WaterSubject

We considered small-scale measurement of permeability in pebbly sands having coarser grains supported in a finer grained matrix (fine packing). Our central question was whether air-based measurements are representative if made with a permeameter tip seal pressed in the sand matrix. We created pebbly sands and variably sorted sands, with systematic variation in aspects of their fine packing. We made permeability measurements by inserting the tip seal of an air permeameter in the matrix of these samples and compared them to the permeability of the composite sample determined by both water-based methods and theory. The air-permeameter measurements made in this way represent the permeability of the composite mixtures of coarser and finer grains and allow for the discernment of permeability between samples with different matrix compositions, ranging from fine to coarse sand. Furthermore, the collective results show that permeability differences in the pebbly sands and variably sorted sands with fine packing, however measured, are primarily due to differences in matrix permeability and not due to differences in the size or the percentage of the coarser grains.

Spherical sandblasting glass beads were sorted into fine, medium, and coarse sand sizes. Larger glass spheres (marbles) were used as model pebbles. Model sediment mixtures were created by homogeneously mixing sediment from among these different size categories and creating samples with a systematic variation in the volume fraction of each category.

To measure permeability, a premixed sample was placed into a clear plastic cylinder (inner diameter of 8.3 cm and length 30.5 cm). An air-based permeameter was used to take measurements as the cylinder was supported vertically and filled, and then, the filled cylinder was capped and served as a constant head permeameter for making water-based measurements. The compressed air-permeameter had inner and outer tip seal diameters of 4 and 26 mm, respectively. Using equations 33a and 33b in, the G_o was determined to be 4.268. More details of the instrument are given in. To serve as a water permeameter, the cylinder and caps had attachments for tubing to carry inflow and outflow and for manometer tubes, spaced 15.3 cm apart.

The premixed sample was added to the cylinder in five stages as it was filled. The air-based measurements were made on each stage before adding the next. The initial stage was 10 cm thick to avoid bottom boundary effects, and each subsequent stage was 5 cm thick. Three measurements were made at each of three locations in the matrix of each stage. The tip seal was inserted at least 2 cm away from the cylinder wall to avoid boundary affects raw air-based measurement of permeability was made by recording the flow rate and injection pressure and using them in. The raw values were then corrected to account for non-Darcian head loss and other factors described in the . The rate of airflow in air permeametry is often so high that inertial forces exceed viscous resistance forces and cause non-Darcian head loss. As with common practice, a correction model based on the Reynolds number was used. The correction model is presented in the and was developed for the instrument used in this study from an independent calibration using samples for which k is independently determined. The symbol ? is used here to represent a corrected value of permeability. Collecting three values of ? at each location and using three locations for each of the five stages gave 45 values of ? for each cylinder of sediment.

The filled cylinder was then converted to a constant head permeameter. The sediment was saturated from the bottom to allow air entrained in the sediment to be displaced (more details are given in. A water-based measurement of permeability, ?, was made by determining the steady-state flow rate and the stable hydraulic gradient between the manometers and computing it with Darcy’s law. This was repeated under different gradients and flow rates to give three ? for the cylinder of sediment. The arithmetic mean of these three measurements, , is taken as representing the permeability of the composite sediment within the cylinder.

For each cylinder of sediment, a bulk average of the air-based permeability measurements, , was determined by the following procedure. The geometric mean of the nine ? values for each stage was computed. Then, the harmonic mean of the five-stage means was computed. The procedure followed from the logic that the harmonic mean would best reflect the influence of any unintended stratification and thus provide the most appropriate comparison to (though we strove to homogeneously mix the sediment sample before adding it uniformly in stages, it was possible that subtle nonuniformities existed, perhaps across the stages). For each mixture ratio, these procedures (for filling a cylinder and determining its and ) were repeated three times.

Sediment mixtures were created by first measuring the desired premixed volumes of each size category in 1000 mL graduated cylinders. ? is defined as the ratio of the premixed volume of the finer sediment to the premixed volume of the finer and coarser grains together. Once mixed, the finer grains occupied pore space between coarser grains and so the postmixed volume of sediment was generally less than the sum of the premixed volumes of each category. r_f is defined as the ratio of the premixed volume of finer sediment to the postmixed volume of the sediment. The magnitude of the change from ? (before mixing) to r_f (after mixing) indicates the relative reduction in pore volume when the components are combined. The volume ratio, r_v, is defined as r_f/? and is greater than or equal to 1.

From the results in these studies, we can draw general conclusions, first, about how permeability varies in pebbly sands and, second, about the use of air permeametry to quantify such differences. In pebbly sands, over the range of fine packing used in these studies, the larger differences in permeability were shown to be primarily due to differences in matrix permeability. The permeability is essentially the permeability of the finer grained matrix. Further differences, such as might be caused by variation in the size or the percentage of the coarse grains, are too small to be discerned with confidence using our water- or air-based methodologies. For example, the permeability of a mixture with fine sand supporting pebble grains is about the same as for fine sand supporting medium sand grains, regardless of the percentage of the coarser grains.

An air-permeameter instrument, pressed into the matrix of the composite mixture, is capable of generating data representing the permeability in pebbly sands. It is also capable of generating data representing the permeability in variably sorted sands with coarse or fine packing.

Previous work showed that in outcrop analogue studies of pebbly sands, air permeametry data from matrix measurements had the same central tendency as pumping test data but a larger variance. Because the permeability of a pebbly sand is essentially that of its matrix, matrix-based air-permeametry measurements should, indeed, capture the central tendency of the composite statistical population. Furthermore, air permeametry in pebbly sands generates data representing the tails of local statistical populations. These tails are not captured very well in the pumping test data because much of the local-scale variation is “hydraulically averaged” within the much larger support scale of the pumping tests.

The collective results from these field and laboratory studies build confidence in using matrix-based air permeametry on outcrop analogue exposures to quantify the statistical populations of local-scale permeability for pebbly sands.