Matthew D. Jackson

Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow

Pore-network models have been used to describe a wide range of properties from capillary pressure characteristics to interfacial area and mass transfer coefficients. The void space of a rock or soil is described as a network of pores connected by throats. The pores and throats are assigned some idealized geometry and rules are developed to determine the multiphase fluid configurations and transport in these elements. The rules are combined in the network to compute effective transport properties on a mesoscopic scale some tens of pores across. This approach is illustrated by describing a pore-scale model for two- and three-phase flow in media of arbitrary wettability. The appropriate pore-scale physics combined with a geologically representative description of the pore space gives a model that can predict average behavior, such as capillary pressure and relative permeability. This capability is demonstrated by successfully predicting primary drainage and waterflood relative permeabilities for Berea sandstone. The implications of this predictive power for improved characterization of subsurface simulation models are discussed. A simple example field study of waterflooding an oil-wet system near the oil/water contact shows how the assignment of physically-based multiphase flow properties based on pore-scale modeling gives significantly different predictions of oil recovery than using current empirical relative permeability models. Methods to incorporate pore-scale results directly into field-scale simulation are described. In principle, the same approach could be used to describe any type of process for which the behavior is understood at the pore scale.

Measurement of streaming potential coupling coefficient in sandstones saturated with natural and artificial brines at high salinity

Measurements of streaming potential can be used to monitor subsurface flow using electrodes installed along boreholes. However, the interpretation of the measurements requires an understanding of the streaming potential coupling coefficient, which dictates the magnitude of the streaming potential for a given pressure difference. Previous laboratory measurements of the coupling coefficient in earth materials focussed on crushed and intact rock samples saturated with artificial NaCl and KCl brines of relatively low salinity: salt concentrations were typically lower than average seawater. However, many subsurface brines are significantly more saline. We have measured the streaming potential coupling coefficient in four different intact sandstone samples saturated with seawater and artificial NaCl brines at concentrations up to 5.3 M/L. We obtain consistent results using three different sets of experimental apparatus. The values we record at low salinity are consistent with those reported previously. As brine salinity increases, the coupling coefficient decreases in magnitude, falling to a value of c. 1.5 x 10-10 V/Pa at 5.3M/L, and remains negative over the entire salinity range. The coupling coefficient measured for seawater is similar to that obtained for NaCl brine of the same ionic strength. The magnitude of the zeta potential also decreases with increasing salinity, but approaches a constant value of c. 17mV at salinities greater than c. 0.4M/L. This behaviour is not captured by current models of the electrical double layer. We hypothesize that ion interactions cause the reduction in thickness of the diffuse layer at high salinity to be less than predicted by the Poisson-Boltzmann equation, in which it is assumed that the ions are point charges. Moreover, the counter-charge required to balance the mineral surface charge is not accommodated entirely within the Stern layer. Consequently, the diffuse layer does not collapse to zero; rather, some of the counter-charge remains mobile within the diffuse layer, at a maximum concentration which is limited by the size of the hydrated counter-ions. Our hypothesis is supported by the observation that the Debye length is c. 0.5 nm at a salinity of 0.4 M/L, which is comparable with the diameter of a hydrated sodium ion. Our results suggest that streaming potential measurements may be used to monitor flow in more saline subsurface environments, such as deep saline aquifers and hydrocarbon reservoirs, than previously thought.

Fluid flow monitoring in oil fields using downhole measurements of electrokinetic potential

Downhole measurements of electrokinetic potential are a promising new technology for hydrocarbon reservoir monitoring.Usinga3Dfinite-elementmodelcombiningbothmultiphase flow and electrokinetic components, we investigated the behavior of electrokinetic streaming potential during oil production in a range of reservoir environments. We found that streamingpotential signals originate at fluid fronts and at geologic boundaries where fluid saturation changes.As water encroaches on an oil production well, the streaming-potential signal associated with the water front encompasses the well even when the front is up to 100 m away, so the potential measured at the well starts to change significantly relative to a distant reference electrode. Variations in the geometry of the encroaching water front can be characterized using an array of electrodes positioned along the well, but a good understanding of the local reservoir geology is required to identify signals caused by the front. The streaming potential measured at a well is maximized in low-permeability reservoirsproducedatahighrateandinthickreservoirswithlow shale content. However, considerable uncertainties remain, particularly relating to the nature of electrokinetic coupling at high salinity and during multiphase flow. Our results suggest that the streaming potential at low salinity 10 3 ‐10 4 mol/L is large 100‐1000 mV but might become too small to resolve 0.1 mV at high salinity 0.5‐2 mol/L, depending on how the available data for the electrokinetic coupling at low salinity are extrapolated into the high-salinity domain. More work remains to determine the behavior of electrokinetic coupling andthereforetheutilityofthistechniqueathighsalinity.

Three-dimensional modeling of a shoreface-shelf parasequence reservoir analog: Part 1. Surface-based modeling to capture high-resolution facies architecture

Conventional reservoir modeling approaches are developed to account for uncertainty associated with sparse subsurface data but are not equipped for detailed reconstruction of high-resolution geologic data sets. We present a surface-based modeling procedure that enables explicit representation of heterogeneity across a hierarchy of length scales. Numerous surfaces are used to construct complex facies-body geometries and distributions prior to generating a grid, allowing sampled and conceptual data to be fully incorporated within field-scale models. Our approach is driven by the improved efficiency that surfaces introduce to reservoir modeling through their geologically intuitive design, rapid construction, and ease of manipulation. Cornerpoint gridding of the architecture defined by the surfaces reduces the number of cells required to represent complex geometries, thus preserving geologic detail and rendering upscaling unnecessary for fluid-flow simulations. The application of surface-based modeling is demonstrated by reconstructing the detailed three-dimensional facies architecture of a wave-dominated shoreface-shelf parasequence from a rich outcrop data set. The studied outcrop data set describes reservoir architecture in a generic analog for many shallow-marine reservoirs. The process of model construction has demonstrated the function of (1) shoreface-shelf clinoforms, (2) paleogeographic changes in shoreline orientation, and (3) storm-event-bed amalgamation in controlling facies architecture. These subtle geometric features cannot be accurately represented using conventional stochastic reservoir modeling algorithms, which results in poor estimation of facies proportions and associated hydrocarbon volumes in place. In contrast, the surface-based modeling approach honors all data and captures subtle geometric facies relationships, thus allowing detailed and robust reservoir characterization.

Quantitative Modeling of Granitic Melt Generation and Segregation in the Continental Crust

[1] We present a new quantitative model of granitic (in a broad sense) melt generation and segregation within the continental crust. We assume that melt generation is caused by the intrusion of hot, mantle-derived basalt, and that segregation occurs by buoyancy-driven flow along grain edges coupled with compaction of the partially molten source rock. We solve numerically the coupled equations governing heating, melting, and melt migration in the source rock, and cooling and crystallization in the underlying heat source. Our results demonstrate that the spatial distribution and composition of the melt depends upon the relative upward transport rates of heat and melt. If melt transport occurs more quickly than heat transport, then melt accumulates near the top of the source region, until the rock matrix disaggregates and a mobile magma forms. As the melt migrates upward, its composition changes to resemble a smaller degree of melting of the source rock, because it thermodynamically equilibrates with rock at progressively lower temperatures. We demonstrate that this process of buoyancy-driven compaction coupled with local thermodynamic equilibration can yield large volumes of mobile granitic magma from basaltic and meta-basaltic (amphibolitic) protoliths over timescales ranging from ∼4000 years to ∼10 Myr. The thickness of basaltic magma required as a heat source ranges from ∼40 m to ∼3 km, which requires that the magma is emplaced over time as a series of sills, concurrent with melt segregation. These findings differ from those of previous studies, which have suggested that compaction operates too slowly to yield large volumes of segregated granitic melt.

Prediction of wettability variation and its impact on flow using pore- to reservoir-scale simulations

We describe a pore- to reservoir-scale investigation of wettability variation and its impact on waterflooding. We use a three-dimensional pore-scale network model of a Berea sandstone to predict relative permeability and capillary pressure hysteresis. We successfully predict experimentally measured relative permeability data for the water-wet case, and demonstrate that the model captures experimentally observed trends in waterflood recovery for mixed-wet media. We then focus upon the effect of variations in initial water saturation associated with capillary rise above the oil–water contact (OWC). This may lead to wettability variations with height because the number of pore-walls which may be rendered oil-wet during primary drainage, increases as the oil saturation increases. We investigate empirical hysteresis models in which scanning curves are used to connect bounding drainage and waterflood curves for a given initial water saturation, and find that if wettability varies with initial water saturation, then the scanning water relative permeability curves predicted by the empirical model are significantly higher than those predicted by the network model. We then use a conventional simulator, in conjunction with the relative permeability curves obtained from the network and empirical models, to investigate the reservoir-scale impact of wettability variations on waterflooding. If the wettability varies with height above the OWC, we find that using the network model to generate scanning relative permeability curves yields a significantly higher recovery than using empirical models or assuming that the reservoir is uniformly oil-wet or water-wet. This is because the scanning water curves are generally low (characteristic of water-wet media), yet the residual oil saturation is also low (characteristic of oilwet media). Our aim is to demonstrate that network models of real rocks may be used as a tool to predict wettability variations and their impact on field-scale flow. D 2003 Elsevier Science B.V. All rights reserved.

Three-dimensional reservoir characterization and flow simulation of heterolithic tidal sandstones

Tidal sandstone reservoirs contain significant intervals of hydrocarbon-bearing heterolithic facies, characterized by the presence of tide-generated sedimentary structures such as flaser, wavy, and lenticular bedding (millimeter to centimeter sand-mud alternations). We have characterized the reservoir properties (sandstone connectivity, effective permeability, and displacement efficiency) of these facies using three-dimensional (3-D) models reconstructed directly from large rock specimens. The models are significantly larger than a core plug, but smaller than a typical reservoir model grid block. We find that the key control on reservoir quality is the connectivity and continuity of the sandstone and mudstone layers. If the sandstone layers form a connected network, they are likely to be productive even at low values of net-to-gross (about 0.30.5). This may explain why the productivity of low net-to-gross, heterolithic tidal sandstones is commonly underestimated or overlooked. Connectivity is the dominant control on the transition between productive (pay) and nonproductive (nonpay) heterolithic facies. However, connectivity is difficult to characterize because core plugs sampled from the subsurface are too small to capture connectivity, whereas two-dimensional outcrop measurements can significantly underestimate the true 3-D value. Our results suggest that core-plug measurements of permeability and displacement efficiency are unlikely to yield representative values at the scale of a reservoir model grid block because the connectivity and continuity of sandstone and mudstone layers varies significantly with length scale.

Upscaling Permeability Measurements Within Complex Heterolithic Tidal Sandstones

We investigate numerically the effect of sample volume on the effective single-phase permeability of heterolithic tidal sandstones, using three-dimensional models reconstructed directly from large rock specimens measuring ∼45 × 30 × 15 cm. We find that both individual and averaged effective permeability values vary as a function of sample volume, which indicates that permeability data obtained from core-plugs will not be representative at the scale of a reservoir model grid-block regardless of the number of measurements taken. However, the error introduced by averaged data may be minimized using the appropriate averaging scheme for a given facies type and flow direction.

Three-dimensional modeling of a shoreface-shelf parasequence reservoir analog: Part 2. Geologic controls on fluid flow and hydrocarbon recovery

Wave-dominated, shoreface-shelf parasequences are commonly modeled as simple layer-cake reservoirs, yet analysis of modern and ancient analogs demonstrates that these intervals contain a more complex physical stratigraphy. We investigate the impact of depositional and diagenetic heterogeneity associated with gently dipping clinoform surfaces on fluid flow and recovery during water flooding, using a three-dimensional model reconstructed from a well-exposed outcrop analog. We demonstrate that the volume of oil in place is affected by variations in facies thickness associated with interfingering along clinoforms, whereas waterflood sweep efficiency is affected by barriers to flow along clinoform surfaces, such as calcite-cemented layers, mudstones, and siltstones. Sweep efficiency is low when water flooding is down depositional dip because oil is bypassed at the toe of each clinothem as water flows preferentially through high-quality sandstone facies in the upper part of the parasequence. Sweep efficiency is higher when water flooding is up depositional dip because the gravity-driven, downward flow of water sweeps poorer-quality sandstone facies in the lower part of the parasequence. In both cases, injectors may offer limited pressure support to producers. Water flooding along depositional strike yields good pressure support but poor sweep because the gravity-driven flow of water into the lower part of the parasequence is significantly reduced. This yields highly variable fluid saturations but a uniform pressure gradient, which is consistent with pressure and fluid saturation data from the mature Rannoch Formation reservoir, Brent field, United Kingdom North Sea. Simple layer-cake models fail to capture the range of flow behaviors described above and overpredict recovery by up to 20% as a result.

A new numerical model of electrokinetic potential response during hydrocarbon recovery

[1] We present results from a new numerical model capable of simulating two-phase flow in a porous medium and the electrical potentials arising due to electrokinetic phenomena. We suggest that, during water-flood of an initially oil-filled reservoir, encroaching water causes changes in the electrokinetic potential at the production well which could be resolved above background electrical noise; indeed, water approaching the well could be detected several 10’s to 100’s of meters away. The magnitude of the measured potential depends upon the production rate, the coupling between fluid and electrical potentials, and the nature of the front between the displaced oil and the displacing water. Citation: Saunders, J. H., M. D. Jackson, and C. C. Pain (2006), A new numerical model of electrokinetic potential response during hydrocarbon recovery, Geophys. Res. Lett., 33, L15316, doi:10.1029/2006GL026835.