Injectivity Errors in Simulation of Foam EOR

Injectivity is a key factor in the economics of foam EOR processes. Poor injectivity of low-mobility foam slows the production of oil and allows more time for gravity segregation of injected gas. The conventional Peaceman equation, when applied in a large grid block, makes two substantial errors in estimating injectivity: it ignores the rapidly changing saturations around the wellbore and the effect of non-Newtonian mobility of foam. When foam is injected in alternating slugs of gas and liquid ("SAG" injection), the rapid increase in injectivity from changing saturation near the well is an important and unique advantage of foam injection. Foam is also shear-thinning in many cases. We use the method-of-characteristics approach of Rossen et al. (2011), which for the first time resolves both changing saturations and non-Newtonian rheology with great precision near the wellbore, and compare to conventionally computed injectivity using the Peaceman equation in a grid block. By itself, the strongly non-Newtonian rheology of the "low-quality" foam regime makes a significant difference to injectivity of foam. Thus for continuous injection of foam in this regime, the Peaceman equation underestimates injectivity by a factor of two even for grid blocks as small as 10 m wide, and by a larger factor for realistic grid-block sizes. However, one could estimate this effect using the equation for injectivity of power-law fluids, i.e. without accounting for changing water saturation near the well, without much error. In SAG processes, however, non-Newtonian rheology is less important than accounting for foam collapse in the immediate near-wellbore region. Averaging water saturation in a large grid block misses this dryout very near the well and the Peaceman equation grossly underestimates the injectivity of gas. We illustrate with examples using foam parameters fit to laboratory data.