ECMOR IX - 9th European Conference on the Mathematics of Oil Recovery
ABSTRACT Subsurface flows are affected by permeability heterogeneity over a range of length scale... more ABSTRACT Subsurface flows are affected by permeability heterogeneity over a range of length scales. It is difficult to fully resolve all of the scales that impact flow and transport through such systems, so models for subgrid effects are often required. In this work, new methods for the coarse scale modeling of flow (i.e., total flow rate for specified wellbore pressures) and transport (movement of injected fluid) in highly heterogeneous deterministic systems are described and applied. The technique for the improved upscaling of flow, referred to as adaptive local-global upscaling, efficiently provides coarse scale transmissibilities (transmissibility is the numerical analog of permeability) that are adapted to a specific flow scenario. Global coarse scale simulations are used to determine the boundary conditions for the local calculation of upscaled properties and a thresholding procedure is introduced for efficiency and to minimize the appearance of spurious transmissibility values. A specialized near-well upscaling is included naturally in the procedure and transmissibilities can be efficiently recomputed when new wells are introduced. The method is applied to both 2D and 3D systems and its improved accuracy over existing procedures is demonstrated. The adaptive local-global transmissibility upscaling is then combined with models for transport. Two approaches are considered for the transport problem. First, a multiscale (dual-grid) technique is presented, in which the fine scale velocity, reconstructed from the coarse scale pressure solution, is used for the solution of advective contaminant transport on the fine scale. This approach provides excellent accuracy but it requires that two grids be used for the simulation. A new generalized convection-diffusion model for transport (so named because of the form of the subgrid terms), in which both flow and transport (single-phase or two-phase) are solved on the coarse grid, is described next. The method is shown to provide significantly improved results compared to those attainable with standard procedures. It is also shown to be well-suited to difficult problems in which well rates or locations change in time.
2006 IEEE International Conference on Evolutionary Computation, 2006
Abstract Geostatistical modeling is a widely used approach to model the heterogeneity of reservo... more Abstract Geostatistical modeling is a widely used approach to model the heterogeneity of reservoir petrophysical prop-erties. This paper investigates a geostatistical-based inversion technique, a hybrid of sequential-self calibration (SSC) and genetic algorithm (GA), to ...
SPE Annual Technical Conference and Exhibition, 2004
Reconciling high-resolution geologic models to production history is a very time-consuming proces... more Reconciling high-resolution geologic models to production history is a very time-consuming process in reservoir modeling. Current practice still involves a tedious history-matching process that is highly subjective and often employs ad-hoc property multipliers. Recently streamline models have shown significant promise in improving the history matching process. In particular, the streamline-based "assisted history-matching" utilizes the streamline trajectories to identify and limit changes only to the regions contributing to the well production history. It is now a well-established procedure and has been applied successfully to numerous field cases. In this paper, we enhance the streamline-based assisted history matching in two important aspects that can significantly improve its efficiency and effectiveness. First, we utilize streamline-derived analytic sensitivities to determine the spatial distribution and magnitude of the changes needed to improve the history match. Sec...
SPE Annual Technical Conference and Exhibition, 1998
Generation of a reservoir model's spatial permeability distribution directly from historical ... more Generation of a reservoir model's spatial permeability distribution directly from historical multiple-well pressure and fractional flow rate data requires an inverse solution of the flow equations. This computation generally utilizes a gradient method to solve the minimization problem. A previously reported geostatistically-based inverse sequential self-calibration (S SC) technique has been shown to significantly reduce the computer time as compared to full inversion solutions and to yield excellent results for single-phase pressure. In this paper we extend the SSC to jointly invert multiple well pressure and multiphase fractional flow data by:adapting a fast streamline simulator for the forward flow solution; andimplementing a new method for computing the sensitivity coefficients for fractional flow rate. The method is fast and robust, and an important consequence of the method is that the spatial correlation structure is honored through the kriging equations in the SSC. This l...
The sequential-self calibration (SSC) method is a geostatistical-based inverse technique that all... more The sequential-self calibration (SSC) method is a geostatistical-based inverse technique that allows fast integration of dynamic production data into geostatistical models. In this paper, we replace the gradient-based optimization in SSC by genetic algorithms (GA). GA, without requiring sensitivity, searches for global minimum. Although GA is computationally intensive, it provides significant flexibility to study parameters whose sensitivities are difficult to compute, e.g., master point locations. A steady-state GA is implemented under the SSC framework for searching the optimal master point locations, as well as the associated optimal perturbations that match the observed pressure, water cut and saturation data. We demonstrate that GA is easy to implement and results are robust. We examine different approaches of selecting master point locations including fixed, stratified random, and purely random methods. Results from this study demonstrate that there are not clear preferential master point locations that are best suited for matching production data for the given well pattern and for the given initial model. This is consistent with the early findings that master point locations can be randomly selected with the stratified random method yielding the best results due to its flexibility and good control for the overall model.
From reservoir exploration to field abandonment, reservoir modeling plays a central role in under... more From reservoir exploration to field abandonment, reservoir modeling plays a central role in understanding and predicting the reservoir key geologic, geophysical, and engineering components. Reservoir models, either as a simple layer cake or as a complex, fully 3D description of structural ...
A high-resolution stratigraphic image of a flume-generated deposit was scaled up to sedimentary b... more A high-resolution stratigraphic image of a flume-generated deposit was scaled up to sedimentary basin dimensions where a natural log hydraulic conductivity (ln(K)) was assigned to each pixel on the basis of gray scale and conductivity end-members. The synthetic ln(K) map has mean, variance, and frequency distributions that are comparable to a natural alluvial fan deposit. A geostatistical analysis was conducted on selected regions of this map containing fluvial, fluvial/floodplain, shoreline, turbidite, and deepwater sedimentary facies. Experimental ln(K) variograms were computed along the major and minor statistical axes and horizontal and vertical coordinate axes. Exponential and power law variogram models were fit to obtain an integral scale and Hausdorff measure, respectively. We conclude that the shape of the experimental variogram depends on the problem size in relation to the size of the local-scale heterogeneity. At a given problem scale, multilevel correlation structure is a result of constructing variogram with data pairs of mixed facies types. In multiscale sedimentary systems, stationary correlation structure may occur at separate scales, each corresponding to a particular hierarchy; the integral scale fitted thus becomes dependent on the problem size. The Hausdorff measure obtained has a range comparable to natural geological deposits. It increases from nonstratified to stratified deposits with an approximate cutoff of 0.15. It also increases as the number of facies incorporated in a problem increases. This implies that fractal characteristic of sedimentary rocks is both depositional process-dependent and problem-scale-dependent.
SELECTIVE UPSCALING OF HYDRAULIC CONDUCTIVITIES XIAN-HUAN WEN AND J. JAIME GOMEZ-HERNANDEZ Depart... more SELECTIVE UPSCALING OF HYDRAULIC CONDUCTIVITIES XIAN-HUAN WEN AND J. JAIME GOMEZ-HERNANDEZ Department of Hydraulic and Environmental Engineering Polytechnic University of Valencia, 46071 Valencia, Spain Abstract A new numerical approach, called ...
A geostatistically-based sequential self-calibration (SSC) method is applied to enhance the estim... more A geostatistically-based sequential self-calibration (SSC) method is applied to enhance the estimation of conductivity field by conditioning on tracer test data, which contains, arguably, the most important information about the aquifer properties related to solute transport, particularly, the information about the high K flow channels embedded within the aquifer. A gradient-based technique, which requires the sensitivity coefficients of the concentrations
ECMOR IX - 9th European Conference on the Mathematics of Oil Recovery
ABSTRACT Subsurface flows are affected by permeability heterogeneity over a range of length scale... more ABSTRACT Subsurface flows are affected by permeability heterogeneity over a range of length scales. It is difficult to fully resolve all of the scales that impact flow and transport through such systems, so models for subgrid effects are often required. In this work, new methods for the coarse scale modeling of flow (i.e., total flow rate for specified wellbore pressures) and transport (movement of injected fluid) in highly heterogeneous deterministic systems are described and applied. The technique for the improved upscaling of flow, referred to as adaptive local-global upscaling, efficiently provides coarse scale transmissibilities (transmissibility is the numerical analog of permeability) that are adapted to a specific flow scenario. Global coarse scale simulations are used to determine the boundary conditions for the local calculation of upscaled properties and a thresholding procedure is introduced for efficiency and to minimize the appearance of spurious transmissibility values. A specialized near-well upscaling is included naturally in the procedure and transmissibilities can be efficiently recomputed when new wells are introduced. The method is applied to both 2D and 3D systems and its improved accuracy over existing procedures is demonstrated. The adaptive local-global transmissibility upscaling is then combined with models for transport. Two approaches are considered for the transport problem. First, a multiscale (dual-grid) technique is presented, in which the fine scale velocity, reconstructed from the coarse scale pressure solution, is used for the solution of advective contaminant transport on the fine scale. This approach provides excellent accuracy but it requires that two grids be used for the simulation. A new generalized convection-diffusion model for transport (so named because of the form of the subgrid terms), in which both flow and transport (single-phase or two-phase) are solved on the coarse grid, is described next. The method is shown to provide significantly improved results compared to those attainable with standard procedures. It is also shown to be well-suited to difficult problems in which well rates or locations change in time.
2006 IEEE International Conference on Evolutionary Computation, 2006
Abstract Geostatistical modeling is a widely used approach to model the heterogeneity of reservo... more Abstract Geostatistical modeling is a widely used approach to model the heterogeneity of reservoir petrophysical prop-erties. This paper investigates a geostatistical-based inversion technique, a hybrid of sequential-self calibration (SSC) and genetic algorithm (GA), to ...
SPE Annual Technical Conference and Exhibition, 2004
Reconciling high-resolution geologic models to production history is a very time-consuming proces... more Reconciling high-resolution geologic models to production history is a very time-consuming process in reservoir modeling. Current practice still involves a tedious history-matching process that is highly subjective and often employs ad-hoc property multipliers. Recently streamline models have shown significant promise in improving the history matching process. In particular, the streamline-based "assisted history-matching" utilizes the streamline trajectories to identify and limit changes only to the regions contributing to the well production history. It is now a well-established procedure and has been applied successfully to numerous field cases. In this paper, we enhance the streamline-based assisted history matching in two important aspects that can significantly improve its efficiency and effectiveness. First, we utilize streamline-derived analytic sensitivities to determine the spatial distribution and magnitude of the changes needed to improve the history match. Sec...
SPE Annual Technical Conference and Exhibition, 1998
Generation of a reservoir model's spatial permeability distribution directly from historical ... more Generation of a reservoir model's spatial permeability distribution directly from historical multiple-well pressure and fractional flow rate data requires an inverse solution of the flow equations. This computation generally utilizes a gradient method to solve the minimization problem. A previously reported geostatistically-based inverse sequential self-calibration (S SC) technique has been shown to significantly reduce the computer time as compared to full inversion solutions and to yield excellent results for single-phase pressure. In this paper we extend the SSC to jointly invert multiple well pressure and multiphase fractional flow data by:adapting a fast streamline simulator for the forward flow solution; andimplementing a new method for computing the sensitivity coefficients for fractional flow rate. The method is fast and robust, and an important consequence of the method is that the spatial correlation structure is honored through the kriging equations in the SSC. This l...
The sequential-self calibration (SSC) method is a geostatistical-based inverse technique that all... more The sequential-self calibration (SSC) method is a geostatistical-based inverse technique that allows fast integration of dynamic production data into geostatistical models. In this paper, we replace the gradient-based optimization in SSC by genetic algorithms (GA). GA, without requiring sensitivity, searches for global minimum. Although GA is computationally intensive, it provides significant flexibility to study parameters whose sensitivities are difficult to compute, e.g., master point locations. A steady-state GA is implemented under the SSC framework for searching the optimal master point locations, as well as the associated optimal perturbations that match the observed pressure, water cut and saturation data. We demonstrate that GA is easy to implement and results are robust. We examine different approaches of selecting master point locations including fixed, stratified random, and purely random methods. Results from this study demonstrate that there are not clear preferential master point locations that are best suited for matching production data for the given well pattern and for the given initial model. This is consistent with the early findings that master point locations can be randomly selected with the stratified random method yielding the best results due to its flexibility and good control for the overall model.
From reservoir exploration to field abandonment, reservoir modeling plays a central role in under... more From reservoir exploration to field abandonment, reservoir modeling plays a central role in understanding and predicting the reservoir key geologic, geophysical, and engineering components. Reservoir models, either as a simple layer cake or as a complex, fully 3D description of structural ...
A high-resolution stratigraphic image of a flume-generated deposit was scaled up to sedimentary b... more A high-resolution stratigraphic image of a flume-generated deposit was scaled up to sedimentary basin dimensions where a natural log hydraulic conductivity (ln(K)) was assigned to each pixel on the basis of gray scale and conductivity end-members. The synthetic ln(K) map has mean, variance, and frequency distributions that are comparable to a natural alluvial fan deposit. A geostatistical analysis was conducted on selected regions of this map containing fluvial, fluvial/floodplain, shoreline, turbidite, and deepwater sedimentary facies. Experimental ln(K) variograms were computed along the major and minor statistical axes and horizontal and vertical coordinate axes. Exponential and power law variogram models were fit to obtain an integral scale and Hausdorff measure, respectively. We conclude that the shape of the experimental variogram depends on the problem size in relation to the size of the local-scale heterogeneity. At a given problem scale, multilevel correlation structure is a result of constructing variogram with data pairs of mixed facies types. In multiscale sedimentary systems, stationary correlation structure may occur at separate scales, each corresponding to a particular hierarchy; the integral scale fitted thus becomes dependent on the problem size. The Hausdorff measure obtained has a range comparable to natural geological deposits. It increases from nonstratified to stratified deposits with an approximate cutoff of 0.15. It also increases as the number of facies incorporated in a problem increases. This implies that fractal characteristic of sedimentary rocks is both depositional process-dependent and problem-scale-dependent.
SELECTIVE UPSCALING OF HYDRAULIC CONDUCTIVITIES XIAN-HUAN WEN AND J. JAIME GOMEZ-HERNANDEZ Depart... more SELECTIVE UPSCALING OF HYDRAULIC CONDUCTIVITIES XIAN-HUAN WEN AND J. JAIME GOMEZ-HERNANDEZ Department of Hydraulic and Environmental Engineering Polytechnic University of Valencia, 46071 Valencia, Spain Abstract A new numerical approach, called ...
A geostatistically-based sequential self-calibration (SSC) method is applied to enhance the estim... more A geostatistically-based sequential self-calibration (SSC) method is applied to enhance the estimation of conductivity field by conditioning on tracer test data, which contains, arguably, the most important information about the aquifer properties related to solute transport, particularly, the information about the high K flow channels embedded within the aquifer. A gradient-based technique, which requires the sensitivity coefficients of the concentrations
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