## Publications

161 results found

Smalley PC, Muggeridge AH, Kusuma CR, 2020, Patterns of water <sup>87</sup>Sr/<sup>86</sup>Sr variations in oil-, gas- and water-saturated rocks: Implications for fluid communication processes, distances and timescales, *Marine and Petroleum Geology*, Vol: 122, ISSN: 0264-8172

© 2020 The Authors This study reviews 87Sr/86Sr depth profiles of formation waters sampled by Sr residual salt analysis (Sr RSA) from >100 oil/gas wells and research sites, including reservoirs with clastic and carbonate host rocks and with gas, oil and water as the continuous fluid phase. Globally, the water data form a smooth trend between low seawater-like 87Sr/86Sr ratios (~0.706) at shallow depths and high (~0.724) ratios in deeply buried rocks, where water-rock interaction dominates. We test the hypothesis that 87Sr/86Sr depth profiles in individual wells could be influenced by diffusional mixing processes by developing 1D diffusion mixing equations to simulate compositional patterns through time and comparing them with observed profiles. Different combinations of boundary and initial conditions generate various patterns characteristic of diffusion, including non-steady-state curves relating to incomplete mixing and steady-state patterns (such as vertical or inclined straight lines) where initial heterogeneities have fully mixed. The dataset yielded 193 occurrences of these patterns. Steady-state patterns are more common and longer in water zones, while non-steady-state patterns are more common and longer in oil and gas zones. The detection of diffusional mixing patterns in hydrocarbon-saturated rocks suggests that diffusion is active, although on average a factor of ~13–18 slower, than in comparable water-saturated rocks. Pattern generation and equilibration times were modelled for each non-steady-state pattern and compared with the time since reservoir filling with oil/gas, revealing that 90% of them could have been generated since filling, but 60% of them would already have mixed to steady state had the initial compositional heterogeneities arisen during or before reservoir filling. This is critical evidence that at least some of the initial heterogeneities must have arisen, and subsequently partially mixed, after filling; these patterns tend

Kostorz WJ, Muggeridge AH, Jackson MD, 2020, An efficient and robust method for parameterized nonintrusive reduced-order modeling, *INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING*, ISSN: 0029-5981

Lei Q, Jackson MD, Muggeridge AH,
et al., 2020, Modelling the reservoir-to-tubing pressure drop imposed by multiple autonomous inflow control devices installed in a single completion joint in a horizontal well, *Journal of Petroleum Science and Engineering*, Vol: 189, Pages: 1-16, ISSN: 0920-4105

Autonomous inflow control devices (AICDs) are used to introduce an additional pressure drop between the reservoir and the tubing of a production well that depends on the fluid phase flowing into the device: a larger pressure drop is introduced when unwanted phases such as water or gas enter the AICD. The additional pressure drop is typically represented in reservoir simulation models using empirical relationships fitted to experimental data for a single AICD. This approach may not be correct if each completion joint is equipped with multiple AICDs as the flow at different AICDs may be different. We use high-resolution numerical modelling to determine the total additional pressure drop introduced by two AICDs installed in a single completion joint in a horizontal well. The model captures the multiphase flow of oil and water through the inner annulus into each AICD. We explore a number of relevant oil-water inflow scenarios with different flow rates and water cuts. Our results show that if only one AICD is installed, the additional pressure drop is consistent with the experimentalzly-derived empirical formulation. However, if two AICDs are present, there is a significant discrepancy between the additional pressure drop predicted by the simulator and the empirical relationship. This discrepancy occurs because each AICD has a different total and individual phase flow rate, and the final steady-state flow results from a self-organising mechanism emerging from the system. We report the discrepancy as a water cut-dependent correction to the empirical equation, which can be used in reservoir simulation models to better capture the pressure drop across a single completion containing two AICDs. Our findings highlight the importance of understanding how AICDs modify flow into production wells, and have important consequences for improving the representation of advanced wells in reservoir simulation models.

Kampitsis AE, Adam A, Salinas P,
et al., 2020, Dynamic adaptive mesh optimisation for immiscible viscous fingering, *COMPUTATIONAL GEOSCIENCES*, Vol: 24, Pages: 1221-1237, ISSN: 1420-0597

Hamid SAA, Muggeridge AH, 2020, Fingering regimes in unstable miscible displacements, *PHYSICS OF FLUIDS*, Vol: 32, ISSN: 1070-6631

Zhou Y, Muggeridge AH, Berg CF,
et al., 2019, Effect of Layering on Incremental Oil Recovery From Tertiary Polymer Flooding, *SPE RESERVOIR EVALUATION & ENGINEERING*, Vol: 22, Pages: 941-951, ISSN: 1094-6470

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Hiller T, Ardevol-Murison J, Muggeridge AH,
et al., 2019, The impact of wetting heterogeneity distribution on capillary pressure and macroscopic measures of wettability, *SPE Journal*, ISSN: 1930-0220

This work investigates how the different length scales of pore scale wetting heterogeneities affect the shape of capillary pressure-saturation (CPS) curves and the derived USBM and Amott-Harvey wettability indices. These macroscopic wettability indices are used to describe bulk rock wettability as the local contact angle (the standard physical measure of wettability) in a sample which is difficult to access andmay vary within and between pores due to changes in mineralogy and the surface coverage of organic materials. Our study combines laboratory experiments and full-scale fluid dynamics simulations employing the multi-phase Stochastic Rotation Dynamics (SRDmc) model. Four model systems were created using monodisperse glass beads. The surface properties of the beads were modified so that half of the surface area in each system was strongly hydrophilic and half was hydrophobic but each system had a different length scaleof wetting heterogeneity, ranging from a fraction of the bead diameter to two bead diameters. There is excellent agreement between the experimental and simulation results. All systems are classified as intermediate wet based on their Amott-Harvey and USBM indices. Examination of the capillary pressure curves shows that the opening of the stable hysteresis loop decreases monotonically as the length scale of the wetting heterogeneities is increased. Hence, our results suggest that macroscopic wettability indices may be used as indicators of ultimate recovery, but are not suited to discriminate between the different flows that occur earlier on in a mixed wettability displacement process.

Abdul Hamid SA, Adam A, Jackson MD,
et al., 2019, Impact of truncation error and numerical scheme on the simulation of the early time growth of viscous fingering, *International Journal for Numerical Methods in Fluids*, Vol: 89, Pages: 1-15, ISSN: 0271-2091

The truncation error associated with different numerical schemes (first order finite volume, second order finite difference, control volume finite element) and meshes (fixed Cartesian, fixed structured triangular, fixed unstructured triangular and dynamically adapting unstructured triangular) is quantified in terms of apparent longitudinal and transverse diffusivity in tracer displacements and in terms of the early time growth rate of immiscible viscous fingers. The change in apparent numerical longitudinal diffusivity with element size agrees well with the predictions of Taylor series analysis of truncation error but the apparent, numerical transverse diffusivity is much lower than the longitudinal diffusivity in all cases. Truncation error reduces the growth rate of immiscible viscous fingers for wavenumbers greater than 1 in all cases but does not affect the growth rate of higher wavenumber fingers as much as would be seen if capillary pressure were present. The dynamically adapting mesh in the control volume finite element model gave similar levels of truncation error to much more computationally intensive fine resolution fixed meshes, confirming that these approaches have the potential to significantly reduce the computational effort required to model viscous fingering.

Tai I, Muggeridge A, 2019, Evaluation of empirical models for viscous fingering in miscible displacement

© 2019 European Association of Geoscientists and Engineers, EAGE. All Rights Reserved. The performance of miscible gas injection projects can be significantly affected by viscous fingering. This is further complicated by the presence of heterogeneities, as depending on the scale of the heterogeneity, there can be a diffusive, advective or channelling effect. To assess the economic feasibility of a miscible gas injection project, reservoir simulations are needed but very fine grids are required for the fingers to be modelled explicitly. This requires a large amount of computational power and time. To get around this issue, many empirical models have been proposed which model the average behaviour of the viscous fingers, allowing predictions of performance, thus reducing grid size and computational time. Many previous studies have investigated the ability of empirical models to represent fingering in line drives but none have considered flow in a quarter five spot pattern. In this study, a two phase, three component higher-order simulator is used to simulate miscible injection in square line drive and quarter five spot models, with and without heterogeneities. The results of the detailed fingering simulations were compared to the Todd & Longstaff and Fayers empirical models. To account for the effect of heterogeneities, the mixing parameter, w, in the Todd & Longstaff was adjusted using Koval's heterogeneity factor, H_k. The growth rate of the fingers, α, and the final fraction of the cross section occupied by the fingers, a+b, were adjusted in the Fayers model to account for heterogeneities and bypassed oil. The empirical models were implemented in a commercial immiscible reservoir simulator, Eclipse-100 using pseudo relative permeabilities. The detailed simulations indicate that the growth rate of the fingers varies non-linearly with mean concentration in radial flows and this is not captured by either of the empirical models. A modification of th

Alem M, Baig T, Muggeridge A, et al., 2019, Predicting the performance of tight gas reservoirs

Copyright 2019, Society of Petroleum Engineers. Engineers need to predict the production characteristics from hydraulically fractured wells in tight gas fields. Decline curve analysis (DCA) has been widely used over many years in conventional oil and gas fields. It is often applied to tight gas, but there is uncertainty regarding the period of production data needed for accurate prediction. In this paper decline curve analysis of simulated production data from models of hydraulically fractured wells is used to to develop improved methods for calibrating decline curve parameters from production data. The well models were constructed using data from the Khazzan field in Oman. The impact of layering, permeability and drainage area on well performance is also investigated. The contribution of each layer to recovery and the mechanisms controlling that contribution is explored. The investigation shows that increasing the amount of production data used to fit a hyperbolic decline curve does not improve predictions of recovery unless that data comes from many years (20 years for a 1mD reservoir) of production. This is because there is a long period of transient flow in tight gas reservoirs that biases the fitting and results in incorrect predictions of late time performance. Better predictions can be made by estimating the time at which boundary dominated flow is first observed (tb), omitting the preceding transient data and fitting the decline curve to a shorter interval of data starting at tb. For single layer cases, tb can be estimated analytically using the permeability, porosity, compressibility and length scale of the drainage volume associated with the well. Alternatively, tb can be determined from the production data allowing improved prediction of performance from 2-layer reservoirs provided that a) there is high crossflow or b) there is no cross-flow and the lower permeability layer either does not experience BDF during the field life time or it is established qui

Alem M, Baig T, Muggeridge A, et al., 2019, Predicting the performance of tight gas reservoirs

Copyright 2019, Society of Petroleum Engineers. Engineers need to predict the production characteristics from hydraulically fractured wells in tight gas fields. Decline curve analysis (DCA) has been widely used over many years in conventional oil and gas fields. It is often applied to tight gas, but there is uncertainty regarding the period of production data needed for accurate prediction. In this paper decline curve analysis of simulated production data from models of hydraulically fractured wells is used to to develop improved methods for calibrating decline curve parameters from production data. The well models were constructed using data from the Khazzan field in Oman. The impact of layering, permeability and drainage area on well performance is also investigated. The contribution of each layer to recovery and the mechanisms controlling that contribution is explored. The investigation shows that increasing the amount of production data used to fit a hyperbolic decline curve does not improve predictions of recovery unless that data comes from many years (20 years for a 1mD reservoir) of production. This is because there is a long period of transient flow in tight gas reservoirs that biases the fitting and results in incorrect predictions of late time performance. Better predictions can be made by estimating the time at which boundary dominated flow is first observed (tb), omitting the preceding transient data and fitting the decline curve to a shorter interval of data starting at tb. For single layer cases, tb can be estimated analytically using the permeability, porosity, compressibility and length scale of the drainage volume associated with the well. Alternatively, tb can be determined from the production data allowing improved prediction of performance from 2-layer reservoirs provided that a) there is high crossflow or b) there is no cross-flow and the lower permeability layer either does not experience BDF during the field life time or it is established qui

Kostorz W, Muggeridge A, Jackson M, et al., 2019, Non-intrusive reduced order modelling for reconstruction of saturation distributions

Copyright 2019, Society of Petroleum Engineers. Two new Non-Intrusive Reduced Order Modelling approaches to estimate time varying, spatial distributions of variables from arbitrary unseen inputs are introduced. One is a generalization of an existing ‘dynamic’ approach which requires multiple surrogate evaluations to model the solutions at different time instances, the other is a ‘steady-state’ approach that evaluates all time instances simultaneously, reducing the local approximation error. The ability of these approaches to estimate the water saturation distributions expected during a gas flood through a 2D, dipping reservoir is investigating for a range of unseen input parameters. The range of these parameters has been chosen so that a range of flow regimes will occur, from a gravity tongue to a viscous dominated Buckley-Leverett displacement. A number of practically relevant model error measures were employed as opposed to the standard L2 (Euclidean) norm. The influence of the number and the structure of training simulations for the model was also investigated, by employing two simple experimental design methods. The results show that POD based NIROM approaches are prone to significant deviations from the true model. The main sources of error are due to the non-smooth variation of system responses in hyperspace and the transient nature of the flows as well as the underlying dimensionality reduction. Since the first two sources are properties of the physical system modelled it may be expected that similar problems are likely to arise independently of the interpolation method and the reduction process used.

Kampitsis A, Salinas P, Pain C, et al., 2019, Mesh adaptivity and parallel computing for 3D simulation of immiscible viscous fingering

© 2019 European Association of Geoscientists and Engineers, EAGE. All Rights Reserved. We present the recently developed Double Control Volume Finite Element Method (DCVFEM) in combination with dynamic mesh adaptivity in parallel computing to simulate immiscible viscous fingering in two- and three-dimensions. Immiscible viscous fingering may occur during the waterflooding of oil reservoirs, resulting in early breakthrough and poor areal sweep. Similarly to miscible fingering it is triggered by small-scale permeability heterogeneity while it is controlled by the mobility ratio of the fluid and the level of transverse dispersion / capillary pressure. Up to this day, most viscous fingering studies have focussed on the miscible problem since immiscible fingering is significantly more challenging. It requires numerical simulations capable to capture the interaction of the shock front with the capillary pressure, which is a saturation dependent dispersion term. That leads to models with very fine mesh in order to minimise numerical diffusion, resulting in computationally intensive simulations. In this study, we apply the dynamic mesh adaptive DCVFEM in parallel computing to simulate immiscible viscous fingering with capillary pressure. Parallelisation is achieved by using the MPI libraries. Dynamic mesh adaptivity is achieved by mapping of data between meshes. The governing multiphase flow equations are discretised using double control volumes on tetrahedral finite elements. The discontinuous representation for pressure and velocity allows the use of small control volumes, yielding higher resolution of the saturation field. We demonstrate convergence of fingers using our parallel numerical method in 2d and 3d, on fixed and adaptive meshes, quantifying the speed-up due to parallelisation and mesh adaptivity and the achieved accuracy. Dynamic mesh adaptivity allows resolution to be automatically employed where it is required to resolve the fingers with lower resolution

Tai I, Muggeridge A, 2019, Evaluation of empirical models for viscous fingering in miscible displacement

© 2019 European Association of Geoscientists and Engineers, EAGE. All Rights Reserved. The performance of miscible gas injection projects can be significantly affected by viscous fingering. This is further complicated by the presence of heterogeneities, as depending on the scale of the heterogeneity, there can be a diffusive, advective or channelling effect. To assess the economic feasibility of a miscible gas injection project, reservoir simulations are needed but very fine grids are required for the fingers to be modelled explicitly. This requires a large amount of computational power and time. To get around this issue, many empirical models have been proposed which model the average behaviour of the viscous fingers, allowing predictions of performance, thus reducing grid size and computational time. Many previous studies have investigated the ability of empirical models to represent fingering in line drives but none have considered flow in a quarter five spot pattern. In this study, a two phase, three component higher-order simulator is used to simulate miscible injection in square line drive and quarter five spot models, with and without heterogeneities. The results of the detailed fingering simulations were compared to the Todd & Longstaff and Fayers empirical models. To account for the effect of heterogeneities, the mixing parameter, w, in the Todd & Longstaff was adjusted using Koval's heterogeneity factor, H_k. The growth rate of the fingers, α, and the final fraction of the cross section occupied by the fingers, a+b, were adjusted in the Fayers model to account for heterogeneities and bypassed oil. The empirical models were implemented in a commercial immiscible reservoir simulator, Eclipse-100 using pseudo relative permeabilities. The detailed simulations indicate that the growth rate of the fingers varies non-linearly with mean concentration in radial flows and this is not captured by either of the empirical models. A modification of th

Kampitsis A, Salinas P, Pain C, et al., 2019, Mesh adaptivity and parallel computing for 3D simulation of immiscible viscous fingering

© 2019 European Association of Geoscientists and Engineers, EAGE. All Rights Reserved. We present the recently developed Double Control Volume Finite Element Method (DCVFEM) in combination with dynamic mesh adaptivity in parallel computing to simulate immiscible viscous fingering in two- and three-dimensions. Immiscible viscous fingering may occur during the waterflooding of oil reservoirs, resulting in early breakthrough and poor areal sweep. Similarly to miscible fingering it is triggered by small-scale permeability heterogeneity while it is controlled by the mobility ratio of the fluid and the level of transverse dispersion / capillary pressure. Up to this day, most viscous fingering studies have focussed on the miscible problem since immiscible fingering is significantly more challenging. It requires numerical simulations capable to capture the interaction of the shock front with the capillary pressure, which is a saturation dependent dispersion term. That leads to models with very fine mesh in order to minimise numerical diffusion, resulting in computationally intensive simulations. In this study, we apply the dynamic mesh adaptive DCVFEM in parallel computing to simulate immiscible viscous fingering with capillary pressure. Parallelisation is achieved by using the MPI libraries. Dynamic mesh adaptivity is achieved by mapping of data between meshes. The governing multiphase flow equations are discretised using double control volumes on tetrahedral finite elements. The discontinuous representation for pressure and velocity allows the use of small control volumes, yielding higher resolution of the saturation field. We demonstrate convergence of fingers using our parallel numerical method in 2d and 3d, on fixed and adaptive meshes, quantifying the speed-up due to parallelisation and mesh adaptivity and the achieved accuracy. Dynamic mesh adaptivity allows resolution to be automatically employed where it is required to resolve the fingers with lower resolution

Kostorz W, Muggeridge A, Jackson M, et al., 2019, Non-intrusive reduced order modelling for reconstruction of saturation distributions

Copyright 2019, Society of Petroleum Engineers. Two new Non-Intrusive Reduced Order Modelling approaches to estimate time varying, spatial distributions of variables from arbitrary unseen inputs are introduced. One is a generalization of an existing ‘dynamic’ approach which requires multiple surrogate evaluations to model the solutions at different time instances, the other is a ‘steady-state’ approach that evaluates all time instances simultaneously, reducing the local approximation error. The ability of these approaches to estimate the water saturation distributions expected during a gas flood through a 2D, dipping reservoir is investigating for a range of unseen input parameters. The range of these parameters has been chosen so that a range of flow regimes will occur, from a gravity tongue to a viscous dominated Buckley-Leverett displacement. A number of practically relevant model error measures were employed as opposed to the standard L2 (Euclidean) norm. The influence of the number and the structure of training simulations for the model was also investigated, by employing two simple experimental design methods. The results show that POD based NIROM approaches are prone to significant deviations from the true model. The main sources of error are due to the non-smooth variation of system responses in hyperspace and the transient nature of the flows as well as the underlying dimensionality reduction. Since the first two sources are properties of the physical system modelled it may be expected that similar problems are likely to arise independently of the interpolation method and the reduction process used.

Alem M, Baig T, Muggeridge A, et al., 2019, Predicting the performance of tight gas reservoirs

Copyright 2019, Society of Petroleum Engineers. Engineers need to predict the production characteristics from hydraulically fractured wells in tight gas fields. Decline curve analysis (DCA) has been widely used over many years in conventional oil and gas fields. It is often applied to tight gas, but there is uncertainty regarding the period of production data needed for accurate prediction. In this paper decline curve analysis of simulated production data from models of hydraulically fractured wells is used to to develop improved methods for calibrating decline curve parameters from production data. The well models were constructed using data from the Khazzan field in Oman. The impact of layering, permeability and drainage area on well performance is also investigated. The contribution of each layer to recovery and the mechanisms controlling that contribution is explored. The investigation shows that increasing the amount of production data used to fit a hyperbolic decline curve does not improve predictions of recovery unless that data comes from many years (20 years for a 1mD reservoir) of production. This is because there is a long period of transient flow in tight gas reservoirs that biases the fitting and results in incorrect predictions of late time performance. Better predictions can be made by estimating the time at which boundary dominated flow is first observed (tb), omitting the preceding transient data and fitting the decline curve to a shorter interval of data starting at tb. For single layer cases, tb can be estimated analytically using the permeability, porosity, compressibility and length scale of the drainage volume associated with the well. Alternatively, tb can be determined from the production data allowing improved prediction of performance from 2-layer reservoirs provided that a) there is high crossflow or b) there is no cross-flow and the lower permeability layer either does not experience BDF during the field life time or it is established qui

Lei Q, Xie Z, Pavlidis D,
et al., 2018, The shape and motion of gas bubbles in a liquid flowing through a thin annulus, *Journal of Fluid Mechanics*, Vol: 285, Pages: 1017-1039, ISSN: 0022-1120

We study the shape and motion of gas bubbles in a liquid flowing through a horizontal or slightly inclined thin annulus. Experimental data show that in the horizontal annulus, bubbles develop a unique ‘tadpole-like’ shape with a semi-circular cap and a highly stretched tail. As the annulus is inclined, the bubble tail tends to vanish, resulting in a significant decrease of bubble length. To model the bubble evolution, the thin annulus is conceptualised as a ‘Hele-Shaw’ cell in a curvilinear space. The three-dimensional flow within the cell is represented by a gap-averaged, two-dimensional model, which achieved a close match to the experimental data. The numerical model is further used to investigate the effects of gap thickness and pipe diameter on the bubble behaviour. The mechanism for the semi-circular cap formation is interpreted based on an analogous irrotational flow field around a circular cylinder, based on which a theoretical solution to the bubble velocity is derived. The bubble motion and cap geometry is mainly controlled by the gravitational component perpendicular to the flow direction. The bubble elongation in the horizontal annulus is caused by the buoyancy that moves the bubble to the top of the annulus. However, as the annulus is inclined, the gravitational component parallel to the flow direction becomes important, causing bubble separation at the tail and reduction in bubble length.

Gago PA, King P, Muggeridge A, 2018, Fractal growth model for estimating breakthrough time and sweep efficiency when waterflooding geologically heterogeneous rocks, *Physical Review Applied*, Vol: 10, ISSN: 2331-7019

We describe a fast method for estimating flow through a porous medium with a heterogeneous permeability distribution. The main application is to contaminant transport in aquifers and recovery of oil by waterflooding, where such geological heterogeneities can result in regions of bypassed contaminants or oil. The extent of this bypassing is normally assessed by a numerical flow simulation that can take many hours of computer time. Ideally the impact of uncertainty in the geological description is then evaluated by the performing of many such simulations using different realizations of the permeability distribution. Obviously, a proper Monte Carlo evaluation may be impossible when the flow simulations are so computationally intensive. Consequently, methods from statistical mechanics, such as percolation theory and random walkers (such as diffusion-limited aggregation), have been proposed; however, these methods are limited to geological heterogeneities where the correlation lengths are smaller than the system size or to continuous permeability distributions. Here we describe a growth model that can be used to estimate the breakthrough time of the water (and hence the sweep efficiency) in most types of geologically heterogeneous rocks. We show how the model gives good estimates of the breakthrough time of water at the production well in a fraction of the time needed to perform a full flow simulation.

Attar A, Muggeridge A, 2018, Low salinity water injection: Impact of physical diffusion, an aquifer and geological heterogeneity on slug size, *JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING*, Vol: 166, Pages: 1055-1070, ISSN: 0920-4105

Abdul Hamid S, Muggeridge AH, 2018, Analytical solution of polymer slug injection with viscous fingering, *Computational Geosciences*, Vol: 22, Pages: 711-723, ISSN: 1420-0597

We present an analytical solution to estimate the minimum polymer slug size needed to ensure that viscous fingering of chase water does not cause its breakdown during secondary oil recovery. Polymer flooding is typically used to improve oil recovery from more viscous oil reservoirs. The polymer is injected as a slug followed by chase water to reduce costs; however, the water is less viscous than the oil. This can result in miscible viscous fingering of the water into the polymer, breaking down the slug and reducing recovery. The solution assumes that the average effect of fingering can be represented by the empirical Todd and Longstaff model. The analytical calculation of minimum slug size is compared against numerical solutions using the Todd and Longstaff model as well as high resolution first contact miscible simulation of the fingering. The ability to rapidly determine the minimum polymer slug size is potentially very useful during enhanced oil recovery (EOR) screening studies.

Abdul Hamid SA, Muggeridge A, 2018, Viscous fingering in reservoirs with long aspect ratios, SPE Improved Oil Recovery Conference

© 2018, Society of Petroleum Engineers. This paper investigates the impact of aspect ratio on the growth rate of viscous fingers using high resolution numerical simulation in reservoirs with aspect ratios of up to 30:1. The behaviour of fingers in porous media with such high aspect ratios has been overlooked previously in many previous simulation studies due to limited computational power. Viscous fingering is likely to adversely affect the sweep obtained from any miscible gas injection project. It can also occur during polymer flooding when using chase water following the injection of a polymer slug. It depends upon the viscosity ratio, physical diffusion and dispersion, the geometry of the system and the permeability heterogeneity. It occurs because the interface between a lower viscosity displacing fluid and a higher viscosity displaced fluid is intrinsically unstable. This means that any small perturbation to the interface will cause fingers to grow. It is therefore almost impossible to predict the exact fingering pattern in any given displacement although many previous researchers have shown that it is possible predict average behaviour (such as gas breakthrough time and oil recovery) provided a very refined grid is used such that physical diffusion dominates over numerical diffusion. It is impossible to use such fine grids in field scale simulations. Instead engineers will tend to use standard empirical models such as the Todd and Longstaff or Koval models, calibrated to detailed simulations, to estimate field scale performance. At late times in high aspect ratio systems, we find that one finger dominates the displacement and that this finger grows with the square root of time, rather than linearly. We also observe that this single finger tends to split, during which time the solvent oil interface length grows linearly with time before one finger again dominates and grows with the square root of time. This cycle can repeat several times. We also find that

Muggeridge AH, Alshawaf M, Krevor S, 2018, Experimental Investigation of Cross-flow in Stratified Reservoirs During Polymer Flooding, SPE IMproved Oil Recovery Conference

Muggeridge AH, Smalley PCC, Dalland M, et al., 2018, Screening for EOR and Estimating Potential Incremental Oil Recovery on the Norwegian Continental Shelf, SPE Improved Oil Recovery Conference

Santo A, Muggeridge A, 2018, An investigation into the benefits of combined polymer-low salinity waterflooding

Copyright 2018, Society of Petroleum Engineers Polymer flooding and low salinity waterflooding are two different but potentially complementary Enhanced Oil Recovery (EOR) techniques. Polymer flooding improves fractional flow and sweep efficiency by improving the mobility ratio for the displacement. Low salinity waterflooding improves pore scale displacement efficiency by changing the wettability of the reservoir rocks toward more water-wet. Reduced salinity water is often used in polymer injection to reduce hydrolysis however the water salinity in this case is typically higher than that needed to obtain a true low salinity effect. This paper describes the outcomes of a systematic study into the potential benefits of combined polymer-low salinity waterflooding versus polymer-high salinity waterflooding, polymer-reduced salinity waterflooding and conventional waterflooding. Numerical simulation, validated against analytical solutions, was used to evaluate the relative performance of these processes. The impacts of layering and reservoir heterogeneity were investigated using two-dimensional (2D) and three-dimensional (3D) reservoir models. Sensitivity studies of injected water salinity and the start time of injection were carried out in each of these models. Outcomes were compared against the recoveries and water cuts predicted using a one-dimensional (1D) analytic solution for the EOR processes to evaluate the impact of sweep versus displacement efficiency on incremental oil recovery and water cut. Combined polymer-low salinity waterflooding shows an improvement in recovery and reduction in water cut compared with the other EOR processes in all cases. We show this is partly due to improving the fractional flow (increasing shock front saturation) but is also due to both the leading and trailing shock fronts in polymer-low salinity waterflooding being more stable than in the other EOR processes, reducing the possibility of viscous finger growth and thus increasing perfo

Santo A, Muggeridge A, 2018, An investigation into the benefits of combined polymer-low salinity waterflooding

Copyright 2018, Society of Petroleum Engineers Polymer flooding and low salinity waterflooding are two different but potentially complementary Enhanced Oil Recovery (EOR) techniques. Polymer flooding improves fractional flow and sweep efficiency by improving the mobility ratio for the displacement. Low salinity waterflooding improves pore scale displacement efficiency by changing the wettability of the reservoir rocks toward more water-wet. Reduced salinity water is often used in polymer injection to reduce hydrolysis however the water salinity in this case is typically higher than that needed to obtain a true low salinity effect. This paper describes the outcomes of a systematic study into the potential benefits of combined polymer-low salinity waterflooding versus polymer-high salinity waterflooding, polymer-reduced salinity waterflooding and conventional waterflooding. Numerical simulation, validated against analytical solutions, was used to evaluate the relative performance of these processes. The impacts of layering and reservoir heterogeneity were investigated using two-dimensional (2D) and three-dimensional (3D) reservoir models. Sensitivity studies of injected water salinity and the start time of injection were carried out in each of these models. Outcomes were compared against the recoveries and water cuts predicted using a one-dimensional (1D) analytic solution for the EOR processes to evaluate the impact of sweep versus displacement efficiency on incremental oil recovery and water cut. Combined polymer-low salinity waterflooding shows an improvement in recovery and reduction in water cut compared with the other EOR processes in all cases. We show this is partly due to improving the fractional flow (increasing shock front saturation) but is also due to both the leading and trailing shock fronts in polymer-low salinity waterflooding being more stable than in the other EOR processes, reducing the possibility of viscous finger growth and thus increasing perfo

Al-Dhuwaihi A, King P, Muggeridge A, 2018, Upscaling for polymer flooding

Copyright 2018, Society of Petroleum Engineers. Polymer flooding is a proven EOR/IOR process for viscous and light oil reservoirs alike. However, it results in the formation of two shocks front that require simulation models with fine grid blocks to represent field scale fluid movement. Therefore, upscaling is required to transfer such fluid behavior to coarser models. However, most upscaling methods are designed for waterflood only, while upscaling techniques for polymer flood are rarely discussed in the literature. In this paper, A new upscaling methodology specifically designed for polymer flooding is presented to address such impracticality. The methodology allows the average flow behavior to be captured, including the effects of small scale heterogeneity whilst compensating for the impact of increased numerical diffusion present in coarse grid models. The method is based on the pore volume weighted method for relative permeability pseudoization first derived by Emanuel and Cook (1974) for waterflooding but extends its implementation to model polymer specific parameters such as adsorption isotherm and viscosity-concentration function. The method is demonstrated on a series of simple reservoir models for a range of different aggregation ratios, showing overall improvement in the prediction of oil recovery, water cut, produced polymer concentration with time, and pressure response in the coarse grid models. This is demonstrated by comparing the predictions from the coarse grid, upscaled models with those from fine grid simulations and coarse grid simulations of the same model reservoir without the new upscaling methodology.

Obidi O, Muggeridge AH, Vesovic V, 2017, Analytical solution for compositional profile driven by gravitational segregation and diffusion, *Physical Review E*, Vol: 95, ISSN: 2470-0045

An improved analytical solution is presented, based on irreversible thermodynamics, that describes the equilibrium distribution of the components of a non-ideal fluid mixture in an 1D, hydrostatic and isothermal system. In such a system, the vertical compositional profile of the fluid at equilibrium will be determined by the interaction of gravitational and chemical potentials. The new analytical solution estimates this profile from the overall composition of the fluid. It is thus more general than the existing solution which requires a knowledge of the fluid composition at a given depth and assumes that the vertical compositional profile of this fluid is already at equilibrium. The solution is demonstrated by comparison against results obtained from previously published molecular dynamics simulations of segregation in a binary mixture and against numerical simulations of a real hydrocarbon reservoir system.

Maes J, Muggeridge AH, Jackson MD,
et al., 2017, Scaling analysis of the In-Situ Upgrading of heavy oil and oil shale, *FUEL*, Vol: 195, Pages: 299-313, ISSN: 0016-2361

The In-Situ Upgrading (ISU) of heavy oil and oil shale is investigated. We develop a mathematical model for the process and identify the full set of dimensionless numbers describing the model. We demonstrate that for a model with nf fluid components (gas and oil), ns solid components and k chemical reactions, the model was represented by 9+k×(3+nf+ns-2)+8nf+2ns dimensionless numbers. We calculated a range of values for each dimensionless numbers from a literature study. Then, we perform a sensitivity analysis using Design of Experiments (DOE) and Response Surface Methodology (RSM) to identify the primary parameters controlling the production time and energy efficiency of the process. The Damköhler numbers, quantifying the ratio of chemical reaction rate to heat conduction rate for each reaction, are found to be the most important parameters of the study. They depend mostly on the activation energy of the reactions and of the heaters temperature. The reduced reaction enthalpies are also important parameters and should be evaluated accurately. We show that for the two test cases considered in this paper, the Damköhler numbers needed to be at least 10 for the process to be efficient. We demonstrate the existence of an optimal heater temperature for the process and obtain a correlation that can be used to estimate it using the minimum of the Damköhler numbers of all reactions.

Alshawaf MH, Krevor S, Muggeridge A, 2017, Analysis of viscous crossflow in polymer flooding, EAGE IOR Symposium 2017

Polymer flooding improves oil recovery by improving flood front conformance compared with waterflooding as well as, in some cases, extracting more oil from lower permeability zones in the reservoir by viscous cross-flow. However viscous cross-flow of water from the low permeability zone may also adversely affect the polymer flood by causing the polymer slug to be diluted and possibly to lose its integrity. The extent to which viscous cross-flow improves or reduces recovery depends upon the permeability contrast between the low and high permeability zones, the viscosity ratios of the fluids (oil, water and polymer solution) and the geometry of the layers. This paper uses inspectional analysis to derive the minimum set of 6 dimensionless numbers that can be used to characterise a polymer flood in a two layered model. A series of finely gridded numerical simulations are then performed to determine the contribution of viscous crossflow to oil recovery from secondary and tertiary polymer flooding in this system. We show that viscous cross-flow will only make a positive impact on oil recovery from secondary polymer flooding when the viscosity ratio values of oil to polymer solution is less than 1 and permeability ratio between the layers is less than 50. Furthermore, we show that there is an inverse relationship between the permeability ratio between layers and the amount of degradation the polymer slug experiences due to viscous crossflow in the high permeability layer. As the permeability contrast between layers increases, the slug degradation decreases. Also, the results show that the desired positive impact from viscous crossflow is higher in secondary polymer foods when compared to tertiary polymer floods. Finally, the results can be used to make initial estimates of the contribution of both viscous cross-flow and mobility control in polymer flooding applications without the need to perform extensive and time consuming numerical simulations.

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