MODULE I: ABIOTIC PROCESSES

Session I-2

Single phase (water only) flow through porous media

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Format. This session contains a overview of basic ground water flow and transport concepts which are relevant to bioremediation of contaminated ground water and soil. Since this material will be covered in detail in the INRA Core course we will limit our coverage to directed reading (Chapters 1, 2 and 3 Fetter), together with a series of annotated figures. A written assignment consisting of specific questions on the reading material will serve to focus attention on key concepts.

Reading Assignment. Contaminant Hydrogeology (C. W. Fetter, Prentice Hall, 2nd ed., 1999).

· Chapter 1  Introduction. This chapter provides a good perspective on ground water contamination and related issues. Particular attention should be given to Section 1.8 (pages 34-43), which describes Darcy’s law, hydraulic head, hydraulic conductivity, scalar, vector, and tensor concepts, along with the development of the general ground water flow equation(s).

· Chapter 2  Mass transport in Saturated Porous Media. Sections 2.1-2.7 (pages 45-58) cover the mass transport concepts of molecular diffusion, advection, and hydrodynamic dispersion. Analytical solution to the advection dispersion equation based on various boundary conditions are presented in sections 2.8-2.9 (pages 58-74). This material will be used later in the course to support the BIOSCREEN and BIOCHLOR models.

· Chapter 3  Transformation, Retardation, and Attenuation of Solutes. This chapter completes the introduction to mass transport through porous media by developing the concepts of sorption, retardation and reaction of solutes. The sorption and retardation are discussed in section 3.1-3.6 (pages 120-142). reaction processes—including biotransformation, are discussed in section 3.7 through 3.9 (pages 147-156).

Ground water flow Concepts. In addition to the material in Fetter, section 1.8 please look over Figures I-3 through I-7 below:

Figure I-3. If we look at a porous media at a scale small enough to see fluids, particles, solutes, and microbial cells moving through individual pore channels we are observing these phenomena at the "Microscale". Note that at this scale the focus is on the interactions between fluid, solid, dissolved or suspended constituents in the fluid, and microorganisms attached to the solid surface. Bulk media properties such as permeability, porosity, hydraulic conductivity and dispersivity are not definable at the Microscale.

 
Figure I-4. If we consider a large enough sample of porous media, like that shown in the one-dimensional packed-bed flow column above, then it becomes possible to define bulk media properties and equations describing porous media flow.

 

Figure I-5. This flowing porous media column represents the experimental apparatus used for the illustration of Darcy’s Law. Note that the Darcian velocity "v" is the total flow rate Q divided by the cross-sectional Area "A". In other words v is the specific discharge through the one-dimensional porous media column. Note how Hydraulic conductivity K is defined along with typical units.

 

Figure I-6. This figure illustrates the relationship between hydraulic conductivity, K, and intrinsic permeability, k. Also note that if the Darcian velocity, v, is divided by the effective porosity n, the result is called the average linear pore velocity.

 

Figure I-7. To further explain the concept of average linear pore velocity consider that a conservative tracer (i.e. chloride or non-sportive dye) is added to the column inflow as shown above. Here the tracer is added to the influent as a "step function" or, in other words, the concentration of traced is raised instantaneously from "0" to C0 and remains constant thereafter. At the effluent end of the column the tracer breakthrough curve would assume a sigmoidal or "S" shape due to the effects of hydrodynamic dispersion. The time required to for the effluent concentration to reach the centroid of the effluent break through curve is the defined as the "travel time" through the column. Conceptually this represents average travel time for tracer to move through the column (some pore channels flow faster, others slower and Tt is the average). The concept which follow here is that average linear pore velocity, as defined in Figure I-6, is equal to the length along the one-dimensional flow path divided by the travel time for the tracer. Note that the actual velocity if water moving through individual porous media flow channels is equal to the average linear pore velocity divided by the tortuosity "T" as shown.

 

Questions. The following questions are intended to focus you on key concepts and information. The page numbers following each question contains the relevant material to answering the question.

I-1. Sketch the experimental apparatus used to illustrate Darcy’s law. (see Figure I-4).

I-2. What are the fundamental units of volumetric flow rate (discharge), hydraulic head hydraulic gradient, and specific discharge (Darcian velocity)?. ( L3/T, L, dimensionless, L/T).

I-3. Explain the difference between a scalar, a vector, and a tensor (pg 37 Fetter). Classify each of the following variables as either a scalar, vector or tensor…hydraulic head, specific discharge, hydraulic gradient, hydraulic conductivity (pg 37-38).

I-4. Explain the concept of "average pore velocity" in the context of a conservative tracer moving through a one-dimensional porous media column (Figures I-6, I-7).

I-5. Specific discharge(Darcian velocity), average pore velocity, and actual pore velocity all have units of velocity (L/T). Explain the relationship between these three variables, (Figures I-6, I-7).

 

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