Perforation Design Calculator

Completions engineering skill covering perforation design for vertical and horizontal wells, skin calculations, underbalance criteria, and limited entry design for multi-cluster hydraulic fracturing.

Important: Penetration depths and flow efficiencies are gun-and-formation specific. API RP 19B test results (Berea sandstone) must be corrected for in-situ conditions. Final design should reference vendor ballistic data.

Module 1 — Phasing and Shot Density Selection

Phasing Comparison

Phasing	Casing Stress	Flow Efficiency	Common Use
0° (inline)	Highest	Low (one plane)	Avoid except casing limitation
180°	Moderate	Low	Rarely used; two opposing planes
120°	Good	Good	General production, some frac jobs
90°	Best for frac	Very good	Hydraulic fracturing preferred
60°	Moderate	Best for flow	Near-wellbore efficiency maximum

def phasing_flow_efficiency(phasing_deg):
    """
    Approximate relative flow efficiency vs. open hole (Karakas-Tariq 1991).
    These are directional — actual values are function of shot density and penetration.
    phasing_deg: 60, 90, 120, 180, 360 (0 degrees)
    """
    efficiency = {60: 0.95, 90: 0.92, 120: 0.87, 180: 0.75, 360: 0.65}
    return efficiency.get(phasing_deg, 0.80)

Shot Density Guidelines

Application	Typical SPF	Notes
Gravel pack / unconsolidated	4–6	Maximize inflow area
Conventional production	4–8	Balance skin vs. casing integrity
Hydraulic fracturing entry	2–4	Control entry, limited entry design
Stimulation (matrix acid)	6–12	Maximize contact area
Horizontal limited entry	1–3	Diversion via friction

Module 2 — Penetration Depth (API RP 19B Correction)

def penetration_depth_insitu(L_berea_in, UCS_berea_psi=6000,
                              UCS_insitu_psi=8000,
                              overburden_psi=6500, pore_psi=3000,
                              cementation_factor=1.0):
    """
    API RP 19B: in-situ penetration correction.
    Step 1: Rock strength correction
      L_rc = L_berea * (UCS_berea / UCS_insitu)^0.36
    Step 2: Effective stress correction (Berea tested at zero confining pressure)
      sigma_eff = overburden - pore_pressure
      correction = (1 - 0.086 * sqrt(sigma_eff / 1000))
    L_insitu = L_rc * correction * cementation_factor
    All lengths in inches; pressures in psi.
    """
    L_rc = L_berea_in * (UCS_berea_psi / UCS_insitu_psi)**0.36
    sigma_eff = overburden_psi - pore_psi
    stress_corr = 1.0 - 0.086 * (sigma_eff / 1000.0)**0.5
    return L_rc * stress_corr * cementation_factor

Typical Appalachian corrections:

Formation	UCS (psi)	L_Berea (in)	Correction factor	L_insitu (in)
Marcellus shale	8,000–14,000	12–18	0.55–0.75	7–14
Utica shale	10,000–16,000	12–18	0.50–0.70	6–13
Onondaga limestone	14,000–20,000	10–14	0.45–0.65	5–9

Module 3 — Perforation Skin (Karakas and Tariq, 1991)

Total perforation skin: S_perf = S_H + S_V + S_wb

import math

def horizontal_skin_sh(k_h, k_v, L_perf_in, r_perf_in, h_perf_ft,
                        phasing_deg):
    """
    S_H: horizontal component of perforation skin
    Simplified form (Karakas-Tariq Table 1 constants for phasing):
    S_H = ln(r_w / r'_w)  where r'_w = a1 * exp(a2 * Lp/r_w) * r_w
    Uses phasing-dependent a1, a2 constants from K-T Table 1.
    This is the dominant term for standard completions.
    """
    # Constants from Karakas-Tariq (1991) Table 1
    params = {
        360: (0.250, -2.091, 0.0453),   # 0° phasing
        180: (0.500, -2.025, 0.0943),
        120: (0.648, -2.018, 0.0634),
         90: (0.726, -1.905, 0.1038),
         60: (0.813, -1.898, 0.1023),
    }
    a1, a2, a3 = params.get(phasing_deg, params[90])
    r_w_ft = 0.365   # typical wellbore radius (ft)
    L_perf_ft = L_perf_in / 12.0
    r_perf_ft = r_perf_in / 12.0
    # Effective wellbore radius
    r_w_prime = a1 * r_w_ft * math.exp(a2 * r_perf_ft + a3 * L_perf_ft)
    return math.log(r_w_ft / r_w_prime)

def wellbore_skin_swb(r_perf_in, L_perf_in, r_w_in, spf, phasing_deg):
    """
    S_wb: wellbore skin (near-wellbore damage not cleaned by perfs).
    Typically small for underbalanced perforating; significant for OBP.
    Approximate: S_wb = c1 * exp(c2 * r_w) for phasing-dependent c1, c2.
    """
    c1_c2 = {360: (1.6e-1, 2.675), 180: (2.6e-2, 4.532),
             120: (6.6e-3, 5.320),  90: (1.9e-3, 6.155), 60: (3.0e-4, 7.509)}
    c1, c2 = c1_c2.get(phasing_deg, c1_c2[90])
    r_w_ft = r_w_in / 12.0
    return c1 * math.exp(c2 * r_w_ft)

def total_perforation_skin(S_H, S_V=0.0, S_wb=0.0):
    """S_total = S_H + S_V + S_wb"""
    return S_H + S_V + S_wb

Module 4 — Underbalanced vs. Overbalanced Perforating

Underbalance Pressure Recommendation (King, 1989)

def recommended_underbalance(reservoir_psi, k_md, fluid="gas"):
    """
    Recommended underbalance pressure (psi) to clean perforation tunnels.
    King (1989) empirical:
      Gas wells:  UB = 250 + 5500/k for k < 10 mD
      Oil wells:  UB = 1000 - 200*k for k in [0.01, 5] mD
                  UB = 200 psi minimum
    k_md: formation permeability (mD)
    """
    if fluid.lower() == "gas":
        ub = 250 + 5500.0 / max(k_md, 0.1)
    else:
        ub = max(200.0, 1000.0 - 200.0 * k_md)
    # Don't exceed reservoir pressure
    return min(ub, reservoir_psi * 0.85)

def is_underbalanced(wellbore_psi, reservoir_psi):
    """Simple check: wellbore_psi < reservoir_psi -> underbalanced."""
    return wellbore_psi < reservoir_psi

Selection guidance:

Condition	Recommended	Notes
k > 50 mD	Either; OBP simpler	Perfs clean up quickly on flow
k = 1–50 mD	Underbalanced preferred	Surge removes crushed zone
k < 1 mD (tight)	Overbalanced + acid or frac	UBP has limited benefit
H2S present	Avoid large UBP	Risk of rapid depressurization
Unconsolidated	Balanced or slight OBP	UBP can cause sand influx

Module 5 — Limited Entry Design (Multi-Cluster Horizontal)

Friction Pressure at Perforation Entry

def perforation_friction_pressure(q_bpm, n_perfs, d_perf_in,
                                   fluid_sg=1.0, Cd=0.9):
    """
    dP_perf = 0.2369 * (rho / Cd^2) * (q / n / d^2)^2
    q_bpm:    total injection rate (bbl/min)
    n_perfs:  total number of perforations in cluster
    d_perf_in: entry hole diameter (inches)
    fluid_sg: fluid specific gravity
    Cd:       discharge coefficient (0.85–0.95 typical)
    Returns: friction pressure (psi) across perforations
    """
    rho_ppg = fluid_sg * 8.34   # lb/gal
    q_per_perf_bpm = q_bpm / n_perfs
    return 0.2369 * (rho_ppg / Cd**2) * (q_per_perf_bpm / d_perf_in**2)**2

Diversion Efficiency (Limited Entry)

def limited_entry_diversion(q_total_bpm, n_clusters, spf_per_cluster,
                              d_perf_in, delta_stress_psi, fluid_sg=1.0,
                              Cd=0.9):
    """
    Equal entry when dP_perf >> delta_stress between clusters.
    Rule of thumb: dP_perf per cluster > 2 × stress contrast to ensure
    >80% of clusters accept fluid.
    Returns: dP_perf for a single cluster and diversion ratio estimate.
    """
    n_perfs_cluster = spf_per_cluster
    q_per_cluster_bpm = q_total_bpm / n_clusters
    dp = perforation_friction_pressure(q_per_cluster_bpm,
                                        n_perfs_cluster, d_perf_in,
                                        fluid_sg, Cd)
    ratio = dp / delta_stress_psi if delta_stress_psi > 0 else float("inf")
    efficiency = min(1.0, 0.5 + 0.5 * min(ratio / 2.0, 1.0))
    return {"dP_perf_psi": dp, "diversion_ratio": ratio,
            "estimated_cluster_efficiency": efficiency}

Appalachian limited entry parameters:

Typical stress contrast between clusters: 200–800 psi
Target dP_perf: 500–1,500 psi for adequate diversion
Entry hole diameter: 0.38"–0.50" for most perforating charges at 2–4 SPF

Output Format

## Perforation Design — [Well / Zone]
**Formation:** [Name] | **Depth:** X,XXX–X,XXX ft | **k:** X.X mD

### Gun/Charge Selection
| Parameter | Value |
|-----------|-------|
| Charge type | [API RP 19B class] |
| Berea penetration (in) | |
| In-situ penetration (in) | [corrected] |
| Entry hole diameter (in) | |
| Shot density (SPF) | |
| Phasing | |

### Perforation Skin Summary
| Component | Value |
|-----------|-------|
| S_H (horizontal) | |
| S_V (vertical) | |
| S_wb (wellbore) | |
| S_perf (total) | |

### Underbalance Assessment
| Recommended UB (psi) | Achievable UB (psi) | Method |
|---------------------|--------------------|----|
| | | UBP / OBP + acid |

### Limited Entry (Horizontal)
| Cluster spacing (ft) | SPF/cluster | dP_perf (psi) | Stress contrast (psi) | Efficiency |
|---------------------|------------|--------------|----------------------|------------|
| | | | | |

Error Handling

Condition	Cause	Action
S_H very negative	Perfs longer than wellbore radius	Check input units (in vs ft)
dP_perf < stress contrast	Too many perfs or large holes	Reduce SPF or entry diameter
In-situ penetration < 2 in	Very hard rock + deep wells	Consider larger gun OD or jet perforating
UB exceeds reservoir pressure	Calculation error	Cap at 85% of reservoir pressure

Caveats

Karakas-Tariq skin equations are analytical and assume uniform perforation tunnel penetration. In reality, tunnels vary due to rock heterogeneity and gun eccentricity.
API RP 19B Berea strength correction is an empirical approximation. Lab testing of actual formation core is more accurate for penetration prediction.
Limited entry diversion efficiency assumes uniform stress contrast across clusters. Natural fractures and local heterogeneity can override designed diversion.
Perforation friction pressure equations assume Newtonian fluid. For viscoelastic frac fluids, apparent viscosity at perforation velocity is typically much higher — dP_perf will be larger (better diversion).
Near-wellbore tortuosity (not captured here) can dominate treating pressure in tight formations; evaluate with step-down test after perforating.

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