Xian-Huan Wen

A Coupled Local-Global Upscaling Approach for Simulating Flow in Highly Heterogeneous Formations

A new technique for generating coarse scale models of highly heterogeneous subsurface formations is developed and applied. The method uses generic global coarse scale simulations to determine the boundary conditions for the local calculation of upscaled properties (permeability or transmissibility). An iteration procedure assures consistency between the local and global calculations. Transport processes are simulated using a subgrid velocity reconstruction technique applied in conjunction with the local-global upscaling procedure. For highly heterogeneous (e.g., channelized) systems, the new method is shown to provide considerably more accurate coarse scale models for flow and transport, relative to reference fine scale results, than do existing local (and extended local) upscaling techniques. The applicability of the upscaled models for dierent global boundary conditions is also considered.

Computing permeability of fault zones in eolian sandstone from outcrop measurements

The large-scale equivalent permeabilities of strike-slip faults in porous sandstone are computed from detailed field measurements. The faults, which occur in the Valley of Fire State Park, Nevada, were previously characterized, and the flow properties of their individual features were estimated. The faults formed from the shearing of joint zones and are composed of a core of fine-grain fault rock (gouge) and deformation bands and a peripheral damage zone of joints and sheared joints. High-resolution fault-zone maps and permeability data, estimated using image analysis calibrated to actual measurements, are incorporated into detailed finite difference numerical calculations to determine the permeability of regions of the fault zone. Faults with slips of magnitude 6, 14, and 150 m are considered. The computed fault-zone permeabilities are strongly anisotropic in all cases. Permeability enhancement of nearly 1 order of magnitude (relative to the host rock) is observed for the fault-parallel component in some regions. Fault-normal permeability, by contrast, may be 2 orders of magnitude less than the host rock permeability. The fault-normal permeability is a minimum for the fault with the highest slip. For a representative fault region, the fault-parallel component of permeability is highly sensitive to the fracture aperture, although the fault-normal permeability is insensitive. The procedures developed and applied in this article can be used for any type of fault for which detailed structural and permeability data are available or can be estimated.

Use of Border Regions for Improved Permeability Upscaling

A procedure for the improved calculation of upscaled grid block permeability tensors on Cartesian grids is described and applied. The method entails the use of a border region of fine-scale cells surrounding the coarse block for which the upscaled permeability is to be computed. The implementation allows for the use of full-tensor permeability fields on the fine and coarse scales. Either periodic or pressure–no flow boundary conditions are imposed over the extended local domain (target block plus border regions) though averaged quantities, used to compute the upscaled permeability tensor, are computed only over the target block region. Flow and transport results using this procedure are compared to those from standard methods for different types of geological and simulation models. Improvement using the new approach is consistently observed for the cases considered, though the degree of improvement varies for different models and flow quantities.

Upscaling of Channel Systems in Two Dimensions Using Flow-Based Grids

A methodology for the gridding and upscaling of geological systems characterized by channeling is presented. The overall approach entails the use of a flow-based gridding procedure for the generation of variably refined grids capable of resolving the channel geometry, a specialized full-tensor upscaling method to capture the effects of permeability connectivity, and the use of a flux-continuous finite volume method applicable to full tensor permeability fields and non-orthogonal grids. The gridding and upscaling procedures are described in detail and then applied to several two-dimensional systems. Significant improvement in the accuracy of the coarse scale models, relative to that obtained using uniform Cartesian coarse scale models, is achieved in all cases. It is shown that, for some systems, improvement results from the use of the flow-based grid, while in other cases the improvement is mainly due to the new upscaling method.

Probabilistic assessment of travel times in groundwater modeling

A Monte Carlo approach is described for the quantification of uncertainty on travel time estimates. A real (non synthetic) and exhaustive data set of natural genesis is used for reference. Using an approach based on binary indicators, constraint interval data are easily accommodated in the modeling process. It is shown how the incorporation of imprecise data can reduce drastically the uncertainty in the estimates. It is also shown that unrealistic results are obtained when a deterministic modeling is carried out using a kriging estimate of the transmissivity field. Problems related with using sequential indicator simulation for the generation of fields incorporating constraint interval data are discussed. The final results consists of 95% probability intervals of arrival times at selected control planes reflecting the original uncertainty on the transmissivity maps.

Field Experiences with Assisted and Automatic History Matching Using Streamline Models

Reconciling high-resolution geologic models to production history is a very time-consuming process in reservoir modeling. Current practice still involves a tedious historymatching 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 historymatching” 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. Second, we use a “generalized travel time inversion (GTTI)” for model updating via an iterative minimization procedure. Using this approach, we can account for the full coupling of the streamlines rather than changing individual or bundles of streamlines at a time. The approach is more akin to automatic history matching. However, by intervening at every step in the iterative model updating, we can retain control over the process as in assisted history matching. Our approach leads to significant savings in time and manpower during field-scale history matching. We demonstrate the power of our method using two field examples with model sizes ranging from 10 5 to 10 6 grid blocks and with over one hundred wells. The reservoir models include faults, aquifer support and several horizontal/high angle wells. History matching is performed using both assisted history matching and the GTTI. Whereas the general trends in permeability changes are similar for both the methods, the GTTI seems to significantly improve the water cut history matching on a well-by-well basis within a few iterations. Our experience indicates that the GTTI can also be used very effectively to improve the quality of history match derived from the assisted history matching. The changes to the reservoir model from GTTI are found reasonable with no artificial discontinuities or apparent loss of geologic realism.

Production Data Integration in Sand/Shale Reservoirs Using Sequential Self-Calibration and GeoMorphing: A Comparison

The stochastic inversion of spatial distribution of lithofacies from multiphase production data is a difficult problem. This is true even for the simplest case, addressed here, of a sand/shale distribution and under the assumption that reservoir properties are constant within each lithofacies. Two geostatistically based inverse techniques, sequential self-calibration (SSC) and GeoMorphing (GM), are extended for such purposes and then compared with synthetic reference fields. The extension of both techniques is based on the one-to-one relationship existing between lithofacies and Gaussian deviates in truncated Gaussian simulation. Both techniques attempt to modify the field of Gaussian deviates while maintaining the truncation threshold field through an optimization procedure. Maintaining a fixed threshold field, which has been computed previously on the basis of prior lithofacies proportion data, well data, and other static soft data, guarantees preservation of the initial geostatistical structure. Comparisons of the two techniques using 2D and 3D synthetic data show that the SSC is very efficient in producing sand/shale realizations matching production data and reproducing the large-scale patterns displayed in the reference fields, although it has difficulty in reproducing small-scale features. GM is a simpler algorithm than SSC, but it is computationally more intensive and has difficulty in matching complex production data. Better results could be obtained with a combination of the two techniques in which SSC is used to generate realizations identifying large-scale features; then, these realizations could be used as input to GM for a final update to match small-scale details.

Integrating Large-Scale Soft Data by Simulated Annealing and Probability Constraints

Interpretation of geophysical data or other indirect measurements provides large-scale soft secondary data for modeling hard primary data variables. Calibration allows such soft data to be expressed as prior probability distributions of nonlinear block averages of the primary variable; poorer quality soft data leads to prior distributions with large variance, better quality soft data leads to prior distributions with low variance. Another important feature of most soft data is that the quality is spatially variable; soft data may be very good in some areas while poorer in other areas. The main aim of this paper is to propose a new method of integrating such soft data, which is large-scale and has locally variable precision. The technique of simulated annealing is used to construct stochastic realizations that reflect the uncertainty in the soft data. This is done by constraining the cumulative probability values of the block average values to follow a specified distribution. These probability values are determined by the local soft prior distribution and a nonlinear average of the small-scale simulated values within the block, which are all known. For each realization to accurately capture the information contained in the soft data distributions, we show that the probability values should be uniformly distributed between 0 and 1. An objective function is then proposed for a simulated annealing based approach to enforce this uniform probability constraint. The theoretical justification of this approach is discussed, implementation details are considered, and an example is presented.

Interpretation and reservoir characterization of a field dominated by complex fluvial channels, Bohai Bay, China

New oil discoveries in the southwest area of Bohai Bay by CNOOC Limited-Tianjin and other international oil companies are mostly found in the Middle Miocene Minghuazhen Formation. The Minghuazhen reservoirs are dominated by fluvial channels and shallow lacustrine and deltaic systems. On seismic, fluvial channels are often difficult to follow, and a terrestrial succession such as in the Minghuazhen Formation typically lacks continuous reflections to trace on seismic data. These depositional facies, along with complex postdepositional faulting, makes seismic interpretation and reservoir characterization of this field very difficult. Due to these complications, many development wells may miss penetrating the main pay by very small distances. The interpretation workflows presented in this paper were used to characterize and locate channel distributions. As a result, over 20 infill well locations were proposed and water-injection selections were optimized so that each injection well could effectively penetrate...