We investigate supercritical CO${}_2$ injection into a sloping saline aquifer and propose a simple relationship to estimate the maximum gas migration distance in the updip direction. The estimate is derived from the system of governing equations for immiscible flow of gas and formation brine. By writing the equations in non-dimensional form, we guess the scaling law for the migration distance at a late stage of CO${}_2$ injection. Then, we verify the scaling law by means of 3-D reservoir simulations of miscible CO${}_2$ injection with account for the residual and solubility trapping. We derive an estimate that relates the maximum migration distance with the dip angle, the porosity, the anisotropic permeability, and the end-points of saturation functions. We show that the estimate is rather accurate for different reservoir temperatures and brine salinity and in the case of a flue gas injection. The proposed scaling is useful for a quick assessment of the risk of CO${}_2$ reaching a potential leakage site in a large regional aquifer. It can also be applied to estimate the propagation of the uncertainties of reservoir parameters to the uncertainty of the migration distance.

我们研究超临界 CO${}_2$注入倾斜的盐水含水层，并提出一个简单的关系来估计上倾方向上的最大气体运移距离。该估计值来自气体和地层盐水不混溶流动的控制方程组。通过将方程写成无量纲形式，我们推测了CO后期迁移距离的比例律${}_2$注射。然后，我们通过混相 CO 的 3-D 储层模拟来验证比例定律${}_2$注入与帐户的残留和溶解度捕集。我们推导出一个将最大迁移距离与倾角、孔隙度、各向异性渗透率和饱和函数端点联系起来的估计值。我们表明，对于不同的储层温度和盐水盐度以及在烟道气注入的情况下，该估计是相当准确的。建议的缩放比例对于快速评估 CO 的风险很有用${}_2$到达大型区域含水层中的潜在泄漏点。它也可以用于估计储层参数的不确定性对迁移距离的不确定性的传播。