The Growth of Mixing Zone in Heterogeneous Porous Media

Dengan menggunakan penyelesaian analitikal yang merangkumi fraktal eksponen, pembesaran jarak pencampuran telah dapat ditentukan bagi model satu dimensi. Size zon pencampuran didapati meningkat apabila media berliang menjadi semakin heterogen. Dalam media berliang yang heterogen, saiz zon pencampuran meningkat apabila pemalar penyerakan meningkat terutama sekali pada aliran jangkamasa singkat relatif. Terdapat tiga faktor penting mempengaruhi saiz zon pencampuran penyerakan, ΔxD. Perkara terpenting dalam kajian ini ialah keheterogenan takungan, yang dipersembahkan oleh fraktal eksponen, β. Hasil kajian mendapati bahawa apabila β menjadi kecil (media berliang menjadi semakin heterogen), saiz zon pencampuran meningkat. Satu lagi faktor mempengaruhi ΔxD ialah pemalar penyerakan bersandar masa, Κ(tD). Di dalam takungan heterogen, zon pencampuran meningkat dengan peningkatan nilai pemalar penyerakan pada aliran jangkamasa singkat relatif. Bagi aliran jangkamasa panjang relatif, bagaimanapun, ΔxD terus meningkat walaupun Κ(tD) menjadi tetap. Faktor ketiga ialah purata kelajuan bendalir, ν. Zon pencampuran mempunyai perkaitan songsang dengan kelajuan bendalir dengan cara ΔxD meningkat apabila ν berkurangan. Kata kunci: Kehomogenan; keheterogenan; pekali penyerakan; eksponen fraktal; zon pencampuran; media berliang Utilizing currently available analytical solutions that incorporate fractal exponent, the growth of mixing length of injected solvent was determined for a one-dimensional model. Mixing zone size was found to increase as porous medium becomes increasingly heterogeneous. In a heterogeneous porous media, mixing zone size increases as dispersion coefficient increases particularly at relatively short duration of flow. There are three important factors influencing the size of the dispersive mixing zone, ΔxD. Of particular importance in this study is reservoir heterogeneity, which is represented by a fractal exponent, β. It was discovered that as β becomes smaller (porous medium becomes increasingly heterogeneous), the size of the mixing zone increases. Another factor affecting ΔxD is time dependent dispersion coefficient, Κ(tD). In a heterogeneous reservoir, mixing zone increases with increasing value of dispersion coefficient at relatively short duration of flow. For relatively long period of flow, however? ΔxD continues to increase even though Κ(tD) remains constant. The third factor is average fluid velocity, ν. Mixing zones have inverse relationship with fluid velocity in that ΔxD increases as ν decreases. Key words: Homogeneity; heterogeneity; dispersion coefficient; fractal exponent; mixing zone; dimensionless concentration; porous media