SP-3: Formation Damage & Hawkins · GK-22

SP-3 · Topic 3.3 · Formation Damage & Hawkins

SP-3: Damage Anatomy & Acid Treatment Design

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Engineering Question for SP-3

Module 03 PBL · Gashaka GK-22

SP-1 established S_d = +14; SP-2 confirmed all of it is rate-independent. Now you must answer: what is physically causing this damage, how far into the formation does it extend, and what acid formulation and volume will remove it?

Hawkins' formula is the bridge between the petrophysical (k_s/k from core flood) and the reservoir engineering (S_d from PTA). Its inverse form allows you to back-calculate the damage radius r_s from the measured skin and the core-measured permeability impairment ratio. This gives you the physical damage geometry, essential for calculating acid volumes and specifying treatment penetration depth.

Core Flood Data — Use Hub Values Only

The corrected core flood data is published on the Module 03 Hub (Core Flood section). Key values: k_s/k = 0.145 (pay average); post-acid restoration = 76.5% of k_DST (= 65 md). Draft versions of this data contained errors — do not use any values from earlier materials.

Data for SP-3

GK-22 SP-3 Data — Reservoir, Core Flood & Well Geometry

Parameter	Symbol	Value	Units	Source
Formation permeability (DST, undamaged)	k	85	md	Horner PTA kh/h
Wellbore radius	r_w	0.35	ft	Completion data
Pay porosity	φ	0.218	fraction	Core plug analysis
Net pay thickness	h	42	ft	Petrophysical log
Damage skin (confirmed from SP-1 & SP-2)	S_d	+14.00	dimensionless	PTA + SP-2 result
Pay-average k_s/k (core flood — corrected)	k_s/k	0.145	dimensionless	Core flood lab (Hub)
k_s (damaged zone permeability)	k_s	12.33	md	0.145 × 85
Post-acid k restoration (core flood — corrected)	k_acid/k_DST	0.765	fraction (76.5%)	Core flood lab (Hub)
Post-acid k_s,new	k_acid	65.0	md	(92+38)/2 md

Two-Zone Model Parameters (for Task 2)

Zone	Physical Description	k_s/k	r_inner (ft)	r_outer (ft)	S_d contribution
Zone 1 — Mud solids	Overbalanced perforation + drilling mud filter cake solids. GK-2 sample (clay-rich) representative.	0.08	r_w = 0.35	r_s1 = 0.60	To be calculated
Zone 2 — WBM filtrate	18-day WBM filtrate invasion zone. Clay swelling + kaolinite migration. GK-1 representative.	0.25	r_s1 = 0.60	r_s2 = ?	To be calculated

KWL Table

K — Know

Hawkins forward: S_d = (k/k_s−1) × ln(r_s/r_w)
k_s/k = 0.145 from core flood (pay average)
Post-acid restoration = 76.5% (k_acid = 65 md)
18 days WBM = deep filtrate invasion in 85 md sand
Kaolinite migrates; smectite swells on contact with fresh water

W — Want to Know

What r_s is consistent with S_d = +14 and k_s/k = 0.145?
How does the two-zone model reconcile with the single-zone equivalent?
What acid volume penetrates to r_s2 = 8 ft?
Why must acid be placed BEFORE gravel pack?
What post-treatment skin does 76.5% restoration give?

L — Learned

r_s (single-zone) = ________ ft
S_d1 (Zone 1 solids) = +________
S_d2 (Zone 2 filtrate) = +________; r_s2 = ________ ft
S_d,post = +________ (target after acid)
Acid volume = ________ bbl (to penetrate Zone 2)

Just-in-Time Resources

Pull these up as you work SP-3. Each maps to the Module 03 topic behind this sub-problem: read the topic page, watch the matching lectures, then reproduce your numbers with the verified calculator.

Study

Topic 3.3 — Formation Damage & Hawkins' Formula — damage origins, S_d from k_s/r_s, and what acid can and cannot fix.

Topic 3.3 — Formation Damage & Hawkins

Watch

Lecture 3.3a — Formation Damage: Physical Origins and the Skin Connection
Lecture 3.3b — Using Hawkins' Formula
Lecture 3.3c — Pseudodamage vs True Formation Damage: What Acid Can and Cannot Fix

Produced lectures

Self-check

hawkins.py — S_d, two-zone damage, and the single-zone damaged pore volume. Running it confirms the acid pore-volume figure in Task 4.

Verified calculator — reproduce your numbers

Tasks & Requirements

SP-3 Calculation Tasks

Single-zone Hawkins inverse — calculate r_s
Using k_s/k = 0.145 (k/k_s = 6.897) and S_d = +14.0:
r_s = r_w × exp[S_d / (k/k_s − 1)]
Calculate r_s in feet. Then verify by forward calculation: S_d = (k/k_s−1) × ln(r_s/r_w) must return exactly +14.0.
Expected: r_s ≈ 3.76 ft. Note: previous draft materials cited 3.77 ft — this rounding difference is acceptable. Use the most precise value your calculator gives and verify by forward calculation.
Two-zone composite damage model
Zone 1 — Mud solids (r_w = 0.35 to r_s1 = 0.60 ft, k_s1/k = 0.08):
S_d1 = (k/k_s1 − 1) × ln(r_s1/r_w)

Zone 2 — WBM filtrate (r_s1 to r_s2, k_s2/k = 0.25):
S_d2 = S_d,total − S_d1
Then back-calculate: r_s2 = r_s1 × exp[S_d2 / (k/k_s2 − 1)]

Verify: S_d1 + S_d2 = +14.00 exactly.
Expected: S_d1 ≈ +6.20 (mud solids, tight zone), S_d2 ≈ +7.80 (filtrate, r_s2 ≈ 8.08 ft). Physical interpretation: Zone 1 is the highly impaired solids-invasion zone (k reduced to 8% of formation k) over just 0.25 ft; Zone 2 is the filtrate-invaded zone (k reduced to 25% of k) extending to 8 ft. Despite Zone 1 being much more severely damaged, Zone 2 contributes more to total skin because it extends over a much larger radial distance.
Post-acid skin prediction using Hawkins forward
Post-acid k_s,new = 0.765 × 85 = 65.0 md (from core flood acid response)
S_d,post = (k/k_acid − 1) × ln(r_s/r_w)
Use r_s from Task 1 (single-zone equivalent). Report to 2 decimal places.
Expected: S_d,post ≈ +0.73 → rounded to +1.0 for design purposes. The acid reduces damage skin from +14.0 to approximately +1.0 — a 93% reduction. The residual +1 reflects incomplete clay dissolution (chlorite in GK-2 sample inhibits full HF attack) and was confirmed in the core flood at 24-hour soak time.
Calculate the acid volume required to penetrate Zone 2
The acid must penetrate to r_s2 ≈ 8.08 ft to dissolve the filtrate-invasion damage. Calculate the pore volume of the treatment zone:
PV_zone = π × (r_s2² − r_w²) × h × φ [ft³] then convert to bbl (1 bbl = 5.615 ft³), and express per foot of interval in gal/ft.
The design treatment volume = 1 × PV_zone (one displaced pore volume just fills the damaged zone to r_s2). Report the design volume, and also state the 2 × PV value as a conservative full-displacement / overflush upper bound.
Expected: PV_zone = π(8.08² − 0.35²) × 42 × 0.218 ÷ 5.615 ≈ 334 bbl ≈ 1 pore volume. Per foot: 334 bbl × 42 gal/bbl ÷ 42 ft ≈ 334 gal/ft — essentially the canonical T6 mud-acid design target of 350 gal/ft (≈ 1× damaged-zone pore volume). Design basis: 350 gal/ft × 42 ft ≈ 14,700 gal ≈ 350 bbl of 3% HCl/2.5% HF mud acid. The 2× PV figure (≈ 668 gal/ft ≈ 668 bbl) is the conservative full-displacement/overflush upper bound, not the design target.
Design the complete 4-step acid treatment programme
Specify the following treatment stages in sequence, with volumes and physical justification for each:
Stage 1 — TCP Reperforation: Shot density, underbalance pressure (psi), and reason for upgrading from 4 to 8 spf before acid treatment.
Stage 2 — HCl Preflush: Concentration (%), volume (gal/ft), and purpose (neutralise carbonates; prepare formation for HF entry; displace completion brine).
Stage 3 — 3% HCl / 2.5% HF Mud Acid: Volume in gal/ft and total bbl. Placement method (coil tubing? bullhead?). Why not higher HF concentration for GK-2 clay-rich lamina?
Stage 4 — KCl Overflush: Concentration (%), volume, and critical safety reason: why must all HF acid be displaced from the wellbore before gravel pack placement?

Critical Safety: HF Acid Must Not Contact Gravel

HF (hydrofluoric acid) dissolves silicate minerals — including quartz (SiO₂), the primary component of 12/20 mesh Ottawa sand gravel. If spent or live HF contacts the gravel pack, it dissolves gravel grains, producing amorphous silica precipitate that reduces k_g from 800,000 md to near zero, destroying the completion. The KCl overflush volume must be at minimum 1.5× the wellbore volume below the perforations to guarantee all HF is displaced into the formation before gravel slurry is pumped.

Theory Reference

Hawkins' Formula — Forward and Inverse Forms

Hawkins Single-Zone — Forward and InverseFORWARD (ks/k and rs known → Sd): Sd = (k/ks - 1) × ln(rs/rw) INVERSE (Sd and ks/k known → rs): rs = rw × exp[ Sd / (k/ks - 1) ] GK-22 Single-Zone Calculation (ks/k = 0.145): k/ks = 1/0.145 = 6.897 k/ks - 1 = 5.897 rs = 0.35 × exp(14.0 / 5.897) = 0.35 × exp(2.373) = 0.35 × 10.73 = 3.756 ft ≈ 3.76 ft Forward Verification: Sd = (6.897 - 1) × ln(3.756/0.35) = 5.897 × ln(10.73) = 5.897 × 2.373 = 13.99 ≈ +14.0 ✓ Post-Acid Forward (k_acid = 65 md): Sd,post = (85/65 - 1) × ln(3.756/0.35) = (1.3077 - 1) × 2.373 = 0.3077 × 2.373 = 0.730 ≈ +0.73 → target +1.0 Two-Zone Composite ModelZone 1 (solids: rw=0.35 to rs1=0.60, ks1/k=0.08): Sd1 = (1/0.08 - 1) × ln(0.60/0.35) = (12.5 - 1) × ln(1.714) = 11.5 × 0.5390 = +6.198 ≈ +6.20 Zone 2 (filtrate: rs1=0.60 to rs2=?, ks2/k=0.25): Sd2 = 14.00 - 6.20 = 7.80 rs2 = 0.60 × exp(7.80 / (1/0.25 - 1)) = 0.60 × exp(7.80 / 3.0) = 0.60 × exp(2.600) = 0.60 × 13.46 = 8.08 ft Verification: Sd2 = (4.0 - 1) × ln(8.08/0.60) = 3.0 × 2.600 = 7.80 ✓ Total Sd = 6.20 + 7.80 = 14.00 ✓

The two-zone model is internally consistent: both zones sum to the measured S' = +14, and both r_s values are physically reasonable (solids invasion to 0.6 ft; filtrate invasion to 8 ft in an 85 md sand after 18 days overbalanced drilling — consistent with filter cake invasion modelling).

Deliverable

✅ SP-3 Checklist

Single-zone inverse: r_s = 3.76 ft with full Hawkins inverse working. Forward verification: S_d = +14.00 ✓
Two-zone model table: Zone 1 (k_s1/k=0.08, r_s1=0.60 ft, S_d1=+6.20) and Zone 2 (k_s2/k=0.25, r_s2=8.08 ft, S_d2=+7.80). Sum verified = +14.00.
Post-acid prediction: S_d,post = +0.73 → design target +1.0, with full Hawkins forward working and reference to core flood k_acid = 65 md.
Acid volume: Pore volume of Zone 2 in bbl, and required treatment volume in bbl and gal/ft.
4-step treatment programme: Each stage specified with volume, concentration, and physical justification. HF/gravel safety note included.

Locked Outputs for SP-5 and SP-6

S_d,post = +1.0 (treatment target) | r_s = 3.76 ft (single-zone equiv.) | r_s2 = 8.08 ft (filtrate zone depth) | k_acid = 65 md

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