Fos-sur-Mer: what is hydrogen storage worth, and what does doing without the gas reformer cost?

POMMES case study · PERSEE, MINES Paris – PSL · a textbook case, not a forecast.

The industrial zone of Fos-sur-Mer uses 83.5 kt of hydrogen a year (refining, methanol), today made by a steam-methane reformer (SMR) burning natural gas, plus some by-product hydrogen from a chlorine plant (KEM ONE, 43 MW). An electrolyser could make it instead, buying electricity at the hourly price. Two questions:

1. What is a hydrogen storage worth — the Manosque salt cavern, 110 km away — to that electrolyser, and how does that value depend on the electrolyser's investment cost (CAPEX)?
2. What does it cost to do without the gas reformer as a back-up, i.e. to impose 100 % electrolytic hydrogen?

How. Hourly French electricity prices come from a European POMMES model of the 2030 power system (16 zones, 11 weather years, three gas prices; T. Knibiehly, PhD, PERSEE). The hub itself is a one-node linear programme — the reduced model — that chooses electrolyser and cavern sizes and their hourly operation at least annual cost. It reproduces the full POMMES modelling of the Fos hub at every point POMMES solved (section 3). The equations and costs live in regles_parametriques/regles/cavite.py; fos_case.py only reads the frozen data and calls them.

Assumptions, units and sources: hypotheses.yaml. Interactive version: page.html.

import numpy as np, pandas as pd, matplotlib.pyplot as plt
import fos_case as fc, analyse
pd.set_option("display.precision", 2)
print("demand:", round(fc.kt_par_an(fc.DEMANDE_FOS_MW), 1), "kt/yr =", round(fc.DEMANDE_FOS_MW, 1), "MW flat")

demand: 83.5 kt/yr = 317.7 MW flat

1. The electricity prices

What matters for storage is not the average price but the spread between cheap and expensive hours. The gas price sets that spread: gas-fired plants set the price in expensive hours, renewables and nuclear in cheap ones.

fig, ax = plt.subplots(figsize=(8, 4))
for g, c in zip(fc.GAZ, ["#5DA9DE", "#005E9E", "#0B2E4F"]):
    p = np.sort(fc.prix("cy2009", g))[::-1]
    ax.plot(np.arange(len(p)) / len(p) * 100, p, color=c, label=f"gas €{g}/MWh — mean {p.mean():.0f} €/MWh")
ax.set(xlabel="share of the year (%)", ylabel="€/MWh", ylim=(0, 250), title="Price duration curve, France, 2030, weather year 2009")
ax.legend(frameon=False); ax.grid(ls=":")

tab = pd.DataFrame({(a, g): [fc.prix(a, g).mean()] for a in fc.ANNEES for g in fc.GAZ}).T[0].unstack()
tab.columns = [f"gas {g}" for g in tab.columns]
tab.round(1)   # mean French price (€/MWh) by weather year

	gas 15	gas 30	gas 65
cy1983	37.5	50.4	78.2
cy1985	43.6	58.1	90.1
cy1987	45.3	61.9	97.2
cy1990	36.2	48.5	75.2
cy1996	44.4	59.2	92.4
cy2000	37.1	48.1	73.3
cy2003	44.6	61.5	99.3
cy2009	43.7	58.6	85.4
cy2010	48.0	65.7	107.3
cy2012	42.5	57.0	88.2
cy2014	38.5	51.0	77.7

2. One run of the reduced model

100 % electrolytic hydrogen, electrolyser at 1,350 €/kW_e (RTE reference), gas at €30/MWh, weather year 2009. Without the cavern, the electrolyser follows the flat demand and pays the average price. With it, the electrolyser is oversized and runs only in the cheapest hours; the cavern fills in spring and summer and empties in winter.

p = fc.prix("cy2009", 30)
par = fc.parametres(1350, 0.68)
res, sol = fc.cavite.valeur_lp(p, par, avec_solution=True)
print(f"solved in {sol.temps_s:.1f} s — value of the cavern: {res.valeur_eur_par_kg:.3f} €/kg "
      f"({100 * res.part_cout:.1f} % of the cost of electrolytic H2 without it), cavern {sol.E_mwh_h2 / 1e3:.0f} GWh, "
      f"electrolyser {sol.P_mw_h2 / 0.68:.0f} MW_e, running {100 * res.x:.0f} % of the hours")
fig, ax = plt.subplots(2, 1, figsize=(9, 5), sharex=True)
j = np.arange(8760) / 24
ax[0].plot(j, p, lw=0.3, color="#9D9D9D"); ax[0].set(ylabel="€/MWh", ylim=(0, 200))
ax[1].plot(j, sol.s_mwh_h2 / 1e3, color="#005E9E"); ax[1].set(ylabel="cavern level (GWh)", xlabel="day of the year")
for a in ax: a.grid(ls=":")

solved in 10.2 s — value of the cavern: 0.442 €/kg (11.9 % of the cost of electrolytic H2 without it), cavern 200 GWh, electrolyser 1109 MW_e, running 45 % of the hours

3. Check: the reduced model against the full POMMES modelling

POMMES solved the Fos hub (without the steel plant) for three CAPEX levels, 11 weather years, with and without the cavern, at several mandate levels. The reduced model is solved here on a few of those points and compared on the difference of annual cost — the quantity both questions are about.

R = fc.pommes()
rows = []
for annee in ("cy1990", "cy2009", "cy2014"):
    for phi in (0.6, 1.0):
        q = R[(R.niveau_capex == "rte_ref") & (R.gaz_eur_mwh == 30) & (R.demande_europe == 1000) & (R.taxe_eur_t == 100)
              & (R.annee == annee)]
        tot = {s: q[(q.stockage == s) & (q.obligation == phi)].annualised_totex_eur.iloc[0] / 1e6 for s in ("no_storage", "manosque")}
        p = fc.prix(annee, 30)
        par = fc.parametres(1350, 0.68, part_min=phi, gaz=30)
        lp = {cav: fc.systeme(p, par, avec_cavite=cav).cout_meur_an for cav in (False, True)}
        rows.append({"year": annee, "mandate": phi, "value of cavern, POMMES (€m/yr)": tot["no_storage"] - tot["manosque"],
                     "value of cavern, reduced (€m/yr)": lp[False] - lp[True]})
pd.DataFrame(rows).round(3)

	year	mandate	value of cavern, POMMES (€m/yr)	value of cavern, reduced (€m/yr)
0	cy1990	0.6	21.19	21.19
1	cy1990	1.0	50.31	50.31
2	cy2009	0.6	12.02	12.02
3	cy2009	1.0	36.90	36.90
4	cy2014	0.6	18.61	18.61
5	cy2014	1.0	53.77	53.77

4. Question 1 — the value of storage, and the electrolyser's CAPEX

Grid of the reduced model (grille.py stockage): 7 CAPEX × 3 gas prices × 5 hydrogen volumes × 3 cavern caps × 11 weather years. Dots: POMMES (mean of the 11 years).

G = analyse.grille("stockage")
V = analyse.valeur_pommes()
fos = round(fc.kt_par_an(fc.DEMANDE_FOS_MW), 2)
g = G[(G.demande_kt == fos) & (G.volume_max_gwh == 200)]
fig, ax = plt.subplots(figsize=(8, 4.5))
for gaz, c in zip(fc.GAZ, ["#5DA9DE", "#005E9E", "#0B2E4F"]):
    s = g[g.gaz == gaz].groupby("capex").valeur_eur_par_kg.agg(["mean", "min", "max"])
    ax.plot(s.index, s["mean"], color=c, label=f"gas €{gaz}/MWh")
    ax.fill_between(s.index, s["min"], s["max"], color=c, alpha=0.1)
    pv = V[(V.obligation == 1) & (V.gaz_eur_mwh == gaz) & (V.demande_europe == 1000)].groupby("capex_eur_kw").valeur_eur_kg.mean()
    ax.scatter(pv.index, pv.values, facecolor="white", edgecolor=c, zorder=5)
ax.set(xlabel="electrolyser CAPEX (€/kW_e)", ylabel="value of the cavern (€/kg H2)", ylim=(0, None))
ax.legend(frameon=False); ax.grid(ls=":")

# The numbers quoted in the post (POMMES, mean and range over 11 weather years)
t = V[(V.demande_europe == 1000) & (V.obligation.isin([0, 1]))]
t.groupby(["obligation", "gaz_eur_mwh", "capex_eur_kw"]).agg(
    value_eur_kg=("valeur_eur_kg", "mean"), worst_year=("valeur_eur_kg", "min"), best_year=("valeur_eur_kg", "max"),
    share_of_cost=("part_cout", "mean"), value_meur_yr=("valeur_meur_an", "mean")).round(2)

			value_eur_kg	worst_year	best_year	share_of_cost	value_meur_yr
obligation	gaz_eur_mwh	capex_eur_kw
0.0	30	417.0	0.25	0.10	0.39	0.19	20.94
		1000.0	0.03	-0.00	0.08	0.02	2.15
		1350.0	0.00	-0.00	0.00	0.00	0.00
1.0	15	1000.0	0.19	0.04	0.35	0.08	16.27
		1350.0	0.06	-0.00	0.17	0.02	5.35
	20	1000.0	0.35	0.16	0.52	0.13	29.09
		1350.0	0.17	0.00	0.34	0.06	13.78
	25	1000.0	0.52	0.29	0.71	0.17	43.50
		1350.0	0.32	0.09	0.52	0.10	26.38
	30	417.0	1.34	1.21	1.45	0.42	112.29
		1000.0	0.70	0.47	0.89	0.22	58.44
		1350.0	0.48	0.22	0.70	0.14	40.41
	35	1000.0	0.87	0.67	1.07	0.25	73.05
		1350.0	0.65	0.36	0.89	0.17	54.43
	40	1000.0	1.06	0.88	1.25	0.29	88.34
		1350.0	0.83	0.56	1.07	0.21	69.50
	45	1000.0	1.24	1.08	1.42	0.32	103.28
		1350.0	1.01	0.78	1.25	0.24	84.47
	50	1000.0	1.41	1.24	1.59	0.34	117.61
		1350.0	1.18	1.00	1.43	0.27	98.90
	55	1000.0	1.59	1.39	1.77	0.37	132.38
		1350.0	1.36	1.16	1.61	0.29	113.78
	60	1000.0	1.76	1.53	1.97	0.39	147.21
		1350.0	1.54	1.31	1.78	0.32	128.56
	65	1000.0	1.93	1.68	2.20	0.41	161.37
		1350.0	1.71	1.46	1.96	0.34	142.82

Reading. Under a 100 % mandate the cavern always has value, and that value falls as the electrolyser gets dearer: a cheap electrolyser is oversized more, so it can shift more of its purchases to cheap hours. The gas price matters as much as the CAPEX, although no gas is burnt at 100 %: it acts only through the spread of electricity prices. Without a mandate, at the central CAPEX, the cavern is worth nothing: electrolysis is built in only 3 weather years out of 11, to make about 40 % of the hydrogen in cheap hours, and the existing gas reformer provides the flexibility.

The volume of hydrogen

For the same cavern, a smaller demand can be shifted over longer periods (the cavern's autonomy grows), so the value per kg rises; a larger one (Fos with a hydrogen-based steel plant, 287.5 kt/yr) fills the cavern in two weeks. The model is homogeneous: only the ratio cap / demand matters (25 kt/yr with 100 GWh = 50 kt/yr with 200 GWh). Below: gas €30/MWh, 1,350 €/kW_e.

s = G[(G.gaz == 30) & (G.capex == 1350)].groupby(["demande_kt", "volume_max_gwh"]).valeur_eur_par_kg.mean().unstack()
s.columns = [f"cap {c:g} GWh" for c in s.columns]
s.round(2)   # €/kg by hydrogen demand (kt/yr)

	cap 100 GWh	cap 200 GWh	cap 400 GWh
demande_kt
25.00	0.52	0.53	0.53
50.00	0.47	0.52	0.53
83.49	0.42	0.48	0.52
150.00	0.37	0.43	0.49
287.47	0.30	0.37	0.44

A one-line rule

The simplified model of regles/cavite.py replaces the LP by a sort of hourly prices in windows as long as the cavern's autonomy. It needs no solver (~1 ms) — how far is it from the LP?

e = (G.simplifie_eur_par_kg - G.valeur_eur_par_kg)
print(f"simplified − LP over {len(G)} cases: median {e.median():+.3f} €/kg, "
      f"median |error| {e.abs().median():.3f} €/kg, 90th pct |error| {e.abs().quantile(.9):.3f} €/kg")
G.assign(err=e).groupby(["demande_kt"]).err.describe()[["mean", "50%", "min", "max"]].round(3)

simplified − LP over 3465 cases: median -0.010 €/kg, median |error| 0.017 €/kg, 90th pct |error| 0.067 €/kg

	mean	50%	min	max
demande_kt
25.00	-1.60e-02	-1.30e-02	-0.18	0.16
50.00	-1.40e-02	-1.10e-02	-0.18	0.16
83.49	-1.40e-02	-1.20e-02	-0.16	0.17
150.00	-9.00e-03	-7.00e-03	-0.18	0.16
287.47	-7.00e-03	-5.00e-03	-0.15	0.14

5. Question 2 — the cost of doing without the reformer

A mandate fixes a minimum electrolytic share of the hydrogen served. The cost of the mandate is measured against the unconstrained hub (the least-cost hub with no mandate, carbon tax of €100/t included), and read excluding the carbon tax — a transfer, not a cost to society.

⚠️ The chlorine by-product (43 MW, 13.5 % of the hydrogen) emits nothing in the model but counts as non-electrolytic. At an 86.5 % mandate the reformer no longer runs; beyond, electrolysis replaces chlorine and avoids no CO₂.

O = analyse.obligation_pommes()
Gh = analyse.obligation_reduit()
fig, ax = plt.subplots(figsize=(8, 4.5))
for cav, c in ((False, "#C77F00"), (True, "#005E9E")):
    s = Gh[(Gh.niveau_capex == "rte_ref") & (Gh.gaz == 30) & (Gh.avec_cavite == cav)].groupby("obligation").surcout_hors_taxe_meur_an.mean()
    ax.plot(100 * s.index, s.values, color=c, label="with cavern" if cav else "without cavern")
    po = O[(O.niveau_capex == "rte_ref") & (O.avec_cavite == cav)].groupby("obligation").surcout_hors_taxe_meur_an.mean()
    ax.scatter(100 * po.index, po.values, facecolor="white", edgecolor=c, zorder=5)
ax.axvline(100 * (1 - fc.CHLORE_MW / fc.DEMANDE_FOS_MW), ls="--", color="grey")
ax.set(xlabel="mandated electrolytic share (%)", ylabel="extra cost excl. carbon tax (€m/yr)", ylim=(0, None))
ax.legend(frameon=False); ax.grid(ls=":")

# Steps of the mandate: marginal abatement cost (€/tCO2), reduced model, 1,350 €/kW_e
m = analyse.marches(Gh[Gh.niveau_capex == "rte_ref"], ["gaz", "avec_cavite"])
m.pivot_table(index="obligation", columns=["gaz", "avec_cavite"], values="abattement_marginal_eur_t").round(0)

gaz	15		30		65
avec_cavite	False	True	False	True	False	True
obligation
0.15	187.0	187.0	153.0	153.0	NaN	NaN
0.30	187.0	187.0	154.0	154.0	217.0	106.0
0.45	195.0	195.0	205.0	177.0	258.0	106.0
0.60	220.0	209.0	265.0	174.0	458.0	110.0
0.70	222.0	209.0	274.0	180.0	401.0	154.0
0.75	222.0	210.0	274.0	195.0	398.0	227.0
0.80	222.0	214.0	274.0	207.0	398.0	246.0
0.86	265.0	240.0	336.0	230.0	416.0	337.0
0.90	NaN	4794.0	NaN	3215.0	458.0	758.0
0.95	5016.0	NaN	2286.0	NaN	1405.0	2826.0
1.00	4231.0	8214.0	8829.0	NaN	13847.0	NaN

# Same at the POMMES points (gas 30), average and marginal abatement cost
analyse._arrondi(analyse.marches(O, ["niveau_capex", "avec_cavite"]))

	niveau_capex	avec_cavite	obligation	surcout_hors_taxe_meur_an	evite_kt	marche_meur_an	marche_evite_kt	abattement_marginal_eur_t	abattement_moyen_eur_t
0	rte_favorable	False	0.00	-9.7	-118.2	NaN	NaN	NaN	NaN
1	rte_favorable	False	0.30	2.3	-17.1	12.0	101.1	118.6	NaN
2	rte_favorable	False	0.45	22.7	86.0	20.4	103.1	197.9	264.2
3	rte_favorable	False	0.60	55.7	215.8	33.0	129.8	254.3	258.2
4	rte_favorable	False	0.75	90.4	350.5	34.7	134.7	257.3	257.9
5	rte_favorable	False	0.90	123.8	448.6	33.4	98.1	340.9	276.0
6	rte_favorable	False	1.00	156.6	458.4	32.8	9.8	3354.1	341.7
7	rte_favorable	True	0.00	0.0	0.0	NaN	NaN	NaN	NaN
8	rte_favorable	True	0.30	11.8	101.1	11.8	101.1	116.3	116.3
9	rte_favorable	True	0.45	23.4	185.3	11.6	84.1	138.4	126.4
10	rte_favorable	True	0.60	35.4	271.0	12.0	85.7	139.6	130.5
11	rte_favorable	True	0.75	50.3	367.1	14.9	96.1	155.2	137.0
12	rte_favorable	True	0.90	73.9	458.4	23.6	91.2	258.7	161.2
13	rte_favorable	True	1.00	98.2	458.4	24.3	0.0	NaN	214.2
14	rte_ref	False	0.00	0.0	0.0	NaN	NaN	NaN	NaN
15	rte_ref	False	0.30	30.1	196.0	30.1	196.0	153.7	153.7
16	rte_ref	False	0.45	52.9	307.2	22.8	111.2	204.6	172.2
17	rte_ref	False	0.60	88.6	441.9	35.7	134.7	265.2	200.5
18	rte_ref	False	0.75	125.5	576.6	36.9	134.7	274.1	217.7
19	rte_ref	False	0.90	162.3	670.7	36.7	94.0	390.8	242.0
20	rte_ref	False	1.00	196.8	679.6	34.5	9.0	3853.0	289.5
21	rte_ref	True	0.00	0.0	0.0	NaN	NaN	NaN	NaN
22	rte_ref	True	0.30	30.1	196.0	30.1	196.0	153.7	153.7
23	rte_ref	True	0.45	49.8	307.2	19.7	111.2	176.9	162.1
24	rte_ref	True	0.60	73.3	441.9	23.5	134.7	174.1	165.8
25	rte_ref	True	0.75	98.0	575.5	24.7	133.6	185.1	170.3
26	rte_ref	True	0.90	128.2	679.6	30.2	104.1	290.5	188.7
27	rte_ref	True	1.00	156.4	679.6	28.1	0.0	NaN	230.1
28	these	False	0.00	-20.1	-410.8	NaN	NaN	NaN	NaN
29	these	False	0.30	-15.9	-385.8	4.3	25.0	171.1	NaN
30	these	False	0.45	4.7	-303.3	20.6	82.5	249.2	NaN
31	these	False	0.60	39.5	-182.8	34.8	120.5	288.8	NaN
32	these	False	0.75	78.9	-48.1	39.4	134.7	292.3	NaN
33	these	False	0.90	118.8	81.5	39.9	129.5	307.9	1457.9
34	these	False	1.00	155.3	96.1	36.5	14.6	2495.6	1615.9
35	these	True	0.00	0.0	0.0	NaN	NaN	NaN	NaN
36	these	True	0.30	0.0	0.0	0.0	0.0	NaN	NaN
37	these	True	0.45	-0.0	-0.0	-0.0	-0.0	NaN	NaN
38	these	True	0.60	0.0	-0.0	0.0	-0.0	NaN	NaN
39	these	True	0.75	3.1	17.3	3.1	17.3	181.9	181.9
40	these	True	0.90	20.5	80.2	17.3	62.9	275.3	255.2
41	these	True	1.00	43.0	96.1	22.5	15.9	1417.8	447.2

6. What this case does not say — and how to go further

• Prices are exogenous: the electrolyser does not move them. The cavern's cap (200 GWh) is declared, not geological; lifted, POMMES builds much more, so the value here is a lower bound.
• The hub is isolated: a hydrogen network (to Lyon, Spain) would change the value of local storage.
• The EU hourly-correlation rule for renewable hydrogen (RFNBO) is not modelled.
• One European power system (2030); the weather years change, the fleet does not. Replaying the case with the TYNDP 2026 scenarios is a natural next step.

These are the kind of mini-projects a group carries out during the course.