belt rock properties (heterogeneity 3 in Fig. 2) are an important control on oil recovery regardless of whether flow is predominantly horizontal or vertical (Fig. 11). Both OIIP and oil produced are lower in models with mud-dominated EOD belts, but the decrease is more pronounced in OIIP (Fig. 9) than in oil produced (e.g. Fig. 11a); consequently, recovery factor increases, and this effect is more significant when hori-zontal flow dominates (Fig. 11b). These trends are the same regardless of the predominant flow direction. Heterogeneities controlling reservoir architecture and the spatial distribution of EOD belts (i.e. EOD-belt interfingering length and geometry; heterogeneities 1 and 2 in Fig. 2) also have a high impact on oil recovery regardless of whether flow is predominantly hori-zontal or vertical, although the rank order is reversed: EOD-belt interfingering length has a larger impact on vertical flow than EOD-belt geometry (grey bar in Fig. 11), but a smaller impact on horizontal flow (black bar in Fig. 11). Furthermore, switching from a short to a long interfingering length (i.e. from setting (i) to setting (ii) of heterogeneity 1: Fig. 2) yields lower

recovery when flow is predominantly horizontal, but higher recovery when flow is predominantly vertical (compare black and grey bars in Fig. 11). Switching from a purely prograda-tional to a retrogradational–progradational EOD-belt geometry (i.e. from setting (i) to setting (ii) of heterogeneity 2: Fig. 2) always yields lower recovery. Anisotropic permeability (heter-ogeneity 4 in Fig. 2) yields lower oil recovery but, perhaps surprisingly, is ranked relatively low even when flow is pre-dominantly vertical. The character of EOD-belt boundaries (heterogeneity 5 in Fig. 2) is ranked low regardless of the pre-dominant flow direction. This heterogeneity appears last when flow is predominantly vertical, and one place above last when flow is predominantly horizontal (compare black and grey bars in Fig. 11).

dIscussIon

Why do the same heterogeneities have different impacts on production for different completion strategies?

The results we present demonstrate that the same heterogeneities in carbonate reservoirs, in developments with the same fluid properties and well spacing, can have a markedly different impact on flow during production for developments in which the completion strategy promotes predominantly horizontal or verti-cal flow. The most obvious manifestation of this effect, and the easiest to explain, is the presence of laterally continuous, imper-meable barriers along sequence boundaries. These barriers have negligible impact on OIIP because they are modelled as four 10 cm-thick layers, representing approximately 0.2% of the total vertical thickness of the model. The barriers prevent vertical cross-flow and pressure communication; sequence boundaries are also typically marked by dislocations of EOD belts (Fig. 1), which impose a pronounced vertical contrast in permeability across most, but not all, of their lateral extent (models α, γ, η and θ in Fig. 3). The resulting stratigraphically defined pressure compartments are efficiently swept by predominantly horizontal displacements. The presence of laterally continuous, impermea-ble barriers has little impact on production. Other studies have also found that thin, laterally continuous baffles to flow in car-bonate reservoirs, such as dolomudstone layers (Grant et al. 1994; Jennings et al. 2000) and zones of bedding-parallel stylo-lites (Agada et al. 2014; Shekhar et al. 2014), have a small impact on flow for viscous-dominated waterfloods with vertical wells. In contrast, injectors perforated at the base of the reser-voir are not in pressure communication with producers perfo-rated at the top of the reservoir, and the pressure in the uppermost stratigraphic sequence, connected to the producers, falls to the minimum producer BHP after 2–4 years of produc-tion, at which time the wells are shut in (e.g. Figs 6b & 12a). Lateral extent, continuity and textural characteristics of sequence boundaries and other stratigraphic surfaces have been con-strained in outcrop studies of ancient carbonate ramps (e.g. Bachmann & Kuss 1998; Pomar et al. 2002; Asprion et al. 2009; Christ et al. 2012a) and platforms (e.g. Hillgaertner 1998; Sattler et al. 2005; Christ et al. 2012b), and their significance as potential flow barriers is recognized in the subsurface (Wagner et al. 1995; Hillgaertner 1998; Powell & Basem 2012). However, our models contain no structure and we recognize that post-dep-ositional faults with very small throw (< 1 m) could offset such barriers and provide vertical flow paths. If the sequence bounda-ries do not act as continuous barriers to flow, but are still associ-ated with reduced porosity and permeability, their impact on vertical flow decreases significantly, and is similar to that observed for predominantly horizontal flow (compare white and

Fig. 8. Tornado chart showing the impact of the six stratigraphic and sedimentological heterogeneities under investigation (Fig. 2) on OIIP. Each bar represents the impact of changing a heterogeneity from setting (i) to setting (ii); if the bar lies to the right (i.e. is greater than 0) then the impact is positive (i.e. OIIP is increased).





black bars in Fig. 11; see also Fig. 12b). Consequently, patches with no cement within laterally continuous cemented barriers, or disruption of such barriers by post-depositional faulting and fracturing, are likely to allow sufficient vertical flow to enable efficient sweep and water breakthrough.

EOD-belt rock properties (heterogeneity 3 in Fig. 2) are an important control on oil recovery regardless of whether flow is predominantly horizontal or vertical, as noted in previous studies (e.g. Pranter et al. 2006; Ambastha et al. 2009; Hollis et al. 2011). Variations in porosity impact OIIP and, therefore, total oil recovered. Variations in permeability impact the flow rate for a given pressure gradient and, therefore, recovery factor after a given production time; although it is worth noting that the impact of EOD-belt rock properties on recovery factor is much more significant for the unfavourable mobility ratio. We discuss this further in the next section. In this study, we focused on the impact of first-order stratigraphic heterogeneities on flow via use of end-member EOD-belt rock properties. Incorporating addi-tional diagenetic overprints will alter the bulk rock properties, and the relationships between porosity and permeability within a given EOD belt (e.g. Taghavi et al. 2007; Beavington-Penney et al. 2008; Swei & Tucker 2012; Escorcia et al. 2013; Martin-Martin et al. 2013).

Heterogeneities controlling reservoir architecture and the spatial distribution of EOD belts (i.e. EOD-belt interfingering length and geometry: heterogeneities 1 and 2 in Fig. 2) also have a high impact on oil recovery, regardless of whether flow is predominantly horizontal or vertical (e.g. Fig. 13). When hor-izontal flow dominates, a short interfingering length yields higher recovery because the proportion of the reservoir com-prising high-porosity, mid-ramp EOD belts (Table 1) controls the volume of oil produced; thicker, but less laterally continu-ous, EOD belts are produced by the short EOD-belt interfinger-ing length and purely progradational EOD-belt geometry (e.g. models α, γ, ε and ζ in Fig. 3), yielding higher OIIP, thicker high-permeability units and, hence, higher recovery. Similar

behaviour has been observed previously with regard to the thickness and lateral continuity of high-permeability streaks in low-permeability carbonate reservoirs (so-called ‘thief zones’: see, e.g., Masalmeh et al. 2004; Vaughan et al. 2004; Ghedan et al. 2010). The recovery factor is insensitive to the interfin-gering length, at least for a favourable end-point mobility ratio. However, when vertical flow dominates, a short EOD-belt interfingering length yields lower recovery. This result seems counterintuitive, because a shorter interfingering length might be expected to yield less laterally continuous, low-permeability outer-ramp and pelagic EOD belts, less tortuous vertical flow paths and, therefore, higher recovery. The result we obtain here is an unexpected occurrence of aliasing within our experimental design; of the four models without barriers to vertical flow along sequence boundaries, models β and δ have the long EOD-belt interfingering length in combination with the high EOD-belt rock properties (setting (i) of heterogeneity 3), whereas models ε and ζ exhibit the shorter EOD-belt interfingering length with low EOD-belt rock properties (setting (ii) of hetero-geneity 3) (Table 2). As a result, longer EOD-belt interfinger-ing length is associated with the two models yielding highest oil recovery (Fig. 7). If sequence boundaries do not act as con-tinuous barriers to flow, but are still associated with reduced porosity and permeability, production wells in models α, γ, η and θ no longer shut-in after 2–4 years, allowing comparison of the EOD-belt interfingering length within the full parameter space of our experimental design. In these models, switching to a longer EOD-belt interfingering length reduces oil recovery, as observed when flow is predominantly horizontal and consistent with the lower OIIP (compare white and black bars in Fig. 11a).

Permeability anisotropy within the EOD belts (heterogeneity 4 in Fig. 2) decreases oil production and recovery factor (Fig. 9a, b) in displacements dominated by both horizontal and verti-cal flow, consistent with previous case studies of carbonate res-ervoirs (Abbaszadeh et al. 2000; Ates et al. 2005; Hollis et al.

Single imbibition curve set & favorable mobility ratio

Single imbibition curve set & unfavorable mobility ratio

Multiple imbibition curve sets & favorable mobility ratio

Multiple imbibition curve sets & unfavorable mobility ratio

-200 -100 0 100 -200 -10 0 10 20

-10 0 10 100 200

EOD-belt rock properties

EOD-belt interfingering length

EOD-belt geometry

Character of theEOD-belt boundaries

Sequence boundaryrock properties

Anisotropy ofEOD-belt permeability



EOD-belt geometry






EOD-belt geometry




(C) Percentage change in time to water breakthrough

(A) Percentage change in oil produced (B) Percentage change in recovery factor

Fig. 9. Tornado charts showing the impact of the six stratigraphic and sedimentological heterogeneities under investigation (Fig. 2) on (a) total oil production, (b) recovery factor and (c) time to water breakthrough. Each bar represents the impact of changing a heterogeneity from setting (i) to setting (ii); if the bar lies to the right (i.e. is greater than 0) then the impact is positive (e.g. the volume of oil produced has increased). Results are shown for the 4 km line drive (Fig. 5a). The heterogeneities in plots (b) and (c) are ranked according to their impact on oil production (a).





2011). However, the impact of permeability anisotropy on oil production is higher for displacements dominated by vertical flow (compare grey and black bars in Fig. 11a), which is to be expected given that lower vertical permeability yields lower ver-tical flow rates for the fixed pressure gradient imposed by our chosen production constraints. Yet, the relatively low ranking of permeability anisotropy (fifth in Fig. 9a), even in models domi-nated by vertical flow is surprising. One reason may be that the range of permeability anisotropy values investigated in our mod-els (Kv/Kh ratios of 0.1–0.4, Table 1) is too narrow, although it is consistent with those examined by other authors (e.g. Hollis et al. 2011). The impact on vertical flow of some smaller-scale

heterogeneities, such as thinly interbedded mud- and grain-dom-inated depositional facies within inner- and outer-ramp EOD belts, may not have been captured in our estimates of vertical permeability at the grid-block scale. To gain a preliminary understanding of how more extreme permeability anisotropy might impact on the ranking of heterogeneity impact, we have investigated a set of models in which the anisotropic permeabil-ity setting has a much lower kv/kh ratio of 0.001. The impact ranking of heterogeneities on oil production and recovery factor is not changed (Fig. 14), although the actual values differ; per-meability anisotropy remains in fifth place for oil recovery, and in third place for recovery factor (with a favourable end-point

Fig. 10. Radar charts showing the effect of the three production strategies (Fig. 5, Table 4) on the impact of the six stratigraphic and sedimentological heterogeneities under investigation (Fig. 2) on (a) total oil production, (b) recovery factor and (c) time to water breakthrough. For clarity of display, absolute values are shown for all charts, and a logarithmic scale is used for recovery factor (b) and time to water breakthrough (c). Results are shown for a single imbibition curve set (Fig. 4b, e) and favourable mobility ratio (Table 4). The heterogeneities in plots (b) and (c) are ranked, anticlockwise, according to their impact on oil production (a).





mobility ratio). This suggests that the kv/kh ratio within EOD belts has a smaller impact on production, even when flow is pre-dominantly vertical, than might be expected. Heterogeneities controlling reservoir architecture and the spatial distribution of EOD belts (i.e. EOD-belt interfingering length and geometry: heterogeneities 1 and 2 in Fig. 2) are more important, together with the presence of flow barriers along stratigraphic surfaces. An alternative explanation for the low ranking of permeability anisotropy may be that laterally continuous, low-permeability outer-ramp and pelagic EOD belts lower the effective vertical permeability of the models at the inter-well scale, subduing the impact of heterogeneities at the grid-block scale that might oth-erwise control vertical flow.

The character of the EOD-belt boundaries is the heterogene-ity with lowest impact on oil produced, although it has a more significant impact on recovery factor, especially for an unfa-vourable mobility ratio (Fig. 9). Its relatively low impact proba-bly reflects the small volume of the models occupied by transitional EOD-belt boundaries, as is evident in the small impact of this heterogeneity on stock tank oil initially in place (STOIIP) (Fig. 8). Setting (ii) for our transitional EOD-belt boundaries is representative of published outcrop studies, which document interfingering of depositional facies at EOD-belt boundaries over lengths of 100–500 m (e.g. Castel et al. 2007; Koehrer et al. 2010; Pierre et al. 2010; Elrick 2011). However, more extreme cases may exist where interfingering of deposi-tional facies occurs over longer length-scales because of shal-lower depositional slopes or high-frequency variations in the rates of accommodation generation and sediment accumulation. Increasing the lateral extent of transitional EOD-belt boundaries will increase the proportion of each model impacted by this het-erogeneity, which may increase its impact on oil production and recovery factor.

Interaction of rock and fluid properties, and well spacing, with the impact of stratigraphic heterogeneities on flow

In this study, although the volume of oil produced, recovery fac-tor and time to water breakthrough differ if a single set, or mul-tiple sets, of relative permeability and capillary pressure curves are used (Figs 6 & 15), the rank order of heterogeneities is only

slightly altered (Fig. 9). We note here that the various relative permeability and capillary pressure curves applied in our model-ling experiments are realistic in as much as they are simplified from proprietary reservoir data, but show limited variation between permeability classes (e.g. in comparison to Hollis et al. 2011). More variable relative permeability and capillary pressure curves, or use of a different method to assign them, may increase their impact on recovery and the rank order of hetero-geneity. However, the results we present here, for production strategies dominated by horizontal and vertical flow, suggest that the same stratigraphic and sedimentological heterogeneities remain important regardless of how relative permeability and capillary pressure are modelled.

Oil production for an unfavourable mobility ratio is gener-ally lower, consistent with numerous previous studies (e.g. Friedmann et al. 2003; Larue & Friedmann 2005). We find that the rank order for oil produced remains unchanged by the end-point mobility ratio (e.g. Fig. 9a), but the rank order for recov-ery factor and time to water breakthrough are different for favourable and unfavourable displacements. Most significantly, we find that an unfavourable end-point mobility ratio increases the impact of EOD-belt interfingering length and EOD-belt rock properties on recovery factor (Fig. 9b), while a favourable end-point mobility ratio increases the effect of these parameters on breakthrough time (Fig. 9c). EOD-belt rock properties and interfingering length have a larger impact on recovery factor for an unfavourable displacement because the oil viscosity is four times higher, but the pressure gradient between injection and production wells only doubles in order to remain within the likely range in real field development. Consequently, produc-tion rates are halved, and the impact of permeability variations on recovery factor after 20 years of production are commensu-rately higher. Conversely, early water breakthrough is typically observed for an unfavourable displacement regardless of hetero-geneity. As a result, the impact of permeability variations on breakthrough time is more significant for a favourable end-point mobility ratio.

Oil production also depends on well spacing (Fig. 7); when flow is predominantly horizontal, the highest recoveries are always observed for the 1 km repeat line drive well placement (Fig. 4), and this well placement also yields the highest recov-ery in most models where flow is predominantly vertical. This

Fig. 11. Tornado charts showing the impact of the six stratigraphic and sedimentological heterogeneities under investigation (Fig. 2) on (a) oil produced and (b) recovery factor when flow is predominantly vertical and horizontal. Results obtained using a single imbibition curve set (Fig. 4b, e), favourable mobility ratio (Table 4) and 4 km line drive (Fig. 5a).





is to be expected because the 1 km line drive employs the larg-est number of production wells. However, in a few models, higher recovery is observed for predominantly vertical flow for the 4 km line drive. This is because the potential for vertical flow, between the deep completions in the injection wells and the shallow completions in the production wells, increases as the well spacing decreases (Fig. 5). Higher recovery is observed for the larger well spacing in models that have low effective vertical permeability because they have reservoir architectures that are more layer-cake in geometry, containing laterally con-tinuous, pelagic EOD belts of low permeability, and also aniso-tropic permeability within EOD belts. We, again, find that the rank order for oil produced remains unchanged (e.g. Fig. 9a), but the rank order for recovery factor and time to water break-through are different depending on the well spacing. The impact of all heterogeneities, except the sequence boundary rock prop-erties (heterogeneity 6 in Fig. 2), on recovery factor and time to water breakthrough increases as well spacing is reduced from 4 (Fig. 5a) to 0.7 km (Fig. 5c; see also Fig. 10b, c). In particular, the impacts of EOD-belt interfingering length and rock proper-ties (heterogeneities 1 and 3 in Fig. 2) on recovery factor increase significantly at smaller well spacing (Fig. 10b). These results are comparable to those of Hollis et al. (2011), who

found that heterogeneities at the scale of depositional facies had a more significant impact on hydrocarbon production as well spacing decreased.

The rank order of heterogeneity on oil produced remains the same regardless of the variability in dynamic performance between models with a common set of fluid properties, well placement, and relative permeability and capillary pressure curves. The impact of heterogeneities on oil produced is greater than the variability in dynamic performance exhibited by a single model for different mobility ratios, well place-ments, and relative permeability and capillary curves. This suggests that the modelled geology is the most important con-trol on production behaviour for the ranges of parameters con-sidered here.

conclusIons

•• We have used integrated flow simulation and experimental design techniques to investigate the first-order impact of stratigraphic and sedimentological heterogeneities on simu-lated recovery in carbonate ramp reservoirs. We find that the modelled heterogeneities in combination exert a greater influence on production behaviour than fluid properties, well

Fig. 12. Depositional dip sections showing oil saturation after 0, 1 and 5 years of simulated production time, through the centre of model α (a) with and (b) without impermeable barriers along sequence boundaries. Results are shown for a single imbibition curve set (Fig. 4b, e), favourable mobility ratio (Table 4) and 4 km line drive production strategy (Fig. 5a). Location of impermeable barriers to flow are shown by the white lines (solid, impermeable barrier present; dashed, sequence boundary without impermeable barrier).





66 m

66 m

4 km4 km4 km

(A) Permeability section (B) Vertical dominateddisplacement (1 year)

(C) Horizontal dominateddisplacement (1 year)

Model �

Model �

0 50 100Oil Saturation (%)

0.01 10 1000Permeability (mD)

Fig. 13. Depositional dip sections through the centre of simulation models β (top) and ε (bottom), showing (a) permeability, (b) oil saturation after 1 year for a displacement dominated by vertical flow and (c) oil saturation after 1 year for a displacement dominated by horizontal flow. Results are shown for a single imbibition curve set (Fig. 4b, e), favourable mobility ratio (Table 4) and 4 km line drive production strategy (Fig. 5a).

Fig. 14. Tornado charts comparing heterogeneity rankings for displacements dominated by vertical flow on (a) volume of oil produced and (b) recovery factor, with two permeability anisotropy settings: (1) original permeability values defined in Table 1; and (2) reduced vertical permeability such that the kv:kh ratio is 0.001. The heterogeneities in (b) are ranked according to their impact on oil production (a).

placement, and the approach to modelling relative permea-bility and capillary pressure data. Similar heterogeneities control flow behaviour in displacements dominated by both horizontal and vertical flow, although the significance of

heterogeneities controlling vertical flow paths increases when vertical flow dominates.

•• The key heterogeneities for displacements dominated by either horizontal or vertical flow are the EOD-belt rock





properties, and heterogeneities controlling the volume and lateral continuity of the EOD belts (i.e. the EOD-belt interfingering length and geometry). Switching from high, grain-dominated to low, mud-dominated porosities and permeabilities decreases the volume of oil produced, but increases recovery factor. This is because changing rock properties exerts a greater impact on OIIP than on oil recovery. When vertical flow dominates, and continuous barriers to flow are present along sequence boundaries, a long EOD-belt interfingering length yields higher recov-ery, although OIIP is decreased. However, when cemented hardgrounds are represented in our models with only decreased permeability and porosity (i.e. no continuous barriers to vertical flow), a long EOD-belt interfingering length yields lower recovery, consistent with models where horizontal flow dominates, and OIIP is also decreased.

•• Sequence boundaries become the key control on oil recov-ery when displacements are dominated by vertical flow, but only when associated with a continuous, impermeable barrier. The impact of permeability anisotropy within EOD belts on oil production increases with vertical flow poten-tial, but is still of low-ranked importance. The least impor-tant heterogeneity is the character of boundaries between EOD belts.

•• The impact of heterogeneities on OIIP is independent of fluid properties, well spacing and completion strategy. As oil pro-duction is strongly affected by OIIP, the ranking of heteroge-neity impact on oil production is also relatively insensitive to these factors. Recovery factor normalizes the volume of oil produced relative to OIIP, and so the impact ranking is more sensitive to fluids, well spacing and completion strategy. Thus, the rank order for heterogeneities impacting recovery factor and time to water breakthrough varies with end-point mobility ratio and well spacing.

•• Well spacing has little influence on the impact or rank order of heterogeneities for displacements dominated by horizontal flow. Reducing well spacing enhances the potential for verti-cal flow, and so increases the impact of all heterogeneities on recovery factor and time to breakthrough in displacements dominated by vertical flow.

We acknowledge funding and support from the ExxonMobil (FC)2 Research Alliance, and thank the following colleagues from the Alliance: Susan Agar, Greg Benson and Owen Hehmeyer (ExxonMobil), Frédéric Amour and Maria Mutti (University of Potsdam), Nicolas Christ and Adrian Immenhauser (University of Bochum), Graham Felce and Fiona Whitaker (University of Bristol), and Simeon Agada and Sebastian Geiger (Heriot Watt University). Thi Thanh Ha Nguyen is thanked for help in running simulations. We are grateful to Schlumberger for the provision of the Petrel reservoir modelling software and Eclipse flow simulation software, and to Roxar for providing the IRAP RMS reser-voir modelling software via academic software donations. Insightful comments from two anonymous reviewers have greatly improved the manuscript

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Received 08 March 2013; revised typescript accepted 29 September 2013.




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