Abstract
The purpose of this work is to study the motion of a non-Newtonian fluid in a rock fracture, generated by a constant pressure gradient to which a pulsating component is superposed. The momentum equation is faced analytically by adopting a logarithmic constitutive law; the velocity is expressed as a power series of the amplitude of the pulsating component, up to the second order, easily usable for numerical calculations. The results obtained are compared with those provided in the past by the authors, using a three-parameter Williamson model. The comparison highlights that the value of the mean flow rate in a period differs by less than 10% even if the velocity profiles look quite different.
Highlights
It is well known that the fluid flow within a geological formation takes place mainly through fractures that are often connected to each other to constitute a network
A literature overview shows that when an oilfield is flooded with a non-Newtonian fluid, the mobility ratio between the displaced fluid and the displacing fluid becomes favorable with respect to flooding with water
Despite the importance of the effects of roughness in fracture flow—as emphasized in the reference work of Zimmerman and Bodvarsson [5]—the roughness is neglected in the present paper because, for an analytical analysis, the complexity generated by the rheological constitutive law of a non-Newtonian fluid and by the unsteady flow suggests adopting a simplified geometry to solve the problem
Summary
It is well known that the fluid flow within a geological formation takes place mainly through fractures that are often connected to each other to constitute a network. Despite the importance of the effects of roughness in fracture flow—as emphasized in the reference work of Zimmerman and Bodvarsson [5]—the roughness is neglected in the present paper because, for an analytical analysis, the complexity generated by the rheological constitutive law of a non-Newtonian fluid and by the unsteady flow suggests adopting a simplified geometry to solve the problem. The planetounsteady flow of a non-Newtonian fluid has been variation faced by many authors technical even recently, superposing a constant pressure gradient a small periodical has acquired and either for numerical calculation purposes or analytically. The non-linearity of the constitutive equation of pseudoplastic fluids makes the variation of theuses, rate because it allows the growth of the mean discharge with a limited increase of power. Fact that the mean flow rate in a period increases
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