CO2 properties and phase behaviour

Mei Lin's first request from Farid was not a core analysis but a table: the density, viscosity and phase of CO₂ at every point from the compressor discharge to the bottom of the injection wells. “Every calculation in this study needs one of those three numbers,” Farid said, “and CO₂ is not a gas you can treat with a z-factor chart and forget. Near its critical point a few degrees changes its density by half.” Ethan had used CO₂ properties in the enhanced recovery course, but only at reservoir conditions. A storage hub handles it across the whole range, from the vapour leaving a capture plant to the dense fluid in the formation.

The phase diagram

CO₂ has a triple point at −56.6 °C and 518 kPa, below which it cannot exist as a liquid; at atmospheric pressure solid CO₂ (dry ice) sublimes directly to gas at −78.5 °C. Its critical point is at 31.0 °C and 7.38 MPa. Above both the critical temperature and the critical pressure it is a supercritical fluid, with a density close to a liquid's and a viscosity close to a gas's. Between the triple point and the critical point, the vapour pressure curve separates liquid from gas. The critical temperature is close to ordinary ground temperatures, which is what makes CO₂ awkward: a pipeline at 12 MPa (1,740 psia) holds liquid in winter and a supercritical fluid in a hot summer, and a well that warms on the way down can cross from one to the other without any phase boundary at all.

For transport, the useful states are the dense phase, either liquid or supercritical above about 8.5 MPa (1,230 psia), where CO₂ has a density of 600 to 1,000 kg/m³ (62 lb/ft³) and can be pumped like a liquid, and the cold low-pressure liquid used for ships, at about −50 °C and 0.7 MPa (100 psia) near the triple point, or −30 °C and 1.5 to 2 MPa (220 to 290 psia) for medium-pressure ships. Gas-phase pipelines, below about 4.8 MPa (700 psia), are used for short collection lines from capture plants but carry little mass per unit of pipe. The worst place to operate is near the vapour pressure curve, where a small pressure or temperature change can flash liquid to vapour and cause two-phase flow, slugging and erratic pump behaviour.

Density

CO₂ density is the property that decides how much fits in a pipe and in a pore. At standard conditions it is about 1.87 kg/m³ (0.117 lb/ft³), 1.5 times as dense as air, which is why a large release flows downhill and collects in low ground. In the dense phase its density ranges from about 600 to 1,100 kg/m³ (37 to 69 lb/ft³), and it is highly compressible near the critical point. No simple correlation covers that range. The reference equation of state for CO₂, by Span and Wagner (1996), is accurate to a few hundredths of a percent and is the basis of property software. Cubic equations such as Peng-Robinson, familiar from the PVT course, are convenient and usually within about 5 percent of the reference density away from the critical point, reading low for dense CO₂; volume translation reduces the error.

# CO2 density and phase from the Peng-Robinson equation of state (stdlib only).
# Peng-Robinson is within about 5 percent of the reference (Span-Wagner) density away from the critical point; it reads low for dense CO2.
import math
SI = True      # True: metric units (Canadian hub), False: oilfield units (US hub)

R = 8.314462; TC, PC, W, MW = 304.13, 7.3773e6, 0.22394, 0.0440095   # K, Pa, acentric factor, kg/mol

def cubic_roots(a2, a1, a0):
    # real roots of z^3 + a2 z^2 + a1 z + a0 = 0
    q = (3 * a1 - a2 * a2) / 9; r = (9 * a2 * a1 - 27 * a0 - 2 * a2 ** 3) / 54; d = q ** 3 + r * r
    if d > 0:
        s = math.copysign(abs(r + math.sqrt(d)) ** (1 / 3), r + math.sqrt(d))
        t = math.copysign(abs(r - math.sqrt(d)) ** (1 / 3), r - math.sqrt(d))
        return [s + t - a2 / 3]
    th = math.acos(r / math.sqrt(-q ** 3))
    return sorted(2 * math.sqrt(-q) * math.cos((th + 2 * math.pi * k) / 3) - a2 / 3 for k in range(3))

def pr(T, p):
    """Return density kg/m3, compressibility factor z and a phase label for CO2 at T (K) and p (Pa)."""
    k = 0.37464 + 1.54226 * W - 0.26992 * W * W
    a = 0.45724 * R * R * TC * TC / PC * (1 + k * (1 - math.sqrt(T / TC))) ** 2
    b = 0.07780 * R * TC / PC
    A, B = a * p / (R * T) ** 2, b * p / (R * T)
    zs = [z for z in cubic_roots(-(1 - B), A - 3 * B * B - 2 * B, -(A * B - B * B - B ** 3)) if z > B]
    def lnphi(z):
        return z - 1 - math.log(z - B) - A / (2 * math.sqrt(2) * B) * math.log((z + 2.414214 * B) / (z - 0.414214 * B))
    z = min(zs, key=lnphi)                        # stable root: lowest fugacity
    if T > TC and p > PC: ph = 'supercritical'
    elif T > TC: ph = 'gas (above Tc)'
    else: ph = 'liquid' if z == min(zs) and len(zs) > 1 or (len(zs) == 1 and z < 0.3) else 'gas'
    return p * MW / (z * R * T), z, ph

if SI:
    print("Hub conditions (Peng-Robinson, CO2)")
    cases = [("compressor discharge", 45.0, 15000), ("pipeline, winter ground", 4.0, 12000), ("pipeline, summer ground", 15.0, 10000),
             ("wellhead, injecting", 20.0, 9000), ("reservoir, Basal Cambrian", 60.0, 20500)]
    print(f"{'location':28s}{'T, C':>7s}{'p, kPa':>9s}{'rho, kg/m3':>12s}{'z':>7s}  phase")
    for name, t, p in cases:
        rho, z, ph = pr(t + 273.15, p * 1000); print(f"{name:28s}{t:7.0f}{p:9,.0f}{rho:12.0f}{z:7.3f}  {ph}")
    print("\nDensity with depth, 10 kPa/m hydrostatic, 8 C surface, two geothermal gradients")
    print(" depth m   rho at 25 C/km   rho at 35 C/km")
    for d in range(500, 3001, 250):
        p = 101.3e3 + 10.0e3 * d
        r1 = pr(281.15 + 0.025 * d, p)[0]; r2 = pr(281.15 + 0.035 * d, p)[0]
        print(f"{d:8,d}{r1:15.0f}{r2:17.0f}")
else:
    print("Hub conditions (Peng-Robinson, CO2)")
    cases = [("compressor discharge", 113.0, 2175), ("pipeline, winter ground", 50.0, 1740), ("pipeline, summer ground", 80.0, 1450),
             ("wellhead, injecting", 85.0, 1300), ("reservoir, Frio", 160.0, 2640)]
    print(f"{'location':28s}{'T, F':>7s}{'p, psia':>9s}{'rho, lb/ft3':>13s}{'z':>7s}  phase")
    for name, t, p in cases:
        rho, z, ph = pr((t - 32) / 1.8 + 273.15, p * 6894.757); print(f"{name:28s}{t:7.0f}{p:9,.0f}{rho / 16.0185:13.1f}{z:7.3f}  {ph}")
    print("\nDensity with depth, 0.433 psi/ft hydrostatic, 70 F surface, two geothermal gradients")
    print(" depth ft   rho at 1.4 F/100 ft   rho at 2.0 F/100 ft   (lb/ft3)")
    for d in range(2000, 10001, 1000):
        p = (14.7 + 0.433 * d) * 6894.757
        r1 = pr((70 + 0.014 * d - 32) / 1.8 + 273.15, p)[0] / 16.0185; r2 = pr((70 + 0.020 * d - 32) / 1.8 + 273.15, p)[0] / 16.0185
        print(f"{d:9,d}{r1:20.1f}{r2:22.1f}")
print("\nMost of the density gain comes between about 600 and 1,000 m (2,000 and 3,500 ft); below that, CO2 density rises only slowly with depth.")

Hub conditions (Peng-Robinson, CO2)
location                       T, C   p, kPa  rho, kg/m3      z  phase
compressor discharge             45   15,000         703  0.355  supercritical
pipeline, winter ground           4   12,000         978  0.234  liquid
pipeline, summer ground          15   10,000         875  0.210  liquid
wellhead, injecting              20    9,000         810  0.201  liquid
reservoir, Basal Cambrian        60   20,500         704  0.463  supercritical

Density with depth, 10 kPa/m hydrostatic, 8 C surface, two geothermal gradients
 depth m   rho at 25 C/km   rho at 35 C/km
     500            148              138
     750            671              309
   1,000            685              511
   1,250            694              545
   1,500            701              560
   1,750            706              570
   2,000            710              577
   2,250            713              583
   2,500            716              587
   2,750            719              591
   3,000            721              594

Most of the density gain comes between about 600 and 1,000 m (2,000 and 3,500 ft); below that, CO2 density rises only slowly with depth.

The table shows why storage is planned below about 800 m (2,600 ft). In a sedimentary basin with hydrostatic pressure and a normal geothermal gradient, CO₂ density rises steeply with depth through the critical region and then flattens. With a 25 °C/km gradient, density reaches about 670 kg/m³ at 750 m and only 710 kg/m³ at 2,000 m. In a hotter basin the curve is lower and keeps rising. Above the critical depth, CO₂ is a gas, occupying several times more pore space per tonne and much more buoyant. Below it, extra depth gains little density but costs drilling, raises temperature and may lower porosity. For the Basal Cambrian Sands at 2,050 m, the code gives about 704 kg/m³ at 60 °C and 20.5 MPa, and Farid adopted that value for the capacity estimates in Lesson 8, noting that the reference equation would give a few percent more.

Viscosity and buoyancy

Dense CO₂ is much less viscous than brine: about 0.05 to 0.10 mPa·s at storage conditions, against 0.4 to 1.0 mPa·s for formation brine. The mobility ratio of CO₂ to brine is therefore large, about 3 to 5 when the reduced relative permeability of CO₂ is included, and injected CO₂ fingers and overrides rather than displacing brine evenly. It is also lighter than brine. With brine at 1,180 kg/m³ and CO₂ at 704 kg/m³, the density difference of about 475 kg/m³ drives CO₂ upward to the base of the seal, where it spreads laterally as a thin tongue. Buoyancy is the reason storage depends on a caprock, and the combination of low viscosity and buoyancy shapes the plume models of Lesson 9.

Impurities change the phase envelope

Captured CO₂ is never pure. Flue gas capture leaves traces of oxygen, nitrogen and argon; syngas capture leaves hydrogen, carbon monoxide and methane; gas processing CO₂ carries hydrogen sulphide and hydrocarbons; and all streams carry water. Non-condensable impurities such as nitrogen, argon, oxygen and especially hydrogen turn the single vapour pressure curve of pure CO₂ into a two-phase envelope with a bubble point line above it. A few percent of hydrogen can raise the bubble point pressure by several MPa, so the pipeline's minimum operating pressure must rise to keep the stream single-phase. Impurities also lower the density of the dense phase, slightly reducing storage capacity and pipeline throughput, and increase the compression power per tonne.

Water and certain impurities matter for a different reason: corrosion. Dry CO₂ is not corrosive to carbon steel, but free water dissolves CO₂ to form carbonic acid, which corrodes steel at millimetres per year. Pipeline specifications therefore limit water to a few hundred parts per million or less, well below the solubility of water in dense CO₂, so that no free water can form even if the line cools. Combinations of impurities can react inside the pipe: sulphur dioxide, nitrogen dioxide, oxygen, hydrogen sulphide and water can form sulphuric and nitric acid and elemental sulphur at concentrations each well within its own limit. Recent research has shown that cross-reactions of this kind set tighter limits on mixed streams than tests on single impurities suggested, which is a live issue for hubs that combine flue gas and syngas sources.

Sofia drafted that specification after looking at the Heartland hydrogen plant's hydrogen slip and the Heartland cogeneration plant' oxygen. The two streams cannot both arrive at the edge of their limits; the hydrogen plant would add a polishing step, and the flue gas plant would need a catalytic oxygen removal unit. Mei's laboratory would measure each stream's bubble point with the impurities present, rather than trusting an equation of state tuned to pure CO₂.

Joule-Thomson cooling and hydrates

When dense CO₂ expands across a valve or a leak, it cools sharply, more than natural gas, because of its large Joule-Thomson coefficient near the vapour pressure curve. Depressurizing a pipeline section for maintenance can drop the temperature below −50 °C, embrittling carbon steel that is not rated for it, and forming dry ice at the outlet. Blowdown procedures are therefore slow and staged. The same cooling appears at the top of an injection well when the wellhead pressure is low and the CO₂ flashes in the tubing; Lesson 8 returns to it. With free water present, CO₂ forms hydrates at temperatures up to about 10 °C, another reason water must be removed before transport.

Solubility and brine

CO₂ dissolves in water to about 5 percent by weight at storage conditions, more at lower temperature and higher pressure, and less as salinity rises. Water also dissolves in CO₂ to a small degree, which is why dense CO₂ entering a formation dries the rock near the well and can precipitate salt from very saline brines, reducing injectivity. CO₂-saturated brine is about 1 percent denser than the original brine, a small difference that matters greatly over long times: it sinks, setting up convection that speeds dissolution, as Lesson 7 explains.