Analytical Reservoir Simulation and Its Applications to Conventional and Unconventional Resources
Authors: Zhou Wentao , Samson Boris , Krishnamurthy Shalini , Tilke Peter , Banerjee Raj , Spath Jeff , Thambynayagam Michael 
Published: June 2013

To support decision making, reservoir simulation is used by oil and gas companies to model fluid flow in the reservoir. Because of the complexity of reservoirs, well scenarios, and recovery processes, reservoir management decisions regularly require the use of computationally expensive numerical simulations. Meanwhile, petroleum engineers often deploy fast analytical simulation tools in practice to support decision making when time, budget, or expertise are of concern. Because of the fast speed in model setup and computation of results, the industry is experiencing a growth in the application of analytical reservoir simulation to a wide range of problems. This paper reviews analytical reservoir simulation technology and discusses its business applications to conventional and unconventional resources.

The simulation is based on the analytical solution of the diffusion equation in a cuboid homogeneous reservoir, using integral transform method. Isoparametric transformation extends the solution to irregular non-cuboid reservoirs. Regional-scale reservoir heterogeneity is handled by combining solutions on multiple cuboids. The solution is further adapted to complex features such as hydraulic fractures, both planar and fracture network, which are essential for production of unconventional resources.

Analytical forward simulation aids the design and optimization of various aspects of well construction. Examples are given in the paper, from interference test design of multilateral well, sensitivity study of tight gas well, to production behavior of shale gas and liquid wells. This paper also shows a simulation case containing multiple shale liquid wells and a quick-look field development planning case involving 64 hydraulically fractured wells honoring flexible drilling schedule.

The growing application of "digital oilfield" technology is vastly increasing the amount of data available in real time. The traditional approaches of data assimilation into numerical simulation models often prove impractical from a time and data perspective. However, in combination with screening technology, production data interpretation facilitated by analytical reservoir simulation that includes pressure transient analysis (PTA) and rate transient analysis (RTA) uses the data efficiently and supports decision making for on-time production management.

Due to the high speed, analytical reservoir simulation is also used in uncertainty and optimization processes where hundreds of, even thousands of, simulation runs are required. We discuss an example of field development planning (FDP) optimization. The automated workflow accelerates the planning process of well placement in the presence of subsurface uncertainty and operational risks. It allows screening and ranking of field development options in a matter of minutes.

With its simplicity, accessibility, and speed, analytical reservoir simulation complements numerical reservoir simulation as a powerful tool supporting E&P decision making.