水力扩散系数是什么?- 江南体育网页版- - - - -地球科学堆江南电子竞技平台栈交换 最近30从www.hoelymoley.com 2023 - 07 - 09 - t17:48:50z //www.hoelymoley.com/feeds/question/2698 https://creativecommons.org/licenses/by-sa/4.0/rdf //www.hoelymoley.com/q/2698 14 水力扩散系数是什么? Bprodz //www.hoelymoley.com/users/580 2014 - 10 - 27 - t18:23:08z 2019 - 05 - 28 - t13:35:13z < p >我难以把握哪些属性描述土壤的水力扩散系数(有时称为土壤湿度扩散系数基于< a href = " http://en.wikipedia.org/wiki/Groundwater_flow_equation Diffusion_equation_.28transient_flow.29 " > < / >)扩散方程。< / p > < p >什么水力扩散系数描述和它是如何与水力传导率?< / p > //www.hoelymoley.com/questions/2698/-/2703 # 2703 10 答案由AtmosphericPrisonEscape水力扩散系数是什么? AtmosphericPrisonEscape //www.hoelymoley.com/users/489 2014 - 10 - 29 - t14:30:56z 2014 - 10 - 29 - t14:30:56z < p >让我们度过一些定义。我不会讨论这个的推导,但你可以看出来,如果你想在我提供的来源。< / p >

We find ourselves in a porous medium, so we will have always some volume filling factor $\Theta$ of water in rock.

enter image description here (copyright K. Roth, Heidelberg University)

Then we can start with the hydraulic conductivity, that can be defined as $$K = \frac{\Theta \left< \kappa \nabla P \right>}{\mu}$$ Here we have quite some notation to clarify:

  • $\Theta$ is the local filling fraction of water in an aquifer
  • $\mu$ is the molecular diffusivity
  • The brackets $\left< ... \right>$ denote the macroscopic average over the microscopic aquifer structure that is given by Permeability $\kappa$ and local pressure gradient. The Permeability itself is a way to encapsulate how easy water can flow through a given geometry.

This is the most rigorous definition I could find in my notes. The lecture however is unavailable on the internet, so you'll have to take my word for this. I just mention this as I don't know whether you're more interested on the theoretical side, or the pragmatic.

The pragmatic approach is usually to simply state Darcy's law $$ q = - K \frac{dh}{dz} $$ relating the water mass flux $q = \rho v$ to the gradient of hydraulic head. We see now that a flow velocity will result from a pressure gradient, but strongly modified through the microscopic properties encapsulated in K.


The hydraulic diffusivity you search for is then written as $$D = \frac{K}{S}$$ where S is the water storage fraction, with $S \sim \Theta$ (not strictly correct). So in a way this just cancels the $\Theta$ in $K$ and appears in the pressure diffusion equation: $$ \partial_t P = D \Delta P $$ and therefore D gives the local diffusion speed of pressure disturbances (which is interestingly not the speed of sound $c_s$ in aquifers!)

We could now say, for educatory purposes that the difference between $K$ and $D$ is only $\Theta$. This makes sense when we look at the context where those two parameters appear: $K$ gives the strength of mass-flow for the fluid, the better filled the volume is, the more mass will flow.

Pressure, however does not care for the amount of water that flows, as it exists everywhere where water is sitting at a given moment, so the coefficient for its propagation does not depend on the filling of volume.

You can look up the derivations for example here. Tell me in the comments, if anything is unclear.

Baidu
map