To emulate a fractured well in ExcSim, follow these simple steps: - Make sure that the well block is square with X- and Y-dimensions equal to the length of the fracture from tip to tip. I.e dX=2xf and dY=2xf, where xf is the fracture half-length.
- If the fracture is oriented in the X-direction, enter a transmissibility multiplier of 1.5339025 in the well block cell in the X-transmissibility map on the "Grid" worksheet, just below the porosity map. Also add the same transmissibility multiplier in the grid block to the left of the well block.
- If the fracture is oriented in the X-direction, enter a transmissibility multiplier of 0.98666142 in the well block cell in the Y-transmissibility map on the "Grid" worksheet, just below the X-transmissibility map. Add the same transmissibility multiplier in the grid block above the well block.
- If the fracture is oriented in the Y-direction, just switch the two factors.
- Give the well a (negative) skin value of s = - ln(0.407646 xf/rw)
The skin value given in point 5. corresponds to an infinite conductivity fracture. Use a slightly higher skin (less negative) to account for any finite conductivity. Note, however, that very small increases in the skin factor may have significant impacts. A typical skin adjustment, to account for finite conductivity, would be in the +0.01 to +0.1 range. A 2012 study, evaluating several GOM reservoirs, comparing various methods for modeling fractured wells (including use of skin factor, local grid refinement (LGR), and ExcSim's method), concluded that: "Following [ExcSim's] method for infinite conductive fractures, we simulated the fractured vertical well for hydraulic fracture lengths of 75 ft and 200 ft and compared the results with the LGR method as shown in Figure 18 and Figure 19 respectively. They confirm that this up-scaling method provides an accurate estimate when the hydraulic fracture conductivity was 20000 md-ft. In Figure 20 it is shown how a realistic conductive fracture can be modeled by [ExcSim's] method by introducing a small skin factor." It should be noted that to use this method on other simulators (other than ExcSim), the transmissibility multipliers given above must be multiplied by 1.47467 and the pressure equivalent radius, ro, must be set to 0.346 DX (where DX is the sides of the square grid blocks). See our blog on Peaceman for further details.
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Reservoir simulators estimate fluid flow from grid block to grid block until the flow reaches a well somewhere in the simulation model. Inter grid block flow is approximated using Darcy's law, with one noticeable exception: Fluid flow from well blocks to wells within those grid blocks introduces some additional difficulties. Peaceman (1978) noted that "in numerical reservoir simulation, the pressure calculated for a well block is the same as the flowing pressure at an equivalent radius, ro. For a square grid, ro = 0.2 ∆x." The problem is that the equivalent radius should demonstrably be much greater than that. In fact:where ∆x is the length of the sides of the square grid block. The video above shows that Peaceman's correction does not solve the problem noted by Peaceman, it only glosses over it. And in doing so, it introduces the distinct error stated above. Failing to solve the problem correctly may cause significant errors in the calculated fluid saturations and viscosities in the well block.Consequently, ExcSim does not use the Peaceman well correction at all. Instead, ExcSim attacks the cause of the problem and solves it by means of transmissibility corrections. See the video for details. For square grid blocks the equivalent well block radius is given by Fig2, and the transmissibility multiplier is: If the grid blocks are rectangular of size (A x B), then the transmissibility multiplier is a function of the ratio between the grid block sides, C=B/A. The formula below gives the transmissibility multiplier for the colored edges of the well block. The transmissibility multiplier for the other edges is found by inverting C, C’=1/C. The equivalent well block radius for rectangular well blocks is given by Fig. 6 below |
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