Using simple models to describe oil production from unconventional reservoirs
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Shale oil (tight oil) is oil trapped in low permeability shale or sandstone. Shale oil is a resource with great potential as it is heavily supplementing oil production in the United States (U.S. Energy Information Administration, 2013). The shale rock must be stimulated using hydraulic fracturing before the production of shale oil. When the hydrocarbons are produced from fractured systems, the resulting flow is influenced by the fracture, the stimulated rock, and the matrix rock. The production decline rates from shale oil reservoirs experience flow regimes starting with fracture linear flow (fracture dominated), then bilinear flow (fracture and stimulated rock dominated), then formation linear flow (stimulated rock dominated), and finally pseudo-radial flow (unstimulated matrix rock dominated) (Cinco-Ley 1982). In this thesis, daily production rates from a shale oil reservoir are modeled using a simple spreadsheet-based, finite difference serial flow simulator that models the single-phase flow of a slightly-compressible oil. This simulator is equivalent to flow through multiple tanks (subsequent part of the thesis will call these cells) through which flow passes serially through one tank into the other. The simulator consists of 11 tanks. The user must specify the compressibility-pore volume product of each tank and the transmissibility that governs flow from one tank to another. The calculated rate was fitted to the given data using the Solver function in Excel. The fitted matches were excellent. Although we can adjust all 22 parameters (2 per cell) to affect the simulation results, we found that adjusting only the first three cells nearest to the well was sufficient. In many cases, only two cells were enough. Adjusting 4 or more cells resulted in non-unique matches. Furthermore, the properties of the very first cells proved insensitive to the matches when using the 3 cells to match the data. The cells in the 2 cell model represent the stimulated zone and the unstimulated rock. Likewise, the cells in the 3 cell model represent the hydraulic fracture, the stimulated zone, and the unstimulated rock. The accessed pore volume and transmissibility were responsive to the injected sand mass and fluid volume up to approximately 10⁶ kg and 7000 m³ respectively; injecting more sand and fluids than this caused negligible increases in the accessed pore volume and transmissibility. This observation suggests that the sand does not migrate far into the fractures. Similarly, it was observed that the number of stages was positively correlated with cell transmissibility and pore volume up to 20 stages. These results suggest that fracture treatments were significantly over designed and injecting less sand and water in fewer stages would optimize the economics of similar projects. To our knowledge this is the first work to analyze the results of fracture treatments by matching with pore volumes and transmissibility in a simple serial cell flow.