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Summary Augmented waterflooding is when a component is coinjected with water to modify the fractional-flow curve. Examples include polymer flooding, surfactant injection, low-salinity waterflooding, and carbonated-water injection (including applications related to carbon dioxide storage). The numerical simulation of these processes is a challenge for several reasons: The appropriate physical behavior needs to be incorporated consistently into empirical models of the fractional flow, whereas the solutions should minimize numerical dispersion, allowing the correct and accurate tracking of compositional variations. Lower-order numerical simulations of these processes give excessive front smearing, requiring many thousands of gridblocks in one dimension to resolve the fronts adequately, rendering the predictions from 3D simulations dubious at best. These erroneous predictions are not caused by phase dispersion (the improper prediction of water velocity)โas in black-oil simulation, in which the effect is less significantโbut occur because of the coupling of compositional dispersion with fractional flow. Small errors in composition alter the fractional flow, causing the development of incorrect wavespeeds. The same effect is also seen in compositional simulation of gas injection. We propose a simple method for streamline-based simulations that substantially reduces numerical dispersion. The method is rooted in the assumption of segregated flow within a gridblock. After comparing numerical and analytical results in one dimension, we implement the method into a 3D streamline-based simulator of polymer flooding that also incorporates a physically based model of the fluid rheology. We demonstrate that traditional simulation methods can vastly overestimate recovery, potentially leading to poor injection design and management decisions. We demonstrate the utility of our approach by suggesting optimal strategies for the design of polymer injection on the basis of our improved simulation technique.
- Asia (0.93)
- North America > United States > Texas (0.28)
- Asia > China > Heilongjiang > Songliao Basin > Daqing Field > Yian Formation (0.99)
- Asia > China > Heilongjiang > Songliao Basin > Daqing Field > Mingshui Formation (0.99)
Summary Current commercial simulators for polymer flooding often make physical assumptions that are not consistent with available experimental data and pore-scale modeling predictions. This may lead to overly optimistic recovery predictions for shear-thinning polymers, while the potential advantages of reducing flow rate or using shearthickening agents are overlooked. We develop a streamline-based simulator that overcomes these limitations and demonstrate how it can be used to design polymerflooding projects. The simulator implements an iterative approach to solve the pressure field because the pressure depends on the aqueous-phase viscosity, which, in turn for non-Newtonian fluids, depends on shear stress and, hence, the pressure gradients. This is in contrast to the common approach in commercial simulators where this viscosity/pressure interdependence is ignored, leading to overestimation of sweep efficiency. Furthermore, in the simulator, non-Newtonian viscosities are defined to be cell-centered while current simulators use a face-centered approach, thereby overpredicting viscosities and the stability of the displacing fronts. In addition, we use a physically based rheological model where non-Newtonian viscosities in two-phase flow are taken at actual effective stresses instead of single-phase equivalents. To validate the simulator, we construct 1D analytical solutions for waterflooding with a non-Newtonian fluid. We then compare our results to those from commercial simulators. We discuss the significance of current assumptions to demonstrate the effect of non-Newtonian behavior on sweep efficiency and recovery.
- Europe > United Kingdom (0.68)
- North America > United States > Texas (0.28)
Abstract Augmented waterflooding is where a component is co-injected for the purpose of modifying the fractional flow curve: examples include polymer flooding, surfactant injection, low salinity waterflooding and carbonated water injection (including applications related to carbon dioxide storage). The numerical simulation of these processes is a challenge for several reasons: the appropriate physical behavior needs to be incorporated consistently into empirical models of the fractional flow, while the solutions should minimize numerical dispersion, allowing the correct and accurate tracking of compositional variations. Traditional numerical simulations of these processes give excessive front smearing, requiring many thousands of grid blocks in one dimension to resolve the fronts adequately, rendering the predictions from three-dimensional simulations dubious at best. These erroneous predictions are not caused by phase dispersion (the improper prediction of water velocity), as in black-oil simulation, where the effect is less significant, but occurs because of the coupling of compositional dispersion with fractional flow. Small errors in composition alter the fractional flow, causing the development of incorrect wave speeds. The same effect is also seen in compositional simulation of gas injection. We propose a simple method, based on the assumption of segregated flow within a grid block, that substantially reduces numerical dispersion. After comparing numerical and analytical results in one dimension, we implement the method into a three-dimensional streamline-based simulator of polymer flooding that also incorporates a physically-based model of the fluid rheology. We demonstrate that traditional simulation methods can vastly over-estimate recovery, potentially leading to poor injection design and management decisions. We demonstrate the utility of our approach by suggesting optimal strategies for the design of polymer injection based on our improved simulation technique. We also discuss extensions of the method to fully compositional displacements involving many chemical components.
- North America > United States (0.68)
- Asia (0.46)
- Energy > Oil & Gas > Upstream (1.00)
- Water & Waste Management > Water Management > Lifecycle > Disposal/Injection (0.34)
- Asia > China > Heilongjiang > Songliao Basin > Daqing Field > Yian Formation (0.99)
- Asia > China > Heilongjiang > Songliao Basin > Daqing Field > Mingshui Formation (0.99)
- Reservoir Description and Dynamics > Reservoir Simulation (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery > Waterflooding (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery > Chemical flooding methods (1.00)
Summary We propose a physically motivated formulation for the matrix/fracture transfer function in dual-porosity and dual-permeability reservoir simulation. The approach currently applied in commercial simulators (Barenblatt et al. 1960; Kazemi et al. 1976) uses a Darcy-like flux from matrix to fracture, assuming a quasisteady state between the two domains that does not correctly represent the average transfer rate in a dynamic displacement. On the basis of 1D analyses in the literature, we find expressions for the transfer rate accounting for both displacement and fluid expansion at early and late times. The resultant transfer function is a sum of two terms: a saturation-dependent term representing displacement and a pressure-dependent term to model fluid expansion. The transfer function is validated through comparison with 1D and 2D fine-grid simulations and is compared to predictions using the traditional Kazemi et al. (1976) formulation. Our method captures the dynamics of expansion and displacement more accurately. Introduction The conventional macroscopic treatment of flow in fractured reservoirs assumes that there are two communicating domains: a flowing region containing connected fractures and high permeability matrix and a stagnant region of low-permeability matrix (Barenblatt et al. 1960; Warren and Root 1963). Conventionally, these are referred to as fracture and matrix, respectively. Transfer between fracture and matrix is mediated by gravitational and capillary forces. In a dual-porosity model, it is assumed that there is no viscous flow in the matrix; a dual-permeability model allows flow in both fracture and matrix. In a general compositional model (where black-oil and incompressible flow are special cases) we can write[Equation 1], where where Gc is a transfer term with units of mass per unit volume per unit time--it is a rate (units of inverse time) times a density (mass per unit volume). c is a component density (concentration) with units of mass of component per unit volume. The subscript p labels the phase, and c labels the component. Gc represents the transfer of component c from fracture to matrix. The subscript f refers to the flowing or fractured domain. The first term is accumulation, and the second term represents flow--this is the same as in standard (nonfractured) reservoir simulation. We can write a corresponding equation for the matrix, m,[Equation 2] where we have assumed a dual-porosity model (no flow in the matrix); for a dual-permeability model, a flow term is added to Eq. 2.
- North America > United States (0.28)
- Asia > China (0.28)
Predictive Pore-Scale Network Modeling
Valvatne, Per H. (Imperial College) | Blunt, Martin J. (Imperial College)
Abstract We show how to predict flow properties for a variety of rocks using pore-scale modeling with geologically realistic networks. Starting with a network representation of Berea sandstone the pore-size distribution is adjusted to match mercury injection capillary pressure for different rock types, keeping the rank order of pore sizes and the network topology fixed. Then predictions of single and multiphase properties are made with no further adjustment of the model. We successfully predict relative permeability and oil recovery for water- oil- and mixed-wet datasets. For waterflooding we introduce a method for assigning contact angles to match measured wettability indices. The aim of this work is not simply to match experiments, but to use easily acquired data to predict difficult to measure properties. Furthermore, the variation of these properties in the field, due to wettability trends and different pore structures can now be predicted reliably. Introduction In network modeling the void space of a rock is represented at the microscopic scale by a lattice of pores connected by throats. By applying rules that govern the transport and arrangement of fluids in pores and throats, macroscopic properties, for instance capillary pressure or relative permeability, can then be estimated across the network, which typically consists of several thousand pores and throats representing a rock sample of a few millimeters cubed. Until recently most networks were based on a regular lattice. The coordination number can vary depending on the chosen lattice (e.g. 5 for a honeycombed lattice or 6 for a regular cubic lattice). As has been noted by many authors the coordination number will influence the network model behavior significantly, both in terms of breakthrough and relative permeability. In order to match the coordination number of a given rock sample, which typically is between 3 and 8, it is possible to remove throats at random from a regular lattice, hence reducing the connectivity. The pore and throat size distributions will also affect the estimated macroscopic properties. By adjusting the size distributions to match capillary pressure data, relatively good predictions of absolute and relative permeabilities have been reported for unsaturated soils. All these models are, however, still based on a regular topology which does not reflect the random nature of real porous rock. The use of networks derived from a real porous medium was pioneered by Bryant et al. They extracted their networks from a random close packing of equally-sized spheres where all sphere coordinates had been measured. Predictions of relative permeability, electrical conductivity and capillary pressure were compared successfully with experimental results from sand packs, bead packs and a simple sandstone. รren and coworkers at Statoil have extended this approach to a wider range of sedimentary rocks. For more complex sandstones it is usually necessary to create first a 3D voxel based representation of the pore space that should capture the statistics of the real rock. This can be generated directly using X-ray microtomography, where the rock is imaged at resolutions of around a few microns, or by using some numerical reconstruction technique. From this voxel representation an equivalent network (in terms of volume, throat radii, clay content etc) can then be extracted. Using these realistic networks water-wet experimental data have been successfully predicted for Bentheimer and Berea sandstones. Most hydrocarbon bearing reservoirs exhibit mixed-wet characteristics, where parts of the rock are oil-wet with the remainder being water-wet. Following primary drainage it is assumed that the part of the rock in direct contact with hydrocarbon will alter its wettability. From Amott tests and nuclear magnetic resonance (NMR) it is possible to get a bulk indication of the wettability. How the mixed wettability is distributed on the pore scale is, however, much more difficult to evaluate. Kovscek and coworkers proposed a model where the smaller pores become oil-wet while the larger ones remain water-wet. Using cryo- and environmental scanning electron microscopy it is possible to visualize directly the distribution of fluids at the pore scale. These studies suggested that the distribution of clay, in particular kaolinite, plays a very important role in determining what parts of the rock becomes oil-wet. Only very limited mixed-wet experimental data have been predicted using pore-scale network modeling, though some promising results have been shown.
- North America > United States > West Virginia (0.46)
- North America > United States > Pennsylvania (0.46)
- North America > United States > Ohio (0.46)
- North America > United States > Kentucky (0.46)
- Geology > Mineral > Silicate > Phyllosilicate (0.89)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Sandstone (0.88)
Summary We present a method for history-matching production data using a streamline simulation that captures all the pertinent physics, including compressible three-phase flow with gravity. We use an approach based on the assumption of 1D flow along streamlines to find the sensitivity of water flow rate at production wells to changes in permeability. Although the computation of the sensitivities is approximate, we show, using data from a North Sea field, that the method can provide a reasonable history match and good predictions of future performance for problems with significant effects caused by compressibility and gravity. Introduction Several history-matching methods have been proposed to constrain reservoir descriptions to production data, such as water-cut history (see, for instance, Refs. 1 through 8). These techniques use conventional grid-based simulation to compute sensitivity coefficients, which give the change in production data caused by a change in the permeability or porosity of some portion of the simulation model. Using the sensitivity coefficients, the porosity and permeability are adjusted to create a new reservoir model. When another simulation is performed using this model, a better match to the data should be obtained. If the match is still unacceptable, new sensitivity coefficients are computed and used to modify the reservoir model again. Because the sensitivity coefficients are nonlinearly dependent on the reservoir description, many iterations may be needed before a good history match is obtained. For a finely-gridded model, there are many more matching parameters than data, and the match is nonunique. To overcome the problem of having many poorly determined parameters in the reservoir description, methods that reduce the parameter space, such as the use of recursively refined grids, gradzone analysis, and gradual deformation have been proposed. Current history-matching methods are still limited, however, by the time taken to perform the forward simulations. Ideally, history matching would start from a statistical ensemble of equiprobable initial estimates of the reservoir description. Each reservoir description, if it is a fine-scale reservoir model, may contain several million gridblocks. Current simulation techniques may take approximately a week to perform a single simulation of this size, making history matching that may require tens to hundreds of iterations on several models impossible in practice. Approaches where history matching is performed on a much coarser grid than the geological model offer appealing savings in computer time. However, the appropriate manner to upscale or downscale single and multiphase flow properties is not obvious. Furthermore, fine-scale details may be important for future prediction of, say, waterflood or gasflood performance. In these cases, history matching on a coarse grid may yield a poor reservoir description with correspondingly inaccurate predictions of future recovery. Streamline-based simulation offers an attractive alternative to grid-based techniques for history matching for two reasons. The first is that for displacement-type simulations through fine-scale heterogeneous reservoir descriptions, streamline simulation can be considerably faster than comparable grid-based, conventional methods. This enables the forward simulations to be performed much faster, allowing matches to be obtained with fine grids. Vasco et al. introduced the use of streamlines in history matching. A streamline simulator that assumed fixed streamlines without gravity was used to perform the forward simulation, while conventional techniques were applied to the computation of sensitivity coefficients. Because the forward simulation was so fast, impressive results were achieved on a number of synthetic and field case histories. There is, however, a second powerful reason for using streamlines in history matching. The time of flight along a streamline can be used directly to compute sensitivity coefficients. The time of flight of a streamline at a producer indicates the water breakthrough time for that streamline. The water cut is the sum of the production along each streamline reaching the well. The time of flight, from Darcy's law, is inversely proportional to the average permeability, assuming that the streamline locations do not change with small changes in permeability. It is then possible to estimate the change in permeability along a streamline necessary to match production history. Independently, three groups have proposed different methods for using streamlines in history matching by calculating the change in permeability necessary to match water production. These streamline-based history-matching techniques offer considerable promise, but they all suffer from one major limitation: the forward simulations assume incompressible flow without gravity. The theory of streamline-based history matching assumes essentially tracer-like flow - fixed streamlines over time with no gravity or compressibility. This may be a poor approximation for many cases, such as for matching early production history, including periods of primary production, where compressibility is important, or for assessing gas injection schemes, where gravity override is significant. It is possible to obtain a history match from a forward simulation that ignores essential physics. However, the reservoir description obtained may not be representative of the field, and the prediction of future performance will be in error as a consequence.
- North America > United States (1.00)
- Europe > Norway > North Sea (0.84)
- Europe > United Kingdom > North Sea (0.60)
- (2 more...)
- Europe > Norway > North Sea > Central North Sea > Central Graben > PL 018 > Block 2/4 > Greater Ekofisk Field > Ekofisk Field > Tor Formation (0.99)
- Europe > Norway > North Sea > Central North Sea > Central Graben > PL 018 > Block 2/4 > Greater Ekofisk Field > Ekofisk Field > Ekofisk Formation (0.99)
Abstract We use a pore-scale network model of three-phase flow to compute relative permeabilities, saturation paths and capillary pressures for a variety of displacement processes. The model is based on a random network of pores and throats with triangular, rectangular and circular cross-sections that represent the complex pore space observed in sandstones. We model wettability alteration after primary drainage and allow any values for the advancing and receding oil/water, gas/water and gas/oil contact angles. Multiple phases can be present in each pore, in wetting and spreading layers, as well as occupying the center of the pore space. In all, twenty different generic fluid configurations for two- and three-phase flow are analyzed. With a network based on a description of Berea sandstone we can predict relative permeabilities for two-phase flow in a water-wet system and waterflood recoveries for mixed-wet media. We then predict the steady-state oil, water and gas three-phase relative permeabilities measured by Oak. We demonstrate that the predictions obtained by the network model compare favorably with those obtained using standard empirical relative permeability correlations. We then study gas injection into media of different wettability and interpret the results in terms of pore-scale displacement processes. Introduction The simultaneous flow of three phases - oil, water and gas - in porous media occurs in a variety of reservoir and environmental engineering problems. During conventional two-phase mechanisms of oil recovery, such as waterflooding, oil recovery is typically 20 to 50% indicating that oil flows at relatively high saturations. In such circumstances uncertainties in the relative permeability often have little impact on recovery predictions. In contrast, during three-phase recovery processes such as gas injection, gas cap expansion, depressurization, solution gas drive and gravity drainage, to achieve a higher recovery oil may flow at very low saturations, implying that the oil relative permeability can also reach very low values. Direct measurement of relative permeabilities and capillary pressures in this regime is not only very difficult but also time consuming and inaccurate. Since two independent fluid saturations are required to define a three-phase system, there is an infinite number of possible fluid arrangements and displacement paths, making a comprehensive suite of experimental measurements for all three-phase displacements impossible. Consequently, numerical simulations of three-phase flow rely on empirical models to predict relative permeability and capillary pressure from measured two-phase values. However, these models may give predictions that vary as much as an order of magnitude from each other, or from direct measurements, since they have little or no physical basis. In such cases uncertainties in relative permeability, particularly at low oil saturation, may have a very significant impact on recovery predictions.
Abstract Streamline-based methods for history matching are appealing for two reasons. First, the forward simulation is potentially much faster than conventional simulation methods for displacement-type problems. Second, time-of-flight information along the streamlines can be used to find sensitivity coefficients in an efficient and elegant manner. However, current streamline history matching methods use forward simulations that ignore the effects of gravity and compressible flow. These effects may be critical in analyzing early-time performance data. If relevant physical effects are neglected in the forward simulation, the history matched reservoir description may not be consistent with the actual field, and predictions from the model will not be reliable. We present a method for history matching watercut data using a streamline simulation that captures all the pertinent physics, including compressible three-phase flow with gravity. We use a methodology based on the assumption of one-dimensional flow along streamlines to find the sensitivity of water flow rate at production wells to changes in permeability. Although the computation of the sensitivities is approximate, the method provides a good history match for problems with significant effects due to compressibility and gravity. Data from a North Sea field is used to test the technique. Using a full-physics streamline model gives a reasonable history match and a good prediction of future performance. Introduction Several history matching methods have been proposed to constrain reservoir descriptions to production data, such as water-cut history (see, for instance). These techniques use conventional grid-based simulation to compute sensitivity coefficients, which give the change in production data due to a change in the permeability or porosity of some portion of the simulation model. Using the sensitivity coefficients, the porosity and permeability data are adjusted to create a new reservoir model. When another simulation is performed using this model, a better match to the data should be obtained. If the match is still not acceptable, new sensitivity coefficients are computed and used to modify the reservoir model again. Because the sensitivity coefficients are non-linearly dependent on the reservoir description, many iterations may be needed before a good history match is obtained. For a finely-gridded model, there are many more matching parameters than data, and the match is non-unique. To overcome the problem of having many poorly determined parameters in the reservoir description, methods that reduce the parameter space, such as the use of recursively refined grids, gradzone analysis and gradual deformation have been proposed. Current history matching methods are still limited, however, by the time taken to perform the forward simulations. Ideally, history matching would start from a statistical ensemble of equi-probable initial estimates of the reservoir description. Each reservoir description, if it is a fine-scale reservoir model, may contain several million grid blocks. Current simulation techniques may take approximately a week to perform a single simulation of this size, making history matching, that may require tens to hundreds of iterations, on several models, impossible in practice. Approaches where history matching is performed on a much coarser grid than the geological model offer appealing savings in computer time. However, the appropriate manner to upscale or downscale single and multiphase flow properties is not obvious. Furthermore, fine-scale details may be important for future prediction of, say, waterflood or gasflood performance. In these cases, history matching on a coarse grid may yield a poor reservoir description with correspondingly inaccurate predictions of future recovery.
- North America > United States > Texas (0.93)
- Europe > Norway > North Sea (0.84)
- Europe > United Kingdom > North Sea (0.60)
- (2 more...)
- Europe > Norway > North Sea > Central North Sea > Central Graben > PL 018 > Block 2/4 > Greater Ekofisk Field > Ekofisk Field > Tor Formation (0.99)
- Europe > Norway > North Sea > Central North Sea > Central Graben > PL 018 > Block 2/4 > Greater Ekofisk Field > Ekofisk Field > Ekofisk Formation (0.99)
Abstract We present an empirical model for three-phase relative permeability that overcomes the limitations of current formulations, such as Stone's methods.1,2 We provide a self-consistent treatment of wettability, changes in hydrocarbon composition, different saturation paths, and the trapping of oil, water and gas. The theoretical development is motivated by a review of recent three-phase experiments. The model is based on saturation-weighted interpolation between the two-phase values.3 To account for the effects of wettability we apply saturation-weighting to all three phases. By writing the relative permeabilities as unique functions of a flowing saturation, the model predicts the behavior for any sequence of saturation changes and accounts for trapping. Layer drainage, which allows oil relative permeabilities to be extrapolated to low saturation, is included for water-wet media. The model ensures smooth changes in relative permeability with changes in hydrocarbon composition and tends to the appropriate limits as the gas and oil become miscible. The model is tested against the data of Oak and co-workers.4,5 We show that it is necessary to include layer drainage and oil trapping to predict three-phase oil relative permeability at low oil saturation accurately.