The goal of this project is to develop a systematic and cost-effective approach to the design and interpretation of Partitioning Interwell Tracer Tests (PITT) to infer hydrocarbon saturation distribution in highly heterogeneous and fractured reservoirs. The key elements of this approach are a very fast streamline-based flow simulation technique and a rapid and novel history matching technique that exploits an analogy between streamlines and seismic ray tracing. This approach will be orders of magnitude faster than conventional history matching, resulting in significant savings in computation time and manpower. The integrated approach will take advantage of the dense spatial coverage of the seismic data for static modeling and the strong coupling of interwell saturation variations to partitioning tracer response. The outcome of this research will be a systematic approach to the design and interpretation of tracer data and practical, PC-based software tools providing high-resolution saturation estimates in the interwell region by combining well log, seismic, and partitioning tracer data.

Texas Engineering Experiment Station, Texas A&M University, College Station, TX
Petroleum and Geosystems Engineering, University of Texas at Austin, Austin, TX

One of the goals of reservoir characterization, particularly in mature reservoirs, is to identify unswept regions containing high oil or gas saturation for targeted infill drilling or enhanced recovery. The project goal was to develop a systematic and cost-effective approach to the design and interpretation of PITTs to infer hydrocarbon saturation distribution in highly heterogeneous and fractured reservoirs. Unlike other efforts in this area, the focus of this research was to identify the location and distribution of remaining and bypassed hydrocarbons in mature oilfields. This represents an enormous resource—on the order of 100 billion recoverable barrels in domestic fields.

Results
The major project accomplishments to date are the:

• Development of a “generalized travel time” inversion scheme for interpretation of field tracer response via inverse modeling that can result in orders of magnitude savings in computation time and significant cost savings in terms of manpower (days as opposed to months).
• Generalization of the streamline-based simulation to describe fluid transport in naturally fractured reservoirs through a dual-media approach. An examination of the scaling behavior of the computation time indicates that the streamline approach is likely to result in significant cost savings for large-scale field applications.

Benefits
The streamline-based inverse modeling has resulted in a dramatic cost reduction in terms of computation time and manpower when compared with traditional history matching. Field scale tracer test interpretation can now be carried out in a matter of days as opposed to weeks or months, and this makes the technology accessible to small operators. The approach is particularly advantageous for high-resolution geologic models consisting of millions of cells that are now routinely used in the industry. The streamline approach has been generalized to model water injection in naturally fractured reservoirs through the use of a dual media approach. Researchers have shown that the streamline models exhibit a linear scaling of the CPU time as opposed to a quadratic scaling for finite-difference simulators. This has the potential of significant savings in time and manpower for field-scale applications in fractured reservoirs.

Summary
The project utilized the unique features of streamline models to develop an efficient approach for interpretation and history matching of field tracer response. Researchers investigated the relative merits of the traditional history matching (“amplitude inversion”) and a novel “travel time inversion” in terms of robustness of the methods and convergence behavior of the solution. The research shows that the traditional amplitude inversion is orders of magnitude more non-linear and the solution likely to get trapped in local minimum, leading to inadequate history match. This project’s proposed travel time inversion has been shown to be extremely efficient and robust for practical field applications.

The project generalized streamline-based simulation to describe fluid transport in naturally fractured reservoirs through a dual-media approach. Researchers compared their results with a commercial finite-difference simulator for waterflooding in five-spot and nine-spot patterns. For both dual porosity and dual permeability formulation, the streamline approach shows close agreement in terms of recovery histories and saturation profiles, with a marked reduction in numerical dispersion and grid orientation effects. An examination of the scaling behavior of the computation time indicates that the streamline approach is likely to result in significant savings for large-scale field applications.

Project performers have also developed several alternative ways of using PITTs in oilfields for the calculation of oil saturation, swept pore volume, and sweep efficiency and assessing the accuracy of such tests under a variety of reservoir conditions.

(July 2007)
In the third year of the project, the project performers have extended the streamline-based generalized travel time inversion to fractured reservoirs. They analytically computed the sensitivities that define the relationship between the reservoir properties and the production response in fractured reservoirs. The sensitivities are an integral part of the researchers’ approach and can be evaluated very efficiently as 1-D integrals along streamlines. The production data integration is then carried out via a generalized travel time inversion, which has been shown to be robust because of its quasi-linear properties and its use of established techniques from geophysical inverse theory. A no-cost extension of 1 year for the project was granted to examine the validity and practical feasibility of the streamline-based inverse modeling of fractured reservoirs. All the proposed work has been completed.

Funding
This project was selected in response to DOE’s Oil Exploration and Production solicitation DE-FC26-02NT15345.

$630,241

$160,293 (20 percent of total)

NETL -Chandra Nautiyal (chandra.nautiyal@netl.doe.gov or 918-699-2021) 
TEES - Akhil Datta-Gupta (datta-gupta@tamu.edu or 979-847-9030)

Publications
Annual Report June 2004 - June 2005  [PDF-2.50MB]

Datta-Gupta, Akhil, and King, M.J., Streamline Simulation: Theory and Practice, Society of Petroleum Engineers, textbook series (completed; expected publication in 2006).

He, Zhong, Datta-Gupta, A., and Vasco, D.W., Rapid Inverse Modeling of Pressure Interference Tests Using Trajectory-Based Travel Time and Amplitude Matching, Water Resources Research (accepted for publication in 2005).

Efendiev, Y., Datta-Gupta, A., Ginting, V., Ma, X., and Mallick, B., An Efficient Two-Stage Markov Chain Monte Carlo Method for Dynamic Data Integration, Water Resources Research (accepted for publication in 2005).

Al-Harbi, M., Cheng, H., He, Zhong, and Datta-Gupta, A., Streamline-Based Production Data Integration in Naturally Fractured Reservoirs, accepted for publication in SPE Journal, December 2005

Cheng, H, Khargoria, A., He, Z., and Datta-Gupta, A., Fast History Matching of Finite-Difference Models Using Streamline-Derived Sensitivities, SPE Reservoir Evaluation and Engineering, 8 (5), October 2005, pp. 426-436.

King, M.J., Osako, I. and Datta-Gupta A., A Predictor Corrector-Formulation for Rigorous Streamline Simulation, International Journal for Numerical Methods in Fluids, 47, 2005, pp. 739-758.

Cheng, H., Datta-Gupta, A., and He, Zhong., A Comparison of Travel-Time and Amplitude Inversion for Production Data Integration into Geologic Models: Sensitivity, Non-Linearity and Practical Implications," SPE Journal, 10(1), March 2005, pp. 75-90.

Al-Huthali, A., and Datta-Gupta, A., Streamline Simulation of Counter-Current Imbibition in Naturally Fractured Reservoirs, Journal of Petroleum Science and Engineering, 43, 2004, pp. 271-300.

Cheng, H., Datta-Gupta, A., and He, Zhong., A Comparison of Travel-Time and Amplitude Inversion for Production Data Integration into Geologic Models: Sensitivity, Non-Linearity and Practical Implications," SPE Journal, 10(1), March 2005, pp. 75-90.

Al-Huthali, A., and Datta-Gupta, A., Streamline Simulation of Counter-Current Imbibition in Naturally Fractured Reservoirs, Journal of Petroleum Science and Engineering, 43, 2004, pp. 271-300. 

3-D streamline distribution in the fractures and the updated fracture permeability distribution after integrating production data.