Long-distance propagation of foam is one key to deep gas mobility control for enhanced oil recovery and CO₂ sequestration. It depends on two processes: convection of bubbles and foam generation at the displacement front. Prior studies with N₂ foam show the existence of a critical threshold for foam generation in terms of a minimum pressure gradient or minimum total interstitial velocity, beyond which strong-foam generation is triggered. The same mechanism controls foam propagation. There are few data for or for CO₂ foam. We extend previous studies to quantify and for CO₂ foam generation, and relate and with factors including injected quality (gas volume fraction in the fluids injected) - f_g, surfactant concentration - C_s, and permeability - K. In each experiment, steady pressure gradient, ∇p, is measured at fixed injection rate and quality, with total interstitial velocity, v_t, increasing-then-decreasing in a series of steps. The trigger for strong-foam generation features an abrupt jump in ∇p upon an increase in v_t. In most cases, the data for ∇p as a function of v_t identify three regimes: coarse foam with low ∇p, an abrupt jump in ∇p, and strong foam with high ∇p. The abrupt jump in ∇p upon foam generation demonstrates the existence of and for CO₂ foam. We further show how and scale with f_g, C_s and K. Conditions that stabilize lamellae reduce the values of the thresholds: both and increase with f_g and decrease with increasing C_s or K. Specifically, scales with f_g as (f_g)² and scales as (f_g)⁴, and both and scale with C_s as (C_s)^−0.4. The effect of K on the thresholds for foam generation is greater than the effects of f_g and C_s. Our data in artificial consolidated cores show that scales with K as K⁻² for CO₂ foam, in comparison to K⁻¹ for N₂ foam in unconsolidated sand/bead packs. More data are needed to verify the confidence of these correlations. It is encouraging that in the cores with K = 270 mD or greater is less than 0.17 bar/m (~ 0.75 psi/ft), 2 to 3 orders of magnitude less than for N₂ foam. Such low can be easily attainable throughout a formation. This suggests that: limited ∇p deep in formations is much less of a restriction for long-distance propagation of CO₂ foam than for N₂ foam. Foam propagation could still be challenging in low-K reservoirs (~ 10 bar/m for K = 27 mD). Nevertheless, formation heterogeneity and alternating slug injection of gas and liquid help foam generation and may well reduce the values of. More research is needed to predict long-distance propagation of foam under those conditions.