Newly developed, generalized analytic solutions to the heat equation for arbitrary 3D well trajectory in anisotropic media are demonstrated to solve benchmark horizontal- and slanted-well productivity problems with unprecedented speed and accuracy. Arbitrary well trajectory is constructed as an assemblage of spatially integrated, linear well segments, as opposed to a distribution of numerically integrated point sources, to provide advantages in both computational speed and accuracy in singularity handling. Production from each arbitrarily oriented segment is reduced to a combination of purely analytic expressions and rapidly convergent, exponentially damped infinite sum approximations. With offered flexibility in cell boundary conditions, the expressions can yield standalone well-productivity estimates for complex wells or serve as the basis for advanced well equations, if integrated within a numerical reservoir simulator. Transients are also computed with analytical integrations in time, thus requiring no time marching. The breakthrough speed and accuracy in productivity assessment open possibilities for advanced well-testing and reservoircharacterization methods. We further demonstrate the usefulness of analytic methodology with several time-dependent, discrete fracture problems for shale gas production with typical Barnett conditions, allowing direct use of complex fracture patterns, such as those interpreted from microseismic mapping. In addition to uniform-flux and uniform-pressure modeling options, a new analytic model is introduced that is capable of modeling both time-dependent material transport between matrix and a stimulated zone and the interplay between a well and fracture. We illustrate our solution method with Barnett fracturedwell examples from the literature. With optional effects such as gas desorption and stress-dependent fracture conductivity as easy add-ons, we can produce full-operational-life production forecasts for shale or tight gas reservoirs from discrete, complex fracture patterns along with reservoir-pressure mappings in a matter of minutes on common PC platforms.
ASJC Scopus subject areas
- Energy Engineering and Power Technology
- Geotechnical Engineering and Engineering Geology