A fracture design has been placed in front of you. Is it the right answer for an optimum completion? How do you know? Is there too much, too little, or the correct amount of proppant? Is proppant strength correct for the expected closure pressure? Will the chosen fluid have enough viscosity to give the desired height or length? The goal of this newsletter is to highlight the characteristics of a properly designed fracture treatment. For this two terms need to be defined: Dimensionless Fracture Conductivity, and Folds of Increase.Dimensionless Fracture Conductivity
Dimensionless fracture conductivity (Fcd) is defined as fracture conductivity, kfw (md-ft), divided by reservoir permeability (k) multiplied by the fracture half-length, xf (ft) (Equation 1). It provides a means of optimizing the amount of conductivity in a fracture for varying permeability and fracture length.
It can be shown mathematically that for pseudoradial & pseudo-steady-state conditions, the optimum value for well productivity occurs at Fcd of about 2. For a given amount of proppant, two different types of fractures can be generated, a short fat fracture can be created with a high value of kfw, or a longer, narrow fracture can be created with a lower value of kfw. Fracpacks in high permeability zones (>1 md) deal with the short fat fractures with a high kfw, and in low permeability zones (<1 md), a long, lower conductivity fracture is desired.
For example, a partially depleted 50’ thick reservoir with 20 md and areal extent of 40 acres (re = 660’) has a 50’ frac half-length. To achieve Fcd = 2, a kfw of 2,000 md-ft is needed. If this same zone has a permeability of 100 md, the kfw required would be 10,000 md-ft to yield the same Fcd of 2.What is Folds of Increase?
Folds of Increase (FOI) is related to Productivity Index (PI) in a ratio of fractured versus natural completion. The FOI is calculated by determining the flow rates before and after a fracture stimulation treatment or FOI= Qf /Qnat. FOI can be calculated using Equation 2.
Where re is drainage radius, rw is wellbore radius, s is prefrac skin, and rw’ is the equivalent wellbore radius. Values for FOI can vary from 1, no stimulation, to values > 10 for very stimulated.
of 40-60 feet with 5-8 pounds/sqft (9,000-14,000 md-ft) appears to give the best results with FOI between 1.6 to 1.8.Effect of Different Proppants
Conductivity varies with different proppants, and with proppant stress of the formation as seen in Figure 4. If Fcd calculated is very low, investigate increasing the concentration (pounds/sqft) or using higher strength proppant, which would increase the Fcd. Conversely, if Fcd is very high, a weaker (cheaper) proppant might be investigated to see the effect on FOI.How is Fcd Related to Production?
Postfrac production is affected by the skin near the wellbore. The more negative the skin, the lower the near-wellbore pressure drop, the higher the reservoir drawdown, and the higher the production rate. Conversely, with higher positive skin, the additional pressure drop near the wellbore reduces reservoir drawdown, and reduces rate. Fcd can be related directly to the-oretical skin ,that is the skin excluding wellbore jewelry. Theoretical skin can be calculated from Equation 3 by using the Effective Wellbore Radius. In the 20 md example above, skin would be -ln(15/0.5) or s = -3.4.
Post fracture Skins from pressure build-up tests have been plotted for various areas around the world in Figure 5. It can be seen as Fcd increases, skin decreases. If the Fcd is below 2, the fracture can be conductivity limited, meaning the reservoir permeability can deliver more production than the propped fracture can carry to the wellbore. Using FOI can optimize treatments to avoid this.