Porous Media and Aquifers PDF

10/3/2024 (1) Porous Media and Aquifers 1 POROUS MEDIUM: THE C...

10/3/2024 (1) Porous Media and Aquifers 1 POROUS MEDIUM: THE CONTINUOUS APPROACH In most of our representations, a soil is assumed as a porous medium domain that can be regarded as continuum. Two questions arise:  What is a porous medium?  What is a continuum? Soils (aquifers and unsaturated zones) are domains that are occupied by porous media. Sand, fissured rocks, sandstone, and karstic or fractured limestone, are examples of porous media in the most general sense. 2 2 1  10/3/2024 POROUS MEDIUM: THE CONTINUOUS APPROACH Several schematizations of a porous medium have been developed looking at photos like those showed the previous slide: Different types of porous media: A – poorly sorted sedimentary deposit with high porosity; B – well sorted sedimentary deposit having low porosity; C – poorly sorted sedimentary deposit consisting of pebbles that are themselves porous; D – very well sorted sedimentary porosity with very low porosity; E – rock made porous by dissolution; F – fractured rock These are qualitative representations; today we know... 3 3 POROUS MEDIUM: THE CONTINUOUS APPROACH... the actual shape of a porous medium by 3D X‐tomography at the micro‐scale level. 4 4 2  10/3/2024 POROUS MEDIUM: THE CONTINUOUS APPROACH QUESTION: What is common to domains occupied by such materials (as the examples just mentioned)? ANSWER: The two major features of the materials occupying these domains are:  Each domain contains both a solid phase and a void space occupied by one or more fluid phases, e.g., water and/or air.  The entire void space, or at least part of it, is interconnected. As such, it enables the movement of the fluids between any two portions of the domain. The surface that bounds the domain intersects the void space, thus permitting the movement of the fluid through the domain boundary. 5 5 POROUS MEDIUM: THE CONTINUOUS APPROACH However, these two features are not sufficient to describe what is a porous medium. Look at these figures:  (a) there are two sub‐domains: one occupied only by solid, the other only by a void space. It conforms to the above definition of a porous medium as "a domain occupied partly by a solid and partly by a void space“;  (b) shows a channel connecting two pores, and connected to the external world. Hence there is "an interconnected void space that enables flow through it“;  (c) a medium made of grains, but the remaining part of the domain is a void space. 6 6 3  10/3/2024 POROUS MEDIUM: THE CONTINUOUS APPROACH QUESTION: What is missing? Does the figure here look better ?... a solid... a void space... and interconnected...? Or is (c) closer to your perception of a porous medium? ANSWER: The requirement that, for a domain to be grain qualified as a porous medium, both the void space and the solid must be distributed throughout the domain. P interconnected voids 7 7 POROUS MEDIUM: THE CONTINUOUS APPROACH Following Bear (1972)1, a porous medium can be properly defined as: “a portion of space occupied by a number of phases, at least one of which is a solid, for which a Representative Elementary Volume (REV) can be found“ REV concept is intimately correlated to the so called “continuum approach”. Suppose we want to describe and measure the motion of the fluid inside the void space: QUESTION:  Can we accurately describe the geometry of all the interconnected pores?  Can we measure the pressure/velocity of the fluid in a number of pore locations? ANSWER:  Probably yes for very few points of a very small sample in a lab;  Probably no for a sand column in a lab even if with the new supercomputers / micro‐ sensors …;  Surely no, if we consider an aquifer system at a regional scale (the scale of our interest). 1 Bear J. (1972), Dynamics of Fluids in Porous Media. American Elsevier. 8 8 4  10/3/2024 POROUS MEDIUM: THE CONTINUOUS APPROACH What other possibility is available? To overcome the above difficulty, which stems from the heterogeneity of the domain (which is a consequence of the presence of solid and void space sub‐domains), a smoothing operation (averaging) must be performed. When it is asked "what is the value of fluid pressure at point P?", we can take the average value of fluid pressure within a volume representative of the medium (REV) centered in P, and assign it to the considered point. Thus, the value of any state variable (pressure, velocity) or property (density, permeability) at a point within a porous medium domain is the average value of that variable, taken over the REV centered at that point. FROM TO Microscopic level of description Macroscopic level of description of phenomena in a porous of phenomena in a porous medium domain. This is the level medium domain. A macroscopic at which phenomena are value is the average value taken described at points WITHIN each over the REV, centered at the phase, using microscopic values macroscopic point real porous medium “continuum” model of porous medium 9 9 POROUS MEDIUM: THE CONTINUOUS APPROACH QUESTION: What is the size of a REV? The size of a REV should be selected such that the average value of any geometrical characteristic Y of the microstructure at any point in a porous medium, is a single‐valued function (or almost so) of the location of that point only:  for V < Vmin : the value undergo Measurements should strong fluctuations also be taken of these averages.  for Vmin < V Vmax : the value may again these variables. undergo smooth changes 10 10 5  10/3/2024 FROM POROUS TO AQUIFER SYSTEM SCALES Soils (porous media) can be investigated at multiple scales: +  we concentrate our interests here dimension  but sometimes it’s useful scale to think about here ‐ 11 11 FROM POROUS TO AQUIFER SYSTEM SCALES All subsurface domains are made of porous materials. They may have all kinds of geometrical configurations. Basically, they are domains in a three‐dimensional space, and should be treated as such. At the Darcy scale, two main kinds of soils (lithology) can be individuated:  sandy soils: they are composed by gravel to sand particles (i.e., relatively large particles) 5 4 3 2 1 0 large particles large pores  clay soils: they are composed by silt to clay particles (i.e., relatively small particles) small particles small pores Then, a mixing of all the various particles is usually encountered in the field 12 12 6  10/3/2024 FROM POROUS TO AQUIFER SYSTEM SCALES WATER DISTRIBUTION IN THE SUBSURFACE Water moves into the subsurface as a part of the hydrologic cycle. The hydrologic cycle is a term used to describe the circulation of water (in all its states) in nature, starting with evaporation from the oceans, continuing with precipitation and movement as surface (rivers and lakes) runoff and subsurface (unsaturated zone and aquifers) flow, eventually returning to the oceans. A portion of the precipitation infiltrates through land surface and then percolates through the unsaturated zone to an underlying aquifer (saturated zone). On its way, part of it is taken up by plants, eventually transpiring to the atmosphere. Another part may evaporate back to the atmosphere through ground surface. unsaturated zone: only part of the void space is occupied by water, the remainder being occupied by a gaseous (e.g., air) and possibly by a nonaqueous phase liquid. saturated zone: the entire void space is occupied by water or other fluids (e.g., hydrocarbon) if we consider large depth. 13 13 FROM POROUS TO AQUIFER SYSTEM SCALES As we move higher above the saturated zone, the moisture content (defined as the ratio between the volume of water in a soil sample to the latter's total volume) gradually decreases, often reaching some limiting value. The reason for this shape is that as we move higher above the phreatic surface, only the smaller pores contain water. The unsaturated zone is composed by three parts:  the root (or soil water) zone in which the moisture content is strongly variable and affected by conditions at ground surface (e.g., precipitation);  the intermediate zone;  the capillary fringe, a zone where pores are completely filled by water due to capillary forces, whose thickness depends on the soil's texture and homogeneity, ranging from practically zero in a very coarse material to as much as 2 to 3 meters (or more) in fine‐grained soils. 14 14 7  10/3/2024 FROM POROUS TO AQUIFER SYSTEM SCALES AQUIFER CLASSIFICATION At the Field scale, sandy soils and clay soils compose the so‐called aquifers and aquicludes/aquitards: AQUIFER from the Latin words aqua, meaning water, and ferre, meaning to bear ‐‐ is a term used to designate a porous geological formation that:  contains water at full saturation (i.e., the entire interconnected void space is filled with water)  permits water to move through it under ordinary field conditions Thus, whether a geological formation can be referred to as an aquifer, or not, depends on its ability to store and transport water relative to other formations in the vicinity.  Roughly speaking, aquifers are usually composed by sandy soils. AQUICLUDE / AQUITARDS a combination of the Latin words aqua and exclude ‐‐ is a formation which may contain water (sometimes in appreciable quantities, as in a clay formation), but is incapable of transmitting it in appreciable quantities. For all practical purposes, an aquiclude may be considered as an impervious layer.  Roughly speaking, aquiclude are usually composed by clay soils. 15 15 FROM POROUS TO AQUIFER SYSTEM SCALES Aquifers are classified according to the position of the piezometric surface, or the presence of a water table QUESTION: What is a piezometric surface? To understand this term, the concept of piezometric head and pressure head must be introduced:  consider a point P in an aquifer. The elevation of the point is z above some selected datum level. Let p denote the pressure in the fluid at the considered point. The piezometric head h at the considered point is defined as: GROUND SURFACE GROUND SURFACE WATER DEPTH ℎ 𝑧 𝑝/𝛾 PIEZOMETER PIEZOMETER PRESSURE SURFACE TOTAL (OR HEAD p/ with  the unit weight of ELEVATION PIEZOMETER HYDRAULIC) HEAD h DEPTH the water P ELEVATION P HEAD z DATUM (MEAN SEA LEVEL) DATUM (MEAN SEA LEVEL) 16 16 8  10/3/2024 FROM POROUS TO AQUIFER SYSTEM SCALES  the piezometric head expresses the energy per unit weight of For shallow the fluid, due to: aquifer: flow towards the elevation, z, of the point above the datum river. level (potential energy per unit weight) the fluid's pressure head (pressure energy per unit weight)  the piezometric head is not the total head. The latter includes also the kinetic energy (i.e., fluid velocity … usually negligible within a porous medium);  the above definitions of "pressure head", and "piezometric head" apply to a saturated porous medium domain that is regarded as a continuum. Thus, For lower a "point" at elevation z means the elevation of the centroid of a REV, the aquifer: flow pressure, p, means the averaged fluid pressure within the REV, and γ towards the city. denotes the average weight of the fluid within the REV; Here, a cone of depression is  one can draw contours of h x, y C, for different values of the constant present, caused C. In this way we obtain a contour map. It gives the value of the by excessive pumping below piezometric head at every point in the considered planar domain the city. 17 17 FROM POROUS TO AQUIFER SYSTEM SCALES  the phreatic surface, or water table, is a special case of a piezometric surface: an imaginary surface that bounds the saturated zone from above. It is defined as the surface at every point of which the water pressure is atmospheric If the atmospheric pressure is referred to as zero pressure, p = 0. Then, h z at all points of the phreatic surface. This means that at every point on a phreatic surface, the piezometric head is equal to the elevation of that point phreatic aquifer: is bounded from above by a phreatic surface is called a phreatic, or unconfined, aquifer, or a water table aquifer; 18 18 9  10/3/2024 EXAMPLES OF REAL PHREATIC AQUIFERS phreatic aquifer in a wet environment (at the southern margin of the Venice Lagoon, Italy) Venice Lagoon unsaturated zone capillary fringe 0.5 m saturated zone trench in a peat farmland 19 19 EXAMPLES OF REAL PHREATIC AQUIFERS phreatic aquifer in an arid zone (at Wadi El‐Nutrun, Egypt) Nile Delta unsaturated zone 5m saturated zone trench in the desert 20 20 10  10/3/2024 CLASSIFICATION OF AQUIFERS leaky aquifer: a phreatic aquifer that is bounded from below by a semipervious layer, which is usually referred to as an aquitard. This is a layer that is much less pervious than the aquifer overlying it and often is also much thinner. It thus behaves as a "semi‐pervious membrane" through which leakage out of or into the phreatic aquifer from an underlying saturated region is possible; 21 21 EXAMPLES OF REAL LEAKY AQUIFERS semi‐confined (leaky) aquifer: The Portorecanati aquifer (Italy) is located in the lower Holocene formation and is formed by medium to coarse sandy gravels, partially in direct contact with the Potenza River 22 22 11  10/3/2024 CLASSIFICATION OF AQUIFERS artesian aquifer: a portion of a confined aquifer in which the piezometric surface is not only above the ceiling of the aquifer, but also above ground surface, is referred to as an artesian aquifer. A well in an artesian aquifer is a flowing well, i.e., water will flow out of the well without pumping; confined aquifer: is bounded from above and from below by impervious formations. The water level in a well (or a piezometer) that is open (i.e., screened) in such an aquifer is higher than the impervious surface that bounds the aquifer from above 23 23 CLASSIFICATION OF AQUIFERS In reality, the same domain at ground surface may be underlain by quite a number of aquifers of different kinds. The upper phreatic aquifer (A) is underlain by two confined ones (B and C). In the recharge area, aquifer B becomes phreatic. Portions of aquifers A, B, and C are leaky, with directions and rates of leakage determined by the elevations of the piezometric surface of each of these aquifers. 24 24 12  10/3/2024 EXAMPLES OF REAL MULTI-AQUIFER SYSTEM The aquifer system of the A B Emilia‐Romagna plain B A 25 25 EXAMPLES OF REAL MULTI-AQUIFER SYSTEM The aquifer system of the Emilia‐Romagna plain A B B A 26 26 13  10/3/2024 EXAMPLES OF REAL MULTI-AQUIFER SYSTEM fresh‐water multi‐aquifer (confined) system in the Venice inland (Italy) and below the Venice Lagoon 27 27 EXAMPLES OF REAL MULTI-AQUIFER SYSTEM The huge aquifer system in Central Valley, California A’ A A A’ 28 28 14  10/3/2024 EXAMPLES OF REAL MULTI-AQUIFER SYSTEM Layered‐type distributions vs from wells to heterogeneous facies models for the classical model aquifer system of Beijing Beijing from wells to facies model 29 29 AQUIFER SYSTEMS AT DEPTH PERMEABLE FORMATIONS AT LARGE DEPTH In the range 0 ‐ 1000 m (approx.) depth we can still call the permeable units as (fresh – brackish – salty) “aquifer” at least when the target fluid is “water” fresh brackish salt good (sand ‐ aquifer) medium poor (clay – aquitard) 30 30 15  10/3/2024 AQUIFER SYSTEMS AT DEPTH For depth larger than 1000 m (approx.) and when the target fluid is no more water: Seismic sections showing the Aquifer  Reservoir subsurface structure A reservoir is a generally permeable formation (i.e., made by sands) from which I can “easily” remove or Seismic sections inject a fluid Where the hydrocarbon reservoir and the surrounding aquifer are highlighted in yellow and blue, respectively 31 31 AQUIFER SYSTEMS AT DEPTH The larger the depth the higher the probability of faulted reservoirs A reservoir in the The Groningen unfaulted Quaternary reservoir in the faulted sequence of the Rotliegend sandstone Northern Adriatic formation, The basin Netherlands 32 32 16