Static and dynamic methods are used in the oil and gas industry, underground natural gas storage, groundwater and underground disposal of fluids for estimating subsurface volumes. Static methods are volumetric and compressibility-based. The dynamic methods are decline/incline curve analysis, material balance and reservoir simulations, and they can be applied only after the start of active injection; hence only static methods will be summarily described here based on the work of Bachu et al. (2007).
2.4.1 Coal beds
The effective storage capacity McO2e for a given coal bed is given by the relation:
M E A h n V P
CO2e CO2s C L P P
= L
¥ ¥ ¥ ¥ ¥Ê ¥ +
r ËÁ ˆˆ
¯˜ ¥ (1 – – )fa fm
[2.1]
where rcO2s = 1.873 kg/m3 is cO2 density at standard (surface) conditions, A and h are the area and effective thickness of the coal zone, respectively, ủc is the bulk coal density (generally ủc ≈1.4 t/m3), P is pressure, PL and VL are Langmuir pressure and volume, respectively, fa and fm are the ash
and moisture weight fraction of the coal, respectively, and E is the storage efficiency factor. Monte Carlo simulations performed by USDOE (2007) produced a range for E between 28 and 40 % for a 15–85 % confidence range, with an average of 33 % for 50 % confidence. The coal gas saturation (in units of volume of gas per unit of coal mass) is given by GcS and is the coal gas content (dry, ash free) at saturation, assuming that the coal will be 100 % saturated with cO2. It is generally assumed to follow a pressure-dependent Langmuir isotherm of the form:
G V P
CS L P P
= ¥ + L [2.2]
2.4.2 Oil and gas reservoirs
assessments for cO2 storage capacity in oil and gas reservoirs are based on reserves databases that list hydrocarbon reserves and various reservoir characteristics. Solution gas should not be considered in storage capacity calculations because it is implicitly taken into account in oil reservoirs through the shrinkage factor. Since reserves databases indicate the volume of original gas and oil in place (OGIP and OOIP) at surface conditions, the theoretical mass storage capacity for cO2 storage in a reservoir at in situ conditions, McO2t, is given by:
McO2t = rcO2r ¥ Rf¥ (1 – FIG) ¥ OGIP
¥ [(Ps¥ Zr¥ Tr)/(Pr ¥ Zs¥ Ts)] [2.3]
for gas reservoirs, and by:
McO2t = rcO2r ¥ [Rf ¥ OOIP ¥ Bf – Viw + Vpw] [2.4]
for oil reservoirs.
an alternate equation for calculating the cO2 storage capacity in oil and gas reservoirs is based on the geometry of the reservoir (areal extent and thickness) as given in reserves databases:
McO2t = rcO2r ¥ [Rf¥ A ¥ h ¥ f ¥ (1 – Sw) – Viw + Vpw] [2.5]
In the above equations rcO2r is cO2 density at reservoir conditions of temperature and pressure, calculated from equations of state. OGIP and OOIP are the initial gas and oil in place, respectively, Rf is the recovery factor, FIG is the fraction of injected gas, P, T and Z denote pressure, temperature and the gas compressibility factor, respectively, Bf is the formation volume factor that brings the oil volume from standard conditions to in situ conditions, Viw and Vpw are the volumes of injected and produced water, respectively (applicable in the case of oil reservoirs), and A, h, f and Sw are reservoir area, thickness, porosity and water saturation, respectively. If gas or miscible
solvent is injected in oil reservoirs during tertiary recovery, then the mass balance of these should be added to Equations 2.4 and 2.5. The subscripts ‘r’
and ‘s’ denote reservoir and surface conditions, respectively. The volumes of injected and/or produced water, solvent or gas can be calculated from production records. In the case of reservoirs with strong aquifer support (water drive), the volumes of injected and produced water may be negligible by comparison with the amount of invading water.
In the case of reservoirs underlain by aquifers, the reservoir fluid (oil and/
or gas) was originally in hydrodynamic equilibrium with the aquifer water.
as hydrocarbons are produced and the pressure in the reservoir declines, a pressure differential is created that drives aquifer water up into the reservoir, invading the reservoir. If cO2 is then injected into the reservoir, the pore space invaded by water may not all be available for cO2 storage, resulting in a net reduction of reservoir capacity. The pore volume invaded by water from underlying aquifers cannot be estimated without detailed monitoring of the oil–water interface and detailed knowledge of reservoir characteristics.
as cO2 is injected and pressure increases, some of the invading water may be expelled back into the aquifer; however, the hysteresis caused by relative permeability effects and irreducible saturations will prevent complete withdrawal of invaded water, leading to a permanent loss of storage space.
Notwithstanding the effect of an underlying aquifer, three other factors control the effectiveness of the cO2 storage process: cO2 mobility with respect to oil and water; the density contrast between cO2 and reservoir oil and water which leads to gravity segregation; and reservoir heterogeneity.
all these processes and reservoir characteristics that reduce the actual volume available for cO2 storage can be expressed by capacity coefficients (C < 1) in the form:
McO2e = Cm¥ Cb¥ Ch¥ Cw¥ Ca¥ McO2t ∫ E ¥ McO2t [2.6]
where McO2e is the effective reservoir capacity for cO2 storage, the subscripts
‘m’, ‘b’, ‘h’, ‘w’ and ‘a’ stand for mobility, buoyancy, heterogeneity, water saturation and aquifer strength, respectively, and E is the storage efficiency coefficient that incorporates the cumulative effects of all the others.
In the cases where good production (and injection) records are available, and particularly when cumulative production is greater than the estimated original oil or gas in place, a production-based method can be used to estimate cO2 storage capacity, in which basically the product Rf¥ OGIP or Rf¥ OOIP in Equations 2.3 and 2.4 is replaced by the produced gas or oil, respectively.
In some cases, more oil or gas has been produced than originally estimated would be recoverable, resulting in a real Rf > 1. cumulative production data should be used whenever possible to check and update the real Rf.
2.4.3 Deep saline aquifers
Storing cO2 in water-saturated structural and stratigraphic traps is similar to storage in depleted oil and gas reservoirs. If the geometric volume (Vtrap) of the structural or stratigraphic trap down to the spill point is known, as well as its porosity (f) and the irreducible water saturation (Swirr), then the theoretical volume available for cO2 storage (VcO2t) can be calculated with the formula:
VcO2t = Vtrap ¥ f ¥ (1 – Swirr) ∫ A ¥ h ¥ f ¥ (1 – Swirr) [2.7]
where A and h are the trap area and average thickness, respectively. This volume is time-independent, and depends on trap characteristics alone.
Relation (2.7) assumes constant porosity and irreducible water saturation, and is applicable when average or characteristic values are used.
The effective storage volume (VcO2e) is given by:
VcO2e = E ¥ VcO2t [2.8]
where E is a storage efficiency coefficient that incorporates the cumulative effects of trap heterogeneity, cO2 buoyancy and sweep efficiency.
calculating the mass of cO2 that corresponds to the effective storage volume is more difficult because CO2 density (rcO2) depends on the pressure in the trap once it is filled with CO2. This pressure is not known a priori but depends on permeability, relative permeability to formation water and cO2, dimensions and volume, and the nature of trap boundaries, and may vary with the injection strategy (injection rate, number and/or inclination of injection wells, etc.). however, this pressure has to be higher than the initial water pressure in the trap (Pi) in order to achieve cO2 injection, but it has to be lower than the maximum bottomhole injection pressure (Pmax) that regulatory agencies usually impose in order to avoid rock fracturing or breaching of the capillary seal. Thus, the mass of cO2 that would be stored in a structural or stratigraphic trap would be between these two limits (Bachu et al., 2007):
minMcO2e = rcO2(Pi, T) ¥ VcO2e ≤ McO2e ≤ maxMcO2e
= rcO2(Pmax, T) ¥ VcO2e [2.9]
where T is the average temperature in the trap. The mass capacity of a trap may vary in time if pressure varies because, although the volume of the trap remains constant, cO2 density varies with varying pressure. Relations 2.7 –2.9 can also be applied to the case of a plume of cO2 that is not necessarily contained in a stratigraphic or structural trap, but the area and thickness of the cO2 plume have to be known a priori through numerical simulations.
uSDOE (2007) proposes to use the entire volume of the aquifer according to the following relation for calculating the volumetric cO2 storage capacity:
McO2e = E ¥ A ¥ h ¥ f ¥ rcO2 [2.10]
where rcO2 is the average cO2 density evaluated at pressure and temperature that represent storage conditions anticipated for a specific deep saline aquifer, and E is a storage efficiency factor that reflects the total pore volume filled with cO2. Application of Relation 2.10 may be difficult for aquifers of large areal extent and great variability, in which case an integral form of Relation 2.10 should be used:
MCO2e = E¥ ÚÚfrCO2d dA h [2.11]
The effect of irreducible water saturation is not taken into account explicitly in Relation 2.10 as in Relation 2.7, but is included in the efficiency factor E through the pore-scale displacement efficiency. Monte Carlo simulations performed by members of the project team produced a range for E between 1 and 4 % of the bulk volume of a deep saline aquifer for a 15–85 % confidence range, with an average of 2.4 % for 50 % confidence (USDOE, 2007). More recent work shows that the efficiency factor E varies, depending on aquifer lithology, between 1.4 % for limestone aquifers with a 10 % confidence and 6 % for sandstone aquifers with a 90 % confidence (Gorecki et al., 2009).