论文标题
反电流自发吸收的早期和后期预测，缩放分析和毛细管扩散系数的估计
Early- and late-time prediction of counter-current spontaneous imbibition, scaling analysis and estimation of the capillary diffusion coefficient
论文作者
论文摘要
研究解决方案的一维线性反电流自发吸收（COUSI）。扩散问题的缩放仅取决于具有平均值1且没有其他参数的归一化系数λ_n（s_n）。使用（混合润湿和强湿）相对渗透率，毛细管压力和迁移率比的组合生成5500个功能的数据集λ_n。由于λ_n的可能变化似乎有限（平均1，正，在s_n = 0，最大为零），因此生成的函数涵盖了最相关的情况。在所有5500例病例中求解了缩放的扩散方程，并根据时间尺度和早期和晚期行为分析恢复曲线。缩放恢复正好落在平方根曲线RF = T_N^0.5上。缩放时间t_n = t/τt_ch对系统长度l和幅度d的幅度为d和via t_ch的量度为λ_n。缩放恢复的特征是RF_TR（最高恢复为T_N^0.5）和LR，该参数控制了以后吸收率下降的参数。该相关性描述了平均R^2 = 0.9989的5500恢复曲线。当水达到无流量边界时，RF_TR比恢复高0.05至0.2单位。 λ_n的形状由三个馏分z_（a，b）量化。描述λ_n和恢复的参数相关，允许（1）准确预测完整的恢复曲线（不求解扩散方程）； （2）预测解释实验恢复的扩散系数； （3）解释润湿性 /饱和功能，粘度和其他输入对早期和晚期恢复行为之间相互作用的综合影响。
Solutions are investigated for 1D linear counter-current spontaneous imbibition (COUSI). The diffusion problem is scaled to depend only on a normalized coefficient Λ_n (S_n ) with mean 1 and no other parameters. A dataset of 5500 functions Λ_n was generated using combinations of (mixed-wet and strongly water-wet) relative permeabilities, capillary pressure and mobility ratios. Since the possible variation in Λ_n appears limited (mean 1, positive, zero at S_n=0, one maximum) the generated functions span most relevant cases. The scaled diffusion equation was solved for all 5500 cases and recovery profiles were analyzed in terms of time scales and early- and late time behavior. Scaled recovery falls exactly on the square root curve RF=T_n^0.5 at early time. The scaled time T_n=t/τT_ch accounts for system length L and magnitude D of the unscaled diffusion coefficient via τ=L^2/D, and T_ch accounts for Λ_n. Scaled recovery was characterized by RF_tr (highest recovery reached as T_n^0.5) and lr, a parameter controlling the decline in imbibition rate afterwards. This correlation described the 5500 recovery curves with mean R^2=0.9989. RF_tr was 0.05 to 0.2 units higher than recovery when water reached the no-flow boundary. The shape of Λ_n was quantified by three fractions z_(a,b). The parameters describing Λ_n and recovery were correlated which permitted to (1) accurately predict full recovery profiles (without solving the diffusion equation); (2) predict diffusion coefficients explaining experimental recovery; (3) explain the combined impact of interactions between wettability / saturation functions, viscosities and other input on early- and late time recovery behavior.
