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# Post-fracture well behavior

There are many factors that the engineer must consider when analyzing the behavior of a well after it has been fracture treated. The engineer should analyze the productivity index of the well both before and after the fracture treatment. Other factors of importance are ultimate oil and gas recovery and calculations to determine the propped fracture length, the fracture conductivity, and the drainage area of the well. Post-fracture treatment analyses of the fracture treatment data, the production data, and the pressure data can be very complicated and time consuming. However, without adequate post-fracture evaluation, it will be impossible to continue the fracture treatment optimization process on subsequent wells.

## Productivity index increase

Many of the early treatments in the 1950s were designed to increase the productivity index of damaged wells. These treatments were normally pumped to break through damage in moderate- to high-permeability wells. The productivity index of an oil well is

....................(1)

For a gas well,

....................(2)

where and are evaluated at the average pressure of

....................(3)

J is the productivity index in terms of barrels per psi per day or mcf-cp per psi squared per day. Viscosity and compressibility are included in the equation describing the productivity index of a gas well, because they are pressure dependent. McGuire and Sikora[1] published a procedure (Fig. 1) that was the first tool a fracture-treatment design engineer could use to determine the fracture length and fracture conductivity required to achieve a certain fold of increase in the productivity index.

The McGuire and Sikora graph can be used to draw the following conclusions:

• For high-permeability reservoirs, fracture conductivity is more important than fracture length.
• For low-permeability reservoirs, fracture length is more important than fracture conductivity.
• For a given fracture length, there is an optimum value of conductivity ratio.
• Most fracture treatments in undamaged formations should result in stimulation ratios of 2 to 14.

These conclusions have allowed engineers to design successful fracture treatments for more than 40 years.

At approximately the same time as the classic McGuire and Sikora paper was published, Prats[2] published another classic paper. Assuming J is the productivity index for a fractured well at steady-state flow, and Jo is the productivity index of the same well under radial flow conditions, Prats found that

....................(4)

for a well containing an infinite conductivity fracture whose fracture half-length is Lf . Prats explained that a well with a fracture half-length of 100 ft will produce as if the well had been drilled with a 100-ft diameter drill bit. In other words, the hydraulic fracture, if conductive enough, acts to extend the wellbore and stimulate flow rate from the well. If the dimensionless fracture conductivity, CfD (Eq. 5), is equal to 10 or greater, the hydraulic fracture will essentially act as if it is an infinitely conductive fracture.

....................(5)

## Ultimate recovery for fractured wells

Hydraulic fracturing should always increase the productivity index of a well; and, under certain circumstances, the hydraulic fracture can increase the ultimate recovery. Figs. 2 and 3 illustrate the differences that sometimes occur between low-permeability and high-permeability reservoirs. In Fig. 2, when a high-permeability well is fracture treated, the drainage volume and the recovery efficiency in the reservoir are not significantly altered. The fracture treatment increases the flow rate, increases the decline rate, and decreases the producing life of the well. The ultimate recovery is not changed. The same reserves are recovered in a shorter period of time, which reduces overall operating costs. Accelerating the recovery of a fixed volume of reserves is often beneficial. If the well is located in the Arctic or offshore in deep water, where operating costs are very high, then recovering the reserves sooner is very advantageous.

Fig. 3 illustrates the normal situation in low-permeability reservoirs. Without a fracture treatment, most low-permeability wells will flow at low rates and recover only modest volumes of oil and gas before reaching their economic limit. By definition, a low-permeability well will not be economic unless a successful fracture treatment is both designed and pumped into the formation. A successful stimulation treatment has the following effects:

• The flow rate will increase
• The ultimate recovery will increase
• The producing life will be extended.

In fact, many low-permeability wells will produce for 40 or more years, given adequate product prices and minimal operating costs. It is usually very easy to justify fracture treatments in low-permeability wells when the fracture treatment substantially increases the ultimate recovery.

## Post-fracture well-test analyses

Post-fracture well-test analyses are used to compute estimates of the propped fracture length, fracture conductivity, and drainage area of the formation. It is important to keep good records of the flow rates of oil, gas, and water, as well as the flowing pressures after the fracture treatment. If possible, a pressure-buildup test should be run after the well cleanup following the fracture treatment. Lee[3] presented a complete discussion on how to analyze production and pressure data after a fracture treatment to estimate fracture properties.

## Nomenclature

 Cf = fracture conductivity, md-ft CfD = dimensionless fracture conductivity J = productivity index, STB/D/psi Jo = productivity index of unfractured well, STB/D/psi k = formation permeability, L2, md Lf = fracture half-length, L, ft pe = pressure at the extremity of the reservoir, psi pwf = flowing bottomhole pressure, m/Lt2 qg = gas flow rate, Mcf/D qo = oil flow rate, STB/D re = drainage radius, ft μ = fluid viscosity, m/Lt z = gas compressibility factor

## References

1. McGuire, W.J. and Sikora, V.J. 1960. The Effect of Vertical Fractures on Well Productivity. J Pet Technol 12 (10): 72-74. SPE-1618-G. http://dx.doi.org/10.2118/1618-G.
2. Prats, M. 1961. Effect of Vertical Fractures on Reservoir Behavior—Incompressible Fluid Case. SPE J. 1 (2). SPE-1575-G. http://dx.doi.org/10.2118/1575-G.
3. Gidley, J.L., Holditch, S.A., Nierode, D.E. et al. 1989. Postfracture Formation Evaluation. In Recent Advances in Hydraulic Fracturing, 12. Chap. 15, 317. Richardson, Texas: Monograph Series, SPE.

## Noteworthy papers in OnePetro

SPE 168612_Economic Optimization of Horizontal Wells