Combining Gradual Deformation and Upscaling Techniques for Direct Conditioning of Fine Scale Reservoir Models to Dynamic Data

Summary Reconciling multiscale data for reservoir characterization is a crucial issue, because different data types provide different information about the reservoir architecture and heterogeneity. It is essential that reservoir models preserve small-scale property variations observed in well logs and core measurements and capture the large-scale structure and continuity observed in global measures such as well-test and production data. 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. As consequence, both fine- and coarse-scale models are updated by dynamic data during the history matching process. 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. Fluid-flow simulation and 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 characterization process by integrating permanent downhole gauge measurements directly into a 3D-geostatistical model containing about two million gridblocks. 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 history matching. 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 process by integrating dynamic data at both fine geostatistical scale and coarse simulation scale.

In order to run reservoir simulation efficiently, a coarse scale (CS) dynamic model is created by upscaling of a fine scale (FS) static model. All history match (HM) changes usually done in the CS dynamic model need to be downscaled to FS for geological justifications and consistency maintenance between the FS static and CS dynamic models. This paper proposes a robust downscaling method for integration of FS static and CS dynamic models. The proposed method downscales a HMDM (dynamic model) to HMSM (static) in multiple steps. Scale-up the ISM (initial) to CS to create an IDM. Identify the cell changes between HMDM and IDM, and transfer the changes to FS to create a MSM (modified). Scale-up the MSM to CS to create to a MDM and calculate the ratios between HMDM and MDM for all cell properties. Transfer the ratios to FS to create a HMSM. Scale-up the HMSM to CS to confirm its identity to the HMDM. Selection of sampling and zone mapping methods is critical in all steps. The proposed method has been successfully applied in a giant carbonate oil field in the Caspian Sea that consists of a matrix dominated platform and a fracture/karst dominated rim. Due to the field's complex geology and high H2S content (15%), a dual porosity, dual permeability compositional model has been created to model compositional sour crude flow within/between matrix and fracture/karst. The FS static model contains a 236m × 236m horizontal grid with 593 layers while the CS dynamic model has the horizontal cell sizes in a range of 236m to 944m with 73 layers. Rock regions, permeability, and reservoir connectivity in the CS dynamic model were calibrated using the field historical production data (e.g., static pressure, PLT, interference test, and GOR/water-cut data) to create a HMDM. Since the HM process was performed only in the CS dynamic model, the FS static model and HMDM became inconsistent. Appling the proposed downscaling method has helped the HM team to resolve this issue and resulted in a seamless link between the FS static and CS dynamic models for current and future HM and model updates.

With the advance of CPU power, numerical reservoir models have become an essential part of most reservoir engineering applications. These models are used for predicting future performances or determining optimal locations of infill wells. Hence in order to accurately predict, these reservoir models must be conditioned to all available data. The challenge in data integration for numerical reservoir models lies in the fact that each data has its own resolution and area of coverage. The most common data for reservoir characterization are; well-log/core data, seismic data and production data. Most current approaches to data integration are hierarchical. Fine scale models are used for integrating well-log/core and seismic data while coarse models are used to integrate mostly production data. The drawback of such a hierarchical approach is such that once the scale is changed, data conditioning, maintained in the previous scale, is lost. In this paper, we review a general algorithm as a solution to the multi-scale data integration. Instead of proceeding in a hierarchical fashion, a fine model and a coarse model is kept in parallel throughout the entire characterization process. The link between the fine scale and the coarse scale is provided by non-uniform upscaling. An optimization procedure determines the optimal gridding parameters that provide the smallest possible mismatch between fine and coarse scale reservoir models. A synthetic example application is given and demonstration of the methodology. The upgridding is accomplish by a static gridding algorithm, 3DDEGA. This algorithm aims at preserving geology by minimizing heterogeneity within a coarse grid block. The coarse grids are provided in a corner-point geometry fashion, hence this allows for accurate description of the reservoir with fewer number of grid blocks.

Novel permeability upscaling method using Fast Marching Method

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 addition to seismic and well constraints, production data must be integrated into geostatistical reservoir models for reliable reservoir performance predictions. An iterative inversion algorithm is required for such integration and is usually computationally intensive since forward flow simulation must be performed at each iteration. This paper presents an efficient approach for generating fine-scale three dimensional (3D) reservoir models that are conditioned to multiphase production data by combining a recently developed streamline-based inversion technique with a geostatistical downscaling algorithm. Production data can not reveal fine scale details of reservoir heterogeneity. By solving the streamline pressure solution at a coarse scale consistent with the production data we are able to invert numerous geostatistical realizations. Additionally, the streamline method allows fine resolution along the 1D streamlines independent of the coarse grid pressure solution so we do not need to explicitly address multiphase scale-up. Multiple geostatistical fine scale models are up-scaled to a coarse scale used in the inversion process. After inversion, the models are each geostatistically downscaled to multiple fine scale realizations. These fine scale models are now preconditioned to the production data and can be up-scaled to any scale for final flow simulation. A 3D extension of the prior 2D sequential-self calibration method (SSC) is developed for the inversion step. This method updates the coarse models to match production data while preserving as much of geostatistical constraint as possible. A new geostatistical algorithm is developed for the downscaling step. We use Sequential Gaussian Simulation with either block kriging or Bayesian updating to "downscale" the history-matched coarse scale models to fine-scale models honoring fine-scale spatial statistics. Combining these two developments we are able to efficiently generate multiple fine scale geostatistical models constrained to well and production data.

Time-lapse seismic provides a source of valuable information about the evolution in space and time of the distribution of hydrocarbons inside reservoirs. Seismic monitoring improves our understanding of production mechanisms and makes it possible to optimize the recovery of hydrocarbons. Although 4D seismic data are increasingly used by oil companies, they are often qualitative, due to the lack of suitable interpretation techniques.Recent modeling experiments have shown that the integration of 4D seismic data for updating reservoir flow models is feasible. However, methodologies based on sequential interpretation of 4D seismic data, trial and error processes and fluid flow simulation tests require a great effort from integrated teams. The development of assisted history matching techniques is a significant improvement towards a quantitative use of 4D seismic data in reservoir modeling.This paper proposes an innovative methodology based on advanced history matching solutions to constrain 3D stochastic reservoir models to both production history and 4D seismic attributes. In this approach, geostatistical modeling, upscaling, fluid flow simulation, downscaling and petro-elastic modeling are integrated into the same history matching workflow. Simulated production history and 4D seismic attributes are compared to real data using an objective function, which is minimized with a new optimization algorithm based on response surface fitting. The gradual deformation method is used to constrain the facies realization, globally or locally, which populates the geological model at the fine scale. Moreover, a new method is proposed to update facies proportions during the optimization process according to 4D monitoring information.We present here a successful application to the Girassol field. Girassol is a large, complex and faulted turbidite field, located offshore Angola. First, a detailed geostatistical geological model was built to describe reservoir heterogeneity at the fine scale, while respecting 3D base seismic data. Second, the model was constrained to production data and 4D seismic attributes, applying gradual deformation to facies realizations and varying facies proportions. The integration of 4D seismic data led to better production forecasts and improved predictions confirmed by a new seismic survey shot two years after the history matching period. 4D seismic data also contributed to better characterize the spatial distribution of heterogeneities in the field. As a result, the fine scale geological model was improved consistently with respect to the fluid flow simulation model and the observed data. The Girassol study, already presented in (Roggero et al., 2007, 2008), has been updated with recent information and a more detailed presentation concerning the construction of the geological model based on 3D seismic data.

Upscaling of polymer adsorption

History matching of 4D seismic and well production data has been developed recently for reservoir characterization. This is a data driven optimization process to derive reservoir model parameters and constitutes a joint inverse problem. Considering the inherent non‐uniqueness in the inverse problem and the unique feature of Bayesian inference in data integration and uncertainty analysis, this joint inverse problem is formulated in a Bayesian framework and solved stochastically by reconstructing the posterior probability density (PPD) surface using a new multi‐scale Markov Chain Monte Carlo (MCMC) algorithm. In this new MCMC method, a technique of multi‐scaling is used to take advantage of the benefits from both the fine scale model and the coarse scale model. Although the coarse scale does not provide reliable information about the model, it helps speed up the convergence of the fine scale model to a good estimation, and, by exchanging information between the fine and coarse scales, works like a regularization operator to smooth the fine scale model and make it more realistic. The resulting PPD samples can also be used to quantify corresponding uncertainties in order to facilitate risk assessment associated with reservoir decision making and management. We use a numerical example to demonstrate how we derive reservoir's static and dynamic properties as well as quantify uncertainties in a Bayesian framework using the multi‐scale MCMC algorithm.

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.

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.

Geo-cellular model contains millions of grid blocks and needs to be up-scaled before the model can be used as an input for flow simulation. Available techniques for upgridding vary from simple methods such as proportional fractioning to more complicated methods such as maintaining heterogeneities through variance calculations. All these methods are independent of the flow process for which simulation is going to be used, and are independent of well configuration. We propose a new upgridding method which preserves the pressure profile at the upscaled level. It is well established that more complex the flow process, more the detailed level of heterogeneity is needed in simulation model. In general, ideal upscaling is the process which preserves the "pressure profile" from the fine scale model under the applicable flow process. In our method we upgrid the geological model using simple flow equations in porous media. However, it should be remembered that to get a better match between fine scale and coarse scale, we also need to use appropriate upscaling of the reservoir properties. The new methodology is currently developed for single phase flow; however, we used it for both single phase and two phase flows for 2D and 3D cases. The methodology fundamentally differs from the other methods which try to preserve heterogeneities. In those methods, grid blocks are combined which have similar velocities (or other properties) by assuming constant pressure drop across the blocks. Instead, we combine the grid blocks which have similar pressure profiles. The procedure is analytical and hence very efficient, but preserves the pressure profile in the reservoir. The grid blocks (or layers) are combined in a way so that the difference between fine scale and coarse scale pressure profiles is minimized. In addition, we also propose two new criteria that allow us to choose the optimum number of the layers more accurately so that critical level of heterogeneity is preserved. These criteria provide insight into the overall level of heterogeneity in the reservoir as well as effectiveness of the layering design. We compare the results of our method with proportional layering and King et al.'s method (King 2005) and show that, for the same number of layers, the proposed method better captures the results of the fine scale model. We show that the layer merging not only depends on the variation in the permeability between the grid blocks, but also on relative magnitude of the permeability values. We also show that new method can account for additional variables such as grid block thicknesses and the size.

The use of upscaling prior to reservoir simulation studies is a common practice, because of the prohibitively high cost of performing high resolution, full-field simulations. In fact, the resolution of the grid may be also limited by the capabilities of the hardware. Invariably, upscaling is undertaken without consideration of the degree of connectivity of the reservoir to the wellbore A new technique is presented in which the discretized fine scale reservoir description is screened using a reservoir connectivity measure prior to performing the upscaling and the theory is presented to validate its appropriateness and accuracy for upscaling reservoirs in which the reservoir connectivity is less than 100%. The new upscaling approach is applied to a gas reservoir system. Traditional upscaling techniques, such as a pressure solver, are also applied to the fine scale reservoir description and the different sets of upscaled grids are flow simulated — along with the fine scale description. The results of this new upscaling approach are shown to be significantly more accurate in providing an upscaled grid system which more closely approximates the simulation behavior of the fine scale grid. This methodology has been shown to be applicable to the case of primary recovery from gas reservoirs and, while it has not been tested with more complex recovery mechanisms such as waterflooding, the theory is robust enough that it should be generally applicable as an upscaling technique in which reservoir connectivity is an issue. Introduction With current technology and with the much-acclaimed multidisciplinary reservoir management approach, it is now possible to integrate geophysical, geological and reservoir engineering data through geostatistical modeling to create multiple detailed or fine scale reservoir descriptions which honor all these diverse conditioning data sets. These descriptions, insofar as they honor the conditioning data and their statistics, may be considered representative of the underlying reality of the reservoir under study. The objective of creating these descriptions is usually for developing bounds on the uncertainty of the future performance of the reservoir. The accepted methodology for measuring the reservoir performance is the flow simulator. Unfortunately, as alluded to above, this technology is still limited in its capabilities, such that the geostatistical descriptions are typically too large to be easily flow simulated. Table 1 illustrates quite clearly the justification for the use of upscaling: there is a limit on the number of gridblocks we may use for flow simulation for a given computer hardware configuration. Hence there is a need for representative upscaling; i.e. upscaling such that the coarse scale description behaves closely to that of the fine scale one. In a reservoir which is 100% connected, connectivity (defined below) is not an issue in the upscaling Should the reservoir be less than completely connected however, then it becomes important to factor in connectivity into the upscaling Several authors have acknowledged the importance of connectivity in reservoir performance. Alabert and Massonnat have noted that the connectivity of permeable rocks is of major concern for field exploitation and performance forecasting. Thus careful and realistic modeling of connectivities is required to plan future developments, understand and forecast well behaviors and to improve oil recovery. Handyside et al. concurred by stating that an assessment of the impact of sand discontinuities or connectivities in the reservoirs is required for realistic performance predictions and estimation of associated P. 249^

New upgridding method to capture the dynamic performance of the fine scale heterogeneous reservoir

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.