Dimensionless Fracture Conductivity: Better Input Values Make Better Wells
Authors: Pearson C. Mark 
Published: June 2014

Technology Today Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering.

Summary
Dimensionless fracture conductivity is a key design parameter in well stimulation that compares the capacity of the fracture to transmit fluids down the fracture and into the wellbore with the ability of the formation to deliver fluid into the fracture. Its use in fracture design dates back to the earliest days of hydraulic fracturing in the 1950's. Despite the advances in numerical simulation and, perhaps, because of its relative simplicity in presenting such an important concept, it continues to be used as a principal design parameter some 40 years later. However, as with any design parameter, its value is only as good as the data used in its determination.
Both recent testing reported in the literature and other studies from as early as the 1970's show that the source of fracture-conductivity data used by most engineers seriously overestimates the effective permeability of the fracture by more than an order of magnitude. This results in many of today's hydraulic-fracture treatments being capacity constrained and significantly underperforming compared with the potential deliverability from the reservoir. Understanding the test parameters under which the input data are measured enables today's engineers to calculate dimensionless fracture conductivity more accurately and improve the productivity from their wells.

Introduction
Dimensionless fracture conductivity, CfD, can be defined asCfD=kfb/kFLf. (1)
Following wider application of hydraulic fracturing in the late 1950's, it became readily apparent that the conductivity of the fracture had to be matched to the potential deliverability of the reservoir. A number of analytical solutions were developed to calculate fractured-well productivity, all of which included some measure of the relative capacity or conductivity of the fracture.1–4
Prats3 showed that, with a CfD&gt;10, steady-state production could be maximized and the effective wellbore radius is approximated byrw=0.5Lf. (2)
For oilwell fracturing, this is perhaps the crux of hydraulic fracturing. The long-term potential from a fractured well is to increase well production to the equivalent of drilling a well with a radius half the size of the fracture half-length.
In the 1970's, work focused on the nature of the transient-flow period, which is much more significant in lower-permeability gas reservoirs. A number of authors presented transient-producing-rate solutions as functions of dimensionless values of time and fracture conductivity.5–7 To maximize the transient production rate (which is higher than the steady-state flow as analyzed by Prats), it is typically necessary to have even higher values of dimensionless fracture conductivity. Cinco-Ley and Samaniego-V.7 showed that, for a dimensionless time greater than 1, the CfD value must be 30 (using the standard industry definition of CfD given earlier). However, on the basis of both Prats' original work and industry experience, a CfD value of 10 continues to be widely used as a standard design factor in the industry.

Fracture-Conductivity Measurements
Fracture conductivity is the product of fracture permeability and propped fracture width left after the fracture has closed. The permeability typically is measured in the laboratory for the particular proppant being used, while the fracture width may be calculated numerically by use of one of a number of 3D and pseudo-3D fracture-design models that are widely available in the industry.
In the 1980's, the American Petroleum Inst. (API) published a series of standard testing procedures that involve flowing a single-phase liquid (water with 2% KCl) through a 7×1 1/2-in. linear proppant-pack cell at flow rates of 1 to 10 mL/min.8 A pressure drop is measured and a permeability value determined. The stress is then increased in 2,000-psi increments, and subsequent measurements are made to obtain a permeability/conductivity curve for a particular proppant being tested. These test procedures remain in use today except that the flow period at each stress level has been increased to 50 hours to account for transient effects in the measurements. Fig. 1 shows proppant-conductivity curves for some commonly used proppant types.9
The design engineer typically reduces these "long-term" permeability data of the proppant pack to take into account other factors that may compromise the ability of the fracture to transmit fluid. These factors include the following.Amount of embedment into the formation.Amount of damage resulting from gel residue.Any long-term degradation of the proppant.Fines migration and plugging.Flowback of proppant out of the fracture.