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.
1 Comment
Mark Burgoyne
3/2/2017 22:59:52
I've done some work to empirically fit appropriate transmissibility and wellbore connectivity multipliers to reasonably represent fractured well behaviour in coarse grid blocks (as long as grid block size does not impact the material balance, ruling shale fracs out) - meaning engineers can simply use existing grid geometries. Listening to your Peaceman connection post, you may have the capability to put the analytical math behind this (it's beyond me!) to take it beyond convoluted empirical equations to exact analytical solutions and in doing so... Care to try? SPE 156610
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