Abstract
Gaussian solutions of the diffusion equation can be applied to visualize the flow paths in subsurface reservoirs due to the spatial advance of the pressure gradient caused by engineering interventions (vertical wells, horizontal wells) in subsurface reservoirs for the extraction of natural resources (e.g., water, oil, gas, and geothermal fluids). Having solved the temporal and spatial changes in the pressure field caused by the lowered pressure of a well’s production system, the Gaussian method is extended and applied to compute and visualize velocity magnitude contours, streamlines, and other relevant flow attributes in the vicinity of well systems that are depleting the pressure in a reservoir. We derive stream function and potential function solutions that allow instantaneous modeling of flow paths and pressure contour solutions for transient flows. Such analytical solutions for transient flows have not been derived before without time-stepping. The new closed-form solutions avoid the computational complexity of time-stepping, required when time-dependent flows are modeled by superposing steady-state solutions using complex analysis methods.
| Original language | English |
|---|---|
| Article number | 160 |
| Journal | Fluids |
| Volume | 8 |
| Issue number | 5 |
| DOIs | |
| State | Published - May 2023 |
Bibliographical note
Publisher Copyright:© 2023 by the authors.
Keywords
- doublet flow
- equipotential lines
- flow paths
- gaussian solution
- reservoir simulations
- streamlines
ASJC Scopus subject areas
- Condensed Matter Physics
- Mechanical Engineering
- Fluid Flow and Transfer Processes