A new method for estimating heterogeneity in Earth models is presented. The new approach requires running a streamline simulator only a few timesteps, so multi-million cell models are evaluated in minutes. Using streamline time of flight and volumetric flow rate information from the simulation, a flow capacity diagram and sweep efficiency history can be determined. Five different measures of heterogeneity can be obtained from these two diagnostic plots. We then evaluated each of these measures of heterogeneity for 450 models that were constructed using a wide range of Dykstra-Parsons coefficient and correlation lengths, and 2 different well patterns. The measures of heterogeneity were plotted against discounted oil recovery to determine the best measure of heterogeneity. From this study we conclude the Lorenz coefficient - as determined from dynamic data - is the single best measure of heterogeneity. Introduction Uncertainties in reservoir performance under secondary or tertiary displacement arise from a variety of sources. The complex interaction between depositional environment and subsequent diagenesis is poorly understood, but nevertheless gives rise to spatial variability in reservoir properties (e.g., porosity, permeability, rock type, etc.). The methods available to estimate reservoir properties all suffer from concerns of spatial resolution. Some, for example seismic surveys and pressure transient tests, estimate bulk properties at an intermediate scale but cannot provide "local" values. Others such as well logs and core analysis may provide accurate estimates of properties at a single point, but cannot provide information other than at those (sparse) locations. To acknowledge the inherent uncertainty in any given Earth model, a stochastic approach is most frequently taken. A number of equally probable models are constructed to evaluate the effect of parameter uncertainty on reservoir performance. The single biggest drawback to this approach is the investment in time required to scale these multimillion cell models up for simulation, history-matching field performance, and making predictive forward model runs. For this reason, a method for ranking the behavior of alternative Earth models is attractive, so that a minimum number of models are used in full field reservoir simulation. The key to ranking alternative models is to identify a robust indicator of that model's performance under displacement conditions. We submit that an appropriate measure of dynamic heterogeneity is a useful means of ranking models. Primary recovery is less sensitive to heterogeneity; in fact, Walsh and Lake (2007) show primary recovery in heterogeneous media with crossflow can be approximated with a suitably averaged, homogeneous permeability. It is during secondary or tertiary recovery that thief zones or other short circuiting of injected fluids become costly. Static measures of heterogeneity describe the distribution in permeability and porosity of a given model; dynamic measures implicitly include the distribution in flowpath length and the connected structure of the flowpaths. Large dynamic heterogeneity is manifest in premature breakthrough of injected fluids. This early breakthrough may be caused by low volume, high permeability flowpaths (i.e., thief zones), or merely by a distribution in flowpath lengths where some paths are much shorter than the mean. The appropriate heterogeneity measure - and therefore ranking tool - should be sensitive to either of these conditions.
In the last several years a variety of new tools for interpreting interwell tracer tests have been developed. The new methods are based on residence time distributions of the tracer, where much of the previous work used only the mean residence time. Using the distribution of residence times extends the power of moment analysis by allowing for the determination of reservoir properties and flood performance as a function of time. Flow geometry and construction of flow capacity - storage capacity diagrams also follows directly from the analysis. Swept volume vs. time, and sweep efficiency are also determined from the residence time distribution, as is remaining oil saturation. One important key to these new methods is our use of the integrated tracer recovery histories. Estimating residual oil saturation is greatly simplified by our mathematical treatment of slug tracer injection. Examples are presented that show improved saturation estimates even at early times in a tracer test. This paper describes the new analysis methods developed recently and shows by comparisons with analytical and experimental data that the methods are accurate and robust. The method is simple and can be done with a spreadsheet using only produced tracer concentration data; it does not require a reservoir model or numerical simulation. The equations are derived from first principles for a very general case that includes both conservative and partitioning tracers produced from any heterogeneous reservoir. Introduction and Motivation Successful fluid injection programs for improved oil recovery require detailed information on reservoir heterogeneity and connectivity, remaining oil saturation and its distribution, and estimates of reservoir volume contacted as a function of volume injected (i.e., sweep efficiency). Methods for assessing these reservoir and operational properties include repeat seismic interpretation, detailed reservoir simulation, production log analysis, and tracer interpretation methods. While all of these methods offer insight into secondary or tertiary recovery mechanics, only tracer methods provide information at the appropriate interwell scale, with less spatial averaging than typical in numerical methods. Oilfield tracer testing is a mature technology, with more than 50 years of application (Du and Guan, 2005). An extensive literature review by these authors shows 43 tracer tests reported in the literature, 60% of which were aqueous phase tracers, and the balance gas phase tracers. They further report that nearly 70% of the test results were interpreted qualitatively, 25% used analytical interpretation, and 12% were interpreted numerically (in some cases more than one method was used, so these do not sum to 100%). Quantitative tracer analysis was first presented to the oil industry by Brigham and Smith (1965) for homogeneous repeat 5-spots, and Abbaszadeh-Dehghani and Brigham in 1984 for layered media. For unit mobility ratio, and neglecting gravity and capillary forces, they show a general solution to tracer transport for arbitrary well configuration, from which swept pore volume can be determined. They also show an iterative method to estimate individual layers' flow capacity, kh, and storage, ?h, by deconvolving the combined tracer signal into individual layer responses. The fundamental restrictions in their development were the assumption of intra-layer homogeneity and unit mobility ratio. Tang and coworkers (Tang and Harker, 1991a, 1991b; Tang, 1995, 2003) developed a method to estimate residual oil saturation that was based on chromatographic theory. In their original work, they show a tracer breakthrough curve of conservative and non-conservative (partitioning) tracers can be collapsed to a single curve by "correcting" the partitioning tracer's residence time by its partition coefficient and the residual oil saturation. This correction is applied at various points in a tracer test (e.g., tracer breakthrough, 10% recovery, etc.). Tang (2003) also extended the Brigham and Smith (1965) model to estimating oil saturation in individual layers from tracer response. Again, these methods assume constant intra-layer properties.
This report documents the results of an extensive sensitivity study conducted by the Idaho National Engineering and Environmental Laboratory. This study investigated the effects of various operating and design parameters on wellbore heat exchanger performance to determine conditions for optimal thermal energy extraction and evaluate the potential for using a wellbore heat exchanger model for power generation. Variables studied included operational parameters such as circulation rates, wellbore geometries and working fluid properties, and regional properties including basal heat flux and formation rock type. Energy extraction is strongly affected by fluid residence time, heat transfer contact area, and formation thermal properties. Water appears to be the most appropriate working fluid. Aside from minimal tubing insulation, tubing properties are second order effects. On the basis of the sensitivity study, a best case model was simulated and the results compared against existing low-temperature power generation plants. Even assuming ideal work conversion to electric power, a wellbore heat exchange model cannot generate 200 kW (682.4e+3 BTU/h) at the onset of pseudosteady state. Using realistic conversion efficiency, the method is unlikely to generate 50 kW (1 70.6e+3 BTUh).
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