IMPERIAL COLLEGE LONDON

Transcription

1 IMPERIAL COLLEGE LONDON Department of Earth Science and Engineering Centre for Petroleum Studies UNDERSTANDING FLUID FLOW IN COMPLEX, FLUVIAL-DELTAIC RESERVOIRS By Charles Faure-Llorens A report submitted in partial fulfilment of the requirements for the MSc and/or DIC September 2012

2 Understanding fluid flow in complex, fluvial-deltaic reservoirs ii DECLARATION OF OWN WORK I declare that this thesis: Understanding fluid flow in complex, fluvial-deltaic reservoirs Is entirely my own work and that where additional material could be constructed as the work of others, it is fully cited and referenced, and/or with appropriate acknowledgments given. Signature: Name of student: Charles Faure-Llorens Name of supervisors: Pr. M. D. Jackson Dr G. J. Hampson PhD student G. Graham

3 Understanding fluid flow in complex, fluvial-deltaic reservoirs iii ACKNOWLEDGMENT I would like to thank my supervisors, Matthew Jackson and Gary Hampson, for sharing their experience and giving advice throughout this project. I am particularly grateful to Gavin Graham for his hard work, constant advice and for providing the high-resolution three-dimensional model. Thank you to my MSc teachers and external lecturers who taught me everything about petroleum engineering throughout this year.

4 Understanding fluid flow in complex, fluvial-deltaic reservoirs iv TABLE OF CONTENTS DECLARATION OF OWN WORK... ii ACKNOWLEDGMENT... iii LIST OF FIGURES... v LIST OF TABLES... vi Understanding fluid flow in complex, fluvial-deltaic reservoirs...1 Abstract...1 Introduction...1 Static model description...3 Model derived from outcrop: Upper Cretaceous Ferron Sandstone Member of Central Utah Geological setting Model specifications, construction and clinoform modelling Static and dynamic parameters for simulations...5 Rock and fluid properties Production strategy Quality check of the grid...7 Understanding fluid flow...7 Experimental design and petrophysical properties investigated Results... 8 Discussions...12 Impact on flow of clinoforms associated with barriers to flow Comparison with wave-dominated reservoirs results Conclusions for Ferron, constituting an analogue for fluvial-deltaic reservoirs...14 Improvements and further work Nomenclature...15 References...15 APPENDIX A: Critical literature review...17 APPENDIX B: Simulation data...25

5 Understanding fluid flow in complex, fluvial-deltaic reservoirs v LIST OF FIGURES Figure 1. Conceptual model of a fluvial-dominated delta lobe...2 Figure 2. Photopanorama of outcrop, and cross section of our model, highlighting clinoform surfaces...2 Figure 3. Geological setting of Ferron Sandstone reservoir analogue...3 Figure 4. Schematic through the lower shallow-marine tongue of the Last Chance delta...3 Figure 5. Schematic of simulation model showing gross internal facies architecture of PS Figure 6. Schematic of simulation model showing gross internal facies architecture within clinothems...5 Figure 7. Graphs of rock and fluids properties....6 Figure 8. Production strategies for flow simulations...6 Figure 9. Quality check of the simulation model...7 Figure 10. Model cross section of clinoform grid of the quality check simulation showing oil saturation..7 Figure 11. Typical effect produced by presence of barrier coverage along clinoforms....9 Figure 12. Graph of final recovery factor for each of the 96 simulations performed....9 Figure 13. Graph of time to WB and final WC of the average of the 16 runs performed for each case...10 Figure 14. Cumulative distribution function (CDF) plot for recovery factor Figure 15. Tornado charts for simulations with water injection up depositional dip...11 Figure 16. Tornado charts for simulations with water injection down depositional dip...11 Figure 17. Tornado charts for simulations with water injection along depositional strike...12 Figure 18. Cross-section through oil saturation profile with barriers along clinoforms...12 Figure 19. Cross-section through pressure profile with barriers along clinoforms...13 Figure 20. Cross-section through oil saturation profile with water injection up depositional dip...13 Figure 21. Cross-section through oil saturation profile after 1 PV injected Figure B-1. Ratio: Time to WB/simulation time, plotted for each of the 96 simulations performed..25 Figure B-2. Final water-cut of the 96 simulations performed...25 Figure B-3. Example of Matlab plots...35

6 Understanding fluid flow in complex, fluvial-deltaic reservoirs vi LIST OF TABLES Table 1. Facies-Association scheme for fluvial-deltaic environment...4 Table 2. Model specifications...4 Table 3. Rock and fluid properties...5 Table 4. Porosity and permeability of the four facies...6 Table 5. Injection/Production targets and constraints...6 Table 6. Setting levels of investigated parameters...8 Table 7. Experimental design used in this study...8

7 Understanding fluid flow in complex, fluvial-deltaic reservoirs Student name: Charles Faure-Llorens Imperial College Supervisors: Pr. M. D. Jackson, Dr. G. J. Hampson, and PhD student G. Graham Abstract Fluvial-dominated deltaic parasequences are often modeled as simple layercake reservoirs. One aspect of the internal stratigraphy that is often not captured in fluid flow simulations of these parasequences are clinoforms, which control facies architecture and can have a significant influence on recovery, especially if they are associated with barriers to flow. Capturing these heterogeneities is necessary to properly predict reservoir performance; however, most models fail to capture these surfaces. This study investigates the impact of heterogeneity associated with dipping clinoform surfaces, where facies are associated with major contrasts in reservoir properties, such as permeability and porosity on fluid flow and hydrocarbon production during a line-drive water flood. Dynamic simulations are run using high-resolution three-dimensional model of a fluvial deltaic reservoir analogue, constructed from a well-exposed outcrop analog: Ferron Sandstone, Utah, USA. We investigate a range of parameters, such as water flood direction, contrasts in facies petrophysical properties and barriers along clinoform surfaces, utilizing experimental design of the simulations and analysis of variance of the simulation results. This study is based on a previous work about fluviodeltaic stratigraphic architecture and compares the results with another previous study of a wavedominated parasequence containing clinoform surfaces. This study demonstrates that a 90% barrier to flow associated with clinoform surfaces affects pressure support between injectors and producers, and consequently sweep efficiency. Horizontal permeability within proximal delta-front facies plays a key role in hydrocarbon recovery when there are barriers to flow along the clinoform surfaces. When there is no barrier along clinoform surfaces, the horizontal permeability within distal delta-front facies has the highest impact when water injection is either up or down depositional dip. Production strategy and waterflood direction are key aspects in hydrocarbon recovery as well due to the variation in facies architecture and hence petrophysical properties. On the other hand, vertical to horizontal permeability ratio in DDF and capillary pressure have almost no influence on hydrocarbon recovery. Consequently, clinoforms modeling is necessary to predict a realistic production behaviour because of their high impact on hydrocarbon production and because parameters with highest influence on recovery differ with clinoforms. Introduction Almost 30% of global oil and gas reserves are hosted in deltaic reservoirs (Tyler and Finley, 1991). There are three main types of deltaic system: fluvial-dominated, wave-dominated, and tidal dominated (Rich, 1951); the type of shoreline system is traditionally considered to be the key control on the subsequent reservoir heterogeneity (Gani and Bhattacharya, 2005). The principal depositional process acting at the shoreline controls the plan view shape and the abundance of clinoform surfaces and their associated heterogeneity (Howell et al., 2008a). Fluvial-dominated reservoirs can be encountered in the North of Gulf of Mexico (Deveugle et al., 2011; Fisher and McGowen, 1969), in the Wasia formation in Saudi Arabia (Tonellot et al., 2009), in the Prudhoe Bay field in Alaska (Begg et al., 1992), or in eastern Russia (Davies et al., 2005). Production characteristics such as early water breakthrough, poor sweep efficiency, pressure compartmentalization, or lower than expected recovery factor are commonly encountered with these reservoirs (Deveugle et al., 2011). Fluvial-deltaic reservoirs comprise single or multiple stacked parasequences, typically juxtaposed with other types of sandbody (Sech et al., 2009). Within each parasequence, facies architecture plays a key role in controlling fluid flow during production, because facies types are associated with major contrasts in reservoir properties such as permeability and porosity (Deveugle et al., 2011; Wellner et al., 2005). Figure 1 depicts a conceptual model of one parasequence with associated facies (Deveugle et al., 2011). At a smaller scale, clinoforms are produced within each parasequence by the progradation of the delta front. Clinoforms exhibit concave-upwards geometry at this scale and typically, a reduced rate of sediment supply limits accumulation (Howell et al., 2008b). They are thin compared to the overall thickness of the parasequence. Clinoform surfaces can be associated with mudstone or cemented calcite, as well as facies interfingering that make parasequences characterisation difficult (Enge and Howell, 2010; Gani and Bhattacharya, 2005). Clinoforms, therefore, may act as barriers or baffles to horizontal and vertical fluid flow in a reservoir, as they subdivide the reservoir into a series of dipping sandstone beds (clinothems) (Figures 2A and 2B). Breaks in the shale drapes associated with clinoforms can provide tortuous flow paths for fluids and result in trapped hydrocarbons (Howell et al., 2008b). A key aspect to predicting hydrocarbon recovery in fluvial-dominated deltaic

8 Understanding fluid flow in complex, fluvial-deltaic reservoirs 2 reservoirs, which is performed in this study, is to accurately capture clinoform geometries, distribution and associated heterogeneity (Figures 2A and 2B). A B Figure 1. Conceptual model of a fluvial-dominated delta lobe. Plan view (A) and depositional dip cross section (B) of a parasequence and associated facies (modified after Deveugle et al., 20011). A B Figure 2. Photopanorama of outcrop (A) (modified after Graham et al., 2011), and cross section of our model (B), highlighting clinoform surfaces Many studies have carried out a detailed geological description of complex, fluvial-deltaic reservoirs, from mapping different parasequences to capturing clinoforms (Deveugle et al., 2011; Enge and Howell, 2010). They have been well studied at outcrop, but there is still uncertainty in identifying clinoform surfaces from subsurface data (Howell et al., 2008b). Moreover, it is poorly understood how to include them in models of fluvial-deltaic parasequences. Consequently, only a few previous studies have characterized fluid flow in fluvial-deltaic reservoirs, and clinoforms were not studied (Choi et al., 2011; Deveugle et al., 2011). Deveugle et al. (2011) studied heterogeneities at a larger scale without clinoform surfaces, and Enge et al. (2010) focused only on clinoforms without taking into account other facies heterogeneities. Finally, Jackson et al. (2009) and Obembe (2009) have carried out a detailed assessment of impact on recovery of clinoforms and associated heterogeneities in wavedominated environment. But fluvial and wave-dominated environment present important differences in clinoforms geometries (gently dipping in wave-dominated: 0.01 to 2 (Hampson et al., 2008; Jackson et al., 2009; Sech et al., 2009), whereas more steeply dipping in fluvial-dominated: 4 to 8 (Enge and Howell, 2010). Consequently, results may not be similar and have to be cross-compared. Commonly, deltaic reservoirs are modeled in the industry using layer-cake approach, but recovery can be over predicted by up to 20% by these models (Jackson et al., 2009). Therefore, a detailed quantitative assessment of the impact on hydrocarbon recovery of heterogeneities present in complex fluvial-deltaic reservoirs is required to understand fluid flow and properly predict hydrocarbon recovery to understand a complex production behavior during water flooding. The main aim of this study is to identify and characterize fluid flow in these complex, fluvial-deltaic shallow-marine reservoirs using a single parasequence of the Ferron Sandstone as a reservoir analogue. This is performed by investigating a range of parameters such as the production strategy, petrophysical properties and heterogeneity associated with clinoform surfaces to gain an understanding of the production behavior during waterflooding of the Ferron Sandstone analogue. We use an experimental design based method to perform an efficient number of fluid flow simulations to identify what are the key aspects that control hydrocarbon production. This study is based on a previous work performed by Deveugle et al. (2011) that has investigated the impact of stratigraphic architecture such as continuity, orientation, and permeability character of channel-fill sand bodies on recovery, by simulating water flooding. They used a high-resolution three-dimensional model that captures facies architecture at a larger scale: scale of parasequences, delta lobes, and facies-association belts from outcrops of the Ferron

9 Understanding fluid flow in complex, fluvial-deltaic reservoirs 3 Sandstone Member, an analogue for fluvial-dominated deltaic reservoirs, used in this study as well. Our study follows Deveugle et al. (2011) s work and parameters used such as geological setting and stratigraphic architecture are derived from their study. Impact of clinoform surfaces is investigated and they are part of the complex stratigraphic architecture implemented. In the meantime parameters adopted for the experimental design of the simulations come from a companion study (Obembe, 2009) on a wave-dominated parasequence containing clinoform surfaces. A consistent comparison of hydrocarbon recovery in either wave or fluvial-dominated reservoirs is therefore carried out. Static model description Model derived from outcrop: Upper Cretaceous Ferron Sandstone Member of Central Utah. The work is performed focusing on one parasequence of the Ferron Sandstone in East-central Utah (Figure 3A). This study follows a previous work carried out by Deveugle et al. (2011). They provided a detailed characterization of stratigraphic architecture of the Upper Cretaceous Ferron Sandstone Member, Utah, as well as its impact on fluid flow. Here is a brief summary of their geological work; see their paper for more details. The Ferron Sandstone Member of the Mancos Shale outcrops along the Coal Cliffs, south-central Utah. The unit was deposited between the Turonian and the Coniacian (late Cretaceous) on the western margin of the Western Interior seaway, which was an epeiric sea that covered much of the modern North American continent (Gardner, 1995; Leckie et al., 1998). In east central Utah, the Ferron Sandstone Member records the overall northeastward progradation of the Last Chance delta system (Cotter, 1976). These deltaic deposits constitute a basinward-thinning wedge that passes eastward into the offshore deposits of the Mancos Shale (Figure 3B). Because of its easy access and high-quality exposure, it has been very well studied and frequently visited as an analogue for fluvial-dominated deltaic reservoirs (Ryer and Anderson, 2004). A B Figure 3. Geological setting of Ferron Sandstone reservoir analogue, location map (A) and Schematic through Last Chance delta system (B) (modified after Deveugle et al., 2011) Figure 4. Schematic through the lower shallow-marine tongue of the Last Chance delta of the Ferron Sandstone Member (modified after Deveugle et al. 2011) The Last Chance deltaic deposits contain either seven (Ryer, 1991) or eight (Garrison and Van den Bergh, 2008; Ryer and Anderson, 2004) sandstone tongues (Figure 3B). Each tongue can be subdivided into smaller stratigraphic unit, termed parasequence (Deveugle et al., 2011). This study focuses on parasequence 1.6 as interpreted by Deveugle et al. (2011) (Figure 4). The high-resolution 3D model built by Graham et al. (2011) captures a portion of this parasequence (Figure 5B). Geological setting. There are four different facies present in this model. Table 1 describes these facies in terms of lithology and sedimentary structures, porosity, and permeability. This table comes from the work performed by Deveugle et al. (2011). Their values of porosity and permeability for the various facies associations are taken from a mature subsurface analogue (South Timbalier field, Gulf of Mexico (Farrell and Abreu, 2006)). In our study, facies association come from Deveugle et al. (2011) s work, while petrophysical properties were assigned for each facies according to Obembe (2009). The reason for this is the opportunity to cross-compare results with Obembe (2009) s work for wave-dominated environment. Parameters settings used are detailed further down (Table 4), but range is consistent with Deveugle et al. (2011) s description (Table 1).

10 Understanding fluid flow in complex, fluvial-deltaic reservoirs 4 Facies Stream mouth bar (SMB) Proximal delta front (PDF) Distal delta front (DDF) Prodelta mudstones (PD) Table 1. Facies-Association scheme for fluvial-deltaic environment (modified after Deveugle et al. (2011)) Lithology and Sedimentary Interpretation Proportion Porosity Permeability Structures Thick (2-10 m), sharp-based, through cross-bedded, medium-grained sandstones in bodies with mounded or composite mound-and-channel geometry. Bioturbation absent. Amalgamated, sharp-based beds of finegrained sandstone ( cm thick) with rare mudstone interbeds. Parallel lamination, current-ripple crosslamination, and rare hummocky cross-stratification in sandstones. Bioturbation sparse or absent. Thin (<50 cm), sharp-based beds of siltstone and very fine to fine-grained sandstone with mudstone interbeds. Parallellaminated bed bases grade into wave- and current-rippled tops. Sparse, low-diversity bioturbation. Laminated mudstone with thin (<5 cm) beds of current-rippled siltstone and very fine grained sandstone. Sparse to intense bioturbation. From best to worst quality facies Migration of subaqueous, sinuous-crested dunes caused by unidirectional currents. Dunes migrated over the mounded surface of a bar or mound-tochannel transition at the mouth of a shallow channel. Sandstone beds deposited episodically from sediment gravity flows, with minor reworking by storm-generated waves. Scarcity of mudstone interbeds indicates deposition close to deltaic distributary mouth. Mudstone and siltstone interbeds deposited from suspension; sandstone beds deposited episodically from sediment gravity flows generated by river flood events. Minor wave reworking. Abundance of mudstone interbeds indicates distal setting. Laminated mudstone deposited from suspension; siltstone and sandstone beds deposited from unidirectional currents during major storms or river flood events. 8% of volume, lower parasequence set; 20% of volume, upper parasequence set 22% of volume, lower parasequence set; 30% of volume, upper parasequence set 63% of volume, lower parasequence set; 23% of volume, upper parasequence set 6% of volume, lower parasequence set; 25% of volume, upper parasequence set Mean: Φ = 28 % Mean: Φ = 27 % Mean: Φ = 18 % Non reservoir Mean: k h = 1793 md k v/k h = 0.9 Mean: k h = 433 md k v/k h = 0.75 Mean: k h = 71 md k v/k h = Non reservoir Not used in our simulations Model specifications, construction and clinoform modelling. This study used a surface-based modelling approach described by Sech et al. (2009). Top and base boundaries of parasequence 1.6 (Figure 4), as well as associated facies from Deveugle et al. (2011) s delta-lobe conceptual geologic model, were implemented in our model. Then, clinoform surfaces have been added using a numerical algorithm developed in a previous study (Graham et al., 2011). A corner point grid has been generated. The grid builds-up from the base surface, then it truncates against facies boundaries surfaces, clinoform surfaces and finally against top surface. These steps are applied for each clinothem, which located between two clinoform surfaces. Barrier coverage along clinoforms was modelled with an additional transmissibility multiplier (equal to zero) that avoids flow to go through the clinoform. Models with such cemented calcite along clinoform have a randomly distributed 90 % of barrier coverage. That means, 90 % of their area within the model acts as barrier to flow, and there are gaps along clinoform surfaces. Thus, cases without barrier can be compared against extreme cases with presence of 90% barrier coverage. The model captures an area measuring 3 km 750 m of a single parasequence. The average thickness of the parasequence considered is 6 m. Cells dimension is 20 m 20 m 20 cm, and model specifications are summarised in Table 2. Clinoform spacing may differ for each reservoir considered. This study uses a 25 m spacing between each clinoform, and they extent over the whole model. Geometry and spacing outcrop data for clinoforms come from previous studies (Enge and Howell, 2010; Forster et al., 2004). Table 2. Model specifications X-axis Y-axis Z-axis Active cells Average cells area Average layers thickness Models 39 cells 152 cells 2763 layers 160,000 cells 380 m 2 20 cm The very high number of layers is due to the way clinoform surfaces are modelled. Consequently, the model has a huge number of cells as well (16,379,064 cells). However many of them are inactive cells because they are pinched-out: only 1% is active. Consequently, it allows us to simulate without upscaling. Previously, Figure 2 shows clinoform geometries in a cross section of the model. There are pinched-out cells because clinoform surfaces extent over the whole model in the X- direction (West-East), and at one time they all become very thin and stack together on top and base surfaces. Thinnest cells become inactive, while others can generate numerical errors; refer to quality check section for detailed explanations. Finally, two continuous thin layers have been added on top and base to help flow to go through these pinched-out cells and avoid as much as possible numerical errors.

11 Understanding fluid flow in complex, fluvial-deltaic reservoirs 5 Figure 5 shows the gross internal facies architecture of the models (A and C), a plan view facies map of parasequence 1.6 modelled of the Ferron sandstone (B), and facies proportion in our models (D). Figure 6 shows the internal facies architecture: facies are vertically and horizontally ordered from the prodelta to the stream mouth bar within each clinothem (Deveugle et al., 2011). A B C SMB PDF DDF PDF Proportion (%) Dip models Strike model D Figure 5. Schematic of simulation model showing gross internal facies architecture of PS 1.6 of the Ferron Sandstone. Simulation models, for up and down depositional dip injection (A), and for along depositional strike injection (B). Parasequence 1.6 used for model construction with associated facies (C) (modified after Deveugle et al. 2011), and facies proportion in models (D). Figure 6. Schematic of simulation model showing gross internal facies architecture within clinothems Static and dynamic parameters for simulations Rock and fluid properties. This study considers only dead oil and water above bubble point at all-time. The oil-water contact is below the deepest point of models, so no aquifer is considered. Table 3 and Figure 7 summarize rock and fluids properties. These properties are consistent with values used by Obembe (2009) to compare results with wave-dominated environments. The initial water saturation is 0.2, and the residual oil saturation is 0.3. Rock and fluid properties (Table 3) were taken from Jackson et al. (2009), while capillary pressures and oil and water relative permeability (Figures 7A and 7B) come from Obembe (2009). Table 3. Rock and fluid properties Fluid properties Density Formation volume Compressibility (kg/m 3 ) factor (rm 3 /sm 3 ) (bar -1 ) Viscosity (cp) Oil Water Rock compressibility (bar -1 ) Porosity and permeability values of model facies are the same as those used by Obembe (2009) (Stream mouth bar considered the same as upper shoreface, proximal delta front same as proximal lower shoreface, and distal delta front same as distal lower shoreface); see Obembe s (2009) study for more details. The petrophysical properties used (Table 4) depict wavedominated environment, however the range used is consistent with properties described by Deveugle et al. (2011) for fluvialdominated environment (Table 1). Only one set of porosity and permeability is assigned per facies. It is a major simplification but it leads to a better understanding of the impact of clinoforms. Moreover in shallow-marine deltaic environment, important contrasts in petrophysical properties characterise facies (Jackson et al., 2009), we study this contrast as well as impact of clinoforms. In Figure 7B different capillary pressure is used depending on the permeability of each facies described in Table 4.

12 Relative permeability Capillary pressure (bar) Understanding fluid flow in complex, fluvial-deltaic reservoirs 6 Table 4. Porosity and permeability of the four facies (Derived from Obembe (2009)) Porosity Horizontal permeability Vertical to horizontal permeability ratio Stream mouth bar (SMB) 27% 2000 md 1 Proximal delta-front (PDF) 27% 50 or 500 md 0.01 or 0.5 Distal delta-front (DDF) 18% 5 or 25 md or 0.01 Prodelta (PD) Non-reservoir Non-reservoir Non-reservoir kro krw SMB (2000 md) PDF (500 md) PDF (50 md) DDF (25 md) DDF (5 md) B Water saturation (Sw) Water saturation (Sw) Figure 7. Oil and water relative permeability curves (A), and capillary pressure curves (B). Note that different capillary pressure are used depending on the setting (low or high) of each facies. A Production strategy. This study uses a line drive water flood production strategy, in line with Obembe (2009) s work. There are six producers and four injectors. Injection rates and production times (Table 5) result in realistic pore volume (PV) injections: 0.96 PV is planned to be injected in dip models. In the strike model, which has a higher proportion of PDF facies (Figure 5D) so a higher PV than dip models, 0.49 PV is injected. These PV injections depend on constraints commitment. Indeed, when permeabilities are low, and with presence of barrier to flow along clinoform surfaces, pressure constraints are reach (Table 5). The initial reservoir pressure is set at 100 bars. In this study well spacing between injectors and producers is 750 m. Hence results can be compared with Obembe (2009) findings for 0.75 km well spacing. Figure 8 shows the three types of injection strategy performed: up depositional dip, down depositional dip, and along depositional strike. Table 5. Injection/Production targets and constraints Group target surface rate Well BHP limit Well Liquid flow rate limit Injectors 350 sm 3 /d for 10 years or 175 sm 3 /d for 20 years Maximum: 150 bar Producers 350 sm 3 /d for 10 years or 175 sm 3 /d for 20 years Minimum: 50 bar 1589 sm 3 /d A B C D Figure 8. Production strategies for flow simulations. Injection up depositional dip (A), down depositional dip (B), and along depositional strike (C). Schematic of injection strategies (D).

13 Understanding fluid flow in complex, fluvial-deltaic reservoirs 7 Quality check of the grid This study uses a high-resolution model that is very complex, as the fluvial-deltaic environment it captures. The clinoform grid (Figure 2) of this study, has a low percentage of active cells because many are pinched-out (Table 2). These pinched-out cells may introduce numerical errors during flow simulations. Quantifying these numerical artefacts is essential to provide a true assessment of physical effects and understand fluid flow in real situations. Therefore, a quality check of the grid has been carried out. It consists on running simulations for a homogeneous case. All facies have same properties of the SMB (Φ = 28 %, k h = 2000 md, k v /k h = 1), and there is no barrier along clinoform surfaces, because the aim is just to check artefacts generated by the grid itself. The injection rate is 350 sm 3 /d, and all results are analysed after 1 PV injected. It uses a regular grid to investigate numerical errors generated by the clinoform grid used in this study. It checks errors for the three injection strategies. This quality check investigates errors on recovery factor (RF), time to water breakthrough (WB) and water-cut (WC). The bar chart in Figure 9A depicts normalized errors of the simulation model (clinoform grid) versus a regular grid. In the regular grid, water flooding displacement goes straight from injectors to producers, whereas in the clinoform grid the path is more tortuous, particularly for up and down depositional dip injection strategies where dipping clinothems impact fluid flow direction. Thus, there are errors in time to WB, highlighted in Figure 9B. Clinoform grid generates some grid artefacts caused by pinched-out cells where highly dipping clinoforms are present. These artefacts result on trapping oil in some pinched-out cells as flow cannot get through. Indeed highly dipping clinoforms ending on a same corner point result in cells that have one surface with a height equal to zero (Figure 10). This phenomenon explains differences in recovery factor, particularly for water flooding up depositional dip. These errors have to be taken into account in following results. Indeed, a few percentages of errors in recovery factor can lead to a difference in production of several thousand barrels of oil. A Normalized errors (%) B Time to WB Recovery factor Up depositional dip Down depositional dip Water-cut Along depositional strike Figure 9. Quality check of the simulation model (A), and model cross section of clinoform and regular grid at time to WB Figure 10. Model cross section of clinoform grid showing oil saturation after 1 PV injected (A), and conceptual model of a typical pinched-out cell (B) Understanding fluid flow Experimental design and petrophysical properties investigated. This study investigates the impact of six parameters. The experimental design is the same as the one performed by Obembe (2009). Permeability contrast is studied because of the possibility to bypass oil and of an earlier water breakthrough. Vertical to horizontal permeability, rates, and capillary pressure could impact oil displacement and sweep efficiency amongst facies due to their influence on the balance of viscous to gravity and capillary forces. Obembe s (2009) study gives more details about investigated parameters and documentations. Each parameter has two setting levels (low (0) and high (1)) (Table 6). To capture influence of all parameters, a twolevel full factorial design should be performed. That means 2 6 = 64 simulations should be run, but this is not the most efficient way to investigate them (Box et al., 1978). Indeed, there are levels of interactions that are not relevant to study, because they are aliased with others, and it can be time-consuming for an insignificant knowledge. As explained by Box et al. (1978), a frac-

14 Understanding fluid flow in complex, fluvial-deltaic reservoirs 8 tional factorial design is the most efficient solution for experimenters. Here is performed a two-level fractional factorial design Consequently, 16 simulations are run (Table 7), and then a statistical analysis of variance (ANOVA) is performed to estimate main effects of each parameter (White and Royer, 2003). This study uses results from DOE++ software (Design Of Experiments) to perform this analysis of variance and provide main effects of parameters. Influence on final recovery factor, time to water breakthrough and final water-cut is investigated. Recovery factor is used instead of cumulative oil produced as our models (dip and strike) do not have the same STOIIP. This experimental design is applied for 6 cases: injection up depositional dip, injection down depositional dip, and injection along depositional strike; the three of them with and without presence of barrier coverage along clinoforms (either 0% or 90%). Derived from Obembe (2009) Table 6. Setting levels of investigated parameters Kv/Kh PDF Kh PDF Kv/Kh DDF Kh DDF Production/Injection rate Capillary P Low setting = md md 175 sm 3 /d for 20 years Not included High setting = md md 350 sm 3 for 10 years Included Kv/Kh PDF Kh PDF (md) Kv/Kh DDF Kh DDF (md) Prod/Inj rate (sm 3 /d) Capillary P (bar -1 ) Run. name Table 7. Experimental design used in this study (modified after Obembe, 2009) No No Yes Yes Yes Yes No No Yes Yes No No No No Yes Yes Results Important findings for Ferron-Sandstone analogue. This study performs 96 numerical flow simulations using ECLIPSE software. Results processing and displaying is carried out using PETREL software and ECLIPSE Office. This section provides main findings after results processing and interpretations. The most important parameter on hydrocarbon recovery is the presence of barrier coverage along clinoform surfaces (Figure 12), which forces fluids to have tortuous pathways. This reduces the effective reservoir permeability and has significant impact on model performances. Water breakthrough commonly occurs later but this is not always true. Figure 11 depicts typical effect of barrier coverage along clinoform surfaces on oil production rate and water-cut with injection up depositional dip, and on recovery factor with injection up and down depositional dip. Results from run 16 (Table 7) are presented, which yields one of the highest recovery factors. Indeed, in run 16 all parameters are in high setting, except rates (Table 6). Barrier coverage along clinoform surfaces has a very high impact on recovery factor regardless the injection strategy adopted (Figure 12). Final recovery factor varies from less than 5% to more than 50% across the 96 runs performed. Presence of barrier coverage can lower the final recovery factor by up to 75% (Figure 12). Impact of clinoform surfaces on fluid flow and hence on hydrocarbon recovery is non-negligible particularly when associated with high percentage of barriers to flow. When horizontal permeability in PDF and DDF is low, impact of barriers to flow along clinoforms is more important, pressure support is not maintained and wells cannot achieve their targets (Figure 12). Injecting along depositional strike seems to be the best solution without barrier coverage along clinoform (Figure 12), however it is important to note the proportion of good quality facies that is higher in strike model than in dip ones (Figure 5D). Consequently, strike model has a higher effective permeability and less contrasts between facies, which lead to a water front with less interfingering effects during fluids displacement. This better sweep efficiency lower the WC because time to WB occurs later, and there is less bypassed oil, and hence recovery factor is higher (Figures 12 and 13). Without presence of barrier coverage along clinoform surfaces, injecting down depositional dip yields higher recovery factor compared to injecting up depositional dip, but the opposite finding occurs with presence of barriers to flow along clinoforms (Figures 11B and 12).

15 Final recovery factor Field oil production rate (sm 3 /d) Water-cut Recoery factor Understanding fluid flow in complex, fluvial-deltaic reservoirs Barrier coverage from 0 to 90% Barrier coverage from 0 to 90% No barrier (rate) 90% barrier (rate) No barrier (WC) 90% barrier (WC) A B Time (years) Time (years) Figure 11. Typical effect produced by presence of barrier coverage along clinoforms on oil production rate and water-cut (A), and on recovery factor with highlights on injection up and down depositional dip (B). In this figure results from run 16 (Table 7) with injection up and down depositional dip are presented after 20 years of production with 1 PV of water injection Down strategy is more sensitive to presence of barriers Up no barrier Down no barrier Up 90% barrier Down 90% barrier Low Kh in PDF and DDF Barrier coverage from 0 to 90% Run Figure 12. Graph of final recovery factor for each of the 96 simulations performed. Up no barrier Up 90% barrier Down no barrier Down 90% barrier Strike no barrier Strike 90% barrier Figure 13 shows that clinoform surfaces have high influences on time to water breakthrough and water-cut as well. These graphs show averages of 16 runs for the 6 cases considered: injection up and down depositional dip, and along depositional strike, with 0% or 90% of barrier coverage along clinoform surfaces. For dip models, barrier coverage reduces the effective permeability and hence WB occurs later and final WC is lower than without barriers to flow along clinoform surfaces (Figures 13A and 13B). On the opposite, for strike model, the presence of 90% of barrier coverage reduces time to WB, because the reservoir is horizontally compartmentalised and fluids take easiest flow path (Figure 13B). Time to water breakthrough is far higher for injection along depositional strike without barrier compared to injection up and down depositional dip, which have quite the same time to WB across all 16 runs without barrier coverage (Figure 13A). When there is presence of barrier, WB does not occur in some simulations injecting up and down depositional dip with low Kh in PDF and DDF. Final water-cut is linked to time to WB and has mostly an opposite shape: the more WB occurs late the more the final WC should be low (Figures 13A and 13B). However when injection is down depositional dip, WB occurs on average at 1/5 of production time, which results, in other runs, in a final water-cut above 90%, but here it is more around 70% (Figures 13A and 13B).

16 Normalized cumulative distribution function Ratio: Time to WB/Production time Final WC Understanding fluid flow in complex, fluvial-deltaic reservoirs 10 A % 90% Barrier coverage along clinoforms Up (mean of 16 runs) Down (mean of 16 runs) Strike (mean of 16 runs) Figure 13. Graph of time to WB and final WC of the average of the 16 runs performed for each case: injection up and down depositional dip, and along depositional strike; with and without barrier coverage along clinoform surfaces. Production associated with barrier coverage along clinoform is far lower than without. Figure 14 depicts a probability range of recovery factor for each case considered. It shows 6 cases. For each case, this plot is based on the average and the variance of the 16 final recovery factors. Curves on the right hand side have statistically a higher recovery factor. It shows differences in recovery factor and so in sweep efficiency between injecting up and down depositional dip, and along depositional strike with and without barrier coverage along clinoforms. An interesting point is the difference between up and down depositional dip injection strategies with or without barrier coverage along clinoforms. Indeed, down depositional dip injection strategy leads to higher recovery factors without barrier coverage along clinoforms according to Figure 14. However, it leads to lower recovery factor when barriers to flow are present, in comparison with recovery factor for up depositional dip injection strategy. This result has been highlighted previously focusing on run 16 (Figure 11B). B % 90% Barrier coverage along clinoforms Up (mean of 16 runs) Down (mean of 16 runs) Strike (mean of 16 runs) Barrier coverage has more impact on down strategy Up no barrier Down no barrier Strike no barrier 0.4 Up 90 % barrier Final recovery factor Figure 14. Cumulative distribution function (CDF) plot for recovery factor. Down 90 % barrier Strike 90% barrier Sweep efficiency and influence of parameters depending on injection strategy. Results from experimental design are now subject to an analysis of variance using DOE++ software. This section shows the influence of the 6 parameters considered on recovery factor, time to WB and WC. Figures 15 to 17 provide tornado charts for the 6 cases investigated, where experimental design has been applied. Parameters are ranked from the highest impact on recovery factor to the lowest. Then, influence on time to WB and WC are displayed to completely assess parameters influencing the sweep efficiency of each case. These tornado charts represent changes that occur when going from level setting 0 (low) to level setting 1 (high) (Tables 6 and 7), and non-significant effects are not displayed (less than 10% of the overall effect). The most important parameter when there is no barrier coverage along clinoforms with injection up and down depositional dip is Kh in DDF (Figures 15A and 16A). But Kh in PDF has the biggest impact on RF, time to WB, and WC when there is 90 % of barrier coverage along clinoforms for injection up and down depositional dip (Figures 15B, 16B). Besides, when injection is along depositional strike Kh in PDF has always the highest influence on time to WB and RF (Figures 17A and 17B), mostly because of the high proportion of PDF facies within strike model (Figure 5D). Consequently Kh in DDF does not have an important influence at all when injection is along depositional strike. But Kh in DDF is still the second most important parameter after Kh in DDF when injection are up and down depositional dip with 90% of barriers to flow along clinoform surfaces (Figures 15B, and 16B). With barrier coverage along clinoforms, Kv/Kh in PDF and in DDF, have not a significant impact on sweep efficiency and RF (Figures 15B, 16B, and 17B), mostly because this barrier coverage compartmentalise the reservoir in the vertical direction, forcing fluid flow to propagate horizontally. But without barriers, Kv/Kh in PDF is the second most important parameter for the three types of injections (Figures 15A, 16A, and 17A). This parameter avoids vertical segregation and avoids oil to be bypassed by flow in the SMB which is located above the PDF and then gravity force can compensate viscous force.

17 Understanding fluid flow in complex, fluvial-deltaic reservoirs 11 Up depositional dip (0% barrier) Standardized effect in % Kh DDF Kv/Kh PDF Prod/Inj rate Kh PDF Kv/Kh DDF Capillary P A Up depositional dip (90% barrier) Standardized effect in % Kh PDF Kh DDF Prod/Inj rate Kv/Kh DDF Kv/Kh PDF Capillary P B Recovery Factor Time to WB Water-cut Recovery Factor Time to WB Water-cut Figure 15. Tornado charts for simulations with water injection up depositional dip, with 0% of barrier coverage along clinoforms (A), and with 90% (B). Threshold value = 2.132, non-significant effects (below threshold) are not displayed in this chart. Down depositional dip (0% barrier) Standardized effect in % Kh DDF Kv/Kh PDF Kh PDF Prod/Inj rate Kv/Kh DDF Capillary P A Down depositional dip (90% barrier) Standardized effect in % Kh PDF Kh DDF Prod/Inj rate Capillary P Kv/Kh PDF Kv/Kh DDF B Recovery Factor Time to WB Water-cut Recovery Factor Time to WB Water-cut Figure 16. Tornado charts for simulations with water injection down depositional dip, with 0% of barrier coverage along clinoforms (A), and with 90% (B). Threshold value = 2.132, non-significant effects (below threshold) are not displayed in this chart. Rates have a high impact as well for injection up and down depositional dip (Figures 15, and 16), although same PV is injected for both settings (longer time of injection compensates the lower rate) (Table 6). Low production and injection rates during a longer time delay time to WB and increase oil recovery. Low rates avoid interfingering effects and avoid viscous forces to overcome gravity forces. Injection along depositional strike yields different results compared to up and down depositional dip. Indeed, parameters with highest influence, for injection up and down depositional dip, which increase RF, increase at the same time the WC, and decrease the time to WB (Figures 15, and 16). Whereas when injection is along depositional strike, parameters with highest impact on RF can delay time to WB and hence decrease WC. High proportion of SMB and PDF facies in strike model (Figure 5D) explains this phenomenon because without high settings in PDF, flow always take the easiest pathway that is located in the SMB, and thus it affects RF and sweep efficiency. Capillary pressure and Kv/Kh in DDF have almost no influence except for Kv/Kh in DDF, which has a little impact on WC when there is no barrier coverage along clinoforms (Figures 15, 16, and 17).

18 Understanding fluid flow in complex, fluvial-deltaic reservoirs 12 Along depositional strike (0% barrier) Standardized effect in % Kh PDF Kv/Kh PDF Prod/Inj rate Kv/Kh DDF Capillary P Kh DDF A Along depositional strike (90% barrier) Standardized effect in % Kh PDF Prod/Inj rate Kv/Kh PDF Kh DDF Kv/Kh DDF Capillary P B Recovery Factor Time to WB Water-cut Recovery Factor Time to WB Water-cut Figure 17. Tornado charts for simulations with water injection along depositional strike, with 0% of barrier coverage along clinoform (A), and with 90% (B). Threshold value = 2.132, non-significant effects (below threshold) are not displayed in this chart. Discussions Impact on flow of clinoforms associated with barriers to flow. Figure 18 shows the impact of barriers to flow along clinoforms for the three injection strategies. Injecting up depositional dip provides a better sweep efficiency than down depositional dip because it provides a gravity stable displacement, and forces water to flow upward from the poorer quality sands into the better quality sands (Figure 18). Injection down depositional dip depicts trapped oil in the underlying clinothem of each clinoform because of gravity forces (Figure 18). Besides, injection along depositional strike is less affected by the presence of barriers (Figure 18). However the time to WB and the WC decrease because barriers compartmentalise the reservoir in the horizontal direction, so the easiest flow path is taken by fluids, and fewer connections between facies are present (Figure 18). Figure 18. Cross-section through oil saturation profile with barriers along clinoforms after 1PV of water injected up and down depositional dip, and along depositional strike (run 16). Barrier coverage along clinoforms acts as vertical barrier to flow and forces fluids to go upward or downward; gravity drainage becomes important and upper part of clinothems presents oil trapped. The presence of barriers along clinoforms generates a tortuous flow path during water flooding that reduces the effective reservoir permeability. The main consequence is that pressure is not maintained during production through the model because some pressure constraints are rapidly reached (Table 5). Bottom hole pressure (BHP) of injectors is limited otherwise it might fracture the formation. Consequently, pressure maintenance is no longer ensured within the reservoir. Then, BHP of producers is limited to avoid reaching bubble point, and hence oil production decreases. Without barrier coverage, pressure is well spread, whereas with 90% of barrier to flow along clinoform surfaces, clinothems are separated from one another, and pressure maintenance is not well achieved (Figure 19). Figure 19 depicts pressure gradient within a dip cross section after 1 PV of water injection up depositional dip. The reservoir acts like it is compartmentalised, thus pressure support is not achieved and wells reach their BHP limits.

19 Understanding fluid flow in complex, fluvial-deltaic reservoirs 13 Figure 19. Cross-section through pressure profile with water injection down depositional dip after 1 PV injected (run 16) Permeability contrast and clinoform surfaces are key aspects of Ferron-Sandstone analogue. Indeed, facies architecture and their associated petrophysical properties have high impacts on balance between viscous and gravity forces. Kh in DDF has a significant impact when there is presence of barriers along clinoforms because fluid is forced (by dipping clinoforms associated with barriers to flow) to flow downward or upward into DDF facies. Without barriers, DDF can remain almost unswept due to the permeability contrast with PDF and the absence of gravity slumping. Figure 20 shows evidences from simulation results of the impact of the contrast between Kh in PDF and in DDF. Moreover, when Kh in PDF is high, it leads to an earlier WB so a higher WC and hence results in a lower final recovery factor due to the high contrast in horizontal permeability between PDF and DDF (Figures 20). Figure 20. Cross-section through oil saturation profile with water injection up depositional dip after 0.5 PV injected (run 12 and 15) Kh in DDF has the highest impact on RF when water injection is up and down depositional dip without barriers to flow along clinoform surfaces (Figures 15A and 16A). Indeed, all oil in PDF is expected to be swept without barrier to flow, regardless of the horizontal permeability (Figure 20). However, oil in DDF can be much more difficult to sweep, particularly when Kh in DDF = 5mD (low level setting). Besides and as seen previously, oil recovery is much lower in the presence of 90 % of barrier coverage along clinoform surfaces. In this case PDF plays the most important role because it contains much more oil than DDF (27 % porosity compared to 18 %). PDF needs to be well swept first to have a good recovery factor (Figure 20). Kv/Kh in PDF has a very high impact on recovery and water cut for all cases without barrier to flow but has almost no effect for cases with barriers (Figure 15, 16, and 17). This is because a low Kv/Kh ratio acts as vertical barriers to flow (Figure

20 Understanding fluid flow in complex, fluvial-deltaic reservoirs 14 21). Hence, the variation of Kv/Kh becomes negligible when barriers to flow are present within the model (Figure 18). Figure 21 depicts oil bypassed in PDF because of the low Kv/Kh ratio in PDF and the surrounding SMB facies, which is the best quality facies. Figure 21. Cross-section through oil saturation profile after 1 PV injected down depositional dip, and along depositional strike (run 1 and 9). Oil is trapped because of low Kv/Kh in PDF and presence of SMB above. Comparison with wave-dominated reservoirs results. This paper has provided an assessment of the impact of heterogeneities on hydrocarbon production in fluvial-dominated environments. The same experimental design as Obembe (2009) has been performed to compare our findings with theirs, which are related to wave-dominated environments. Horizontal permeability has high impacts on fluid flow compared to Kv/Kh ratio because our well spacing is small. Increasing well spacing results in decreasing viscous forces, thus gravity slumping has a more significant effect (Jackson et al., 2009). This result has also been found by Obembe (2009) for three different well spacing: 0.75 km (ours), 1.5 km, and 3 km in wave-dominated environment. In our study Kv/Kh in PDF has the second highest impact when there is no barrier coverage along clinoforms. Well spacing is 750 m, and effects of gravity forces should become more important than viscous forces with increasing well spacing as seen by Obembe (2009). In their study Kv/Kh in plsf (the equivalent of PDF but for wavedominated environment, detailed by Jackson et al. (2009)) becomes the parameter with the highest impact when increasing well-spacing from 0.75 km to 1.5 km and 3 km. This finding can be expected to be extended for fluvial-dominated environments. Moreover, they found that the presence of barrier coverage along clinoforms reduces the impact of Kv/Kh in plsf and it is Kh in plsf that has the highest impact on fluid flow. Our study also contains this finding. Capillary pressure and Kv/Kh in dlsf (equivalent to DDF) have little impact on fluid flow and hydrocarbon recovery in their study of wave-dominated environments. We find the same result for fluvial-dominated environments. Obembe (2009) concluded that pressure support is not really affected by the presence of barriers to flow with 750 m well spacing and that compartmentalisation is more evident with 3 km well spacing. In our study, presence of barriers yield very bad recovery factor and we have seen evidences of poor pressure maintenance. At 750 m well spacing, they found that production at target rate is achieved, regardless of the flooding direction and with pressure control on wells. We do not find the same result in our study. Indeed, the production at target rate is not achieved with presence of barrier coverage along clinoform surfaces and with low horizontal permeability. At 750 m well spacing, Obembe (2009) found that it is better to inject water down depositional dip than up depositional dip. However our study shows the opposite conclusion. As explained by Jackson et al. (2009), water injection up depositional dip forces water to flow upward from the poorer quality sands into the better quality sands. Capillary pressure has no influence either in this wave-dominated study, but it is suggested that its influence could be more important with more than 3 km well spacing. Conclusions for Ferron, constituting an analogue for fluvial-deltaic reservoirs Fluvial dominated reservoirs that contain huge reserves are encountered all over the world, like in the Gulf of Mexico. This paper has assessed the impact of clinoform surfaces and the possible wrong estimation of hydrocarbon recovery with a lack of understanding of fluid flow observed in these complex reservoirs. Some parameters require much more attention than others because of their high impact on hydrocarbon recovery, as seen for Kh in PDF. However, having high uncertainty on others can be acceptable as for Kv/Kh when there is barrier coverage along clinoform surfaces. On the other hand, focusing on analogue studies is necessary to determine the lateral extent of clinoform surfaces as we have seen their impact on hydrocarbon recovery, particularly when associated with barrier coverage. Some important differences exist between fluvial-dominated environment and wave-dominated, although they share similarities. It is recommended to inject water up depositional dip in fluvial-dominated instead of down depositional dip in wavedominated when there is presence of barriers to flow along clinoforms is the biggest difference observed. Making a clear distinction between these two types of depositional environment during the exploration phase is an important investment, because hydrocarbon recovery can be greatly affected.

21 Understanding fluid flow in complex, fluvial-deltaic reservoirs 15 Here is a summary of key findings that this study demonstrated to understand fluid flow in complex, fluvial-deltaic reservoirs: 1. Percentage of barrier coverage along clinoforms is the most important parameter. It can greatly lower hydrocarbon recovery. Models which do not capture these heterogeneities lead to an over prediction of hydrocarbon production. 2. Permeability contrast between SMB, PDF, and DDF is a key parameter. With presence of barrier coverage, Kh in PDF is the parameter which has the highest impact for up and down depositional dip injections. Whereas it is Kh in DDF when there is no barrier coverage along climoforms in these cases. 3. Waterflood direction and production strategy are key parameters. In our study injecting water along depositional strike is the best strategy to adopt, but the high proportion in PDF facies present in this model has to be taken into consideration. As much as possible, it is better to produce at low rates since it provides a better sweep efficiency. With presence of barrier coverage along clinoform surfaces it is preferable to inject up depositional dip compared to down depositional dip. 4. Kv/Kh in PDF has almost no influence with the three types of injection if there is presence of barrier coverage If that is not the case, it is necessary to take careful attention on this parameter because its impact becomes the second most important after Kh. 5. Capillary pressure and Kv/Kh in DDF have almost no impact on fluid flow. Improvements and further work. Combining results with uncertainties on parameters such as percentage of barrier coverage is necessary because there are still uncertainties in identifying clinoforms from subsurface data. Another improvement for this study is to stack other parasequences. In these kinds of shallow-marine reservoirs, there are many parasequences are stacked. Indeed, a 40 m thick model would give more relevant results for a reservoir simulation than a 6 m thick one. However, the models used in this study have already more than 16 million cells. This huge number of cells is due to the way adopted to build clinoforms. Many of them are not active cells (99%) since they are too thin. However, huge quantity of data has to be handled, and simulations take a longer time. Nomenclature SMB Stream-mouth bar Kh Horizontal permeability RF Recovery factor BHP Bottom hole pressure PDF Proximal delta-front Kv Vertical permeability WB Water breakthrough md MilliDarcy DDF Distal delta-front N North WC Water-cut sm 3 Surface cubic meter PD Prodelta Φ Porosity PS Parasequence kr Relative permeability References Begg, S.H., Gustason, E.R., and Deacon, M.W., 1992, Characterization of a fluvial-dominated delta: Zone 1 of the Prudhoe Bay field: SPE, v Box, G., Hunter, W., and Hunter, J., 1978, Statistics for experimenters: an introduction to design, data analysis, and model building (Chapters ): New York, Wiley Press. 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Fisher, W.L., and McGowen, J.H., 1969, Depositional systems in the Wilcox Group (Eocene) of Texas and their relation to occurrence of oil and gas: AAPG Bulletin, v. 53, p Forster, C.B., S. H. Snelgrove, S.H., and Koebbe, J.V., 2004, Modeling permeability structure and simulating fluid flow in a reservoir analog: Ferron Sandstone, Ivie Creek area, east-central Utah: AAPG Studies in Geology v. 50, p Gani, R.M., and Bhattacharya, J.P., 2005, Lithostratigraphy versus Chronostratigraphy in Facies correlations of Quaternary Deltas: Application of Bedding Correlation: SEPM Special Publication, v. 83, p Gardner, M.H., 1995, Tectonic and eustatic controls on the stratal architecture of mid-cretaceous stratigraphic sequences, central Western Interior foreland basin of North America: SEPM Special Publication, v. 52, p Garrison, J.J.R., and Van den Bergh, T.C.V., 2008, High resolution depositional sequence stratigraphy of the Upper Ferron

22 Understanding fluid flow in complex, fluvial-deltaic reservoirs 16 Sandstone Last Chance delta: An application of coal-zone stratigraphy: AAPG Studies in Geology v. 50, p Graham, G.H., Jackson, M.D., Hampson, G.J., Sech, R.P., and Deveugle, P.E.K., 2011, Three-dimensional numerical modeling of clinoforms in deltaic shoreface reservoirs: EAGE Conference & Exhibition incorporating SPE EUROPEC Workshop 10, Capturing Realistic Sedimentary Architecture in Geo-cellular Reservoir Models: State of the Art and Advances from Object and Process Modelling, to Multipoint Statistics, Vienna, Austria. Hampson, G.J., Rodriguez, A.B., Storms, J.E.A., Johnson, H.D., and Meyer, C.T., 2008, Geomorphology and high-resolution stratigraphy of progradational wavedominated shoreline deposits: Impact on reservoir-scale facies architecture: SEPM Special Publication v. 90, p Howell, J.A., Skorstad, A., MacDonald, A., Fordham, A., Flint, S., Fjellvoll, B., and Manzocchi, T., 2008a, Sedimentological parameterization of shallow-marine reservoirs: Petroleum Geoscience, v. 14, p Howell, J.A., Vassel, A., and Aune, T., 2008b, Modelling of dipping clinoform barriers within deltaic outcrop analogues from the Cretaceous Western Interior Basin, U.S.A.: Geoligical Society (London) Special Publication, v. 309, p Jackson, M.D., Hampson, G.J., and Sech, R.P., 2009, Three-dimensional modelling of a shoreface-shelf parasequence reservoir analog: Part2. Geologic controls on fluid flow and hydrocarbon recovery: AAPG Bulletin, v. 93, p Leckie, R.M., Yuretich, R.F., West, O.L.O., Finkelstein, D., and Schmidt, M., 1998, Paleoceanography of the southwestern Western Interior sea during the time of the Cenomanian Turonian boundary (Late Cretaceous): SEPM Special Publication, v. 6, p Obembe, A., 2009, Impact of heterogenity on flow in wave-dominated shallow-marine reservoirs: thesis submitted for the Individual MSc research Project (Petroleum Engineering) at Imperial College London. Rich, J.L., 1951, Three critical environments of deposition and criteria for recognition of rocks deposited in each of them: Geological Society of America Bulletin, v. 62, p Ryer, T.A., 1991, Stratigraphy, facies and depositional history of the Ferron Sandstone in the Canyon of Mudstonedy Creek, east-central Utah: Geology of east-central Utah: Utah Geological Association Publication v. 19, p Ryer, T.A., and Anderson, P.B., 2004, Facies of the Ferron Sandstone, east-central Utah: AAPG studies in Geology, v. 50, p Sech, R.P., Jackson, M.D., and Hampson, G.J., 2009, Threedimensional modeling of a shoreface-shelf parasequence reservoir analog: Part I: Surface-based modeling to capture high-resolution facies architecture: AAPG Bulletin, v. 93, p Tonellot, T., Burnstad, R., and Fitzmaurice, J., 2009, Seismic Inversion Workflow for Sand stringers characterization in offshore Saudi Arabia: SPE, v Tyler, N., and Finley, R.J., 1991, Architectural controls on the recovery of hydrocarbons from sandstone reservoirs: SEPM Concepts and Models in Sedimentology and Paleontology 3, p Wellner, R., R. Beaubouef, R., J. C. Van Wagoner, J.C., H. H. Roberts, H.H., and Sun, T., 2005, Jet-plume depositional bodies The primary building blocks of Wax Lake delta: Transactions of the Gulf Coast: Association of Geological Societies, v. 55, p White, C.D., and Royer, S.A., 2003, Experimental design as a framework for reservoir studies: SPE, v

23 APPENDIX A: Critical literature review MILESTONES Paper n o Year Title Author(s) Contribution JPT, V. 30, p 1978 Deltaic environment reservoir Types and Their characteristics Wiley Press, New York AAPG Memoir 71, p AAPG Studies in Geology 50 AAPG Bulletin, V.93, NO.9, pp AAPG Bulletin, V.94, NO.2, pp EAGE; v.17; p AAPG Bulletin, V. 95, NO. 5, pp Statistics for experimenters: an introduction to design, data analysis, and model building (Chapters ) 1999 Reservoir Characterization- Recent Advances / Chapter 5: Predicting Interwell Heterogeneity in Fluvial-deltaic Reservoirs: Effects of Progressive Architecture Variation Through a Depositional Cycle from Outcrop and Subsurface Observations 2004 Searching for Modern Ferron Analogs and Application to Subsurface Interpretation 2009 Three-dimensional modelling of a shoreface-shelf parasequence reservoir analog: Part2. Geologic controls on fluid flow and hydrocarbon recovery 2010 Impact of deltaic clinothems on reservoir performance: Dynamics studies of reservoir analogs from the Ferron Sandstone Member and Panther Tongue, Utah 2011 Predicting the impact of sedimentological heterogeneity on gas oil and water oil displacements: fluvio-deltaic Pereriv Suite Reservoir, Azeri Chirag Gunashli Oilfield, South Caspian Basin 2011 Characterization of stratigraphic architecture and its impact on fluid flow in a fluvialdominated deltaic reservoir analog: Upper Cretaceous Ferron Sandstone Member, Utah Sneider, R. M., Tinker, C. N., and Meckel, L. D. Box, G., Hunter, W., and Hunter, J. Knox, P. R., and Barton, M. D. (Chapter 5) Edited by Schatzinger, R. A., and Jordan, J. F. Bhattacharya, J. P., and Tye, R. S. Jackson, M. D., Hampson, G. J., and Sech, R. P. Enge, H. D., and Howell, J. A. Choi, K., Jackson, M. D., Hampson, G. J., Jones, A. D.W., and Reynolds, A. D. Deveugle, P. E. K., Jackson, M. D., Hampson, G. J., Farrell, M. E., Sprague, A. R., Stewart, J., and Calvert, C. S. First presentation and complete summary of processes responsible for creating the end members of a continuum of deltaic sedimentation and the characteristics of reservoirs created by these processes. First detailed explanation of fractional factorial design concepts for experimenters to increase research efficiency. It shows the basic simplicity of the designs and how they fit naturally into iterative scientific method. Have carried out studies of outcrop reservoir analogues and of reservoirs that suggest that variability is predictable if assessed within the framework of depositional cycles and that differences between adjacent high-frequency cycles can substantially impact production behaviour and reserve-growth potential. Quantitative approach to selecting modern-depositional settings analogous to those of the Cretaceous Ferron Sandstone is presented. Have investigated the impact of clinoform-controlled, intraparasequence depositional and diagenetic heterogeneity on water flood efficiency in wave-dominated, shoreface-shelf reservoirs using 3D-model of a single parasequence exposed at outcrop. Dynamic study focused on the impact of deltaic clinothems on reservoir performance based on reservoir analogues. Permeabilities and mudstones barriers are the key parameters studied. First detailed assessment of the impact of large and intermediate-scale heterogeneities on flow in fluvial-deltaic reservoirs. First comparison of water-oil and gas-oil displacements in fluvial-deltaic reservoirs using 3D geologic/simulation models derived from outcrop and subsurface data. This study documents a high-resolution three-dimensional reservoir-scale model of delta-complex deposits from the Upper Cretaceous Ferron Sandstone Member of central Utah.

24 Understanding fluid flow in complex, fluvial-deltaic reservoirs 18 JPT, V. 30, p (1978) Deltaic environment reservoir Types and Their characteristics Authors: R. M. Sneider, C. N. Tinker, and L. D. Meckel Contribution: First presentation and complete summary of processes responsible for creating the end members of a continuum of deltaic sedimentation and the characteristics of reservoirs created by these processes. Objective of the paper: Better understanding of the quality, distribution, and continuity of the reservoir and its contained fluids. They provide the knowledge needed of (1) the distribution and quality of pore space in terms of porosity, permeability, and capillary pressure properties, and (2) the location of barriers to flow, both internal and external, to enhance the ultimate recovery from this important source of oil and gas. Methodology used: Summary paper, which is based solely on and distilled from information available in published sources. Conclusion reached: 1. The most important factor controlling reservoir quality is the initial size and sorting of grains. Thus, the best reservoir-quality sand in bar deposits is at or near the top. 2. The best reservoir-quality sand in channels is in the bottom. 3. High energy sand deltas have the best continuity of both bars and channel sands, while the low-energy mud deltas display much more discontinuity of sands because of the more continuous clay/silt interbeds. Comments: More recent studies can complete this paper.

25 Understanding fluid flow in complex, fluvial-deltaic reservoirs 19 Wiley Press, New York (1978) Statistics for experimenters: an introduction to design, data analysis, and model building. (Chapters ) Authors: Box G. Hunter, W. and Hunter, J. Contribution: Detailed explanation of fractional factorial design concepts. They are one means available to experimenters to increase research efficiency. It shows the basic simplicity of the designs and how they fit naturally into iterative scientific method. Objective of the paper: The number of runs required by a full 2 k factorial design increases geometrically as k is increased. It turns out, however, that when k is not small the desired information can often be obtained by performing only a fraction of the full factorial design. A part of this book describes how suitable fractions can be generated and discusses their advantages and limitations. Methodology used: Usually it is most efficient to estimate the effects of several variables simultaneously. Each experimental design will then contain a group of experimental runs. After many sensitivity runs of a two-level factorial design, effects can be estimated but all are not of appreciable size. There tends to be a certain hierarchy. In terms of absolute magnitude, main effects tend to be larger than two-factor interactions, which in turn tend to be larger than three-factor interactions, and so on. The idea is to reduce the number of runs (experiments) needed to analyse an effects, avoiding too many useless interactions. Conclusion reached: At some point, higher order interactions tend to become negligible and can properly be disregarded. Also, when a moderately large number of variables is introduced into a design, it often happens that some have no distinguishable effects at all. There tends to be redundancy in a 2 k design if k is not small; redundancy in terms of an excess number of interactions that can be estimated and sometimes in an excess number of variables that are studied. Fractional factorial design exploits this redundancy. Comments: In sequential experimentation, unless the total number of runs for a full or replicated factorial is needed to achieve sufficient precision, it is usually better to run fractional factorial designs. The fractions, used as building blocks, can build up to the full factorial design if this is necessary.

26 Understanding fluid flow in complex, fluvial-deltaic reservoirs 20 AAPG Memoir 71, p (1999) Reservoir Characterization-Recent Advances / Chapter 5: Predicting Interwell Heterogeneity in Fluvialdeltaic Reservoirs: Effects of Progressive Architecture Variation Through a Depositional Cycle from Outcrop and Subsurface Observations Authors: Edited by Richard A. Schatzinger and John F. Jordan / Chapter 5: Paul R. Knox and Mark D. Barton Contribution: Have carried out studies of outcrop reservoir analogues and of reservoirs that suggest that variability is predictable if assessed within the framework of depositional cycles and that differences between adjacent high-frequency cycles can substantially impact production behaviour and reserve-growth potential. Objective of the paper: Benefits range from improved prospect ranking to improved development efficiency and better prioritization of mature fields for acquisition or characterization. Application of these techniques to fluvial-deltaic reservoirs could improve near-term reserve-growth potential, preventing permanent loss of strategic resources by curtailing premature field abandonments. Methodology used: Detailed investigation of two fluvial-influenced upper delta-plain reservoirs. To investigate changes in architecture through depositional cycles, the hierarchy of depositional cyclicity has been identified and the depositional facies assessed at the scale of the smallest identifiable cycle. Differing sets of terminology have been applied to describe the hierarchy of scales of depositional cycles, such as, from smallest to largest, parasequences, high-frequency sequences, sequences and composite sequences, etc Conclusion reached: Outcrop studies of the Cretaceous Ferron sandstone of Utah have demonstrated that: 1. Incised fluvial deposits in progradational parts of low-frequency depositional cycles tend to be narrow, deep, and internally homogeneous, whereas those in retrogradational parts of such cycles tend to be wider, internally heterogeneous, and display lateral channel migration 2. River-dominated delta-front styles are more common in progradational parts of intermediatefrequency cycles, whereas wave-dominated delta-front styles are more common in retrogradational parts. Comments: The application of these findings to other reservoir intervals and other basins should be made with appropriate caution. Nothing said about clinoforms and potential barriers to flow.

27 Understanding fluid flow in complex, fluvial-deltaic reservoirs 21 AAPG Bulletin, V.93, NO.9, pp (2009) Three-dimensional modelling of a shoreface-shelf parasequence reservoir analog: Part2. Geologic controls on fluid flow and hydrocarbon recovery Authors: Matthew D. Jackson, Gary J. Hampson, and Richard P. Sech Contribution: Have investigated the impact of clinoform-controlled, intra-parasequence depositional and diagenetic heterogeneity on water flood efficiency in wave-dominated, shoreface-shelf reservoirs using 3D-model of a single shoreface-shelf parasequence exposed at outcrop. Objective of the paper: This study investigates the impact of depositional and diagenetic heterogeneity associated with gently dipping clinoform surfaces on fluid flow and recovery during water flooding, using three-dimensional model reconstructed from a well-exposed outcrop analogue. Methodology used: Well placement during water flooding is influenced by reservoir structure, but different production strategies have been tried. Various typical Rock and fluid properties of wave-dominated Shoreface-shelf reservoirs in the North Sea are used. A layer-cake model was generated for each production scenario to reflect the changing location of the control data at modelled wells. The simple barrier bodies modelled in this study will capture the impact on flow of these other types of heterogeneity associated with clinoforms. Conclusion reached: 1. Although clinoform surfaces control facies architecture, they have little impact on the waterflood recovery factor unless they are associated with calcite-cemented layers or other barriers to flow. 2. Layer-cake models can yield poor predictions of the volume of oil in place if they fail to capture variations in facies thickness associated with interfingering along clinoform surfaces. If the clinoform surfaces are associated with calcite-cemented layers, which act as barriers to flow, and the layers occupy a significant proportion of each surface, then clinoforms can have a significant impact on waterflood recovery that is not captured by simple layer-cake model. 3. The largest impact on waterflood recovery factor is observed if water flooding is oriented parallel to depositional strike. 4. Pressure support of producers is reduced if water flooding is oriented parallel to depositional dip. Barrier-lined clinoforms have more significant impact on water flooding down depositional dip than up depositional dip. Comments: Sensitivity runs with only a few parameters. Study of the impact of heterogeneities by performing an experimental design: Obembe et al Note that the presence and lateral extent of clinoform-related barriers may be difficult to characterize in the subsurface because they may be extensive enough to impact waterflood sweep and pressure communication, but may not be associated with diagnostic breaks in pressure.

28 Understanding fluid flow in complex, fluvial-deltaic reservoirs 22 AAPG Bulletin, V.94, NO.2, pp (2010) Impact of deltaic clinothems on reservoir performance: Dynamics studies of reservoir analogs from the Ferron Sandstone Member and Panther Tongue, Utah Authors: Havard D. Enge and John A. Howell Contribution: Dynamic study focused on the impact of deltaic clinothems on reservoir performance based on reservoir analogs. Permeabilities and mudstones barriers are the key parameters investigated. Objective of the paper: A key aspect of the modelling is to accurately capture clinoforms geometries and their effect on simulated flow. Clinoforms are commonly draped with low-permeability mudstones that produce reservoir heterogeneity by subdividing the deltaic sand body into a series of dipping sandstone beds (clinothems). Methodology used: The study presented in this article used highly geometrical digital geological outcrop data collected using ground-based laser scanning (light detection and ranging [LIDAR]) to build and test three-dimensional geocellular models of deltaic reservoir analogues. Portions of the two deltaic systems were dynamically analysed in a reservoir modelling software by simulating production in 41 models. These models tested a range of mudstone barrier continuities and permeability. Conclusion reached: 1. Clinothems and associated heterogeneities have significant influence on production. 2. When the clinothems do not extend between wells, they have a greater influence on production than when represented as field-wide reservoir elements. 3. Introduction of thicker bedsets barriers enhanced recovery maybe because of increased sweep efficiency. If heterogeneities are close to continuous and have low-enough permeability, steeper dipping and closer spaced clinothems lower the recovery factor. 4. Spacing of injector and producer should be guided by clinothems spacing and the permeability of the mudstone drapes on the clinoforms. Comments: Difficult to assess the applicability of these results because of the very particular analog chosen. Steeper dipping and others parameters are different between the two base case (the low net-to-gross one and the high one). PVT properties remain the same in the whole study. Petrophysical sensitivity only run on permeability.

29 Understanding fluid flow in complex, fluvial-deltaic reservoirs 23 EAGE, v. 17, p (2011) Predicting the impact of sedimentological heterogeneity on gas oil and water oil displacements: fluviodeltaic Pereriv Suite Reservoir, Azeri Chirag Gunashli Oilfield, South Caspian Basin Authors: Choi, K., Jackson, M. D., Hampson, G. J., Jones, A. D.W., and Reynolds, A. D. Contribution: First detailed assessment of the impact of large and intermediate-scale heterogeneities on flow in fluvial-deltaic reservoirs. First comparison of water-oil and gas-oil displacements in fluvialdeltaic reservoirs using 3D geologic/simulation models derived from outcrop and subsurface data. Objective of the paper: Understand fluid flow and impact on oil recovery in fluvial-deltaic environment characterized by laterally continuous layers of variable net-to-gross (NTG). Before, predictions were based on reservoir models which do not explicitly capture the full range of geologic heterogeneity present in the Pliocene Pereriv Suite reservoirs (major reservoir interval of ACG Oilfield). Methodology used: Reservoirs modelling approach starts with the simplest possible model then progressively add increasing levels of geologic heterogeneity. Simulation-based sensitivity analysis has been carried out and experimental design and analysis of variance to identify the key heterogeneities which have major impact on recovery. A two-level fractional-factorial design was employed. Conclusion reached: It shows the importance of the presence of communications between adjacent low and high net-to-gross layers. It significantly improves oil recovery, providing pressure support and a route for oil production from sandbodies within the low NTG layers which otherwise be isolated. Impact on recovery is much more significant when heterogeneity is located in low NTG layers than one high NTG layers. I most case, same significant heterogeneities impact on both water and gas displacements (rates are set to obtain a stable displacement). Comments: Petrophysical properties were assumed to be uniform. Overlap between the sensitivity parameters describing channel stacking and channel dimensions. A wider range of heterogeneity scale is needed for a complete understanding of flow-fluid behaviour. Major simplifications have been done on PVT properties; it could be interesting to assess the additional impact of more realistic modelling of the fluid properties.

30 Understanding fluid flow in complex, fluvial-deltaic reservoirs 24 AAPG Bulletin, V. 95, NO. 5, p (2011) Characterization of stratigraphic architecture and its impact on fluid flow in a fluvial-dominated deltaic reservoir analog: Upper Cretaceous Ferron Sandstone Member, Utah Authors: Peter E. K. Deveugle, Matthew D. Jackson, Gary J. Hampson, Michael E. Farrell, Anthony R. Sprague, Jonathan Stewart, and Craig S. Calvert Contribution: This study documents a high-resolution three-dimensional reservoir-scale model of deltacomplex deposits from the Upper Cretaceous Ferron Sandstone Member of central Utah. Objective of the paper: Use of the model to investigate the impact of stratigraphic architecture, and some of the associated uncertainties in interpretation, on fluid flow during hydrocarbon production. The goals of this paper are threefold: (1) to capture stratigraphic architecture at delta-lobe scale using high resolution three-dimensional model; (2) to derive the characteristic dimensions and spatial organization of the delta lobes and their constituent facies-association belts; (3) to identify some of the key heterogeneities of delta-lobe stratigraphic architecture that impact fluid flow and hydrocarbon recovery via a simulationbased sensitivity analysis. Methodology used: Several methods have been developed last decade for the digital collection of outcrop data sets. This study use simpler and more conventional techniques because traditional field geology techniques provide sufficient accuracy to characterize the modelled facies-association belt; there was abundance of existing digital and non-digital data available for the study. The outcrop model was built following a hybrid of the hierarchical surface-based modelling work-flow and a conventional grid-based approach. Conclusion reached: 1. Detailed characterization of the stratigraphic architecture. 2. During water flooding, sweep efficiency of the model is controlled by four parameters: the continuity, orientation, and permeability character of channel-fill sand bodies; the vertical permeability of heterolithic distal delta-front deposits; the direction of sweep relative to the orientation of channel-fill and delta-lobe sand bodies; and well spacing. 3. The first two parameters are likely to be uncertain in subsurface data sets but have a large impact on predicted sweep efficiency, which must be assessed via modelling of different interpreted scenarios. Comments: The sensitivity analysis is more qualitative than quantitative. The main point is to characterize the stratigraphic architecture. Very favourable end-point mobility ratios, without compressibility, capillary or gravity effects are used in the Streamline-based tracer simulations to investigate the impact of stratigraphic architecture and facies-dependent permeability contrasts on sweep efficiency. Larger and smaller scales of stratigraphic heterogeneity should be take into account in future studies.

31 Water-cut Normalised time to WB Understanding fluid flow in complex, fluvial-deltaic reservoirs 25 APPENDIX B: Simulation data Here is an example of final results (time to WB and WC) of the 96 runs, although, key findings have been exposed in the main body: up 0 barrier up 90 barrrier down 0 barrier down 90 barrier strike 0 barrier strike 90 barrier Run Figure B-1. Ratio: Time to WB/simulation time plotted for each of the 96 simulations performed up 0 barrier up 90 barrrier down 0 barrier down 90 barrier strike 0 barrier strike 90 barrier Run Figure B-2. Final water-cut of the 96 simulations performed. Here is an example of.data file used to run simulation in ECLIPSE software: RUNSPEC DEBUG 51*0/ SAVE/ TITLE Clinoform cD DIMENS -- Nx Ny Nz / -- Phases present -- Only dead oil and water above bubble point at all time

32 Understanding fluid flow in complex, fluvial-deltaic reservoirs 26 OIL WATER METRIC -- Note units used throughout.data file START 01 'jan' 2005 / UNIFIN UNIFOUT WELLDIMS -- NWMAX NWMAXZ NGMAX NWGMAX / TABDIMS -- NTSFUN NTPVT NSSFUN NPPVT / NSTACK 80/ MESSAGES / -- All else is defaulted MEMORY 1428 / GRID NEWTRAN -- Use NEWTRAN for irregular grids and OLDTRAN for Cartesian grids PSEUDOS --Write restart file containing initial water saturations etc. --Switch off output to the PRT file during grid loading for easier debugging NOECHO --Include file containing COORD, ZCORN, PORO, PERMX, PERMY, PERMZ data --Load grid INCLUDE 'Includes/25M.GRDECL' / -- PORO, PERMX etc. are included in separate files, they depend on level setting INCLUDE 'Includes/PORO.GRDECL' / INCLUDE 'Includes/PERMX00.GRDECL' / INCLUDE 'Includes/PERMZ0100.GRDECL'/ COPY PERMX PERMY / --Include MULTZ data (if calcite cement present) INCLUDE 'Includes/MULTX90.GRDECL'/ INCLUDE 'Includes/MULTY90.GRDECL'/ INCLUDE 'Includes/MULTZ90.GRDECL'/ -- Set up NNC's across pinched-out cells PINCH 0.01 'GAP' / -- Produce initial file for GRAF INIT

33 Understanding fluid flow in complex, fluvial-deltaic reservoirs 27 EDIT PROPS CORRECT NOW -- oil/water relative permeability and capillary pressure are tabulated as -- a function of water saturation -- SMB --Sw krw kro Pc (Bar) SWOF E / -- pdf low --Sw krw kro Pc (Bar) / -- ddf low --Sw krw kro Pc (Bar) / -- OT --Sw krw kro Pc (Bar)

34 Understanding fluid flow in complex, fluvial-deltaic reservoirs / / -- Specify fluid properties -- OIL WATER GAS -- (KG/M3) (KG/M3) (KG/M3) DENSITY / -- Specify rock properties -- REF.PRES ROCK-COMPRESSIBILITY -- (BAR) (1/BAR) ROCK / -- Dead oil PVT table (FVF and Viscosity must vary with pressure) -- Oil phase press. Oil FVF Oil compressibility Oil Viscosity -- (BAR) (Rm3/Sm3) (1/bars) (CPoise) PVCDO / -- Water PVT table -- Ref. press. FVF-WATER Compressibility Viscosity Viscosibility -- (BAR) (RM3/SM3) (1/BAR) (CPoise) (1/BAR) PVTW / REGIONS Create regions and assigne associated properties INCLUDE 'Includes/SATNUM9.GRDECL' / SOLUTION DATA FOR INITIALISING FLUIDS TO POTENTIAL EQUILIBRIUM EQUIL -- DATUM PRESSURE DEPTH OWC DEPTH GOC INIT INIT INTE -- DATUM OWC CAP GOC CAP TYPE TYPE N -- PRESS PRE LO DO / SUMMARY DATE -- Specify creation of summary file RPTSMRY 1 / -- Specify summary file in LOTUS format LOTUS -- Specify output of producer wells to summary file GOPR 'P' / GWPR 'P' / GWCT

35 Understanding fluid flow in complex, fluvial-deltaic reservoirs 29 'P' / GWIT 'I' / -- Specify output of oil and water in place to summary file FOIP FWIP FOPT --well oil production total WOPT 'P1' / WOPT 'P2' / WOPT 'P3' / WOPT 'P4' / WOPT 'P5' / WOPT 'P6' / --water prod total WWPT 'P1' / WWPT 'P2' / WWPT 'P3' / WWPT 'P4' / WWPT 'P5' / WWPT 'P6' / --well BHP WBHP / --water inj total WWIT 'I1' / WWIT 'I2' / WWIT 'I3' / WWIT 'I4' / SCHEDULE CONTROL ON OUTPUT AT EACH REPORT TIME RPTSCHED 'FIP=1' 'WELLS' 'SUMMARY=2' / -- 'FIP=1' 'WELLS' 'SUMMARY=2' 'RS' 'SGAS' 'SOIL' 'SWAT' 'PRESSURE' / RPTRST 'BASIC=2' / --Load wells specifications INCLUDE 'Includes/WELSPECS-EXAMPLE-DOWN-3km.txt' /

36 Understanding fluid flow in complex, fluvial-deltaic reservoirs 30 GCONPROD -- NAME PROD OIL WAT GAS LIQ PROCE FREE GRP DEF PROC PROC PROC RES PROD -- RATE TAR TAR TAR TAR EXC RES PRO GUI EXCW EXCG EXCL FLU BAL 'P' 'LRAT' 3* 350 / / GCONINJE -- NAME PHA INJ WAT RES RINJ TOTAL FREE GRP DEF -- MODE TAR VOL TAR VOID RES INJ GUI 'I' 'WATER' 'RATE' 350 / / WCONPROD -- NAME STATUS CONTMODE OILT WATT GAST LIQT RESVT BHPT TOHT PROVFP ART 'P1' 'OPEN' 'GRUP' 3* * 50/ 'P2' 'OPEN' 'GRUP' 3* * 50/ 'P3' 'OPEN' 'GRUP' 3* * 50/ 'P4' 'OPEN' 'GRUP' 3* * 50/ 'P5' 'OPEN' 'GRUP' 3* * 50/ 'P6' 'OPEN' 'GRUP' 3* * 50/ / WCONINJE -- NAME INJPHASE OP/SH CONTMODE SURFLOWRATE RESFLOWRATE BHPLIMIT THPTARGET VFPTABLE RS/OR/RV 'I1' 'WATER' 'OPEN' 'GRUP' * 150 / 'I2' 'WATER' 'OPEN' 'GRUP' * 150 / 'I3' 'WATER' 'OPEN' 'GRUP' * 150 / 'I4' 'WATER' 'OPEN' 'GRUP' * 150 / / ECHO TUNING / / 2* 50/ DATES 1 MAR 2005/ 1 MAY 2005/ 1 JUL 2005/ 1 SEP 2005/ 1 NOV 2005/ 1 JAN 2006/ 1 MAR 2006/ 1 MAY 2006/ 1 JUL 2006/ 1 SEP 2006/ 1 NOV 2006/ 1 JAN 2007/ 1 JAN 2008/ 1 JAN 2009/ 1 JAN 2010/ 1 JAN 2011/ 1 JAN 2012/ 1 JAN 2013/ 1 JAN 2014/ 1 JAN 2015/ / END

37 Understanding fluid flow in complex, fluvial-deltaic reservoirs 31 Here is an example of well specifications.txt file: -- WELL SPECIFICATION DATA -- NAME GROUP WH-i WH-j BHPdatum flowing phase drainradius WELSPECS P1 P * 'OIL' / P2 P * 'OIL' / P3 P * 'OIL' / P4 P * 'OIL' / P5 P * 'OIL' / P6 P * 'OIL' / I1 I * 'WATER' / I2 I * 'WATER' / I3 I * 'WATER' / I4 I * 'WATER' / / -- COMPLETION SPECIFICATION DATA -- NAME I J KUP KLOW OPEN/ST SATABLE CONFACTR WELLINTDIM EFF/KH SKINF DFACTOR PENETDIR PREEQUIRAD COMPDAT P1 1* 1* OPEN 1* 1* 0.31 / P2 1* 1* OPEN 1* 1* 0.31 / P3 1* 1* OPEN 1* 1* 0.31 / P4 1* 1* OPEN 1* 1* 0.31 / P5 1* 1* OPEN 1* 1* 0.31 / P6 1* 1* OPEN 1* 1* 0.31 / I1 1* 1* OPEN 1* 1* 0.31 / I2 1* 1* OPEN 1* 1* 0.31 / I3 1* 1* OPEN 1* 1* 0.31 / I4 1* 1* OPEN 1* 1* 0.31 / Here is the Matlab code used for results processing: % cut and reorganize the.rsm (output from ECLIPSE simulations) file previously imported in matlab prompt = {'Last row of first sequence?'}; dlg_title = 'Input value'; num_lines = 1; def = {''}; answer = inputdlg(prompt,dlg_title,num_lines,def); lastrow = str2num(answer{1,1})'; x = lastrow; y = lastrow+9; z = lastrow-1; sorted_data(1:x,1:9) = data(1:x,1:9); sorted_data(1:x,10:18) = data(y:y+z,1:9); y = y+z+9; sorted_data(1:x,19:27) = data(y:y+z,1:9); y = y+z+9; sorted_data(1:x,28:36) = data(y:y+z,1:9); y = y+z+9; sorted_data(1:x,37:45) = data(y:y+z,1:9); y = y+z+9; sorted_data(1:x,46:47) = data(y:y+z,1:2); STOIIP (1,1) = sorted_data (1,19); RF (1:x,1) = sorted_data (1:x,21)/STOIIP (1,1); sorted_data (1:x,48) = RF (1:x,1); n=1; for n=1:x;

38 Understanding fluid flow in complex, fluvial-deltaic reservoirs 32 if < sorted_data (n,17) < 0.02 WC_at_WB = sorted_data (n,17); WB_time(1,1) = sorted_data (n,1); end end j = x/40; k = floor(j); i=1; l=1; while i<=x small_data (l,1) = sorted_data (i,1); small_data (l,2) = sorted_data (i,5); small_data (l,3) = sorted_data (i,6); small_data (l,4) = sorted_data (i,17); small_data (l,5) = sorted_data (i,18); small_data (l,6) = sorted_data (i,19); small_data (l,7) = sorted_data (i,20); small_data (l,8) = sorted_data (i,21); small_data (l,9) = sorted_data (i,48); l=l+1; i = i+k; end small_data (42,1) = sorted_data (x,1); small_data (42,2) = sorted_data (x,5); small_data (42,3) = sorted_data (x,6); small_data (42,4) = sorted_data (x,17); small_data (42,5) = sorted_data (x,18); small_data (42,6) = sorted_data (x,19); small_data (42,7) = sorted_data (x,20); small_data (42,8) = sorted_data (x,21); small_data (42,9) = sorted_data (x,48); PV_inj (1,1) = small_data (42,5)/(small_data (1,6)+small_data (1,7)); results (1,1) = small_data (42,4); results (1,2) = small_data (42,9); results (1,3) = WB_time(1,1); results (1,4) = small_data (42,8); results (1,5) = small_data (42,5); results (1,6) = PV_inj (1,1); % create RF and WC vs Time subplot(4,2,1); plot(sorted_data(1:x,1),rf(1:x,1),'--r','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,17),'-.b','markersize',1,'linewidth',1); grid on; whitebg([ ]); xlabel('time(years)'); ylabel('rf and WC'); legend('rf','wc','location','northeast') title('recovery Factor and Water Cut versus Time'); axis([]); % create GOPR and GWPR vs Time subplot(4,2,2); plot(sorted_data(1:x,1),sorted_data(1:x,5),'--r','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,6),'-.b','markersize',1,'linewidth',1); grid on;

39 Understanding fluid flow in complex, fluvial-deltaic reservoirs 33 whitebg([ ]); xlabel('time(years)'); ylabel('rates(sm3/d)'); legend('gopr','gwpr','location','northeast') title('group Oil and Water production rates versus Time'); axis([]); % create GWIT and FOPT vs Time subplot(4,2,3); plot(sorted_data(1:x,1),sorted_data(1:x,18),':r','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,21),'b','markersize',1,'linewidth',1); grid on; xlabel('time(years)'); ylabel('cumulative(sm3)'); legend('gwit','fopt','location','northeast') title('group Water Injected and Field Oil Produced versus Time'); axis([]); % create FOIP and FWIP vs Time subplot(4,2,4); plot(sorted_data(1:x,1),sorted_data(1:x,19),'r','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,20),'b','markersize',1,'linewidth',1); grid on; xlabel('time(years)'); ylabel('initially in place(sm3)'); legend('foip','fwip','location','northeast') title('field Oil and Water Initially in Place versus Time'); axis([]); % create WBHP vs Time subplot(4,2,5); plot(sorted_data(1:x,1),sorted_data(1:x,7),'r','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,8),'b','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,9),'y','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,10),'g','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,11),'c','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,12),'color',[0.5.6],'markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,13),'m','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,14),'w','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,15),'k','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,16),'color',[1.4.6],'markersize',1,'linewidth',1); grid on; xlabel('time(years)'); ylabel('pressure(bars)'); legend('p1','p2','p3','p4','p5','p6','i1','i2','i3','i4','location','northeast') title('well Bottom Hole Pressure versus Time'); axis([]); % create WOPT vs Time

40 Understanding fluid flow in complex, fluvial-deltaic reservoirs 34 subplot(4,2,6); plot(sorted_data(1:x,1),sorted_data(1:x,22),'r','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,23),'m','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,24),'y','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,25),'g','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,26),'c','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,27),'b','markersize',1,'linewidth',1); grid on; xlabel('time(years)'); ylabel('oil Production(sm3)'); legend('p1','p2','p3','p4','p5','p6','location','northeast') title('well Oil Cumulative Production versus Time'); axis([]); % create WWPT vs Time subplot(4,2,7); plot(sorted_data(1:x,1),sorted_data(1:x,28),'r','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,29),'m','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,30),'y','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,31),'g','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,32),'c','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,33),'b','markersize',1,'linewidth',1); grid on; xlabel('time(years)'); ylabel('water Production(sm3)'); legend('p1','p2','p3','p4','p5','p6','location','northeast') title('well Water Cumulative Production versus Time'); axis([]); % create WWIT vs Time subplot(4,2,8); plot(sorted_data(1:x,1),sorted_data(1:x,44),'r','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,45),'m','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,46),'y','markersize',1,'linewidth',1); plot(sorted_data(1:x,1),sorted_data(1:x,47),'g','markersize',1,'linewidth',1); grid on; xlabel('time(years)'); ylabel('water Injection(sm3)'); legend('i1','i2','i3','i4','location','northeast') title('well Water Cumulative injection versus Time'); axis([]);

41 Understanding fluid flow in complex, fluvial-deltaic reservoirs 35 Here is a figure displaying all output results obtained after each simulation using the Matlab code: Figure B-3. Example of Matlab plots (Run 2, Injection up deositioal dip without barriers) Here is the code used to create CDF plot: sdata=sort(data); average=mean(sdata); variance=std(sdata); P=normcdf(sdata,average,variance); plot(sdata,p,'-');