Furui: Generalized Skin Equation

Introduction

In 2002, Furui et al introduced a new skin factor for horizontal wells, which considered various completion styles. Furui developed a comprehensive set of equations to predict the performance of horizontal well completions:

1. Convergent flow to perforations in slots

2. Effect of formation damage

3. Effect of crushed zone due to perforating jet

4. Effect of slot plugging

5. Turbulence effects

6. and interaction of the above

General Form of a Skin Equation

According to Furui:

s = Rate-Independent Skin + Rate-Dependent Skin

Where:

s0 = Rate Independent Skin

f_tF_o,w = Rate-Dependent Skin

Fo,w = Forcheihmer number

In most literature, the above equation is cast into the following form w/r to flow rate:

Completions Investigated

OpenHole Completions & Formation Damage

Furui presented a series of equations to estimate the combined effect for an open-hole completion considering static formation damage and anisotropy.

Loss Due to Slotted Linear	Schematic
used for all related discussion here and below.

Slotted Liners

Furui looked at slotted liners as shown below, and then combined with the effect of convergence flow skin with formation damage as well as anisotropy - and of course turbulent flow as before.

Losses to Flow Pattern	Schematic
For unplugged slots, k >> k, the linear flow component skin is negligible. for skin losses inside the slot, there must be plugging and an effective permeability

Plugging of slots may be a major problem in unconsolidated formation. As the flow of the slot becomes a porous medium as opposed to closed conduit flow, the pressure losses can be substantial.

Discussion	Schematic
Slotted Liners: The overall performance becomes poor for both the rate-independent skin and the turbulence scale factors [Furui, 2003]
Perforated Liners: The overall performance becomes poor for both the rate-independent skin and the turbulence scale factors [Furui, 2003]
For unplugged slots, k >> k, the linear flow component skin is negligible. for skin losses inside the slot, there must be plugging and an effective permeability

Although the work was extended to include anisotropic conditions, Furui showed that formation anisotropy is not significant for slotted liner completions IF THERE WERE 4 OR MORE SLOT UNITS AROUND THE circumference of liner (see below). Also, the slider orientation relative to the permeability field has no significant effect.

Perforated Liners

Furui stated that The flow geometry of perforated liners is similar to that of slotted liners, and that the convergent flow to the perforations (milled) were more likely to be hemispherical rather than radial flow.

where the rest of the equations are similar to the slotted liner scenario.

Pressure Contours: Perforated Liner	Pressure Contours: Slotted Liner

Slotted (Or Perforated) Liners + Formation Damage

In openhole completions, the effect of damage is classically given by the Hawkins equation; however, the Hawkins equation does not consider convergent flow. Furui followed the work of Karakas and Tariq [1991] who derived a model for these interactions in cased and perforated wells.

The solution was given as:

for unplugged slots

for slots plugged by sand

In the above equation, conventional formation damage (s_fo) which is also linked to the Liner geometry skin via the dimensionless permeability ratio (an amplication factor of Beta also applies to the turbulent region)

Furui also showed:

where:

rsH = damage penetration in the horizontal direction

Loss Due to Slotted Linear	Schematic
The important fact is that the effect of formation damage on slotted liner completions is even worse than openhole completions. The reduced permeability region magnifies the skin due to the convergent flow inside the damaged zone

Cased and Perforated Wells

Skin factor models for perforated wells already exist. Furui [] extened the work for perforation orientation, and extended the work account for formation damage and crushed zone.

Some of the scenarios are presented below:

Loss Due to Slotted Linear	Schematic
Perforations extend beyond the damaged zone. As expected, for perforations beyond the damage zone, the effect of formation damage is not substantial. The perforations can create flow paths through the damaged zone; however, Furui [2003] states that the flow concentration around the tip of the perforations can increase additional pressure drop/
Perforations within the damaged zone, combined with anisotropy
Inclusion of crushed zone effects

References:

• K. Furui, D. Zhu, & A. D. Hill, A Comprehensive Model of Horizontal Well Completion Performance, SPE 84401, 2003.

• K. Furui, A Comprehensive Skin Factor Model for Well Completions Based on Finite Element Simulations. PhD, University of Texas At Austin, 2004