Multistage horizontal fracture design

Now the pieces come together. The 4-22H will have a lateral of about 9,800 ft, a cemented 4-1/2 in liner tied back to surface for fracturing, and a plug-and-perf completion like the 3-22H. Ethan has to decide how many stages, how many clusters in each, how many holes in each cluster, what rate, what fluid and how much proppant, and he has to check that the frac string can take the pressure. Tom gives him one rule: 'Every cluster you shoot should get its share of fluid and sand. A cluster that takes nothing is money you spent on a hole in the casing.'

This lesson covers the design of a multistage treatment along a horizontal well: landing the lateral, spacing stages and clusters, limited-entry perforating to share fluid between clusters, pumping schedules, rates and pressures, and the logistics of water, proppant and equipment.

Landing and lateral placement

The design starts before the well is drilled, with the choice of landing zone and lateral direction. The lateral is drilled roughly along the minimum horizontal stress direction so that fractures are transverse (lesson 7). Its vertical position within the target is chosen where the rock is most productive and where fractures will grow into the best rock: often in the more brittle, higher-quality layers, with stress barriers to keep height under control. Geosteering keeps the well in the zone (PET-310). Well spacing between neighboring laterals is chosen with the fracture half-length in mind; wells that are too close interfere with each other and share the same rock, while wells too far apart leave rock undrained.

Stages and clusters

A stage is the length of lateral fractured in one pumping operation, isolated from the rest by plugs or packers. Each stage contains several perforation clusters, short perforated intervals, each meant to start its own fracture. Over the past two decades, operators have moved toward shorter stages, more clusters and closer cluster spacing, on the theory that more fractures contact more rock. Typical modern designs have stages of about 150 to 300 ft with three to eight clusters, and cluster spacing of about 30 to 80 ft.

Closer spacing has limits. Stress shadows from neighboring fractures (lesson 8) can stop middle clusters growing; too many clusters per stage divide the rate so much that some never break down; and costs rise with stage count. Many operators now test spacing on pilot wells with fiber-optic or tracer diagnostics before changing their standard design.

Limited entry

When several clusters are open at once, fluid goes preferentially to the cluster with the lowest breakdown and closure stress. Limited-entry design counters this by deliberately restricting the number and size of perforation holes, so that the friction across the holes is large. The pressure inside the casing must then rise well above the fracturing pressure of every cluster, and each cluster takes a similar share of the rate, because small differences in stress become small compared with the perforation friction.

The pressure drop across a set of perforations comes from Bernoulli's equation, with a discharge coefficient Cd that accounts for the shape of the entry hole. With q the rate through the cluster, ρ the fluid density, n the number of holes and d their diameter:

In oilfield units, with q in bbl/min, ρ in lbm/gal and d in inches, the equation becomes Δp = 0.2369 q² ρ/(n² d⁴ Cd²), in psi. Erosion by proppant enlarges the holes and rounds their edges during the job, so Cd rises and the friction falls; designers allow for this, sometimes using equal-entry charges that make consistent round holes.

# Multistage design: limited-entry perforation friction, rate split between clusters, stage volumes and surface pressure
import math
SI = False  
if SI:   # 03-22 Cardium: kPa, m3/min, mm, kg/m3
    q_stage, rho, d_hole, cd = 8.0, 1010.0, 9.5, 0.80
    stresses = [23200.0, 23500.0, 23050.0, 23900.0]          # closure stress at each of 4 clusters, kPa
    net = 2500.0
    def pf(q, n):                                             # perforation friction, kPa, for q m3/min through n holes
        qs = q / 60.0; a = math.pi / 4 * (d_hole / 1000.0) ** 2
        return 8 * rho * qs**2 / (math.pi**2 * cd**2 * n**2 * (d_hole / 1000.0) ** 4) / 1000.0
    stages, fluid_per_stage, prop_per_stage = 20, 260.0, 30.0   # m3, metric tons
    tvd, md, fr_grad, hydro_grad, burst = 1560.0, 3258.0, 2.45, 9.9, 53400.0
    pu, qu, fu, mu_ = "kPa", "m3/min", "m3", "t"
    trials, design = (12, 6, 4), 6
else:    # 3-22H Bakken: psi, bbl/min, in, lbm/gal
    q_stage, rho, d_hole, cd = 80.0, 8.45, 0.40, 0.80
    stresses = [8040.0, 8110.0, 7990.0, 8200.0, 8060.0]     # 5 clusters
    net = 450.0
    def pf(q, n): return 0.2369 * q**2 * rho / (n**2 * d_hole**4 * cd**2)
    stages, fluid_per_stage, prop_per_stage = 40, 6500.0, 250000.0   # bbl, lbm
    tvd, md, fr_grad, hydro_grad, burst = 10450.0, 20520.0, 0.19, 0.44, 12410.0
    pu, qu, fu, mu_ = "psi", "bbl/min", "bbl", "lbm"
    trials, design = (12, 6, 5, 4), 5
def split(n_holes):
    lo, hi = min(stresses), max(stresses) + 10 * net + pf(q_stage, n_holes) * 50
    for _ in range(200):
        p = (lo + hi) / 2; qs = []
        for s in stresses:
            dp = p - s - net
            if dp <= 0: qs.append(0.0); continue
            # invert pf: q = sqrt(dp / pf(1, n))
            qs.append(math.sqrt(dp / pf(1.0, n_holes)))
        if sum(qs) > q_stage: hi = p
        else: lo = p
    return p, qs
for holes in trials:
    p, qs = split(holes)
    share = ", ".join(f"{x/q_stage:4.0%}" for x in qs)
    print(f"{holes:2d} holes per cluster: perf friction {pf(q_stage/len(stresses), holes):6,.0f} {pu}; cluster shares {share}")
p, qs = split(design)
bhtp = p
print(f"design: {design} holes per cluster")
stp = bhtp - hydro_grad * tvd + fr_grad * md
print(f"pressure inside the casing at the perforations {bhtp:,.0f} {pu}; hydrostatic {hydro_grad*tvd:,.0f}; pipe friction {fr_grad*md:,.0f}")
print(f"surface treating pressure {stp:,.0f} {pu}; 80% of casing burst {0.8*burst:,.0f} {pu} -> {'acceptable' if stp < 0.8*burst else 'too high'}")
print(f"totals for {stages} stages: fluid {stages*fluid_per_stage:,.0f} {fu}, proppant {stages*prop_per_stage:,.0f} {mu_}")
print(f"hydraulic power at the pumps: {stp*q_stage/(60.0 if SI else 1.0)*(1.0 if SI else 1/40.8):,.0f} {'kW' if SI else 'hp'}")

12 holes per cluster: perf friction    217 psi; cluster shares  22%,  19%,  24%,  14%,  21%
 6 holes per cluster: perf friction    869 psi; cluster shares  20%,  20%,  21%,  19%,  20%
 5 holes per cluster: perf friction  1,251 psi; cluster shares  20%,  20%,  21%,  19%,  20%
 4 holes per cluster: perf friction  1,955 psi; cluster shares  20%,  20%,  20%,  19%,  20%
design: 5 holes per cluster
pressure inside the casing at the perforations 9,782 psi; hydrostatic 4,598; pipe friction 3,899
surface treating pressure 9,083 psi; 80% of casing burst 9,928 psi -> acceptable
totals for 40 stages: fluid 260,000 bbl, proppant 10,000,000 lbm
hydraulic power at the pumps: 17,810 hp

For the 4-22H, with five clusters per stage at 80 bbl/min and closure stresses differing by up to 210 psi, twelve holes per cluster give only about 220 psi of friction, and the shares range from 14 to 24 percent. Six holes give about 870 psi and shares within 19 to 21 percent. Ethan chooses five holes, with about 1,250 psi of friction. The surface treating pressure is about 9,100 psi, under 80 percent of the frac string's burst rating of about 12,400 psi, but with less margin than he would like; the pumps need about 17,800 hydraulic horsepower.

Rate and surface pressure

The rate is chosen to give enough rate per cluster to break down and grow each fracture and to carry proppant in slickwater, and it is limited by surface pressure and available horsepower. The surface treating pressure is the bottomhole treating pressure minus the hydrostatic pressure of the fluid column plus the friction in the pipe and the perforations.

Friction reducers cut pipe friction to a fraction of plain water's, and pipe friction is often the largest controllable term in long laterals. The casing or frac string must hold the maximum surface pressure with a margin; operators commonly limit treating pressure to about 80 percent of the burst rating of the weakest component, and set the pump pressure relief and the automatic shutdown below that. Proppant-laden slurry is heavier than water, which raises the hydrostatic and slightly lowers the surface pressure, while proppant in the perforations erodes them and lowers the friction during a stage. A screenout, in which proppant bridges in the fracture or perforations and the pressure rises sharply, ends the stage and must be cleaned out, often with coiled tubing.

The pumping schedule

Each stage follows a schedule. An acid spearhead may be pumped first to clean the perforations and lower breakdown pressure. A pad of clean fluid opens the fractures and supplies leak-off. Proppant is then added in steps of rising concentration, so that the fracture is filled with sand as it closes from the tip back. Finally, a flush of clean fluid displaces the last proppant slurry out of the casing, stopping just short of the perforations so as not to overdisplace and leave the near-wellbore part of the fracture unpropped.

Slickwater stages in unconventional wells commonly use low concentrations of fine sand, ramped up through the stage; gel jobs in conventional rock use higher concentrations of coarser proppant, sometimes ending with a tail-in of resin-coated sand. Designers size the stage volumes from models calibrated with past jobs and with production results, not only from simple geometry models.

Logistics

A multistage job is an industrial operation. A large frac spread includes a dozen or more high-pressure pumps, blenders that mix proppant and chemicals into the fluid, a data van, sand storage and conveyors, chemical trailers, water tanks or pits, iron and manifolds, and often a wireline unit and crane for plug-and-perf. Zipper fracturing alternates stages between two or more wells on the same pad so that the wireline work on one well happens while the other is being pumped, keeping the pumps busy. Simultaneous fracturing pumps two wells at once from one spread.

Water supply drives the schedule. The 4-22H needs about 260,000 bbl, about 11 million gallons, for 40 stages. North Dakota requires water permits from the State Water Commission for new sources; Prairie Crest sources much of its fracturing water from permitted depots supplied by groundwater and the Missouri River system, plus recycled produced water, piped where possible to reduce truck traffic. Fuel, dust control and noise are planned with landowners and neighbors, and traffic is a real concern for nearby residents.

Equipment and emissions

Frac pumps were traditionally diesel-driven. Many operators now use dual-fuel pumps that burn natural gas with diesel, or electric pumps powered by gas turbines or the grid, which cut fuel cost, emissions and noise. Field gas from nearby wells can fuel them, turning a waste stream into an energy source. These choices feed into the program's cost and its environmental assessment.

Checking the design

Before finalizing, Ethan checks the design against the well and the rock. The casing and wellhead ratings exceed the maximum pressure with margin. The tubing and casing temperature and pressure loads are acceptable. The cement bond log shows isolation between stages and above the top stage. The stage and cluster positions avoid faults identified on seismic, and keep a safe distance from offset wells, whose operators are notified as required. The water, proppant and equipment are available on the planned dates. And the expected production gain justifies the cost, which is the subject of the capstone.