Monday, November 20, 2017

Progress in Fracture Treatment Design chapter 2

Pivotal to designing the treatment- and to deciding whether to do one at all -is cost benefit analysis , relating cost of the fracture job to increased well productivity. The more fracture length for a given fracture conductivity, the more productivity, but also the more costly the fracture job. This analysis, called net present value, is done with simulators that find the optimum fracture length and conductivity for a given payback schedule. Too short a fracture, or too low a conductivity, and the increase in well productivity won't cover the cost of fracture treatment ; too long, and the extra fracture length will add significantly to cost but negligibly to production. Some simulators model fracturing economics in longer terms ; they tell , for example, for a well with a given deliverability, amortized at a certain rate, how much should be spent on hydraulic fracturing given a future oil price.


 Fracture Geometry Modeling

The need to understand hydraulic fracturing stimulated advances in basic rock mechanics. A key finding was of Hubbert and Willis, in 1957, showing that fractures in the earth are usually vertical, not horizontal. They reasoned that because a fracture is a plane of parting in rock, the rock will open in the direction of least resistance. At the depth of most pay zones, overburden exerts the greatest stress, so the direction of least stress is therefore horizontal. Fractures open perpendicular to this direction and are therefore vertical. In shallow wells, or where thrusting is active, horizontal stress may exceed vertical stress and horizontal fractures may form.

By the 1960s, fractures created below 1000 or 2000 ft were accepted as vertical. Operators then posed some difficult questions : How high does the fracture grow? How can we prevent it from extending into the gas or water zone? How does fracture height relate to fracture width and lenght? And how do we optimize fracture dimensions?

 A major task of rock mechanics became the prediction of fracture height, length and width for a given injection rate, duration of injection and fluid leakoff. Needed for this prediction is a model of how a fracture propagates in rock.







Today, a number of models occupy a continuum from 2D to pseudo-three dimensional (P3D) and fully 3D. The basic difference between 2D and 3D models is that in 2D models, fracture height is fixed or set equal to length , whereas in 3D models, fracture height, length, and width can all vary somewhat independently. 

The 3D approach is more realistic because fracture height is not determined by lithology but by vertical variation in the magnitude of least principal stresses, which often but always follow lithologic units. The greater the vertical contrast in least principal stresses, the better fracture height is contained.

The perf and the frac : what's the link?

Field wisdom holds that the ideal perforation lies in the plane normal to the minimum far-field stress direction. This perforation links most directly with the induced fracture, minimizing pressure drop near the borehole. Other perforations probably connect with the fracture indirectly, if at all. But because fracture azimuth is generally not known and because alignable perforating guns are not readily available, conventional guns shooting at closely spaced angles around 360 degree are generally used. These are called phased guns. The closer the angle (phasing) between perforations, the better chance of having more perforations in or near the ideal plane. Not until recently, however, were large-scale experiments performed to evaluate the relationship between perforations and hydraulic fractures. 

Behrmann and Elbel of Schlumberger and Dowell Schlumberger , respectively , used full-scale perforators on steel casing cemented into sandstone blocks placed in a  triaxial stess cell. They made several observations about the relationship between perforation orientation and stress direction. They found that fractures initiate from the wellbore wall in the optimum hydraulic fracture direction, from perforations nearest this direction, or both. Fractures tend not to form at other perforations. 

The best perforation-to-fracture communication is achieved when perforations are within 10 degree of the far-field minimum horizontal stress. This means that perforations not optimally oriented may result in a large pressure drop, or proppant bridging, when pad and slurry flow around the annulus to the fracture. As expected , the maximum number of perforations in communication with the fracture is achieved with a perforating gun having the smallest possible angle between shots. 
 

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