Martin J. Blunt

Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques

This paper presents the results of the Tenth SPE Comparative Solution Project on Upscaling. Two problems were chosen. The first problem was a small 2D gas injection problem, chosen so that the fine grid could be computed easily, and both upscaling and pseudoisation methods could be used. The second problem was a waterflood of a large geostatistical model chosen so that it was hard (though not impossible) to compute the true fine grid solution. Nine participants provided results for one or both problems. Introduction The SPE Comparative Solution Projects provide a vehicle for independent comparison of methods and a recognized suite of test datasets for specific problems. The previous nine comparative solution projects – 9 have focussed on black-oil, compositional, dual porosity, thermal or miscible simulations, as well as horizontal wells and gridding techniques. The aim of the tenth comparative solution project was to compare upgridding and upscaling approaches for two problems. Full details of the project, and data files available for downloading can be found on the project web site. The first problem was a simple 2000 cell 2D vertical cross section. The tasks specified were to apply upscaling or pseudoization methods and obtain solutions for a specified coarse grid, and a coarse grid selected by the participant. The second problem was a 3D waterflood of a 1.1 million cell geostatistical model. This model was chosen to be sufficiently detailed that it would be hard, though not impossible, to run the fine grid solution and use classical pseudoisation methods. We will not review the large number of upscaling approaches here. For a detailed description of these methods see any of the reviews of upscaling and pseudoisation techniques, for example – . Description of Problems Model 1 The model is a 2-phase (oil and gas) model that has a simple 2D vertical cross-sectional geometry with no dipping or faults. The dimensions of the model are 762 meters long by 7.62 meters wide by 15.24 meters thick. The fine scale grid is 100 x 1 x 20 with uniform size for each of the grid blocks. The top of the model is at 0.0 metres with initial pressure at this point of 100 psia. Initially the model is fully saturated with oil (no connate water). The permeability distribution is a correlated geostatistically generated field, shown in Fig 1. The fluids are assumed to be incompressible and immiscible. The fine grid relative permeabilities are shown in Fig 2. Capillary pressure was assumed to be negligible in this case. Gas was injected from an injector located at the left of the model and dead oil was produced from a well on the right of the model. Both wells have a well internal diameter of 1.0 ft and are completed vertically throughout the model. The injection rate was set to give a frontal velocity of 0.3 m/d (about 1 foot/day or 6.97 m per day), and the producer is set to produce at a constant bottom pressure limit of 95 psia. The reference depth for the bottom hole pressure is at 0.0 meters (top of the model). The tasks specified were to apply upscaling or pseudoization method in the following scenarios: 1. 2D – 2D uniform 5 x 1 x 5 coarse grid model 2. 2D – 2D nonuniform coarsening. Max 100 cells. Directional pseudo relative permeabilities were allowed if necessary. Model 2 This model has a sufficiently fine grid to make use of any method that relies on having the full fine grid solution almost impossible. The model has a simple geometry, with no top structure or faults. The reason for this choice is to provide maximum flexibility in selection of upscaled grids. SPE 66599 Tenth SPE Comparative Solution Project: A Comparison of Upscaling Techniques M A Christie, SPE, Heriot-Watt University, and M J Blunt, SPE, Imperial College 2 M A CHRISTIE & M J BLUNT SPE 66599 At the fine geological model scale, the model is described on a regular cartesian grid. The model dimensions are 1200 x 2200 x 170 (ft). The top 70 ft (35 layers) represents the Tarbert formation, and the bottom 100 ft (50 layers) represents Upper Ness. The fine scale cell size is 20 ft x 10 ft x 2 ft. The fine scale model has 60 x 220 x 85 cells (1.122x10 cells). The porosity distribution is shown in Fig 3. The model consists of part of a Brent sequence. The model was originally generated for use in the PUNQ project. The vertical permeability of the model was altered from the original: originally the model had a uniform kv/kh across the whole domain. The model used here has a kv/kh of 0.3 in the channels, and a kv/kh of 10 -3 in the background. The top part of the model is a Tarbert formation, and is a representation of a prograding near shore environment. The lower part (Upper Ness) is fluvial. Participants and Methods Chevron Results were submitted for model 2 using CHEARS, Chevron’s in house reservoir simulator. They used the parallel version and the serial version for the fine grid model, and the serial version for the scaled-up model. Coats Engineering Inc Runs were submitted for both model 1 and model 2. The simulation results were generated using SENSOR. The simulator runs used the conventional 5or 7-point finite difference formulation, zero capillary pressure, and no directional relative permeability. GeoQuest A solution was submitted for model 2 only, with coarse grid runs performed using ECLIPSE 100. The full fine grid model was run using FRONTSIM, a streamline simulator, to check the accuracy of the upscaling. The coarse grid models were constructed using FloGrid, GeoQuest’s gridding and upscaling application. Landmark Landmark submitted entries for both model 1 and model 2 using the VIP simulator. The fine grid for model 2 was run using parallel VIP. Phillips Petroleum Solutions were submitted for both model 1 and model 2. The simulator used was SENSOR. Roxar Entries were submitted for both model 1 and model 2. The simulation results presented were generated using Roxar’s Black Oil, Implicit Simulator, Nextwell. The upscaled grid properties were generated using Roxar’s Geological Modelling software, RMS, in particular the RMSsimgrid option. Streamsim Streamsim submitted an entry for model 2 only. Simulations were run using 3DSL, a streamline based simulator. TotalFinaElf TotalFinaElf submitted a solution for model 2 only. The simulator used for the results presented was ECLIPSE; results were checked using the streamline code 3DSL. University of New South Wales The University of New South Wales submitted results for model 1 only using CMG’s IMEX simulator. Results Model 1 Fine Grid Solution All participants were able to compute the fine grid solution, and the solutions from the different simulators used were very close, as shown in Fig 4. The University of New South Wales fine grid solution departs slightly from the other fine grid solutions; it was not possible to track down the source of this discrepancy in the short time between receiving this solution and the paper submission deadline. Upscaled Solutions Participants were asked to generate solutions on a 5 x 5 grid, and on a grid of their choice with a maximum of 100 cells. The reason for the choice of the 5 x 5 grid was that, with that grid size, the coarse grid boundaries fall on high permeability streaks which is generally a problem for upscaling methods which don’t compute the fine grid solution. The solutions submitted for the 5 x 5 grid used single phase upscaling only (Roxar), or single phase upscaling plus regression based pseudoisation of relative permeabilities (Coats, Phillips, Landmark). The solutions with pseudo relative permeabilities are very close to the fine grid solution, and Roxar’s solution using only single phase upscaling shows a significant discrepancy (Fig 5). A second set of solutions was presented by some participants (shown in Fig 6). Here Roxar used single phase upscaling in conjunction with a streamline approach to generate local grid refinements (with a total of 96 cells) which captured the details of the flow in the early, mid, and late-time regions. Coats showed that good results could also be obtained with homogeneous absolute permeability and no alteration of relative permeability, and Phillips showed that good results could be obtained from a 6 x 2 grid. The University of New South Wales solution was based on a global upscaling and upgridding approach which attempts to minimize the variance of permeability within a cell. Their solution is close to their fine grid solution, although the difference between their fine grid solution and the other fine grid solutions tends to make their method appear to perform less well. Model 2 Fine Grid Solution Five participants provided fine grid results as well as an upscaled solution. Landmark and Chevron ran the full fine grid on a parallel reservoir simulator. GeoQuest and SPE 66599 TENTH SPE COMPARATIVE SOLUTION PROJECT: A COMPARISON OF UPSCALING TECHNIQUES 3 Streamsim provided results using streamline codes (TotalFinaElf also provided streamline results using 3DSL. We have not shown their production curves as they are the same as Streamsim’s). A comparison of the fine grid results is shown in Fig 7, 8, 9, 10. All the figures shows very good agreement between all four fine grid submissions. Although only producer 1 well plots are shown here for reasons of space, plots of the remaining well rates and watercuts show equally high levels of agreement between the four fine grid solutions. The differences that occur likely to be due to either different time steps early on, where the production rate is very sensitive to the transient pressure response, or to different treatment of the injection well, which was at the corner of four cells in the fine model, leading to different injectivity indices. Upscaled Solutions There were two methodologies used to generate the upscaled solutions. Some participants used finer scale information in some way, and then history matched a coarser grid to the finer grid results. Others made no use of fine sc

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.

Flow in porous media — pore-network models and multiphase flow

In the last 3 years there has been a huge increase in the use of pore-scale modeling to study multiphase flow and transport in porous media. Starting from single pore models of fluid arrangements, computations of relative permeability, interfacial area, dissolution rate and many other physical properties have been made. Combined with a realistic description of the pore space, predictive modeling of a variety of processes, including waterflood relative permeability and mass transfer coefficients, is now possible. This review highlights some of the major advances, with an emphasis on models of wettability and three-phase flow.

Carbon dioxide in enhanced oil recovery

Abstract Oil reservoirs are deep underground, with the oil and gas contained in porous rock at high temperatures and pressures. Around 5 – 20%, of the oil can be produced from the field under its own pressure (primary production), but in most fields water is injected to displace the oil. This still leaves at least 50% of the oil behind in the reservoir. Further recovery can be obtained by injecting carbon dioxide that both displaces and dissolves the remaining oil. At least 71 projects worldwide use CO 2 flooding and produce a total of over 170 000 barrels of oil a day, worth around

Relative permeabilities from two- and three-dimensional pore-scale network modelling

1.3 billion a year. The cost of producing an extra barrel of oil ranges from

Three-dimensional modeling of three phase imbibition and drainage

5 to

Modelling two-phase flow in porous media at the pore scale using the volume-of-fluid method

8 and thus is profitable at the present price of nearly

A New Model of Trapping and Relative Permeability Hysteresis for All Wettability Characteristics

20 a barrel. In the majority of these cases, the carbon dioxide comes from natural underground sources and is piped to the oil field. The potential use of CO 2 flooding would be considerably greater, if large quantities of the gas, extracted from power stations, were available at low cost. For every kilogramme of CO 2 injected, approximately one to one quarter of a kilogramme of extra oil will be recovered. For most projects about as much carbon dioxide is disposed of in the reservoir as is generated when the oil is burnt. When CO 2 is at a sufficiently high pressure to form mixtures with the crude oil that are miscible in laboratory tests, up to 40% of the oil remaining in the field after water flooding can be recovered. Approximately half the water flooded oil fields in the US could be exploited profitably by CO 2 injection. Carbon dioxide flooding of the larger North Sea fields is a particularly attractive prospect, because the crude oil is light (composed of low molecular weight hydrocarbons) and the geology of the reservoirs is less heterogeneous than the American fields. A profitable project would be possible if the gas could be provided and piped to the reservoir at a cost of around

Physically-based network modeling of multiphase flow in intermediate-wet porous media

3.50 per thousand cubic feet or less.

Pore‐scale modeling of longitudinal dispersion

We present a computer study of two-phase flow in a porous medium. The porous medium is represented by an isotropic network of up to 80 000 randomly placed nodes connected by thin tubes. We then simulate two-fluid displacements in this network and are able to demonstrate the effects of viscous and capillary forces. We use the local average flow rates and pressures to calculate effective saturation dependent relative pemeabilities, fractional flows and capillary pressures. Using a radial Buckley-Leverett theory, the mean saturation profile can be inferred from the solution of the fractional flow equation, which is consistent with the computed saturation. We show that the relative permeability may be a function of both viscosity ratio and capillary number.