Upscaling of polymer adsorption

Heterogeneity of the fine-scale models will result in full tensor effects for the upscaled models, especially in reservoirs with channels or fractures. A flow-based upscaling approach integrating multiple flow scenarios is developed to effectively capture the full-tensor effects when upscaling from fine-scale discrete fracture models. The new approach is proposed to deliver computationally affordable simulation models under precision comparable to the high-resolution models. The approach starts with several sets of flow-based single scenario upscaling procedures. A fine-scale discrete fracture model is built up as the reference model for all the successive procedures and comparisons. Then several flow cases (referred as scenarios) are determined according to the target simulation conditions. A global upscaling technique under multipoint flux approximation scheme is introduced to each flow scenario. An integrated output least squares method, which aims to minimize the total bias of simulation results of all the flow scenarios, is adopted to obtain the optimal transmissibility connection list of the coarse-scale models. We design and implement several examples including two synthetic conceptual cases and a real field case. In each case, comparisons are provided for the simulation results of the proposed approach and previous upscaling approaches based on two point flux approximation schemes. The coarse-scale models upscaled by different methods are based on the same fine-scale (reference) model in each case. The results of the upscaled models are also compared to the reference model. The numerical results show that the new approach generates coarse-scale models which are closer to the fine-scale model. Although under certain conditions, traditional upscaling methods can achieve equivalent results, it is proven that the new approach is more robust when applied to more general flow scenarios. It can be noted that it may take a bit more time for the numerical simulation of coarse-scale models upscaled by the new method, due to the introduction of the non-neighbor connections. When compared to the fine- scale model, however, the improvement of computational efficiency is still pretty significant. The last case is a real field case with about 500,000 fine-scale grids and 10,000 coarse-scale grids, which demonstrates the ability of the new approach to be applied in the industry. The novelty of the proposed approach is the optimization technique integrating multiple scenarios to generate a high precision coarse-scale model under multipoint flux approximation scheme. The new method effectively capture the anisotropic features of the coarse-scale models, which is a challenge for flow-based upscaling procedures because a single flow simulation is usually inadequate to obtain full tensor information of the upscaled models.

In sandstone reservoirs, one of the most important challenges is the effective upscaling of a fine scale model. A conventional upscaling process is not adequate when significant percentage of shale distribution exists in the reservoir. In the fine scale model, significant discontinuity exists in sand bodies. Some sand bodies are connected to the wells, and some are not. As the fine scale model is upscaled, some discontinuous sand bodies are combined with other connected sands. This results in two potential problems: the connected volume to the existing wells increases, thus making the production from those wells more optimistic, and the production from in fill wells do not show as much additional potential since some of the new volumes which should have been connected to the new well are already drained by the existing wells. A new procedure1 is developed to overcome this problem. In a new procedure, we first determine the connected sand volume to the existing wells. We remove the dis-connected sand bodies from the fine scale model. We then upscale the model to a desired level. We simulate the flow performance till a desired time when either new wells are drilled or some well are shut-in. At that point, we start from the fine scale model again and determine new connected volume due to additional of new wells. We combine the new virgin sands with depleted sands in the upscaled model and determine the saturation and pressure in the upscaled model using an appropriate material balance technique. We re-start the simulation using newly connected volume till we reach a point of drilling additional wells. The key difference between the proposed method and the existing methods, is our ability to add new hydrocarbon volumes (as well as new conductivity) in the model as a function of time. The proposed method was applied to a giant oil field in Siberia which is in turbite environment with large amounts of discontinuous sand bodies. We were able to demonstrate the advantage of the proposed method by comparing the performance of upscaled simulation model to the fine scale geologic model. As the percentage of sand decreases in a given reservoir, the difference between the conventional and a proposed method becomes significant. Using the new approach, we would be able to evaluate the infill potential much more accurately.

Integration of dynamic data typically requires the solution of an inverse problem that can be computationally intensive and practically infeasible for fine scale reservoir models. In this paper we present a new methodology to directly update fine scale geostatistically-based reservoir models by combining gradual deformation parameterization for the fine scale geostatistical model and an upscaling technique for the coarse scale flow simulation model. The proposed methodology includes: Perturbation of the fine scale geostatistical model using the gradual deformation parameterization. Gradual deformation ensures the preservation of the overall geostatistical properties of the fine model. Generation of the coarse scale flow simulation model by upscaling the fine scale geostatistical model. Sensitivity computation of the flow simulation results with respect to the fine scale parameterization. This sensitivity computation is analytical and takes into account the upscaling process. Direct updating of the fine scale geostatistical model using classical optimization process. Direct updating ensures consistency between the fine and coarse scale models. The accuracy of the proposed methodology was improved by calibrating the flow simulation model. The objective of this calibration is to reduce the error introduced by the upscaling step during the flow simulation. We applied successfully our methodology for fine scale reservoir description by integrating permanent down-hole gauge measurements directly into a three-dimensional geostatistical model containing about two million grid blocks. This test is designed to highlight several key issues of the proposed methodology: Efficiency of the upscaling step coupled with gradient-based optimization to speed up the history matching process. Usefulness of the calibration step for a correct integration of upscaling techniques in history matching. Capability of the methodology for maintaining consistency and coherency between fine scale and coarse scale models. Improvement of the reservoir characterization by integrating dynamic data at the fine geostatistical scale. We conclude that the proposed methodology can be used effectively and efficiently for reservoir characterization purposes.

Infill well placement optimization in two-dimensional heterogeneous reservoirs under waterflooding using upscaling wavelet transform

This paper presents the development of a static model for a naturally-fractured High-Pressure-High-Temperature (HPHT) gas sand reservoir located in the Tarim basin, Western China. The study is part of a well placement optimization study. It is motivated by the big challenges of drilling a well at depths ranging from 6800m-8000m[AG1] in a HPHT environment. A detailed fine-scale model is required as input for the dynamic model. The static model is developed through an integration [AG2]process. It consists of both matrix and fractures. The matrix modeling started by integrating 3D seismic and log data to build the structural model. A new rock type scheme was developed by reconciling log and core data, including capillary pressures. Additionally, permeabilities are estimated at each uncored location using a two-step approach, namely trend estimation by regression analysis and variability simulation by 1D Gaussian simulation. The 3D modeling was executed in the order of least dependent to most dependent variable (i.e., from facies, to rock type, then followed by porosity, permeability and saturation respectively). From the geology, the sand bodies were interpreted to be continuous throughout the field. Discontinuous mudstone layers are sandwiched in-between the sand bodies. This information, together with outcrop data, is used to guide the spatial relationships in the model. Facies, rock type, porosity and permeability are simulated using geostatistical procedures. Meanwhile, saturation is generated based on the Leverett J-Function. To quantify the uncertainty in the various data, especially in the capillary pressure data, the porosity-permeability relationship, the gas-water contact and the surface tension of the gas-water system, a probabilistic model of the Gas Initially in Place (GIP) is created through uncertainty and sensitivity analysis. The origin of the fracture system was analyzed by developing a prototype of a conceptual model. The understanding from the prototype model is coupled with the 3D seismic, outcrops, drilling information, rock mechanics, image log, core, and dynamic data, to develop fracture characteristics and correlations. The discrete fracture system is modelled using a stochastic simulation approach, constraining it to the seismically-inverted fracture density map for each zone through well-seismic correlations and a nonlinear inversion [AG3]to build the Discrete Fracture Network (DFN). Finally, the fracture model is integrated with the matrix model by upscaling the DFN model into the grid system. Following the creation of the static model, a dual porosity model was prepared for dynamic modeling by maintaining consistency between the fine scale and upscaled models throughout the upscaling process. The methodology described above has produced a detailed fine scale model that shows consistency between properties and geology. This is a direct consequence of the new rock type system and the order in which the simulation was conducted. The facies model shows the continuity of the sand bodies, and the discontinuity of the mudstone, as indicated by the geological interpretation. The 3D Poro-Perm relationship shows the variability which is a reflection of the variability of the core data. The probabilistic distribution of the GIP is in agreement with the results of conventional reservoir engineering analyses, namely Material Balance and Rate Transient Analysis. Furthermore, the fracture distribution confirms the information both at the wells, as well as in-between the wells as given by the seismic interpretation. This study demonstrates that a reliable fine scale model can be developed to match the available data and interpretation by properly preparing the pre-requisite inputs and following the order of dependency in the reservoir attributes.

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 123671, ’Dynamic Updating of Reservoir Models,’ by Harun Ates and Asnul Bahar, SPE, Kelkar and Associates, and Vitaly Krasnov, SPE, Rosneft, and Mohan Kelkar, SPE, University of Tulsa, prepared for the 2009 SPE Annual Technical Conference and Exhibition, New Orleans, 4-7 October. The paper has not been peer reviewed. In sandstone reservoirs, an important challenge is scaling up a fine-scale model effectively. Conventional methods are not adequate when significant shale distribution exists in the reservoir. In the fine-scale model, some sand bodies are connected to the wells and some are not. As the fine-scale model is scaled up, some discontinuous sand bodies become combined with connected sands. A new procedure was developed to overcome this problem. Introduction Traditional reservoir modeling involves developing a fine-scale geocellular model that incorporates the small-scale static uncertainties. Once such a description is created, it is scaled up to an appropriate scale such that it can be flow simulated to understand the dynamic performance of the reservoir. It is difficult to flow simulate a fine-scale model because it is computationally demanding. Some sandstone reservoirs tend to be highly discontinuous, with sand and shale dispersed within the reservoir. The continuity of the sand bodies may not be known precisely and reflects an uncertainty in static models. The problem becomes even more complex if the reservoir is thick and contains multiple thin sand bodies. When a fine-scale model is constructed, it may contain many vertical layers to account for all the thin sands present in the reservoir. Scaling up of such models is very difficult because of the following. If the model is coarsened (scaled up) significantly, many of the discontinuous sands will connect to other sands, and this will increase the pore volume (PV) “connected” to the wellbore, changing the transmissibility (connectivity) distribution between wells. In the scaled-up model, because of artificially connected sands, infill wells would not indicate true potential of additional recovery because some of the virgin sands that would have been connected to the newly drilled wells would show to have been drained already by existing wells in the model. If the model is maintained at relatively fine scale, the simulation can be computationally demanding. The dynamic modeling (e.g., history matching) would be more time consuming. Therefore, many uncertainties may not be investigated correctly.

Numerical reservoir simulation often requires upscaling of fine-scale detailed models and coarse-scale models are necessary to reduce computational time for dynamic evaluations. However, these simplifications may degenerate results due to loss of resolution of the small-scale phenomena, averaging of sub-grid heterogeneity and numerical dispersion, especially in oil fields where miscible gas is injected. Most of the existing upscaling techniques focus on reproducing the results of a specific geological realization, in a deterministic approach. Nowadays, however, reservoir simulation studies commonly include uncertainty quantifications, which is performed by simulating multiple geological realizations. For that, the use of fine-scale models can be computationally prohibitive and this requires a proper procedure to upscale the coarse-scale simulation models in multiple realizations environment. In this work, we propose and test an ensemble-level upscaling technique for compositional systems with miscible gas injection. The new approach considers the classical Koval factor, calculated for the fine-scale models, as a guide for selecting representative fine-scale models to train pseudo-functions for the coarse-models. Only a few fine models are simulated (about 1%), and the uncertainty quantification process with coarse-scale models can be significantly improved. The proposed workflow is guided by ranking the fine-scale models in increasing order of their Koval Factor. We selected representative models and applied a two-step methodology to improve upscaled coarse-scale results for these models. We then propose a consistent procedure to expand the fitted pseudo-functions to all the coarse models, providing an effective ensemble-level upscaling. The correlation between Koval factor and oil recovery is a useful guide to extrapolate the pseudo-functions obtained for each selected representative model, enabling better coarse-scale simulation results when multiple realizations are considered. This procedure can be applied for continuous miscible gas injection and can be adapted for WAG scheme. This work was motivated by the lack of practical procedures to improve coarse-scale results at the ensemble-level. With our approach, we can better represent uncertainty quantification using coarse-scale models with reduced computational cost and requiring only a few fine-scale simulation runs.

Characterization of naturally fractured reservoirs is complicated. The reservoir model of such reservoirs must represent both fracture and matrix systems and interaction between the two. It is important to choose correct dual continuum model parameters to build the most representative of a fractured reservoir. In this study, we try to improve our understanding of interaction between matrix and fracture and how this can be captured by dual porosity/permeability model. We look at a homogeneous, a simple heterogeneous and a detailed pore-type based heterogeneous model. Fracture act as boundary conditions. First, interaction of forces during various depletion scenarios is studied. Then, oil recovery by gas/water injection is simulated in the fine scale. Dual continium models corresponding to the fine scale models have been built and it has been tried to achieve a good match between fine scale and dual continuum model, by adjusting dual continium model parameters. Observations from this study highlight the importance of capturing the fine scale heterogeneity in fractured reservoir modeling. Furthermore, the ability of reproducing fine scale results, by final simulation model will depend upon selected upscaling/coarsening methodology and how parameters of the coarse scale model are generated/tuned.

A new upscaling technique based on Dykstra–Parsons coefficient: evaluation with streamline reservoir simulation

Geostatistical models of reservoir properties can be hundreds of millions of cells; it is impractical to use them directly in flow simulation due to computational cost. Upscaling techniques are applied to average fine scale permeability values onto coarser flow simulation blocks. In cases where unstructured grids are used or the geology inside the grid block is not aligned with the block geometry, full permeability tensors arise instead of a diagonal tensor. The focus of this work is on development of a method to characterize the full permeability tensor for an unstructured grid block using fine scale heterogeneity information. A single phase flow-based upscaling is performed and a prototype program called ptensor is developed based on the random boundary conditions and optimization technique. Full, symmetric and diagonal permeability tensors are calculated for 2-D and 3-D blocks and sensitivity analysis is performed. Introduction Geostatistical modeling of petrophysical properties can generate fine scale models with hundreds of millions of cells. Using those fine scale models directly in flow simulation is computationally inefficient. Upscaling techniques scale the fine scale models to coarser scale models while preserving the fine scale heterogeneity. A simple averaging is sufficient and reasonable for variables that average linearly; however, in the case of permeability which does not average linearly, a simple arithmetic averaging is inadequate. For complex cases with heterogeneity, flow-based upscaling techniques yield more accurate results (1). In this type of upscaling the flow equation is solved for pressure and the results are used to calculate the block permeability. Commonly unstructured grids are used in order to better capture the flow response near complex reservoir features such as faults and wells. Usually cases that involve the use of irregular block or a heterogeneous permeability field at fine scale require calculation of the full permeability tensor. White and Horne(2) and Gomez-Hernandez(3) proposed different methods to calculate permeability tensor for regular coarse blocks. In recent years, some approaches are presented by Durlofsky(4), Prevost(5) and He(6) to calculate the full permeability tensor for irregular shape grid blocks. This paper introduces a simple, fast and accurate method to calculate full, symmetric or diagonal permeability tensor for any corner point geometry grids. The unstructured grid is surrounded by a bounding box and the geometry is simplified with the fine resolution grid. The steady state flow equation is solved, via finite difference, for the input fine grid cells within a bounding box. The results are used to calculate the permeability tensor of corresponding coarse regular or irregular blocks. Randomly assigned boundary conditions are used and the results are optimized to get the desired full, symmetric or diagonal tensor. Methodology Flow based upscaling is used to calculate effective permeability of coarse block. Consider a single rectangle (2-D) or a cube (3-D) imposed on a fine scale model. The idea here is to calculate the pressure at fine scale with specific boundary conditions applied at the boundary of the coarse block and then use the solution to calculate the full permeability tensor for that coarse block.

In this work, we present an upscaled model for mixed dimensional coupled flow problem in fractured porous media. We consider both embedded and discrete fracture models (EFM and DFM) as fine scale models which contain coupled system of equations. For fine grid discretization, we use a conservative finite-volume approximation. We construct an upscaled model using the non-local multicontinuum (NLMC) method for the coupled system. The proposed upscaled model is based on a set of simplified multiscale basis functions for the auxiliary space and a constraint energy minimization principle for the construction of multiscale basis functions. Using the constructed NLMC-multiscale basis functions, we obtain an accurate coarse grid upscaled model. We present numerical results for both fine-grid models and upscaled coarse-grid models using our NLMC method. We consider model problems with (1) discrete fracture fine grid model with low and high permeable fractures; (2) embedded fine grid model for two types of geometries with differnet fracture networks and (3) embedded fracture fine grid model with heterogeneous permeability. The simulations using the upscaled model provide very accurate solutions with significant reduction in the dimension of the problem.

In simulating enhanced oil recovery processes, it is critical that all the flow behaviors are properly accounted for in the simulation. Due to computation limitations, long calculation time, and complexity of physics, geological models cannot be directly used for field wide simulations. Upgridding reduces the number of grid blocks in the simulation model and hence make the simulation more efficient. An appropriate upgridding process needs to preserve the dynamic behavior of fine scale model. We propose such a methodology. Previous methodologies were based on preservation of variability in the fine scale models. However, those methodologies do not necessarily account for the dynamic flow behavior. Instead, our new methodology is based on preserving the fractional flow character. In upgridding the fine scale model, we have developed a criterion by which the sequence in which the fine scale layers are combined is proposed such that fractional flow characteristics based on fine scale model are honored. Using this methodology, we can not only determine the sequence in which layers are combined, but also, to what extent we can upgrid the fine scale model. The proposed methodology is developed for two-phase, two-dimensional flow under the effect of gravity segregated displacement. However, it is also tested for three-phase, three-dimensional flow in gravity dominated displacement with moderate effect of viscous and capillary forces. The proposed solution is analytical; therefore, computationally efficient. We have validated the methodology using both synthetic and field examples and demonstrate that the proposed methodology is superior to variance based methodologies.

We introduce a pseudoisation method to upscale polymer flooding in order to capture the flow behaviour of fine scale models. This method is also designed to improve the predictability of pressure profiles during this process. This method controls the numerical dispersion of coarse grid models so that we are able to reproduce the flow behaviour of the fine scale model. To upscale polymer flooding, three levels of analysis are required such that we need to honour (a) the fractional flow solution, (b) the water and oil mobility and (c) appropriate upscaling of single phase flow. The outcome from this analysis is that a single pseudo relative permeability set that honours the modification that polymer applies to water viscosity modification without explicitly changing it. The shape of relative permeability can be chosen to honour the fractional flow solution of the fine scale using the analytical solution. This can result in a monotonic pseudo relative permeability set and we call it the Fractional-Flow method. To capture the pressure profile as well, individual relative permeability curves must be chosen appropriately for each phase to ensure the correct total mobility. For polymer flooding, changes to the water relative permeability included the changes to water viscosity implicitly thus avoiding the need for inclusion of a polymer solute. We call this type of upscaling as Fractional-Flow-Mobility control method. Numerical solution of the upscaled models, obtained using this method, were validated against fine scale models for 1D homogenous model and as well as 3D models with randomly distributed permeability for various geological realisations. The recovery factor and water cut matched the fine scale model very well. The pressure profile was reasonably predictable using the Fractional-Flow-Mobility control method. Both Fractional-Flow and Fractional-flow-Mobility control methods can be calculated in advance without running a fine scale model where the analysis is based on analytical solution even though produced a non-monotonic pseudo relative permeability curve. It simplified the polymer model so that it is much easier and faster to simulate. It offers the opportunity to quickly predict oil and water phase behaviour.

Qualified asset management requires optimum re-development scheme to the matured fields applying IOR options. The keys for successful re-development planning are to evaluate the uncertainty of the reservoir properties and how to integrate technology available in the reservoir simulation study targeting realistic flow modeling. A reservoir re-development scheme was formulated for a highly heterogeneous limestone reservoir which has production history for more than 35 years. Systematic approach was made to improve the accuracy of the reservoir simulation model when water or associated gas injection was considered. The uncertainty range of the reservoir rock properties was first investigated to assess the past reservoir practice. Then, the evaluation of the gas injection was performed with high resolution reservoir simulation. After examining PVT properties, discussions were made to preserve the fluid flow characteristics in the heterogeneous reservoir on the coarse gridded flow simulation model, which was up-scaled from the fine scale model realized by the geostatistical approach. The grid block size was carefully selected by a number of numerical experiments to simulate the heterogeneous nature. The impact of the up-scaled vertical permeability on the gas injection performance was also evaluated. The 3D-flow based up-scaling technique for near-well region was examined in order to simulate the horizontal well performance in the reservoir scale simulation model. It was concluded thatthe rigid IOR assessment was achieved presenting superior performance of gas injection than that of water injection through high resolution reservoir simulation, thatthe application of streamline method for evaluating vertical permeability of up-scaled grid made well-preserved heterogeneity in the fine scale model and thatThe 3D well model for horizontal well is required only when the duration of the displacement front advancement in near well region significantly exceeds the time step size. Introduction The Khafji Oil Field is situated in the offshore neutral zone between the Kingdom of Saudi Arabia and the State of Kuwait. The studied limestone reservoir in the field has been producing heavy crude oil for more than 35 years. Since the reservoir has little natural support of driving energy noticed by the sharp decline of its pressure, IOR application is essential for efficient reservoir development. This paper describes the systematic approach to improve the reliability of numerical reservoir simulation for the IOR assessment. Recently, intensive geological and reservoir engineering studies were carried out to clarify the reservoir nature, and the results were integrated into a fine scale geostatistical model and a coarse grid flow simulation model. The geostatistical model satisfactorily described the spatial distribution of the petrophysical characteristics, and the up-scaled flow simulation model adequately reproduced the past reservoir performances. 1 However, when the reservoir development scheme with IOR is adopted, the reservoir is going to encounter at the extreme pressure / saturation conditions which have never happened in the past production history. Modeled reservoir elements which may affect the simulation results should be examined and re-evaluated to assure the reliability of prediction.

Well data reveal reservoir layering with relatively high vertical resolution but are areally sparse, whereas seismic data have low vertical resolution but are areally dense. Improved reservoir models can be constructed by integrating these data. The proposed method combines stochastic seismic inversion, finer-scale well data, and geologic continuity models to build ensembles of geomodels. Stochastic seismic inversions operating at the mesoscale (≈10 m) generate rock property estimates that are consistent with regional rock physics and true-amplitude imaged seismic data. These can be used in a cascading workflow to generate ensembles of fine-scale reservoir models, wherein each realization from the Bayesian seismic inversion is treated as an exact constraint for an associated finer scale stochastic model. We use two-point statistical models for the fine-scale model, modeling thickness and porosity of multiple facies directly. The update of these fine-scale models by the seismic constraints yields highly correlated truncated Gaussian distributions. These generate potentially rich pinchout behavior and flexible spatial connectivities in the fine scale model. The seismic constraints confine the fine-scale models to a posterior subspace corresponding to the constraint hypersur-face. A Markov Chain Monte Carlo samples the posterior distribution in this subspace using projection methods that exploit the reduced dimensionality that comes with the exact constraints. These methods are demonstrated in three-dimensional flow simulations on a cornerpoint grid, illustrating the effects of stratigraphic variability on flow behavior.