Particle tracking analysis using the USGS particle tracking program MODPATH (Pollock, 1994) determined the contributing recharge area, (CRA) and ground-water travel times for each known pumping well or well field in the study area. MODPATH uses the hydraulic heads and flow distribution output from MODFLOW to calculate the flow paths and travel times of imaginary particles of water moving through the simulated ground-water flow system. The accuracy of particle tracking analysis must be known for correct interpretation of MODPATH results. Limitations of particle-tracking analysis are discussed at length by Pollock (1994) but several important factors that influence particle-tracking results follow. Particle movement and ground-water travel times computed by MODPATH are based on advective ground-water flow and no dispersion, diffusion, or chemical or microbiological retardation are incorporated into the calculations. Therefore, the movement of contaminants within ground-water are not fully described by MODPATH results alone. The spatial discretization of the ground-water flow model also may limit the accuracy of particle tracking results because cells containing sinks that do not discharge at a rate large enough to consume all the water entering the cell introduce uncertainty into the computed path of an imaginary water particle. However, the most significant factor affecting the accuracy of particle tracking analysis is the accuracy of the hydraulic head and flow distribution computed by the ground-water flow model. Therefore, all of the limitations associated with the ground-water flow model also apply to the particle-tracking analysis.
The porosity of the alluvial aquifer must be known for MODPATH to compute ground-water velocities. At the same ground-water discharge through a unit cross-sectional area of porous material, a material with a high porosity will have a lower average ground-water flow velocity than a material with a low porosity. This occurs because the higher porosity material has more openings per unit area of porous material than does a lower porosity material, thereby allowing the same amount of discharge at a lower average ground-water velocity than in a lower porosity material. Porosity was distributed among model cells based on the distribution of lithology and typical values of porosity (Driscoll, 1986; Freeze and Cherry, 1979).
Steady state ground-water flow was simulated for five different combinations of well pumping and river stage. Particle tracking analysis then determined the CRA for pumping wells in each of the following scenarios: (1) low pumping rate, low river stage (LPLR); (2) low pumping rate, high river stage (LPHR); (3) quasi-steady state conditions of January 1993 (QUASI); (4) high pumping rate, low river stage (HPLR); and (5) high pumping, high river stage (HPHR).
The river-surface altitude was defined for each river cell in the model for the quasi-steady-state calibration and for each stress period of the transient calibration. High and low river-stage data sets were chosen from the transient stress period data based on a comparison of the river stage at the USGS gage located in Kansas City, Missouri with the average annual high and low stages calculated from 1958 to 1994. The annual mean discharge from 1958 to 1994 at the USGS gage in Kansas City, Missouri was 54,890 ft3/s (cubic feet per second) which corresponds to a river surface altitude of 219.62 m at the gage. High river-stage conditions were represented by the September 26, 1993 river stage data when the average river surface altitude at the USGS gage in Kansas City, Missouri was 221.65 m (93,160 ft3/s discharge). A discharge of 91,200 ft3/s, corresponds to a river surface altitude of 221.55 m, and was exceeded 10 percent of the time between 1958 and 1994 (Reed, Perkins, and Gray, 1994). The river-stage altitude at the USGS gage in Kansas City, Missouri for the January, 1993 quasi-steady-state river stage conditions was 218.51 m (39,930 ft3/s discharge). Low river-stage conditions were represented by the January 16, 1994 river-stage data when the average river-surface altitude at the USGS gage in Kansas City, Missouri was 217.95 m (28,980 ft3/s discharge). A discharge of 23,400 ft3/s corresponds to a river-surface altitude of 217.5 m and was exceeded 90 percent of the time between 1958 and 1994 (Reed, Perkins, and Gray, 1994).
Well-pumping rates used in the quasi-steady-state simulation for January 1993 depended on the availability of data and were either average pumping rates for the month of January 1993 or average annual pumping rates. High well pumping rates were set at 1.25 times average annual pumping rates; and low pumping rates were set at 0.75 times average annual pumping rates.
For each scenario, one imaginary particle of water was placed on the water table in the center of the top-most active model cell and tracked to its eventual discharge point. Particles were placed in this manner for two reasons: (1) most water entering the alluvial aquifer comes from direct infiltration by precipitation or from the major rivers, and (2) the primary source of potential contamination to the alluvial aquifer is from leaks or spills that occur on the land surface. Consequently, the CRAs computed by MODPATH include the source area of water to each well or well field and advective ground-water travel times from the land surface and the major rivers to each well or well field. The starting locations and travel times of the particles that discharged to a well were saved and input into the GIS. Particles with travel times from 0 to 1 year, 1 to 5 years, 5 to 10 years, 10 to 100 years, and 100 to 1,000 years were grouped to create 1-, 5-, 10-, 100-, and 1,000-year CRAs for each scenario.
The shape, size, and ground-water travel time within the CRA for each well or well field is affected by changes in river stage and pumping rates and by the location of the well or well field with respect to the major rivers, alluvial valley walls, and other pumping wells. Similarities in the shapes of CRAs between different wells and well fields can be attributed to similarities in the pumping rate, and the position of the wells or well fields in relation to the major rivers, the alluvial valley walls, or other well fields. A typical CRA for a well located within an aquifer such that effects from any hydrologic boundary are negligible will have a bull's-eye pattern. The CRAs for each public water supply well field are discussed individually followed by a discussion of the CRAs of the industrial well fields.
The effect of well pumping and river stage on the total CRA of well fields in the study area is complex because: (1) Each well field has a unique orientation with respect to the geometry of the aquifer, the alluvial valley walls, the rivers, and the other pumping wells in the study area; (2) The hydraulic properties of the aquifer in the vicinity of each well field are different in both magnitude and spatial orientation; and (3) Each well field pumps at a different rate. For most well fields an increase of well pumping increases the CRA for both low and high river stage scenarios (see below). However, the total CRAs for well fields of National Starch Inc. and Phillips Petroleum decreased with increased pumping for the low-river-stage scenarios and the total CRAs for well fields of the Missouri Cities Water Company; National Starch Inc. and Independence, Missouri decreased with increased pumping for the high-river-stage scenarios. The largest effect of a change in river stage is the change in the potentiometric surface gradient. Typically, an increase of river stage lowers the regional ground-water gradient between the alluvial valley walls and the rivers in the study area. Most total CRAs increased with increased river stage (see below). However, the effect of a change in the ground-water gradient on the CRA is different for each well field. For instance, the total CRAs for the well fields of Gladstone, Missouri; Chevron Chemical, Liberty, Missouri Community Water Company, Tri-County Water Company and Phillips Petroleum (well field number 18) decreased with increased river stage for the low pumping scenarios and the well fields of the Missouri Cities Water Company; Gladstone, Missouri, Independence, Missouri, Tri-County Water Company, Phillips Petroleum (well field number 23); Sealright Company; and Reichhold Chemical/Certain-Teed decreased with increased river stage for the high pumping scenarios.
Change in recharge area and pumpage of wells (11.6 kb)
Change in recharge area and change in river altitude (11.7 kb)Proximity to a major river reduces the size of the CRA because the well or well field obtains a large part of its water from recharge induced from the river. A comparison of the Liberty, Missouri well field with the North Kansas City, Missouri well field illustrates this difference. The simulated high pumping rate for the Liberty, Missouri well field is 13,254 m3/day which corresponds to a total CRA of over 23 km2 for both the low and high river stage scenarios. However, simulated high pumping rate for the North Kansas City, Missouri well field of 16,476 m3/day corresponds to a total CRA of just over 1 km2 for both low and high river stage scenarios.
Induced recharge because of proximity of a well field to a river may also affect the spatial distribution of individual CRAs within the total CRA for each well field. For example, the Independence, Missouri well field is located close to the Missouri River and has the 1-year CRA located near the river but a 5-, or 10-year CRA in the area closest to the wells for all scenarios because the distance from the bottom of the riverbed to the screened interval of the well is less than the distance from the land surface to the screened interval of the well. Also, because the bottoms of larger rivers typically intersect alluvial material of higher hydraulic conductivity, ground water travels more quickly at this depth than at shallower depths where alluvial deposits of lower hydraulic conductivity are found.
The vertical conductance term limits water flow between layers of the model to simulate the vertical anisotropy of hydraulic conductivity within the alluvial aquifer. This anisotropy is greatest in the heterogeneously distributed finer-grained deposits present at shallow depths and represented in the model by layer 1 and to a lesser degree in the more homogeneously distributed silt and sand present in deeper parts of the aquifer and represented in the model by layers 2 and 3. The distribution of vertical conductance between layers 1 and 2 and between layers 2 and 3 affect the relative distribution of CRAs within the total CRA of each well or well field. For example, the Liberty, Missouri well field has a part of the 100-year CRA located closer to the well field than a part of the 10-year CRA because a low rate of vertical water movement caused by the presence of clay near the land surface increased the travel time of water from the water table to deeper parts of the aquifer. The part of the 10-year CRA located farther from the same well field is there because a high rate of vertical water movement caused by coarse deposits at the land surface decreased the travel time of water from the water table to deeper parts of the aquifer. Because the hydraulic conductivity values in the deeper parts of the aquifer are higher and more uniformly distributed, the rate of water movement there is faster and more uniform than in shallower parts of the aquifer. Therefore. the rate of water flow vertically from the shallower parts of the aquifer to the deeper parts often controls the time of travel of water from the water table to the screened interval of a pumping well and the distribution of the CRA of a well or well field.
Interference between pumping well fields also affects the size and shape of CRAs of well fields. Well interference between the Independence, Missouri and Liberty, Missouri well fields has already been discussed. However, the CRAs of well fields located just north of the confluence of the Missouri and Kansas rivers show the greatest well interference effects. Well fields located in the upgradient direction of the regional flow field will intercept ground water before it reaches well fields located in the downgradient direction. This effectively cuts off the ground-water supply to the well fields located downgradient and limits the upgradient extent of the downgradient CRAs. This is shown for the Phillips Petroleum Company, Sealright Company and Reichhold Chemical/Certain-Teed well fields (well field numbers 18, 25, and 27 respectively).
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![Low Pumping Rate, Low River Stage [28.8 kb]](images/lplrplot.gif){kind=link}
![Low Pumping Rate, High River Stage [28.5 kb]](images/lphrplot.gif){kind=link}
![Quasi-Steady State Conditions of January1993 [28.6 kb]](images/steadplot.gif){kind=link}
![High Pumping Rate, Low River Stage [29.0 kb]](images/hplrplot.gif){kind=link}
![High Pumping, High River Stage [29.2 kb]](images/hphrplot.gif){kind=link}