Question 5 of 5: Production Casing Design — Burst, Collapse and Tensile

Question 5: Production Casing Design — Burst, Collapse and Tensile (equal value)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. $7$ in production casing to $12{,}000$ ft TD; open hole $8\tfrac34$ in; mud weight $14.1$ ppg; pore-pressure gradient $13.5$ ppg; fracture gradient $15.5$ ppg; salt-water gradient $0.45$ psi/ft; design factors $DF_{burst}=1.1$, $DF_{collapse}=1.0$, $DF_{tensile}=1.6$; three available N-80/P-110 casing weights (table above); methane is the produced fluid.

Find. A casing program (grade, weight, length of each section) satisfying burst, collapse and tensile design factors over the full 12,000 ft.

Approach. Collapse governs at the SHOE (external mud column, casing assumed fully evacuated — worst case); burst governs at the SURFACE (a methane kick displacing mud all the way up, backed up externally by a degraded salt-water column). Build both load profiles vs. depth, apply the design factors, find where each available casing satisfies both simultaneously, taper the string to use the lighter/cheaper casing wherever it qualifies, then confirm tensile is not exceeded anywhere in the tapered string.

1. Collapse load (worst case: evacuated casing, full external mud column). $P_{collapse}(D)=0.052\,MW\,D$; at TD, $P_{collapse}(12{,}000)=0.052(14.1)(12{,}000)$, so $\boxed{P_{collapse,TD}=8{,}798\ \text{psi}}$, required rating $=8{,}798\times1.0=8{,}798$ psi (max, at the shoe).
2. Burst load (worst case: methane kick reaches surface, salt-water backup outside). Pore pressure at TD $=0.052(13.5)(12{,}000)=8{,}424$ psi. Assuming a methane gradient of $0.1$ psi/ft in the kick column, surface shut-in casing pressure $SICP=8{,}424-0.1(12{,}000)$, so $\boxed{SICP=7{,}224\ \text{psi}}$. Net burst (internal minus salt-water backup, $0.45$ psi/ft) at depth $D$: $P_{net}(D)=\left[SICP+0.1D\right]-0.45D=7{,}224-0.35D$, maximum at the surface: $\boxed{P_{net}(0)=7{,}224\ \text{psi}}$, required rating $=7{,}224\times1.1=7{,}946$ psi (max, at surface); at TD it falls to $7{,}224-0.35(12{,}000)=3{,}024$ psi.
3. Screen each casing against both requirements. N-80 26# (burst 7,240, collapse 5,410): satisfies burst $\times1.1\le7{,}240$ only for $D\ge1{,}835$ ft, and collapse $\times1.0\le5{,}410$ only for $D\le7{,}379$ ft — usable ONLY in the middle interval $1{,}835$–$7{,}379$ ft. N-80 32# (burst 10,040, collapse 10,320): required burst never exceeds $7{,}946$ psi and required collapse never exceeds $8{,}798$ psi anywhere in the well, so it is $\boxed{\text{adequate over the FULL 0–12,000 ft length}}$.
4. Design the tapered string. Use the cheaper N-80 26# wherever both checks clear it, bracketed by N-80 32# where either check fails: $\boxed{0\text{–}1{,}850\ \text{ft: N-80, 32 lb/ft}}$ (burst-critical zone, rounded conservatively below the 1,835 ft crossover), $\boxed{1{,}850\text{–}7{,}350\ \text{ft: N-80, 26 lb/ft}}$ (checked: burst req. at 1,850 ft $=1.1(7{,}224-0.35(1{,}850))=7{,}234\le7{,}240$ ✓; collapse req. at 7,350 ft $=0.052(14.1)(7{,}350)=5{,}389\le5{,}410$ ✓), $\boxed{7{,}350\text{–}12{,}000\ \text{ft: N-80, 32 lb/ft}}$ (collapse-critical zone).
5. Tensile check (buoyed weight, buoyancy factor $BF=1-14.1/65.5=0.785$). Air weight of the full string $=1{,}850(32)+5{,}500(26)+4{,}650(32)=351{,}000$ lbf, buoyed $=351{,}000(0.785)=275{,}441$ lbf, carried at the wellhead by the top (N-80 32#) joint: $SF_{top}=745{,}000/275{,}441=2.70$. Weight hanging below the top of the middle section (26# $+$ bottom 32#) $=291{,}800$ lbf air, $228{,}985$ lbf buoyed, carried by N-80 26# body strength: $SF_{mid}=604{,}000/228{,}985=2.64$. Both clear $\boxed{SF\ge1.6}$ with margin — tensile does not govern this design.