Many questions relative to fracture flow characteristics remain under investigated. How big does a fracture need to be? How can fines migration potential be alleviated with a fracture? What is the fracture production contribution versus the radial contribution? How much production is directed through out-of-phase perforations? How close can the fracture be to an aquifer?
A three dimensional radial reservoir model was developed to answer these questions. The model integrates the reservoir, wellbore, formation damage, fracture, and the completion hardware.
Historically, researchers have modeled the fracture as one dimensional. By modeling the fracture in 2 and 3 dimensions one can visualize the flow patterns around a fractured well. By analyzing these flow patterns, one can better understand the impacts the fracture is having. Results are presented (both vector and contour plots) that highlight the flows within and around the fracture. Conclusions are presented that quantify fracture effectiveness vs. length and comparisons are made to previous work.
Fracture flow visualization provides insight into the formation fluid velocities that could lead to fines migration. The effects a fracture has on formation velocity reduction will be quantified. While no generalized theory exists for fines transport velocity thresholds (only formation specific values to date), this type of analysis is an effective way to quantify those velocities and to aid in designing completions and setting production targets that prevent further formation damage through fines migration.
The production fraction from perforations out-of-phase with the fracture are also quantified. Conclusions are drawn about the relative importance of cleaning and/or stimulating these perforations.
A benefit of using a three dimensional reservoir/fracture simulator is it provides a method of determining the water influx when the fracture extends near an aquifer. Results are shown that detail hydrocarbon and water production versus aquifer proximity to the fracture.
The following work makes use of two separate, but similar, numerical models. A two dimensional high resolution radial model was used for all but the water coning analysis. For these cases a lower fidelity three dimensional cylindrical model was used.
SINDA/FLUINT fluid flow analysis software was used for the reservoir simulator. A more detailed description of using SINDA/FLUINT for reservoir analysis can be found in reference 1.
The nodalization for the high resolution model can be seen in Figures 1 and 3. In order to take advantage of symmetry, half of the formation and one fracture wing were modeled. The model has 36 logarithmically spaced radial divisions, and 36 linearly space angular divisions. Each angular element represents 5 degrees.
A rectangular fracture wing of constant width was used. A no-flow boundary was placed at the edge of the fracture that contacted the formation (at radius L). This was done to compensate for the idealized constant width assumption.
Formation damage, when included in the analysis, was assumed to have depth of 1 foot from the sandface. The sandface was assumed to have a permeability of either 20% or 10% of the native formation. This permeability reduction was varied logarithmically along the formation radius until a radius of 1 foot was reached and the formation permeability retained it original value. This approach results in skin numbers of 4.3 and 9.8, respectively.
Whenever perforations were used they were modeled as damaged. The perforation tunnels were modeled as cylinders with a 6 inch formation penetration. The compaction zone was modeled as a 1/2 inch radial zone with a permeability 20% of that of the surrounding formation. This is shown in Figure 2. The perforation pattern used was 12 shots per foot with a 60 degree phasing.