Realistic reservoir models are essential for efficient field management and accurate forecasting of hydrocarbon production. Such models, based on the physical description of the reservoir, need to be calibrated or conditioned to historical production data. The process of incorporating dynamic data in the generation of reservoir models, known as history matching, is traditionally done by hand and is a very tedious, time-consuming procedure that, in addition, returns only one single matched model. It has been shown that the best matched model may well not be a good predictor of future performance. In this work, one of the first field applications of the Neighbourhood Algorithm (NA) is presented. The NA is a stochastic sampling algorithm that explores the parameter space, finds an acceptable ensemble of data fitting models and extracts robust information from this ensemble in a Bayesian framework. The aim is to forecast hydrocarbon production accurately and to assess the related uncertainty by means of multiple reservoir models. The NA methodology was extensively applied to an offshore gas field and compared to a previously manually matched model. The Mistral field has been producing for 6 years from 7 wells. Gas and water productions and pressure data were available and the uncertainty quantification was consistently obtained. Algorithm control parameters and objective function definition effects were investigated. The posterior probability density functions of each unknown parameter, calculated taking into account the observed production data, were evaluated. The hydrocarbon production was forecast using Bayesian inference and the economic risk estimated. The overall process was carried out with a significant time reduction compared with the previous manual approach. The results presented suggest that use of stochastic sampling techniques in a Bayesian framework may well be a valid alternative methodology to the traditional industry workflow for the uncertainty quantification in producing fields. Introduction History matching is a very complex non-linear and ill-posed problem. Like most inverse problems, it is characterised by non-uniqueness of solution [24]. For this reason different combinations of the model parameters may lead to acceptable representations of the history of the reservoir. Traditionally, history matching is done by hand and is a very tedious, time-consuming procedure where the reservoir parameters are varied until a satisfactory match is obtained. In addition, this standard practice leads only to a single production forecast making unfeasible any assessment of uncertainty. Recently, thanks to increasing computer power and technology, computer-aided history matching techniques are becoming gradually more adopted by the oil industry. This is due to the great time-saving benefits they can offer over conventional trial-and-error approaches [25]. "Automatic" and "Assisted history match" techniques automatically vary reservoir parameters until a defined stopping criteria is achieved. In literature they can be divided into three main groups:Deterministic methods;Stochastic methods;Hybrid methods. During the last decades the application of stochastic methods has spread over all the disciplines of the oil industry [12, 13, 14, 15, 20]. However, even if the nature of the history matching problem has been widely recognized, the majority of the approaches adopted return only one matched model that eventually will be used to forecast production. Alternative solutions (i.e. other acceptable models) are usually not sought because of computational and human time constraints. However, neglecting the non-uniqueness of the inverse problem and selecting only one reservoir model could lead to errors in the prediction of the production as cleverly highlighted in the work of Tavassoli et al. [25]. In addition only one model does not allow an assessment of uncertainty in prediction.
Summary We present a detailed investigation on the reliability of some of the dynamic pseudofunctions used to upscale flow properties in reservoir simulation. A one-dimensional example (1D) and a real field application are used to evaluate methods developed by Kyte and Berry and Stone, and a new flux weighted potential(FWP) method. A derivation of Stone's method (based on the description given by Stone above) is presented, which is found to give an inconsistent set of equations. Stone's analytical example was used to illustrate how pseudo relative permeabilities that exhibit non-physical behavior may still give acceptable results, but this success can disappear with changes in boundary conditions. The pseudofunctions from a field application were not able to match the 2Dsimulations from which they were calculated, even when a different pseudofunction was used for each coarse grid block. Improvements were obtained when directional pseudofunctions were used, but still the results were not satisfactory. Similar results were found when comparing fine and coarse grid 3D simulations for a quarter of a five-spot pattern in this field. The results presented in this article suggest that dynamic pseudofunctions, as applied here and as commonly used in industry, may not be an adequate approach to up-scaling. The possibility of large errors and the difficulty in predicting when they may occur make the use of pseudofunctions examined in this paper unreliable. Introduction Oil and gas reservoirs are very complex systems in which rock and flow properties vary at all scales (pore to reservoir scale). Rock properties(e.g., porosity and absolute permeability) and saturation functions (e.g., relative permeability and capillary pressure) show variations that can be significant to oil recovery at scales below the size of common simulation grid blocks. One of the most important problems in reservoir simulation is that of accurately accounting for such small scale variations. In addition to the low resolution, coarse grid solutions can be strongly affected by numerical diffusion. Many pseudofunction techniques have been proposed to reproduce fine grid results(including detailed descriptions of heterogeneity and with minimum numerical diffusion) using the typical coarse grids of field simulations. Baker and Dupouy1 have a useful review of some of the competing alternatives methods (including Kyte and Berry2 and Stone3 methods). For example, they discuss a variation of the Kyte and Berry method which requires averaging pressures over the volume of a coarse grid cell, rather than using the mobility weighted average pressure over a face. The volume weighting method is more consistent with the derivation of the simulator's finite difference equations and avoids the occurrence of directional pseudocapillary pressures. However, at the coarse grid sizes usually deployed, the capillary pressure would have negligible influence. Another upscaling method is introduced in this paper similar to the Kyte and Berry method. It is based on a flux weighting of potentials at a face, referred to as the flux weighted potential(FWP). Except for certain specific analytic upscaling methods (Li et al.4), there are three broad approaches to upscaling which are pursued in the petroleum industry with varying degrees of success. These may be summarized as follows.Solve a fine grid 3D problem for a large representation area of the reservoir to be modeled, and apply an upscaling algorithm to the proposed coarse grid in this area. It is then necessary to demonstrate that the resulting pseudofunctions used in the coarse grid solution adequately reproduce the fine grid results. Some ad hoc decisions are then required on how to allocate the derived family of pseudofunctions to the whole reservoir. The difficulties with this approach can be the large cost with the fine grid solution, failure to reproduce it adequately with the coarse grid, and that the chosen area is not representative of other parts of the reservoir. One of the principal advantages is that the geometry of some of the real wells can be properly included in the large model area.Choose a few moderately small representative elements of volume (REV), and obtain a fine grid solution for the REVs, and the corresponding pseudofunctions for the coarse grid of the intended reservoir model. 2D cross sections are frequently used for this purpose. They have the merit of being much less expensive than a large area model. However, cross sections do not give any representations of the changing viscous to gravity ratios associated with areal sweep effects. Sometimes this is alleviated using a typical stream-tube geometry as a varying width in the cross section (Hewett and Berhens5), but this cannot deal with the 3D problem caused by areal heterogeneities. Interactions between real wells are neglected, and the allocation of the generated families of pseudofunctions to the coarse grid reservoir model becomes more problematic.A procedure referred to as successive renormalization6–8 is used. In this approach the central idea is to use fast solutions of flow problems in small Cartesian blocks as a basis for upscaling. The small blocks have artificial boundary conditions applied (e.g., constant pressure on two opposing faces and no flows on the other faces). The block solutions can be very fast, being independent of each other, and no special ad hoc assumptions are made about representative volumes. Successive sweeps can then be made at increasing block sizes, until the desired coarse grid size is attained for the large reservoir simulation. The choice of block size (King6 used 2×2×2 blocks) and the number sweeps is arbitrary. For some problems, error canceling between successive sweeps can occur, but in others, such as with complicated shale distributions, the cancellation does not occur. For two-phase renormalization, the use of a water injection only boundary condition on a block can generate large errors, and the influences of gravity slumping are ignored.
Production from heavy oil reservoirs has always been a challenge due mainly to one factor in particular high oil viscosity, implying low oil mobility within porous media. Different methods have been implemented over the years in order to reduce oil viscosity. Well-known methods include steam injection (e.g., Steam Drive, Steam Assisted Gravity-SAGD), CO2 injection, chemical injection etc. These types of application are mainly applied to onshore fields where space is available and operating costs are much lower with respect to offshore fields. Moreover they may not be feasible for shallow reservoirs where injection could be an issue due to uncertainties regarding the cap-rock sealing. The scope of this paper is to present a patented nonconventional EOR method for heavy oil reservoirs using radio frequency/microwave heating. An adequate completion design and well-reservoir connection is used for heating the oil, thus solving the problems that impede RadioFrequency /MicroWave (RF/MW) penetration into the reservoir. Consequently, oil viscosity may be reduced, thus allowing its continuous production to surface (eventually by means of an artificial lift system included in the well completion). This method could be also suitable for offshore fields because it doesn't require high energy consumption, or large surface areas, or high operating costs. It can also be suitable for those shallow reservoirs not suitable for injection processes. This paper presents details of this new technology and associated simulation results showing its range of implementation.
Three-phase flow is present in many oil recovery processes of interest to the oil industry. It occurs in processes such as primary production below bubble point pressure in reservoirs with water drive, in gas or water alternating gas (WAG) injection into waterflooded reservoirs, in thermal oil recovery, and in surfactant flooding. Despite its common occurrence, our ability to reliably model three-phase flow using numerical simulation is questionable. This paper shows the importance of three-phase flow at typical oil field conditions. It also shows the uncertainties in the predictions of oil recovery due to the three-phase relative permeability model. Numerical simulations of immiscible gas and WAG injection into a waterflooded one eighth of a five-spot were performed to determine the importance of the three-phase flow at conditions that are of interest to the oil industry. Consistent oil-water imbibition and oil-gas drainage relative permeability and capillary pressure were derived for this purpose, including a new form for imbibition capillary pressure. Dimensionless scaling groups for three-dimensional three-phase flow in porous media were developed. The scaling groups were used to design simulations at various conditions of gravity, viscous and capillary force interactions. In addition, several simulations were made to determine the uncertainty of the results due to the model for three-phase relative permeabilities. The results of this study show that there is a significant uncertainty associated with the selection of the three-phase relative permeability model for field scale simulations of gas and WAG injections. This uncertainty is translated into doubtful simulation results in terms of distribution of the fluids inside large volumes of the reservoir, total oil recovery, and fluids production rates. It is shown that additional oil recovery due to gas injection after a waterflood can be different by a factor of two depending on the model for three-phase relative permeability. It is also shown that the producing gas oil ratio (GOR) varies considerably depending on the model for three-phase relative permeability, while maintaining the same two-phase relative permeabilities. Accurate predictions of oil recovery in processes that exhibit three-phase flow need more rigorous models for three-phase relative permeability. Large three-phase flow regions were present for most of the conditions simulated. The size of the three-phase flow regions ranged from 20% to 80% of the volume of the reservoir. The size of the three-phase flow region was a strong function of the kro model used. Thus, an argument asserting that only a small part of the reservoir is affected by the uncertainties in the three-phase relative permeability model is not supported by these results.
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