Chemical EOR · Capillary desaturation · HTHS carbonates

What applied trapping number is required to mobilize residual oil in our carbonates?

The underlying manuscript measures, on aged mixed-to-oil-wet carbonate reservoir core plugs, the applied force required to mobilize residual oil during low-IFT surfactant flooding (σ_os = 3.07×10⁻³ mN/m, as reported in the preprint). Each experiment maps a capillary desaturation curve (CDC) — remaining oil saturation versus the applied trapping number N_t — and resolves the critical trapping number N_t,crit at which residual oil first mobilizes. On this SAMPLE set the onsets for mixed-to-oil-wet carbonates fall 31–140× above the water-wet sandstone reference used by default in screening tools, reproducing the manuscript's qualitative finding — a shift that directly changes surfactant-flood design for these reservoirs.

Explore field-rate scaling

CDC corefloods completed: 3of 4
N_t,crit — reservoir Core B: 1.37×10⁻³
above water-wet sandstone onset: 31–140×
of residual oil mobilized (Core B, SF1): 72%

SAMPLE DATAThe SAMPLE records reach the same screening conclusions as the manuscript with different values; the measured records are not published here.

Manuscript: Critical Trapping Numbers and Capillary Desaturation in Mixed-to-Oil-Wet Carbonates under High-Temperature, High-Salinity Surfactant Flooding — under review at Geoenergy Science and Engineering; preprint on SSRN. The preprint has not been peer reviewed.

Preprint record (SSRN)

The central finding — mobilization-force ladderSAMPLE DATA

log scale · SAMPLE onsets vs water-wet benchmark

Program contributions

scope

Centrifuge-conditioned CDC and N_t,crit measurements for crude-aged carbonates at 100 °C and 243,028 ppm TDS connate salinity — a dataset range not previously available. The residual-oil baseline is corrected for the capillary end effect that biases classical low-rate waterflood endpoints.
Carbonate-specific mobilization thresholds in place of transferred water-wet sandstone correlations — a shift in N_t,crit of 1.5–2.1 orders of magnitude (31–140× on this SAMPLE set) attributed primarily to wettability.
A multi-rate CDC protocol executed to completion at 100 °C and 243,028 ppm TDS using a thermally stable low-IFT GAC/IOS formulation (σ_os = 3.07×10⁻³ mN/m; aqueous-stable ≥ 21 days at 120 °C) — conditions under which conventional sulfate surfactants hydrolyze.
Field-rate translation of the thresholds into velocity–viscosity screening targets, implemented as a live calculator alongside the data.

Gaps this work closes

why it was needed

HTHS experimental gap: extended multi-rate CDC protocols rarely survive surfactant degradation, divalent-ion precipitation and phase instability at these temperatures and salinities — HTHS-condition carbonate CDC datasets are correspondingly limited.
Baseline-definition gap: historical CDCs anchor S_orw on low-rate waterflood endpoints; in mixed-to-oil-wet rock these terminate at an apparent remaining saturation, biasing N_t,crit downward and rendering chemical-EOR forecasts non-conservative.
Data-scarcity gap: conditioned mixed-wet carbonate CDC datasets are limited, and reservoir models default to water-wet correlations — a transfer that is not conservative for these systems.
Screening-transfer gap: no carbonate-specific benchmark existed to assess whether field-achievable trapping numbers (u ≈ 1 ft/day) can initiate desaturation; CDC#2 places the SF1 baseline just below the measured onset — the primary screening result of this work.

Program statusSAMPLE DATA

CDC#1

Core A

Outcrop reference

Completed

CDC#2

Core B

Reservoir carbonate

Completed

CDC#3

Core C

Reservoir carbonate

Completed

CDC#4

New core

—

Planned

CDC#5

New core

—

Planned

Definition. The trapping number N_t combines injection velocity, displacing-phase viscosity, and interfacial tension into a single dimensionless measure of the applied mobilizing force. The critical trapping number N_t,crit is the value at which residual oil first mobilizes: under the tested conditions, incremental recovery was not observed below this onset; above it, recovery increased with the applied trapping number. Reservoir-specific thresholds — rather than water-wet sandstone correlations — are required for reliable surfactant-flood screening in these systems.

What is in this report

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Experiment record · complete

CDC#1 — Core A

Complete rate-step record for CDC#1: centrifuge-conditioned baseline, seawater pre-flush, SF1 rate escalation at low IFT (σ_os = 3.07×10⁻³ mN/m), and salinity-gradient post-flush. All trapping numbers computed with the manuscript conventions.

Prepared by Imad A. Adel

Core identity

Experiment	CDC#1
Core label	Core A
Type	Outcrop reference
Temperature	100 °C
Status	Completed

S_orw baseline: 16.00 %; centrifuge-conditioned
S_orc after SF1: 8.11 %; end of rate escalation
S_o,post: 8.11 %; after salinity post-flush
N_t,crit: 5.86×10⁻⁴; last no-oil SF1 step
S_orw recovered: 49.3 %; share of residual oil mobilized

SAMPLE DATAKPI values above are computed from the SAMPLE record, not the manuscript.

Core properties

bulk-volume check: πD²·L·φ/4 = 14.18 cm³ vs PV 14.20 cm³ (0.2%)

Parameter	Value	Unit
Length, L	5.000	cm
Diameter, D	3.800	cm
Pore volume, PV	14.200	cm³
Porosity, φ	0.2500	frac.
Initial water sat., S_wi	0.2800	frac.
Residual oil baseline, S_orw	0.1600	frac.
Aqueous viscosity, μ	0.40	cP
Density difference, Δρ	200	kg/m³
Cross-sectional area, A = πD²/4	1.1341×10⁻³	m²
Permeability at S_orw, k (from ΔP block)	45.001	mD

Constants: g = 9.81 m/s² · α = 0° (horizontal) · cos θ = 1 (mechanical baseline) · σ_SW/post = 24.3 mN/m · σ_SF1 = 3.07×10⁻³ mN/m.

Permeability at S_orw — Darcy law

ΔP–Q correlation R² = 1.0000 · mean k = 45.001 mD

Step	Q (cm³/min)	ΔP (psi)	ΔP (Pa)	k (mD)
1	0.500	0.4799	3,308.8	45.004
2	1.000	0.9599	6,618.3	44.999
3	4.000	3.8395	26,472.4	45.000
4	8.000	7.6790	52,944.8	45.000

Stage schedule & trapping numbers

u = Q/A · N_c = uμ/(φσ) · N_b = kΔρg/(φσ) · N_t = √(N_c²+N_b²)

Stage	Fluid	Q (cm³/min)	σ (mN/m)	u (ft/day)	v = u/φ (ft/day)	N_c	N_b	N_t
SW pre-flush	SW	0.500	24.3	2.083	8.33	4.84×10⁻⁷	1.43×10⁻⁸	4.84×10⁻⁷
	SW	1.000	24.3	4.166	16.66	9.68×10⁻⁷	1.43×10⁻⁸	9.68×10⁻⁷
	SW	4.000	24.3	16.663	66.65	3.87×10⁻⁶	1.43×10⁻⁸	3.87×10⁻⁶
	SW	8.000	24.3	33.326	133.31	7.74×10⁻⁶	1.43×10⁻⁸	7.74×10⁻⁶
SF1 surfactant flood	SF1	0.075	3.07×10⁻³	0.312	1.25	5.74×10⁻⁴	1.14×10⁻⁴	5.86×10⁻⁴
	SF1	0.250	3.07×10⁻³	1.041	4.17	1.91×10⁻³	1.14×10⁻⁴	1.92×10⁻³
	SF1	0.500	3.07×10⁻³	2.083	8.33	3.83×10⁻³	1.14×10⁻⁴	3.83×10⁻³
	SF1	1.000	3.07×10⁻³	4.166	16.66	7.66×10⁻³	1.14×10⁻⁴	7.66×10⁻³
	SF1	2.000	3.07×10⁻³	8.332	33.33	1.53×10⁻²	1.14×10⁻⁴	1.53×10⁻²
	SF1	6.000	3.07×10⁻³	24.995	99.98	4.60×10⁻²	1.14×10⁻⁴	4.60×10⁻²
	SF1	8.000	3.07×10⁻³	33.326	133.31	6.13×10⁻²	1.14×10⁻⁴	6.13×10⁻²
	SF1	12.000	3.07×10⁻³	49.990	199.96	9.19×10⁻²	1.14×10⁻⁴	9.19×10⁻²
Salinity-gradient post-flush	DSAL1	0.250	24.3	1.041	4.17	2.42×10⁻⁷	1.43×10⁻⁸	2.42×10⁻⁷
	DSAL2	0.250	24.3	1.041	4.17	2.42×10⁻⁷	1.43×10⁻⁸	2.42×10⁻⁷

N_t,crit — last SF1 step with no measurable oil · First production — first SF1 step with measurable oil. Step volumes and minimum durations (1.5 PV per plateau) are given in the protocol duration calculator.

Post-flush fluids: DSAL1 = 3:1 SW:DI dilution (75% salinity ≈ 32.5 kppm TDS); DSAL2 = 1:1 (50% ≈ 21.7 kppm TDS) — injected at low rate to isolate the phase-behavior response without an additional increase in the applied trapping number. Post-flush stages are tabulated here but excluded from the CDC figures.

Recovery & saturation chain

total oil 1.120 cm³ · N_t,crit = 5.86×10⁻⁴ (highlighted row) · first oil at 1.92×10⁻³

Stage	Q (cm³/min)	N_t	Oil recovered (cm³)	Cumulative (cm³)	S_o (%PV)	S_o/S_orw	S_orw mobilized (%)
SW	0.500	4.84×10⁻⁷	0.000	0.000	16.00	1.0000	0.00
SW	1.000	9.68×10⁻⁷	0.000	0.000	16.00	1.0000	0.00
SW	4.000	3.87×10⁻⁶	0.000	0.000	16.00	1.0000	0.00
SW	8.000	7.74×10⁻⁶	0.000	0.000	16.00	1.0000	0.00
SF1	0.075	5.86×10⁻⁴	0.000	0.000	16.00	1.0000	0.00
SF1	0.250	1.92×10⁻³	0.160	0.160	14.87	0.9296	7.04
SF1	0.500	3.83×10⁻³	0.200	0.360	13.46	0.8415	15.85
SF1	1.000	7.66×10⁻³	0.240	0.600	11.77	0.7359	26.41
SF1	2.000	1.53×10⁻²	0.180	0.780	10.51	0.6567	34.33
SF1	6.000	4.60×10⁻²	0.140	0.920	9.52	0.5951	40.49
SF1	8.000	6.13×10⁻²	0.120	1.040	8.68	0.5423	45.77
SF1	12.000	9.19×10⁻²	0.080	1.120	8.11	0.5070	49.30
DSAL1	0.250	2.42×10⁻⁷	0.000	1.120	8.11	0.5070	49.30
DSAL2	0.250	2.42×10⁻⁷	0.000	1.120	8.11	0.5070	49.30

Desaturation responseSAMPLE DATA

S_o (%PV) vs N_t · pre-flush + SF1

Normalized CDCSAMPLE DATA

S_o/S_orw vs N_t · pre-flush + SF1

Experiment record · complete

CDC#2 — Core B

Complete rate-step record for CDC#2: centrifuge-conditioned baseline, seawater pre-flush, SF1 rate escalation at low IFT (σ_os = 3.07×10⁻³ mN/m), and salinity-gradient post-flush. All trapping numbers computed with the manuscript conventions.

Prepared by Imad A. Adel

Core identity

Experiment	CDC#2
Core label	Core B
Type	Reservoir carbonate
Temperature	100 °C
Status	Completed

S_orw baseline: 34.00 %; centrifuge-conditioned
S_orc after SF1: 10.54 %; end of rate escalation
S_o,post: 9.41 %; after salinity post-flush
N_t,crit: 1.37×10⁻³; last no-oil SF1 step
S_orw recovered: 72.3 %; share of residual oil mobilized

SAMPLE DATAKPI values above are computed from the SAMPLE record, not the manuscript.

Core properties

bulk-volume check: πD²·L·φ/4 = 20.24 cm³ vs PV 20.25 cm³ (0.0%)

Parameter	Value	Unit
Length, L	5.100	cm
Diameter, D	3.800	cm
Pore volume, PV	20.250	cm³
Porosity, φ	0.3500	frac.
Initial water sat., S_wi	0.2200	frac.
Residual oil baseline, S_orw	0.3400	frac.
Aqueous viscosity, μ	0.40	cP
Density difference, Δρ	200	kg/m³
Cross-sectional area, A = πD²/4	1.1341×10⁻³	m²
Permeability at S_orw, k (from ΔP block)	9.000	mD

Constants: g = 9.81 m/s² · α = 0° (horizontal) · cos θ = 1 (mechanical baseline) · σ_SW/post = 24.3 mN/m · σ_SF1 = 3.07×10⁻³ mN/m.

Permeability at S_orw — Darcy law

ΔP–Q correlation R² = 1.0000 · mean k = 9.000 mD

Step	Q (cm³/min)	ΔP (psi)	ΔP (Pa)	k (mD)
1	0.500	2.4477	16,876.3	9.000
2	1.000	4.8954	33,752.6	9.000
3	4.000	19.5815	135,009.7	9.000
4	8.000	39.1630	270,019.4	9.000

Stage schedule & trapping numbers

u = Q/A · N_c = uμ/(φσ) · N_b = kΔρg/(φσ) · N_t = √(N_c²+N_b²)

Stage	Fluid	Q (cm³/min)	σ (mN/m)	u (ft/day)	v = u/φ (ft/day)	N_c	N_b	N_t
SW pre-flush	SW	0.500	24.3	2.083	5.95	3.46×10⁻⁷	2.05×10⁻⁹	3.46×10⁻⁷
	SW	1.000	24.3	4.166	11.90	6.91×10⁻⁷	2.05×10⁻⁹	6.91×10⁻⁷
	SW	4.000	24.3	16.663	47.61	2.76×10⁻⁶	2.05×10⁻⁹	2.76×10⁻⁶
	SW	8.000	24.3	33.326	95.22	5.53×10⁻⁶	2.05×10⁻⁹	5.53×10⁻⁶
SF1 surfactant flood	SF1	0.075	3.07×10⁻³	0.312	0.89	4.10×10⁻⁴	1.62×10⁻⁵	4.11×10⁻⁴
	SF1	0.250	3.07×10⁻³	1.041	2.98	1.37×10⁻³	1.62×10⁻⁵	1.37×10⁻³
	SF1	0.500	3.07×10⁻³	2.083	5.95	2.74×10⁻³	1.62×10⁻⁵	2.74×10⁻³
	SF1	1.000	3.07×10⁻³	4.166	11.90	5.47×10⁻³	1.62×10⁻⁵	5.47×10⁻³
	SF1	2.000	3.07×10⁻³	8.332	23.80	1.09×10⁻²	1.62×10⁻⁵	1.09×10⁻²
	SF1	6.000	3.07×10⁻³	24.995	71.41	3.28×10⁻²	1.62×10⁻⁵	3.28×10⁻²
	SF1	8.000	3.07×10⁻³	33.326	95.22	4.38×10⁻²	1.62×10⁻⁵	4.38×10⁻²
	SF1	12.000	3.07×10⁻³	49.990	142.83	6.57×10⁻²	1.62×10⁻⁵	6.57×10⁻²
Salinity-gradient post-flush	DSAL1	0.250	24.3	1.041	2.98	1.73×10⁻⁷	2.05×10⁻⁹	1.73×10⁻⁷
	DSAL2	0.250	24.3	1.041	2.98	1.73×10⁻⁷	2.05×10⁻⁹	1.73×10⁻⁷

N_t,crit — last SF1 step with no measurable oil · First production — first SF1 step with measurable oil. Step volumes and minimum durations (1.5 PV per plateau) are given in the protocol duration calculator.

Post-flush fluids: DSAL1 = 3:1 SW:DI dilution (75% salinity ≈ 32.5 kppm TDS); DSAL2 = 1:1 (50% ≈ 21.7 kppm TDS) — injected at low rate to isolate the phase-behavior response without an additional increase in the applied trapping number. Post-flush stages are tabulated here but excluded from the CDC figures.

Recovery & saturation chain

total oil 4.980 cm³ · N_t,crit = 1.37×10⁻³ (highlighted row) · first oil at 2.74×10⁻³

Stage	Q (cm³/min)	N_t	Oil recovered (cm³)	Cumulative (cm³)	S_o (%PV)	S_o/S_orw	S_orw mobilized (%)
SW	0.500	3.46×10⁻⁷	0.000	0.000	34.00	1.0000	0.00
SW	1.000	6.91×10⁻⁷	0.000	0.000	34.00	1.0000	0.00
SW	4.000	2.76×10⁻⁶	0.000	0.000	34.00	1.0000	0.00
SW	8.000	5.53×10⁻⁶	0.000	0.000	34.00	1.0000	0.00
SF1	0.075	4.11×10⁻⁴	0.000	0.000	34.00	1.0000	0.00
SF1	0.250	1.37×10⁻³	0.000	0.000	34.00	1.0000	0.00
SF1	0.500	2.74×10⁻³	0.900	0.900	29.56	0.8693	13.07
SF1	1.000	5.47×10⁻³	1.150	2.050	23.88	0.7023	29.77
SF1	2.000	1.09×10⁻²	0.850	2.900	19.68	0.5788	42.12
SF1	6.000	3.28×10⁻²	0.750	3.650	15.98	0.4699	53.01
SF1	8.000	4.38×10⁻²	0.650	4.300	12.77	0.3755	62.45
SF1	12.000	6.57×10⁻²	0.450	4.750	10.54	0.3101	68.99
DSAL1	0.250	1.73×10⁻⁷	0.150	4.900	9.80	0.2883	71.17
DSAL2	0.250	1.73×10⁻⁷	0.080	4.980	9.41	0.2767	72.33

Desaturation responseSAMPLE DATA

S_o (%PV) vs N_t · pre-flush + SF1

Normalized CDCSAMPLE DATA

S_o/S_orw vs N_t · pre-flush + SF1

Experiment record · complete

CDC#3 — Core C

Complete rate-step record for CDC#3: centrifuge-conditioned baseline, seawater pre-flush, SF1 rate escalation at low IFT (σ_os = 3.07×10⁻³ mN/m), and salinity-gradient post-flush. All trapping numbers computed with the manuscript conventions.

Prepared by Imad A. Adel

Core identity

Experiment	CDC#3
Core label	Core C
Type	Reservoir carbonate
Temperature	100 °C
Status	Completed

S_orw baseline: 19.00 %; centrifuge-conditioned
S_orc after SF1: 8.80 %; end of rate escalation
S_o,post: 8.80 %; after salinity post-flush
N_t,crit: 2.66×10⁻³; last no-oil SF1 step
S_orw recovered: 53.7 %; share of residual oil mobilized

SAMPLE DATAKPI values above are computed from the SAMPLE record, not the manuscript.

Core properties

bulk-volume check: πD²·L·φ/4 = 10.10 cm³ vs PV 10.10 cm³ (-0.0%)

Parameter	Value	Unit
Length, L	4.950	cm
Diameter, D	3.800	cm
Pore volume, PV	10.100	cm³
Porosity, φ	0.1800	frac.
Initial water sat., S_wi	0.1400	frac.
Residual oil baseline, S_orw	0.1900	frac.
Aqueous viscosity, μ	0.40	cP
Density difference, Δρ	200	kg/m³
Cross-sectional area, A = πD²/4	1.1341×10⁻³	m²
Permeability at S_orw, k (from ΔP block)	5.000	mD

Constants: g = 9.81 m/s² · α = 0° (horizontal) · cos θ = 1 (mechanical baseline) · σ_SW/post = 24.3 mN/m · σ_SF1 = 3.07×10⁻³ mN/m.

Permeability at S_orw — Darcy law

ΔP–Q correlation R² = 1.0000 · mean k = 5.000 mD

Step	Q (cm³/min)	ΔP (psi)	ΔP (Pa)	k (mD)
1	0.500	4.2763	29,484.0	5.000
2	1.000	8.5525	58,967.4	5.000
3	4.000	34.2100	235,869.6	5.000
4	8.000	68.4200	471,739.3	5.000

Stage schedule & trapping numbers

u = Q/A · N_c = uμ/(φσ) · N_b = kΔρg/(φσ) · N_t = √(N_c²+N_b²)

Stage	Fluid	Q (cm³/min)	σ (mN/m)	u (ft/day)	v = u/φ (ft/day)	N_c	N_b	N_t
SW pre-flush	SW	0.500	24.3	2.083	11.57	6.72×10⁻⁷	2.21×10⁻⁹	6.72×10⁻⁷
	SW	1.000	24.3	4.166	23.14	1.34×10⁻⁶	2.21×10⁻⁹	1.34×10⁻⁶
	SW	4.000	24.3	16.663	92.57	5.38×10⁻⁶	2.21×10⁻⁹	5.38×10⁻⁶
	SW	8.000	24.3	33.326	185.15	1.08×10⁻⁵	2.21×10⁻⁹	1.08×10⁻⁵
SF1 surfactant flood	SF1	0.075	3.07×10⁻³	0.312	1.74	7.98×10⁻⁴	1.75×10⁻⁵	7.98×10⁻⁴
	SF1	0.250	3.07×10⁻³	1.041	5.79	2.66×10⁻³	1.75×10⁻⁵	2.66×10⁻³
	SF1	0.500	3.07×10⁻³	2.083	11.57	5.32×10⁻³	1.75×10⁻⁵	5.32×10⁻³
	SF1	1.000	3.07×10⁻³	4.166	23.14	1.06×10⁻²	1.75×10⁻⁵	1.06×10⁻²
	SF1	2.000	3.07×10⁻³	8.332	46.29	2.13×10⁻²	1.75×10⁻⁵	2.13×10⁻²
	SF1	6.000	3.07×10⁻³	24.995	138.86	6.38×10⁻²	1.75×10⁻⁵	6.38×10⁻²
	SF1	8.000	3.07×10⁻³	33.326	185.15	8.51×10⁻²	1.75×10⁻⁵	8.51×10⁻²
	SF1	12.000	3.07×10⁻³	49.990	277.72	1.28×10⁻¹	1.75×10⁻⁵	1.28×10⁻¹
Salinity-gradient post-flush	DSAL1	0.250	24.3	1.041	5.79	3.36×10⁻⁷	2.21×10⁻⁹	3.36×10⁻⁷
	DSAL2	0.250	24.3	1.041	5.79	3.36×10⁻⁷	2.21×10⁻⁹	3.36×10⁻⁷

N_t,crit — last SF1 step with no measurable oil · First production — first SF1 step with measurable oil. Step volumes and minimum durations (1.5 PV per plateau) are given in the protocol duration calculator.

Post-flush fluids: DSAL1 = 3:1 SW:DI dilution (75% salinity ≈ 32.5 kppm TDS); DSAL2 = 1:1 (50% ≈ 21.7 kppm TDS) — injected at low rate to isolate the phase-behavior response without an additional increase in the applied trapping number. Post-flush stages are tabulated here but excluded from the CDC figures.

Recovery & saturation chain

total oil 1.030 cm³ · N_t,crit = 2.66×10⁻³ (highlighted row) · first oil at 5.32×10⁻³

Stage	Q (cm³/min)	N_t	Oil recovered (cm³)	Cumulative (cm³)	S_o (%PV)	S_o/S_orw	S_orw mobilized (%)
SW	0.500	6.72×10⁻⁷	0.000	0.000	19.00	1.0000	0.00
SW	1.000	1.34×10⁻⁶	0.000	0.000	19.00	1.0000	0.00
SW	4.000	5.38×10⁻⁶	0.000	0.000	19.00	1.0000	0.00
SW	8.000	1.08×10⁻⁵	0.000	0.000	19.00	1.0000	0.00
SF1	0.075	7.98×10⁻⁴	0.000	0.000	19.00	1.0000	0.00
SF1	0.250	2.66×10⁻³	0.000	0.000	19.00	1.0000	0.00
SF1	0.500	5.32×10⁻³	0.220	0.220	16.82	0.8854	11.46
SF1	1.000	1.06×10⁻²	0.280	0.500	14.05	0.7394	26.06
SF1	2.000	2.13×10⁻²	0.200	0.700	12.07	0.6352	36.48
SF1	6.000	6.38×10⁻²	0.150	0.850	10.58	0.5571	44.29
SF1	8.000	8.51×10⁻²	0.100	0.950	9.59	0.5050	49.50
SF1	12.000	1.28×10⁻¹	0.080	1.030	8.80	0.4633	53.67
DSAL1	0.250	3.36×10⁻⁷	0.000	1.030	8.80	0.4633	53.67
DSAL2	0.250	3.36×10⁻⁷	0.000	1.030	8.80	0.4633	53.67

Desaturation responseSAMPLE DATA

S_o (%PV) vs N_t · pre-flush + SF1

Normalized CDCSAMPLE DATA

S_o/S_orw vs N_t · pre-flush + SF1

New experiment — working sheet · planned

CDC#4 — New coreflood

Blank working sheet for a future coreflood. Fill the identity, core properties, ΔP readings and — during the flood — the incremental oil per step. Every output, table and figure generates automatically in the standard program format, and the cross-core comparison updates to include this experiment.

Prepared by Imad A. Adel

Core identity

Core label
Status	New — to be conducted

S_orw baseline: —; centrifuge-conditioned
S_orc after SF1: pending; end of rate escalation
S_o,post: pending; after salinity post-flush
N_t,crit: —; last no-oil SF1 step
S_orw recovered: pending; share of residual oil mobilized

Core properties · editable inputs

enter core properties to activate

Parameter	Value	Unit
Length, L		cm
Diameter, D		cm
Pore volume, PV		cm³
Porosity, φ		frac.
Initial water sat., S_wi		frac.
Residual oil baseline, S_orw		frac.
Aqueous viscosity, μ		cP
Density difference, Δρ		kg/m³
Cross-sectional area, A = πD²/4	—	m²
Permeability at S_orw, k (from ΔP block)	pending	mD

Constants: g = 9.81 m/s² · α = 0° (horizontal) · cos θ = 1 (mechanical baseline) · σ_SW/post = 24.3 mN/m · σ_SF1 = 3.07×10⁻³ mN/m.

Permeability at S_orw — Darcy law · ΔP editable

pending — ΔP measured during the pre-flush

Step	Q (cm³/min)	ΔP (psi)	ΔP (Pa)	k (mD)
1	Q, step 1 (cm³/min)	ΔP, step 1 (psi)	—	—
2	Q, step 2 (cm³/min)	ΔP, step 2 (psi)	—	—
3	Q, step 3 (cm³/min)	ΔP, step 3 (psi)	—	—
4	Q, step 4 (cm³/min)	ΔP, step 4 (psi)	—	—

Stage schedule & trapping numbers

u = Q/A · N_c = uμ/(φσ) · N_b = kΔρg/(φσ) · N_t = √(N_c²+N_b²)

Stage	Fluid	Q (editable) (cm³/min)	σ (mN/m)	u (ft/day)	v = u/φ (ft/day)	N_c	N_b	N_t
SW pre-flush	SW	Q, SW step 1 (cm³/min)	24.3	—	—	—	—	—
	SW	Q, SW step 2 (cm³/min)	24.3	—	—	—	—	—
	SW	Q, SW step 3 (cm³/min)	24.3	—	—	—	—	—
	SW	Q, SW step 4 (cm³/min)	24.3	—	—	—	—	—
SF1 surfactant flood	SF1	Q, SF1 step 5 (cm³/min)	3.07×10⁻³	—	—	—	—	—
	SF1	Q, SF1 step 6 (cm³/min)	3.07×10⁻³	—	—	—	—	—
	SF1	Q, SF1 step 7 (cm³/min)	3.07×10⁻³	—	—	—	—	—
	SF1	Q, SF1 step 8 (cm³/min)	3.07×10⁻³	—	—	—	—	—
	SF1	Q, SF1 step 9 (cm³/min)	3.07×10⁻³	—	—	—	—	—
	SF1	Q, SF1 step 10 (cm³/min)	3.07×10⁻³	—	—	—	—	—
	SF1	Q, SF1 step 11 (cm³/min)	3.07×10⁻³	—	—	—	—	—
	SF1	Q, SF1 step 12 (cm³/min)	3.07×10⁻³	—	—	—	—	—
Salinity-gradient post-flush	DSAL1	Q, DSAL1 step 13 (cm³/min)	24.3	—	—	—	—	—
	DSAL2	Q, DSAL2 step 14 (cm³/min)	24.3	—	—	—	—	—

N_t,crit — last SF1 step with no measurable oil · First production — first SF1 step with measurable oil. Step volumes and minimum durations (1.5 PV per plateau) are given in the protocol duration calculator.

Post-flush fluids: DSAL1 = 3:1 SW:DI dilution (75% salinity ≈ 32.5 kppm TDS); DSAL2 = 1:1 (50% ≈ 21.7 kppm TDS) — injected at low rate to isolate the phase-behavior response without an additional increase in the applied trapping number. Post-flush stages are tabulated here but excluded from the CDC figures.

Recovery & saturation chain · incremental oil editable

enter core properties first

Stage	Q (cm³/min)	N_t	Oil recovered (editable) (cm³)	S_o (%PV)	S_o/S_orw	S_orw mobilized (%)
SW	0.500	—	Oil recovered, SW step 1 (cm³)	—	—	—
SW	1.000	—	Oil recovered, SW step 2 (cm³)	—	—	—
SW	4.000	—	Oil recovered, SW step 3 (cm³)	—	—	—
SW	8.000	—	Oil recovered, SW step 4 (cm³)	—	—	—
SF1	0.075	—	Oil recovered, SF1 step 5 (cm³)	—	—	—
SF1	0.250	—	Oil recovered, SF1 step 6 (cm³)	—	—	—
SF1	0.500	—	Oil recovered, SF1 step 7 (cm³)	—	—	—
SF1	1.000	—	Oil recovered, SF1 step 8 (cm³)	—	—	—
SF1	2.000	—	Oil recovered, SF1 step 9 (cm³)	—	—	—
SF1	6.000	—	Oil recovered, SF1 step 10 (cm³)	—	—	—
SF1	8.000	—	Oil recovered, SF1 step 11 (cm³)	—	—	—
SF1	12.000	—	Oil recovered, SF1 step 12 (cm³)	—	—	—
DSAL1	0.250	—	Oil recovered, DSAL1 step 13 (cm³)	—	—	—
DSAL2	0.250	—	Oil recovered, DSAL2 step 14 (cm³)	—	—	—

Desaturation response

S_o (%PV) vs N_t · pre-flush + SF1

Normalized CDC

S_o/S_orw vs N_t · pre-flush + SF1

Required inputs for this sheet — everything else computes automatically:

Identity: a core label (top of page).
Core properties: L, D, PV, φ, S_wi, S_orw (centrifuge-conditioned baseline), μ (0.40 cP at 100 °C unless re-measured), Δρ (200 kg/m³ default).
Permeability block: the four pre-flush ΔP readings at Q = 0.5 / 1 / 4 / 8 cm³/min — these back-calculate k at S_orw, which also feeds N_b.
Rate schedule: keep the standard protocol rates or edit Q per step to match the run sheet.
Recovery: incremental oil (cm³, ±0.05 resolution) per step during the flood — N_t,crit, S_orc, S_o,post, E_D and both CDC figures resolve as you type, and this core joins the cross-core comparison automatically.

Added corefloods live in this browser session — use Export scenario to save the data; it can be re-entered afterwards.

New experiment — working sheet · planned

CDC#5 — New coreflood

Blank working sheet for a future coreflood. Fill the identity, core properties, ΔP readings and — during the flood — the incremental oil per step. Every output, table and figure generates automatically in the standard program format, and the cross-core comparison updates to include this experiment.

Prepared by Imad A. Adel

Core identity

Core label
Status	New — to be conducted

S_orw baseline: —; centrifuge-conditioned
S_orc after SF1: pending; end of rate escalation
S_o,post: pending; after salinity post-flush
N_t,crit: —; last no-oil SF1 step
S_orw recovered: pending; share of residual oil mobilized

Core properties · editable inputs

enter core properties to activate

Parameter	Value	Unit
Length, L		cm
Diameter, D		cm
Pore volume, PV		cm³
Porosity, φ		frac.
Initial water sat., S_wi		frac.
Residual oil baseline, S_orw		frac.
Aqueous viscosity, μ		cP
Density difference, Δρ		kg/m³
Cross-sectional area, A = πD²/4	—	m²
Permeability at S_orw, k (from ΔP block)	pending	mD

Constants: g = 9.81 m/s² · α = 0° (horizontal) · cos θ = 1 (mechanical baseline) · σ_SW/post = 24.3 mN/m · σ_SF1 = 3.07×10⁻³ mN/m.

Permeability at S_orw — Darcy law · ΔP editable

pending — ΔP measured during the pre-flush

Step	Q (cm³/min)	ΔP (psi)	ΔP (Pa)	k (mD)
1	Q, step 1 (cm³/min)	ΔP, step 1 (psi)	—	—
2	Q, step 2 (cm³/min)	ΔP, step 2 (psi)	—	—
3	Q, step 3 (cm³/min)	ΔP, step 3 (psi)	—	—
4	Q, step 4 (cm³/min)	ΔP, step 4 (psi)	—	—

Stage schedule & trapping numbers

u = Q/A · N_c = uμ/(φσ) · N_b = kΔρg/(φσ) · N_t = √(N_c²+N_b²)

Stage	Fluid	Q (editable) (cm³/min)	σ (mN/m)	u (ft/day)	v = u/φ (ft/day)	N_c	N_b	N_t
SW pre-flush	SW	Q, SW step 1 (cm³/min)	24.3	—	—	—	—	—
	SW	Q, SW step 2 (cm³/min)	24.3	—	—	—	—	—
	SW	Q, SW step 3 (cm³/min)	24.3	—	—	—	—	—
	SW	Q, SW step 4 (cm³/min)	24.3	—	—	—	—	—
SF1 surfactant flood	SF1	Q, SF1 step 5 (cm³/min)	3.07×10⁻³	—	—	—	—	—
	SF1	Q, SF1 step 6 (cm³/min)	3.07×10⁻³	—	—	—	—	—
	SF1	Q, SF1 step 7 (cm³/min)	3.07×10⁻³	—	—	—	—	—
	SF1	Q, SF1 step 8 (cm³/min)	3.07×10⁻³	—	—	—	—	—
	SF1	Q, SF1 step 9 (cm³/min)	3.07×10⁻³	—	—	—	—	—
	SF1	Q, SF1 step 10 (cm³/min)	3.07×10⁻³	—	—	—	—	—
	SF1	Q, SF1 step 11 (cm³/min)	3.07×10⁻³	—	—	—	—	—
	SF1	Q, SF1 step 12 (cm³/min)	3.07×10⁻³	—	—	—	—	—
Salinity-gradient post-flush	DSAL1	Q, DSAL1 step 13 (cm³/min)	24.3	—	—	—	—	—
	DSAL2	Q, DSAL2 step 14 (cm³/min)	24.3	—	—	—	—	—

N_t,crit — last SF1 step with no measurable oil · First production — first SF1 step with measurable oil. Step volumes and minimum durations (1.5 PV per plateau) are given in the protocol duration calculator.

Post-flush fluids: DSAL1 = 3:1 SW:DI dilution (75% salinity ≈ 32.5 kppm TDS); DSAL2 = 1:1 (50% ≈ 21.7 kppm TDS) — injected at low rate to isolate the phase-behavior response without an additional increase in the applied trapping number. Post-flush stages are tabulated here but excluded from the CDC figures.

Recovery & saturation chain · incremental oil editable

enter core properties first

Stage	Q (cm³/min)	N_t	Oil recovered (editable) (cm³)	S_o (%PV)	S_o/S_orw	S_orw mobilized (%)
SW	0.500	—	Oil recovered, SW step 1 (cm³)	—	—	—
SW	1.000	—	Oil recovered, SW step 2 (cm³)	—	—	—
SW	4.000	—	Oil recovered, SW step 3 (cm³)	—	—	—
SW	8.000	—	Oil recovered, SW step 4 (cm³)	—	—	—
SF1	0.075	—	Oil recovered, SF1 step 5 (cm³)	—	—	—
SF1	0.250	—	Oil recovered, SF1 step 6 (cm³)	—	—	—
SF1	0.500	—	Oil recovered, SF1 step 7 (cm³)	—	—	—
SF1	1.000	—	Oil recovered, SF1 step 8 (cm³)	—	—	—
SF1	2.000	—	Oil recovered, SF1 step 9 (cm³)	—	—	—
SF1	6.000	—	Oil recovered, SF1 step 10 (cm³)	—	—	—
SF1	8.000	—	Oil recovered, SF1 step 11 (cm³)	—	—	—
SF1	12.000	—	Oil recovered, SF1 step 12 (cm³)	—	—	—
DSAL1	0.250	—	Oil recovered, DSAL1 step 13 (cm³)	—	—	—
DSAL2	0.250	—	Oil recovered, DSAL2 step 14 (cm³)	—	—	—

Desaturation response

S_o (%PV) vs N_t · pre-flush + SF1

Normalized CDC

S_o/S_orw vs N_t · pre-flush + SF1

Required inputs for this sheet — everything else computes automatically:

Identity: a core label (top of page).
Core properties: L, D, PV, φ, S_wi, S_orw (centrifuge-conditioned baseline), μ (0.40 cP at 100 °C unless re-measured), Δρ (200 kg/m³ default).
Permeability block: the four pre-flush ΔP readings at Q = 0.5 / 1 / 4 / 8 cm³/min — these back-calculate k at S_orw, which also feeds N_b.
Rate schedule: keep the standard protocol rates or edit Q per step to match the run sheet.
Recovery: incremental oil (cm³, ±0.05 resolution) per step during the flood — N_t,crit, S_orc, S_o,post, E_D and both CDC figures resolve as you type, and this core joins the cross-core comparison automatically.

Added corefloods live in this browser session — use Export scenario to save the data; it can be re-entered afterwards.

Synthesis

Cross-core comparison

All SAMPLE desaturation responses on a common trapping-number basis, benchmarked against the classical water-wet sandstone reference (Chatzis & Morrow, 1984; converted to the N_t convention of this study). This page updates automatically as corefloods are completed or added.

Prepared by Imad A. Adel

Oil saturation vs trapping numberSAMPLE DATA

S_o (%PV) · pre-flush + SF1 · semilog

Normalized CDCs vs water-wet benchmarkSAMPLE DATA

S_o/S_orw

Endpoint saturations by stageSAMPLE DATA

S_o/S_orw · baseline → SF1 → post-flush

Program summarySAMPLE DATA

SAMPLE endpoints & thresholds

Parameter	CDC#1 Core A	CDC#2 Core B	CDC#3 Core C	CDC#4 new core	CDC#5 new core
Absolute (brine) permeability, k_abs (mD)	45.00	9.00	5.00	—	—
Permeability at S_orw (mD)	45.00	9.00	5.00	—	—
Porosity, φ (frac.)	0.2500	0.3500	0.1800	—	—
S_orw baseline (%)	16.00	34.00	19.00	—	—
N_t,crit	5.86×10⁻⁴	1.37×10⁻³	2.66×10⁻³	pending	pending
S_orc after SF1 (%)	8.11	10.54	8.80	—	—
S_o,post (%)	8.11	9.41	8.80	—	—
S_orw recovered after SF1 (%)	49.3	69.0	53.7	—	—
E_D after post-flush (%)	49.3	72.3	53.7	—	—
× water-wet onset (1.9×10⁻⁵)	≈31×	≈72×	≈140×	—	—
* live value from the working sheet — provisional until the experiment is completed and verified.

N_t,crit is reported operationally: the highest tested trapping number before measurable desaturation. S_orw recovered = (S_orw − S_o)/S_orw at the stated stage.

Reading the comparison (SAMPLE records): both reservoir cores and the outcrop reference core mobilize oil only at trapping numbers 31–140× above the water-wet sandstone onset ((1.9 ± 0.6)×10⁻⁵). Core B shows a sharp desaturation once its threshold is crossed; Core A and Core C exhibit a more gradual desaturation over an order of magnitude in N_t — consistent with oil held in films, rough surfaces and micro-porosity of mixed-to-oil-wet carbonates rather than as discrete ganglia. Direct transfer of water-wet CDC correlations to these systems would materially overestimate mobilization at field-achievable forces.

Synthesis

Field-rate scaling — is the threshold achievable?

At a representative field Darcy velocity of u = 1 ft/day, the SF1 aqueous baseline (μ = 0.40 cP, σ_os = 3.07×10⁻³ mN/m) delivers N_t ≈ 1.31×10⁻³ in the Core B SAMPLE system — below its SAMPLE onset of 1.37×10⁻³. Displacing-phase viscosity is the primary optimization parameter. This calculator translates any velocity–viscosity pair into an applied trapping number for each SAMPLE core system.

Prepared by Imad A. Adel

Interactive scaling calculatorSAMPLE DATA

N_c = uμ/(φσ) · N_b from core k · σ_os = 3.07×10⁻³ mN/m

How to useSet the core, u and μ; the figure, readouts and viscosity table recompute.

Select the core system — this sets the porosity φ and the measured permeability at S_orw, which fix the Bond-number contribution N_b.
Set the Darcy velocity u with the first slider (the field range 0.5–2 ft/day is shaded in the chart).
Set the aqueous-phase viscosity μ with the second slider.

The cards below report the applied N_c, N_b and N_t and compare N_t against the selected core’s measured N_t,crit; the table gives the viscosity required at the selected velocity to reach the onset and the N_t ≈ 10⁻² target. Hover any curve for values; drag to zoom; use Reset axes in the figure toolbar, or double-click the plot.

Darcy velocity u

Aqueous viscosity μ

Core system

Trapping number vs Darcy velocityviscosity scenarios · shaded band = field range 0.5–2 ft/day

Applied N_t: 1.31×10⁻³; u = 1.00 ft/day · μ = 0.40 cP
Threshold N_t,crit: 1.37×10⁻³; Core B
Margin vs onset: 0.96×; below onset — no mobilization
Target N_t ≈ 10⁻²: 13.1%; of the high-E_D target trapping number

What it showsEach curve is a viscosity scenario, the red dashed line is the selected core’s N_t,crit, and the open marker is the selected scenario.

Viscous and buoyancy componentsSAMPLE DATA

Applied N_c: 1.31×10⁻³; viscous component
Applied N_b: 1.62×10⁻⁵; buoyancy component

Viscosity requirements & polymer screening

computed live at selected u

Target at u = 1.00 ft/day — Core B	Required μ (cP)	Polymer screening (literature)
Reach onset (N_t,crit = 1.37×10⁻³)	0.42	none — baseline suffices
Reach N_t ≈ 10⁻² (high microscopic displacement efficiency)	3.05	≈3,500–4,000 ppm ATBS

Implementation constraints (screening, not measured here): at ~2 mD, viscous polymer injection is bounded by injectivity, mechanical degradation, filtration/face-plugging and fracture-pressure limits. Under 100 °C / 243k ppm TDS, HTHS-stable chemistries (e.g. ATBS-based synthetic polymers) are required rather than conventional HPAM. Literature screening: ≈1,500–2,000 ppm active ATBS for ~2 cP; ≈3,500–4,000 ppm for ~10 cP. Polymer rheology, retention and propagation were not directly measured in this work.

Reference

Fluids & formulation

Brine compositions, post-flush dilutions, crude oil, and the SF1 surfactant formulation with its phase-behavior and interfacial-tension basis — the boundary conditions behind every trapping number in this report.

Prepared by Imad A. Adel

Brine compositions — Table 1

synthetic FW & injection SW

Ion / property	Formation water	Seawater
Na⁺	66,130	13,662
Ca²⁺	23,246	539
Mg²⁺	2,674	1,583
K⁺	—	498
Cl⁻	150,675	27,092
SO₄²⁻	230	0
HCO₃⁻	—	0
TDS (ppm)	243,028	43,373
Hardness (ppm as CaCO₃)	26,520	2,122
Viscosity (cP, 25 °C)	1.57	1.02
Density (g/cm³, 25 °C)	1.17	1.04

Density and viscosity at ambient conditions (25 °C, 1 atm). FW establishes connate conditions; SW is the injection base fluid and surfactant solvent.

Post-flush brine	Dilution (SW : DI water)	Salinity vs SW	≈ TDS (ppm)
DSAL1	3 : 1	75%	32,530
DSAL2	1 : 1	50%	21,687

Salinity-gradient post-flush: after the maximum viscous step, diluted seawater is injected at low rate (Q = 0.25 cm³/min) to probe phase-behavior-driven mobilization without an additional increase in the applied trapping number. Dilution shifts the local environment from near-optimum Winsor III toward under-optimum Winsor I.

SF1 formulation — Table 3

properties at 100 °C

Parameter	Value	Unit
Optimal salinity, S^*	45,000	ppm TDS
Optimal solubilization ratio, R^*	9.5	cm³/cm³
Chun–Huh IFT, σ_Huh = C/(R^*)²	3.32×10⁻³	mN/m
Spinning-drop IFT, σ_os (100 °C)	3.07×10⁻³	mN/m
Baseline pendant-drop IFT, σ_ow	24.3	mN/m
Aqueous stability limit	70,000	ppm TDS
Aqueous slug viscosity, μ	0.40	cP
Microemulsion type	Winsor III	—

SF1 composition, as reported in the preprint: sodium Guerbet alkoxy carboxylate (GAC, C24–35PO–30EO–COONa, 0.5 wt% active) with internal olefin sulfonate (IOS) co-surfactants and an ethoxylated phenol co-solvent (0.5 wt% active), formulated in seawater.

Phase behavior — solubilization scan

Winsor I → III → II · S^* = 45 kppm · R^* = 9.5

Oil–surfactant IFT vs temperature

spinning drop · power-law fit R² = 0.998

Reference

Formulation calculator

Batch-preparation calculator for multi-component surfactant formulations in a seawater-concentrate basis. Preloaded with a generic SAMPLE recipe — illustrative component percentages, not the manuscript’s formulation. Blue cells are editable; all masses recompute live.

Prepared by Imad A. Adel

Batch setupSAMPLE DATA

final salinity = 1.0× SW after dilution

How to useSet the batch and the brine basis; the recipe and the mass balance recompute.

Set the batch size — enter the target total batch mass (g).
Set the brine basis — the SW concentrate factor (default 1.5×); the brine mass fraction is 1/factor, so the final batch salinity is 1.0× SW regardless of the factor chosen.
Enter the formulation — for each component, the target active wt% in the final batch and the active fraction of the stock solution as assayed (%).
Read the recipe — the required active mass, the stock mass to weigh, and the DI-water balance recompute instantly. The mass-balance check must equal the batch mass.
Mix in the listed order — brine concentrate first, then the surfactant stocks, then the co-solvent, then DI water to the target mass.

Target total batch mass

SW concentrate factor

Batch compositionmass balance: 1,000.00 g = batch (closes)

Brine mass fraction of batch (= 1/factor): 0.6667; fraction
Brine concentrate mass: 666.67; g

Brine basis. The formulation is prepared in a concentrated synthetic-seawater brine so that, after the surfactant stocks and DI water are added, the final batch salinity equals 1.0× SW (43,373 ppm TDS). Stocks and DI water dilute the concentrate back to the target salinity.

Component table — active targets and stock assaysSAMPLE DATA

total active = 1.00 wt% · 10.0 g active in batch

Component	Target active wt% (editable)	Stock active % (editable)	Required active mass (g)	Stock mass to add (g)	Stock (% of batch)	Notes
SAMPLE surfactant A (generic anionic blend)		Stock active fraction, SAMPLE surfactant A (generic anionic blend)	4.00	33.33	3.333%	illustrative stock, 12.0% active
SAMPLE surfactant B (generic co-surfactant blend)		Stock active fraction, SAMPLE surfactant B (generic co-surfactant blend)	3.00	16.67	1.667%	illustrative stock, 18.0% active
SAMPLE co-solvent (generic ethoxylate)		Stock active fraction, SAMPLE co-solvent (generic ethoxylate)	3.00	3.00	0.300%	assumed neat (100% active)
Total active surfactant	1.00 wt%		10.00	53.00	5.300%

Final batch recipe — mass to add, in mixing orderSAMPLE DATA

Addition (in order)	Mass to add (g)	% of batch
1.5× SW brine concentrate	666.67	66.67%
SAMPLE surfactant A (generic anionic blend) stock	33.33	3.33%
SAMPLE surfactant B (generic co-surfactant blend) stock	16.67	1.67%
SAMPLE co-solvent (generic ethoxylate) stock	3.00	0.30%
DI water (balance)	280.33	28.03%
TOTAL	1,000.00	100.00%

Worked SAMPLE example at 1,000 g: brine concentrate 666.67 g · Surfactant A stock 33.33 g · Surfactant B stock 16.67 g · Co-solvent 3.00 g · DI water 280.33 g — total 1,000.00 g.

Reference

Experimental protocol — CDC coreflood

Execution-ready procedure for SF1 capillary-desaturation corefloods at 100 °C, organized as checked phases with acceptance criteria. Every quantity in this procedure feeds the CDC#4 working sheet directly.

Prepared by Imad A. Adel

System: HPHT coreflood; 1,200 psi confining · 200 psi back pressure
Temperature: 100 °C; thermal equilibration before injection
Plateau criterion: ≥ 1.5 PV; stable ΔP and fractional flow
Primary output: S_o vs N_t; capillary desaturation curve

0Pre-job preparation & fluid QCMaterials verified before the core is loaded

Synthesize and verify brines against Table 1 targets: FW 243,028 ppm TDS; SW 43,373 ppm TDS; confirm density and viscosity against reference values (FW 1.17 g/cm³, 1.57 cP; SW 1.04 g/cm³, 1.02 cP at 25 °C).
Prepare 50%-diluted seawater for the post-flush; label DSAL.
Prepare SF1 in seawater (GAC 0.5 wt% active + IOS co-surfactants + ethoxylated phenol co-solvent 0.5 wt% active); confirm the solution is clear and single-phase at test temperature before loading.
Filter crude through 0.5 µm inline filter; record dead-oil viscosity at 100 °C (reference 1.25 cP).
Record core identity, dimensions, PV, φ, S_wi and centrifuge-conditioned S_orw in the working sheet (CDC#4 tab) — these drive every computed output.
Verify pump calibration at 0.075 and 12 cm³/min (lowest and highest protocol rates).

1System setup & thermal equilibrationHPHT coreflood configuration

Load core into the HPHT holder; confirm sleeve, end-pieces and flow-line routing.
Apply confining pressure 1,200 psi and back pressure 200 psi.
Heat to 100 °C; hold until temperature is stable at all sensors before any injection.
Leak/integrity check: stable ΔP baseline, no bypass, no abnormal pressure excursions.

2Baseline seawater pre-flushEstablish injection salinity and confirm a stable residual baseline

Inject SW at Q = 0.5, 1, 4, 8 cm³/min; hold each rate ≥ 1.5 PV (volumes and minimum durations auto-computed below).
Record ΔP at each stable plateau — these four readings back-calculate k at S_orw by Darcy’s law (enter in the ΔP table of the working sheet; target R² ≥ 0.95 for the ΔP–Q trend).
Return to the reference rate Q = 0.25 cm³/min and confirm zero incremental oil at this rate.
If oil is produced during the pre-flush, update the S_orw baseline in the working sheet before starting SF1 — the CDC must start from a verified stable baseline.

3SF1 rate escalation — the CDC measurementStepwise increase of the trapping number

Start SF1 at Q = 0.075 cm³/min; hold until oil cut ceases and ΔP is stable.
Escalate through Q = 0.25, 0.5, 1, 2, 6, 8, 12 cm³/min; each plateau ≥ 1.5 PV.
Advance rate only when BOTH ΔP and effluent fractional flow approach stable values.
Record incremental oil per step to the burette resolution (±0.05 cm³); enter values live in the working sheet — S_o, S_o/S_orw and N_t update automatically.
The last step with zero measurable oil before the first producing step defines N_t,crit (flagged automatically in the sheet).

4Salinity-gradient post-flushSeparate phase-behavior effects from the applied viscous force

After the 12 cm³/min plateau, inject a seawater chase.
Inject 50%-diluted brine at Q = 0.25 cm³/min (low rate by design — any additional oil here is phase-behavior-driven, not viscous).
Monitor oil production and ΔP; record any late-stage mobilization as the post-flush endpoint S_o,post.

5Shut-down & data packageClose out the experiment

Cool and depressurize per lab SOP; unload and preserve the core.
Confirm the working sheet is complete: core data, four ΔP readings, all incremental-oil entries.
Export the scenario file from the working sheet and archive with raw logger data.
Verify headline outputs (N_t,crit, S_orc, S_o,post, E_D) against the cross-core comparison page.

Rate schedule & live duration calculator

enter the core pore volume

Pore volume, PV cm³

Stage	Q (cm³/min)	1.5 PV volume (cm³)	Minimum duration
SW pre-flush	0.500	18.36	0:36:43
	1.000	18.36	0:18:22
	4.000	18.36	0:04:35
	8.000	18.36	0:02:18
SF1 escalation	0.075	18.36	4:04:48
	0.250	18.36	1:13:26
	0.500	18.36	0:36:43
	1.000	18.36	0:18:22
	2.000	18.36	0:09:11
	6.000	18.36	0:03:04
	8.000	18.36	0:02:18
	12.000	18.36	0:01:32
Post-flush	0.250	18.36	1:13:26

Acceptance criteria — every step

data quality gates

Check	Acceptance criterion
Injected volume	≥ 1.5 PV per rate step (see calculator)
Pressure response	ΔP stable or approaching a plateau before rate change
Effluent fractional flow	Stable or approaching stable values
Oil reading resolution	Incremental oil recorded to ±0.05 cm³; "measurable desaturation" means above this resolution
ΔP–Q linearity (pre-flush)	R² ≥ 0.95 across the four Darcy steps for k determination
Mass balance	Reasonable closure before accepting the step
System integrity	No leakage, bypass, or abnormal pressure excursions
Operating conditions	Temperature and back pressure stable throughout the step
IFT assignment	σ = 24.3 mN/m for SW/post-flush stages; σ = 3.07×10⁻³ mN/m for SF1 stages (used in N_t processing)

Reference

Model & equations — scientific basis

Every relationship used in this report, with conventions, constants and assumptions. All tables and figures across the site derive from these equations through one shared computation engine — outputs are retraceable end to end.

Prepared by Imad A. Adel

Governing equations — implemented convention

as implemented in this report

N_c = v · μ / σ = u · μ / (φ · σ · cos θ)

Eq. 1

Capillary number

Interstitial-velocity convention; μ = aqueous displacing-phase viscosity; cos θ = 1 (mechanical baseline, wettability term omitted).

v = u / φ

Eq. 2

Interstitial velocity

u = Q/A with Q in m³/s (1 cm³/min = 1.6667 × 10⁻⁸ m³/s), A = πD²/4.

N_b = k · Δρ · g / (φ · σ · cos θ)

Eq. 3

Bond number (implemented)

k = Darcy-law average permeability at S_orw (1 mD = 9.869233 × 10⁻¹⁶ m²); Δρ = 200 kg/m³. The Pope et al. (2000) form omits φ; this implementation includes it. N_b is 2–3 orders of magnitude below N_c in the reservoir cores, so the distinction does not affect N_t.

N_t = √(N_c² + 2 · N_c · N_b · sin α + N_b²)

Eq. 4

Total trapping number

Vector combination of viscous and buoyancy forces (Pope et al., 2000).

N_t = √(N_c² + N_b²)

Eq. 5

Horizontal simplification

α = 0° for all corefloods in this work — used throughout.

σ = C / (R^*)²

Eq. 6

Chun–Huh IFT

C = 0.3 mN/m; with R^* = 9.5 gives σ_Huh = 3.32 × 10⁻³ mN/m — independent check on the spinning-drop extrapolation (agreement within 8%).

N_t = N_c,2 · (k_rw / φ)

Eq. 7–8

Water-wet reference conversion

Chatzis & Morrow N_c,2 = k_w·ΔP/(L·σ) converted to this study’s basis; Berea BL-2 anchor (k_rw = 0.202, φ = 0.225) gives multiplier ≈ 0.9 — visually negligible on a log axis.

S_o,i = S_orw − (Σ oil recovered)_i / PV

Saturation chain

Normalized as S_o/S_orw; mobilized fraction = 1 − S_o/S_orw; E_D = (S_orw − S_orc)/S_orw.

k = Q · μ · L / (A · ΔP)

Darcy-law permeability

ΔP end-to-end, converted at 6,894.757 Pa/psi; k reported as the average of the four rate steps with the ΔP–Q correlation R² as a quality flag.

N_t,crit = highest tested N_t before measurable desaturation

Critical trapping number (operational)

The empirical bracket extends to the next rate step at which oil was produced; both bounds are reported.

Constants & conversions

1 cm³/min	1.6667×10⁻⁸ m³/s
1 mD	9.869233×10⁻¹⁶ m²
1 psi	6,894.757 Pa
1 m/s	283,464.6 ft/day
g	9.81 m/s²
Δρ	200 kg/m³ (assumed)
μ (100 °C)	0.40 cP — SW and SF1-in-SW (formulation did not change aqueous baseline viscosity)
σ_{SW / post-flush}	24.3 mN/m (pendant drop, 100 °C)
σ_SF1	3.07×10⁻³ mN/m (spinning-drop, power-law extrapolated to 100 °C)

Assumptions & limitations

S_orw baselines are centrifuge-conditioned reference values — protocol- and rock-dependent, not universal residual saturations.
Wetting state (mixed-to-oil-wet) is inferred from the 21-day / 100 °C aging protocol and displacement response; it was not independently quantified by Amott, USBM or contact angle.
cos θ = 1 and the mechanical N_c, N_b baseline isolate applied forces from rock–fluid interaction terms; the results are a defined mechanical baseline, not a complete wettability-dependent trapping criterion.
σ_os at 100 °C is extrapolated above the 90 °C measurement limit (power-law, R² = 0.998); the same phase environment is assumed to persist 90→100 °C. SF1 aqueous stability ≥ 21 days at 120 °C supports plausibility.
N_t,crit is an operational bracket (last no-oil step → first producing step), not a continuously resolved onset.
μ is the aqueous displacing-phase viscosity — the applied force is referenced to a defined fluid property, not to in-situ microemulsion rheology.
One reservoir plug per rock type and one outcrop reference core: CDC-slope contrasts are sample-bounded; the outcrop response is a reference measurement, not a reservoir prediction.
Field-rate scaling identifies screening constraints only; polymer rheology, retention, injectivity and fracture-pressure limits were not measured in this work.
The fourth SAMPLE record (Experiment 4) has not been flooded; its sheet carries no identity or petrophysics and the coreflood recovery is intentionally blank.

Reference

Nomenclature

All symbols, subscripts, units and abbreviations used across this report.

Prepared by Imad A. Adel

Symbols

Symbol	Definition	Unit
A	Cross-sectional area of the core plug	m²
E_D	Microscopic displacement efficiency	fraction
g	Gravitational acceleration (9.81)	m/s²
k	Permeability at S_orw (Darcy-law average)	mD
k_abs	Absolute (brine) permeability	mD
L	Core plug length	cm
N_b	Bond number	—
N_c	Capillary number	—
N_t	Total trapping number	—
N_t,crit	Critical trapping number	—
PV	Pore volume	cm³
Q	Volumetric injection rate	cm³/min
R^*	Optimal solubilization ratio	cm³/cm³
S^*	Optimal salinity	ppm TDS
S_o	Oil saturation	fraction
S_orc	Residual oil saturation after chemical flood	fraction
S_orw	Residual oil saturation after waterflood (centrifuge-conditioned baseline)	fraction
S_o,post	Oil saturation after the salinity-gradient post-flush	fraction
S_wi	Initial water saturation	fraction
u	Darcy (superficial) velocity	m/s or ft/day
v	Interstitial velocity, v = u/φ	m/s or ft/day
V_o/V_s	Oil solubilization ratio	cm³/cm³
V_w/V_s	Water solubilization ratio	cm³/cm³
α	Dip angle (0° in this work)	degrees
ΔP	Differential pressure (end-to-end)	psi or Pa
Δρ	Aqueous–oleic density difference (200)	kg/m³
θ	Contact angle (cos θ = 1 baseline)	degrees
μ	Aqueous displacing-phase viscosity (0.40 at 100 °C)	cP
σ_os	Oil–surfactant interfacial tension (3.07×10⁻³ at 100 °C)	mN/m
σ_ow	Oil–seawater interfacial tension (24.3)	mN/m
φ	Porosity	fraction

Abbreviations

Abbreviation	Definition
CDC	Capillary desaturation curve
DI	Deionized (water)
DSAL	Diluted-salinity brine (salinity-gradient post-flush)
EOR	Enhanced oil recovery
FW	Formation water (243,028 ppm TDS)
GAC	Guerbet alkoxy carboxylate
HPHT	High-pressure, high-temperature (coreflood system)
HTHS	High-temperature, high-salinity
IFT	Interfacial tension
IOS	Internal olefin sulfonate
SF1	Surfactant formulation 1 (GAC + IOS blend in seawater)
SW	Synthetic seawater (43,373 ppm TDS)
TDS	Total dissolved solids

What applied trapping number is required to mobilize residual oil in our carbonates?

The central finding — mobilization-force ladderSAMPLE DATA

Program contributions

Gaps this work closes

Program statusSAMPLE DATA

What is in this report

Core A — outcrop reference (SAMPLE)

Core B — reservoir carbonate (SAMPLE)

Core C — reservoir carbonate (SAMPLE)

Planned experiment — no measured results

Sample calculator sheet

Cross-core comparison

Field-rate scaling

Fluids & formulation

Formulation calculator

Experimental protocol

Model & equations

Nomenclature

CDC#1 — Core A

Core identity

Core properties

Permeability at Sorw — Darcy law

Stage schedule & trapping numbers

Recovery & saturation chain

Desaturation responseSAMPLE DATA

Normalized CDCSAMPLE DATA

CDC#2 — Core B

Core identity

Core properties

Permeability at Sorw — Darcy law

Stage schedule & trapping numbers

Recovery & saturation chain

Desaturation responseSAMPLE DATA

Normalized CDCSAMPLE DATA

CDC#3 — Core C

Core identity

Core properties

Permeability at Sorw — Darcy law

Stage schedule & trapping numbers

Recovery & saturation chain

Desaturation responseSAMPLE DATA

Normalized CDCSAMPLE DATA

CDC#4 — New coreflood

Core identity

Core properties · editable inputs

Permeability at Sorw — Darcy law · ΔP editable

Stage schedule & trapping numbers

Recovery & saturation chain · incremental oil editable

Desaturation response

Normalized CDC

CDC#5 — New coreflood

Core identity

Core properties · editable inputs

Permeability at Sorw — Darcy law · ΔP editable

Stage schedule & trapping numbers

Recovery & saturation chain · incremental oil editable

Desaturation response

Normalized CDC

Cross-core comparison

Oil saturation vs trapping numberSAMPLE DATA

Normalized CDCs vs water-wet benchmarkSAMPLE DATA

Endpoint saturations by stageSAMPLE DATA

Program summarySAMPLE DATA

Field-rate scaling — is the threshold achievable?

Interactive scaling calculatorSAMPLE DATA

Viscous and buoyancy componentsSAMPLE DATA

Viscosity requirements & polymer screening

Fluids & formulation

Brine compositions — Table 1

SF1 formulation — Table 3

Phase behavior — solubilization scan

Oil–surfactant IFT vs temperature

Formulation calculator

Batch setupSAMPLE DATA

Component table — active targets and stock assaysSAMPLE DATA

Final batch recipe — mass to add, in mixing orderSAMPLE DATA

Experimental protocol — CDC coreflood

Rate schedule & live duration calculator

Acceptance criteria — every step

Model & equations — scientific basis

Permeability at S_orw — Darcy law

Permeability at S_orw — Darcy law

Permeability at S_orw — Darcy law

Permeability at S_orw — Darcy law · ΔP editable

Permeability at S_orw — Darcy law · ΔP editable