Completion Science, LLC®
Completion Science, LLC®
Completion Science, LLC®


How to size for bridging on slots?
What is the design process for sizing the particles used in diverting treatments in the shale formations?

The simple answer to this is pump the biggest particles you can and size the other particles to seal on and around these. This may seem over simplistic, but it requires a good amount of engineering understanding to get there. There are a number of oilfield related applications that involve sizing particles to bridge or seal. Some good examples are sizing the bridging particles in a drill-in fluid or sizing diverting materials to bridge on a perforation.

Extensive research has been conducted in the past to answer the question about bridging on perforations or pores. A classic is “Particle Transport Through Perforations,” SPE 7006, Gruesbeck, C., Exxon Production Research Co., Collins, R.E., U. of Houston. See Figure 6 of that paper for rules on sizing bridging particles relative to the perforation diameter and the effects of particle slurry concentration. (Note: We are requesting permission from SPE for use of the graphs discussed in this page. Check back at a later date)

The take home message from this chart is that at low concentrations, a particle nearly as big as the perforation may be needed. As the concentration increases, a bridge could form with particles that are actually significantly smaller than the perforation hole. In fact particles that are only 1/5 the size of the perf would be expected to form a bridge at concentrations of 6 lbs/gal or higher (with sand).

So that’s all well and good, but what about sealing or bridging on a fracture or slot inlet. We will start with a slot of sufficient length such that end effects can be ruled out (in engineering terms, an infinite slot). If we took this case and went to the laboratory with the expectation of getting results similar to the above, we would be sorely disappointed. After many frustrating attempts, we would have to conclude that the only predictable and stable results are those with particles at least as big as the slot.

So, let’s go back to the round hole case and work our way toward a slot. The simplest case would be to make a “hole” that is a very short slot, basically, a square hole. Testing on this would give us results not too much different from the above perforation example. We could then move to a slot that is twice as long as wide. Then we could double the length, then double it again. Similar testing to this was carried out and reported in SPE 126310 “Correlating Flowing Time and Conditions for Plugging of Rectangular Openings, Natural Fractures, and Slotted Liners by Suspended Particles,” T.V. Tran, F. Civan, Univ. of Oklahoma; I. Robb, Halliburton. See Figure 6 from that paper.

With a bit of extrapolation, one could generalize this by saying that in a slot twice as long as wide, it would take about 3 or 4 particles to bridge the width (bigger particles, than the square). In a slot 4 times as long as wide, we would start noticing that we are now needing particles big enough that two of them bridge the slot. As we kept getting the aspect ratio (length to width) bigger it would get harder and harder to get predictable results unless we had particles as big as the slot width itself. We can see from this that the “end” effects are important. Having an “end” of the slot to help hold particles in place greatly improves the conditions of bridging. An analogy to this would be how easy it would be to set a tripod over a hole, but difficult to set it over a crack if there is no place for the third leg to sit. The additional dimension is critical for bridge stability. There are other factors which also contribute to the instability and they are covered well in SPE 67298, “Proppant Holdup, Bridging, and Screen-out Behavior in Naturally Fractured Reservoirs,” R.D Barree, M.W. Conway. The conclusion of this paper regarding stable bridges across a fracture is that there are some additional factors involving fluid flow that enter the discussion (warning, topics like Bernoulli’s equation are going to come up).

Once the larger particles used for fracturing diverting are sized, sizing the remaining particles becomes simple. Note the relationship below between three adjacent particles and the resulting “pore throat.” 

The pore throat is about 1/6 the size of the particles. We could choose something just slightly larger than this, say 1/5 to ensure quick bridging (actually plugging). We could even add particles that are 1/5 of these smaller particles we just added as well. The motivation for this is to get down to small enough pore throats to get filtration in addition to bridging. The pack now is capable of filtering out polymers (guar or friction reducer) or other small, soft material (let’s face it, the water we use for fracturing is not hospital clean). This filtration that takes place gives a very good, final seal to the pack.

The smaller particles are generally not sized in discrete steps but are taken from the grinding process with a natural particle size distribution that includes the sizes discussed.

So, what do we know about the size of the fractures near the wellbore in naturally fractured rock like shale? Well, not much. Not only do we not know how wide the fractures are, we don’t know how many are intersecting the perforation tunnels. In fact, there really isn’t a perforation tunnel left after the erosion that has taken place outside the casing after a fracturing treatment was placed. There is some type of eroded cavity there now.

Consider these statements:
1. A sand slurry is erosive to rock (and cement and steel).
2. A large amount of sand slurry pumped eroded out a cavity downstream of the perforation (jet orifice). 
3. Looking at shale cores, we see it is broken up in chunks.
4. The eroded cavity probably intersects one or more of these chunks. 
5. The fracture(s) initiated between these chunks.
6. At the end of pumping, the fractures are probably not 100% sand filled. 

Can we be sure about statement 6? If the fracture were completely sand filled, we could pump a diverter that had particles only big enough to seal on the sand pore throats. If you try this, it will fail miserably. So, there is something other than 100% sand filled fractures near the wellbore.

But how wide are they? We don’t know, but we could just pump the biggest particle we can get through the pumps and see what happens (or we could rig up some kind of downstream injector if the pumpable particles aren’t big enough, but that is not an easy solution to get to). And that is basically how we got to where we are. There were attempts to apply engineering, but it was soon obvious that the amount of engineering effort that would have to be expended to understand such a complex system would not be worth the expense. A field trial was cheaper and faster.