Description of the Model

We use a compositional simulation model in this study to represent concepts such as oil/gas component exchange and miscibility development, oil swelling and oil viscosity reductions. Todd provides a full review of different aspects that need to be correctly represented in a CO2 flooding simulation (Todd 1979). CMG-GEM is the compositional

flow simulator used in this study (CMG-GEM 2014.10). The fluid model for this study is taken from the Jema field in the United States characterised by Khan et al. (Khan et al. 1992, Ghomian et al. 2008). However, the properties are slightly modified to make an oil of desired density and viscosity. Table 2.1 shows the properties of this fluid model.

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Table 2.1: Detail of the fluid model properties used in this study (Khan et al. 1992)

Comp. Zi Mw Weight Fraction Pc (psi) Tc (°R) Vc (ft3_/lb- mole) 𝝎 Parachor 𝜸_{𝑪𝑶𝟐−𝒊} CO2 0.0192 44.0 0.0054 1069.8 547.5 1.5057 0.2250 49.0 0 C1 0.0693 16.0 0.0071 667.1 300.0 1.5858 0.0080 71.0 0.05 C2-3 0.1742 36.0 0.0401 660.3 609.8 2.8277 0.1260 135.7 0.05 C4-6 0.1944 59.9 0.0876 488.6 839.0 4.9850 0.2439 231.6 0.05 C7-16 0.3138 125.1 0.2950 303.8 1100.0 9.5 0.6386 439.1 0.09 C17-29 0.1549 256.2 0.2982 230.3 1400.0 18.0 1.0002 788.2 0.09 C30+ 0.0742 478.3 0.2667 229.7 1750.0 35.0 1.2812 1112.4 0.09

Table 2.2 shows estimated oil properties using this fluid model at two different representative reservoir conditions of onshore Permian Basin and offshore North Sea provinces (Fayers et al. 1981, Warner 1977).

Table 2.2: Calculated oil properties at two different representative reservoir conditions

ρo (lb/ft3₎ ρCO2 (lb/ft3₎ μo (cP) μCO2 (cP) BBP (psi) MMP (psi) Bo (Rb/stb) GOR (scf/stb) Offshore, North Sea

(5000psi, 212°F) 44.98 43.75 0.657 0.059 778 2400 1.18 232

Onshore, Permian Basin

(3000psi, 113°F) 45.86 50.34 0.796 0.069 577 1200 1.23 232

The relative permeability data used for this work are also taken from the work of Dria et al. (1993) for experimental CO2 core flooding with the endpoints and exponents

illustrated in Table 2.3 and Figure 2.1. The Stone-1 model was used for the representation of 3-phase oil relative permeability. Spiteri and Juanes thoroughly investigated and compared the performances of Stone 1, Stone 2 and Saturated Weighted Index (SWI) relative permeability models (Spiteri & Juanes 2006) and concluded that the Stone 1 model is the one that agrees best with experimental data.

Hysteresis was only modelled in the gas phase with a trapped gas saturation of Sgc=0.16.

Hysteresis was not modelled in the water phase, as it has been assumed that the formations are water-wet and hysteresis in the wetting phase is very small. Care was also taken to smooth the relative permeability curves for the separation which may occur around the critical point for the sharp transition between gas and oil phases (CMG-GEM 2014.10). Certain features such as capillary pressure effects and water blocking (Muller & Lake 1991) were not considered in this study.

Table 2.3: Relative permeability model parameters (Dria et al. 1993)

Phase 𝒌_𝒓𝒋𝒐 𝒔_𝒋𝒓 𝜸_𝒋

water 0.36 0.36 3.1

oil (with water) 0.57 0.37 2.9 oil (with gas) 0.57 0.16 2.9

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Figure 2.1: water-oil (left) and gas-oil (right) relative permeabilities adopted for this study (Dria et al. 1993)

This set of relative permeability data has been used by a number of researchers. Roper et al. (1992) used these data to analyse the tertiary CO2 injectivity. Chang et al. (1994) also

used them to investigate the actual CO2 flow patterns under multiple contact miscibility

conditions.

Figure 2.2 shows the fractional flow curves, respectively for water and gas displacing oil. The fractional flow curve for water displacing oil has been generated assuming a mobility ratio of 3.3 for water displacing oil (water and oil viscosities of 0.28cP and 0.92cP respectively). Similarly, the fractional flow curve for CO2 displacing oil was generated

based on a mobility ratio of 18.4 (gas and oil viscosities of 0.05cP and 0.92cP respectively).

Figure 2.2: Fractional flow curves for water (left) and gas (right) displacing oil for the set of relative permeability depicted in Table 2.3

A significant amount of the findings depicted in this study relies on the set of the relative permeability that have been selected in this study. In this section an alternate set of relative permeability data has been identified and then is compared with the default set, and is depicted in Table 2.3. This will allow comparison of the characteristics of the two

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relative permeability models. The alternate set of relative permeability data has been taken from the simulation work of Goodyear et al. (2003) with the end point’s and exponents depicted in Table 2.4 and Figure 2.3 (Goodyear et al. 2003, SHARP6 Reports 2001).

Table 2.4: The relative permeability parameters for the alternate set of relative permeability data (Goodyear 2003, SHARP Reports 2001)

Phase 𝒌_𝒓𝒋𝒐 𝒔_𝒋𝒓 𝜸_𝒋

water 0.3 0.25 2

oil (with water) 0.57 0.25 4

oil (with gas) 0.57 0 4

gas 0.57 0.025 2

Figure 2.3: Alternate set of relative permeability model (Table 2.4); water-oil (left) and gas- oil (right).

Figure 2.4 compares the fractional flow curves between the two sets of relative permeability models depicted above and for water and gas displacing oil under the same mobility ratios of 3.3 (w/o) and 18.4 (g/o).

Figure 2.5 compares the actual water/gas saturation profiles after 0.2HCPV gas/water injection in a one dimensional model (with 500 grid blocks) and with the mobility ratios described above. The saturation of the shock front has also depicted in each figure for both water and gas displacing the oil phase; note that there is fair agreement between the magnitude of shock front saturations which can be inferred from Figure 2.4 and Figure 2.5.

A significant difference between the two sets of relative permeability is the extent of multiphase region that is created upon using each of them in a given simulation. For the base set of relative permeability (Table 2.3), the created multiphase region is apparently much smaller and thus a rather piston-like displacement may be obtained.

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Figure 2.4: Fractional flow curves for water (left) and gas (right) displacing oil; Blue: the base set of relative permeability (Table 2.3), Green: the alternate set of relative permeability

(Table 2.4)

Figure 2.5: water (left) and gas (right) saturations after 0.2HCPV water/gas injection in a 1D model. The solid-green data represent the alternate set relative permeability model. The

dashed-blue data represent the base set relative permeability model.

Figure 2.5 shows that the location of the water front is roughly similar between the two relative permeability models. However, for gas this is not the case as the critical gas saturation is fundamentally different between the two models. The alternate relative permeability model predicts a much wider two phase region and accordingly a gas saturation front that is ahead compared to that of the base set of relative permeability model with resultant earlier gas breakthrough. Another important difference between the two relative permeability models is the significance of gravity upon using either of them. The alternate set of relative permeability model (Table 2.4) predicts a larger multiphase region, which in turn may increase the contact between different phases with consequent larger gravity effects. Note that the two relative permeability models may generate the same gravity number (Appendix-2) as the oil relative permeability endpoint is similar in both of them. However, since the two phase regions of either of the relative permeability models are different, the effect of gravity could be different upon using each of them.

Figure 2.6 compares the three phase oil relative permeabilities obtained by Stone-1 correlation between the two relative permeability models. The white regions in each

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figure shows the region that either oil does not exist or cannot flow. It can be seen that the base set of relative permeability predicts a much smaller mobile oil window. The relative distribution of each oil relative permeability ranges is roughly identical between the two models. Note, however, that the two sets of relative permeability have the same oil endpoint relative permeability.

Figure 2.6: 3-phase oil relative permeability calculated with Stone-1 model; left: the base set relative permeability model (Table 2.3), right: the alternate set relative permeability model

(Table 2.4)

For the majority of the discussions presented in this chapter and later studies in Chapter 3 and 5, we use the first set of relative permeability depicted in Table 2.3. However, the second set of relative permeability model will be used in Chapter 3 to compare the likely performance of cross sectional North Sea and Permian Basin representative models with an alternate sets of relative permeability model in addition to the default set of relative permeability. This will allow investigation weather the obtained results are sensitive to the chosen set of relative permeability model. It will be shown that although the results are quantitatively different, they are qualitatively very similar (Figure 3.18).