Hydraulic Fracturing Overview

Introduction

Hydraulic fracturing is a well stimulation technique that creates conductive flow channels in the reservoir rock by injecting fluid at pressures exceeding the formation fracture gradient. The induced fracture dramatically increases the effective wellbore contact area, enabling economic production from formations that would otherwise be unproductive.

Petroleum Office provides analytical models for fracture geometry prediction, leakoff analysis, and proppant transport calculations covering the classical 2D fracture models and supporting design computations.

Why Hydraulic Fracturing?

Hydraulic fracturing is performed when the natural reservoir deliverability is insufficient for economic production:

• Low permeability -- tight sandstones, shales, and carbonates where matrix flow is too slow
• Near-wellbore damage -- drilling damage (positive skin) that restricts inflow
• Thin pay zones -- limited productive interval requiring enhanced contact area
• Bypassing heterogeneity -- reaching past near-wellbore barriers to undamaged rock

The Skin Analogy

An unfractured damaged well has a positive skin factor $S > 0$ that reduces productivity. A hydraulic fracture creates an equivalent negative skin, dramatically increasing effective wellbore radius:

$$r_w' = r_w e^{-S}$$

For a propped fracture of half-length $x_f$ and finite conductivity $F_{cD}$, the equivalent skin can reach $S = -4$ to $-6$, corresponding to effective wellbore radii tens to hundreds of times larger than the physical wellbore.

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Fracture Geometry Fundamentals

How a Fracture Propagates

When fluid is injected above the fracture pressure:

                    Injection
                       │
                       ▼
        ┌──────────────┬──────────────┐
        │              │              │  Overburden
        ├──────────────┼──────────────┤  ─── Stress Barrier (upper)
        │     ◄────────┼────────►     │
        │   Fracture   │  Fracture    │  Pay Zone
        │     wing     │   wing       │  (height h)
        ├──────────────┼──────────────┤  ─── Stress Barrier (lower)
        │              │              │  Underburden
        └──────────────┴──────────────┘

              xf             xf
        ◄──────────►  ◄──────────►
           Half-length    Half-length

The fracture propagates as a bi-wing crack extending symmetrically from the wellbore. The geometry -- width, length (or radius), and height -- depends on the balance between:

1. Fluid pressure inside the fracture
2. In-situ stress resisting fracture opening
3. Rock stiffness (Young's modulus) resisting deformation
4. Fluid leakoff into the formation walls

Key Geometric Parameters

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2D Fracture Geometry Models

Three classical analytical models describe fracture geometry under different assumptions about height confinement and deformation mode:

Model Overview

    PKN Model              KGD Model            Radial Model
    (confined height)      (confined height)    (unconfined)

    ┌────────────┐         ┌────────────┐
    │  │         │         │            │           ╱  ╲
    │  │ ellipse │         │ rectangle  │         ╱      ╲
    │  │ cross-  │         │ cross-     │       ╱    ●     ╲
    │  │ section │         │ section    │         ╲      ╱
    │  │         │         │            │           ╲  ╱
    └────────────┘         └────────────┘        penny-shaped

    w varies along L       w uniform along h     w varies with R
    w_max at wellbore      w_max at center       w_max at center
    Plane strain: vert.    Plane strain: horiz.  Axial symmetry

Decision Guide: PKN vs KGD vs Radial

Rule of thumb:

• If $x_f / h_f > 1$ (fracture longer than tall): PKN
• If $x_f / h_f < 1$ (fracture shorter than tall): KGD
• If height is unconstrained: Radial

Detailed Documentation

• Fracture Geometry Models -- PKN, KGD, and Radial equations with leakoff

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Leakoff and Fluid Efficiency

Carter Leakoff Model

Not all injected fluid goes into creating fracture volume. A significant portion leaks off into the permeable formation walls. Carter (1957) described the leakoff velocity as:

$$u_L = \frac{C_L}{\sqrt{t - \tau}}$$

Where:

• $u_L$ = leakoff velocity, ft/min
• $C_L$ = total leakoff coefficient, ft/min$^{1/2}$
• $t$ = current time
• $\tau$ = time at which the fracture face was first exposed

Three Leakoff Mechanisms

The total leakoff coefficient combines all three:

$$\frac{1}{C_L} = \frac{1}{C_I} + \frac{1}{C_{II}} + \frac{1}{C_{III}}$$

Fluid Efficiency

Fluid efficiency ($\eta$) is the fraction of injected volume that remains in the fracture at any time:

$$\eta = \frac{V_{frac}}{V_{injected}}$$

Fluid efficiency directly affects fracture dimensions -- higher leakoff means shorter, narrower fractures for the same injection volume.

Detailed Documentation

• Fracture Geometry Models -- Leakoff equations and efficiency calculations

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Proppant Transport

Purpose

After pumping stops, the induced fracture closes under in-situ stress. Proppant (sand, ceramic beads, or resin-coated particles) is placed inside the fracture during the treatment to keep it propped open, maintaining a conductive flow path from the reservoir to the wellbore.

Key Considerations

                Fracture Width (w)
                ◄─────────────►
    ┌───────────────────────────────────┐
    │  ○ ○   ○  ○ ○  ○   ○  ○  ○  ○   │  ▲
    │ ○  ○ ○  ○   ○  ○ ○  ○  ○  ○  ○  │  │
    │  ○  ○ ○  settling  ○  ○  ○   ○   │  │  Fracture
    │   ○ ○  ▼  ○ ○  ○ ○   ○  ○ ○  ○  │  │  Height
    │ ○  ○ ○  ○  ○ ○  ○  ○  ○  ○ ○  ○ │  │  (h)
    │○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ │  │
    │○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○○│  ▼
    └───────────────────────────────────┘
           Proppant bank (settled)

Proppant settling during pumping determines the final proppant distribution:

• Settling velocity depends on particle size, density contrast, and fluid rheology
• Wall effects slow settling when particles are large relative to fracture width
• Concentration effects reduce settling in dense slurries (hindered settling)
• Fluid rheology -- power-law fluids used in fracturing significantly reduce settling

Transport Ratio

The transport ratio compares horizontal proppant velocity to settling velocity, indicating whether proppant reaches the fracture tip or banks near the wellbore.

Detailed Documentation

• Proppant Transport -- Settling velocity, wall effects, hindered settling, power-law corrections

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Available Calculation Categories

Fracture Geometry

Proppant Transport

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Practical Workflow

Step 1: Characterize the Formation

1. Determine in-situ stress profile (closure stress, barriers)
2. Obtain rock mechanical properties (Young's modulus, Poisson's ratio)
3. Assess formation permeability and leakoff potential
4. Define pay zone thickness and barrier locations

Step 2: Select Geometry Model

Step 3: Estimate Leakoff

1. Determine leakoff coefficient from mini-frac or lab data
2. Calculate fluid efficiency for the planned pump rate and volume
3. Adjust treatment volume to achieve target fracture dimensions

Step 4: Design Proppant Placement

1. Calculate settling velocity for chosen proppant and fluid
2. Assess transport ratio -- will proppant reach the tip?
3. Determine proppant concentration schedule
4. Verify fracture width exceeds 3x proppant diameter for placement

Step 5: Predict Fracture Dimensions

1. Calculate width, length/radius, and net pressure
2. Verify fracture stays within target zone (height containment)
3. Estimate propped fracture conductivity
4. Calculate equivalent skin and productivity improvement

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Related Documentation

Fracture Models and Proppant

• Fracture Geometry Models -- PKN, KGD, Radial equations and comparison
• Proppant Transport -- Settling, wall effects, hindered settling

Production Impact

• Well Flow Overview -- IPR and skin factor effects on productivity
• Productivity Index -- Equivalent skin from fracture stimulation
• Pipe Flow Overview -- Post-frac production system analysis

Rock and Fluid Properties

• PVT Overview -- Fluid property correlations for leakoff calculations

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References

1. Economides, M.J. and Nolte, K.G. (2000). Reservoir Stimulation, 3rd Edition. John Wiley & Sons.

2. Valko, P. and Economides, M.J. (1995). Hydraulic Fracture Mechanics. John Wiley & Sons.

3. Carter, R.D. (1957). "Derivation of the General Equation for Estimating the Extent of the Fractured Area." Appendix to: Howard, G.C. and Fast, C.R., "Optimum Fluid Characteristics for Fracture Extension." Drilling and Production Practice, API, pp. 261-270.

4. Perkins, T.K. and Kern, L.R. (1961). "Widths of Hydraulic Fractures." Journal of Petroleum Technology, 13(9), pp. 937-949. SPE-89-PA.

5. Geertsma, J. and de Klerk, F. (1969). "A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures." Journal of Petroleum Technology, 21(12), pp. 1571-1581. SPE-2458-PA.