Computation of the time-varying flow rate from an artesian well in central Dade County, Florida, by analytical and numerical simulation methods

Abstract

Simulation of the development of a plume of brackish water in a surficial aquifer caused by discharge from a flowing artesian well required an accurate estimate of the rate of flow during a 40-year period. The rate of flow from the well, constructed with 12-inch casing in 1944, was measured to be 2,350 gallons per minute 2 months after completion and 1,170 gallons per minute in 1964, 1965, and 1969. The rates measured 20 years apart appeared to be mutually inconsistent unless the difference could be explained by the: (1) drawdown of the aquifer over time, (2) raising of the altitude at which the water was discharged, (3) installation of 80 feet of 8-inch liner, or (4) deterioration of the condition of the well over time. The latter possibility implies losses of flows through holes in the casing and increased friction losses. Application of an analytical solution relating the time-varying rate of flow to a constant opposing head (a rewriting of the "constant drawdown" formula) failed to reconcile the measured rates, though estimates provided by use of the formula differed by only about 15 percent. Numerical simulation techniques were also used to estimate the rate of artesian flow from the source aquifer, a permeable zone at about 1,200 feet below land surface, near the top of the Upper Floridan aquifer in southeastern Florida. The selected simulation code contained a well-riser model that was used to account for friction losses in the well. Construction of a highly generalized model of the Floridan aquifer system for the flow-rate analysis, and the determination of a set of predevelopment head values for use as an initial condition, permitted simulation of the effects of recharge through leaky confining layers or from aquifer boundaries at a finite distance from the well. The conceptual model supported by the calibration of the model of the Floridan aquifer system is that a hydraulically uniform Lower Floridan aquifer ("Boulder Zone") provides recharge to the Upper Floridan aquifer through a leaky middle confining unit, and head variations in the Upper Floridan aquifer are related to variations in the thickness of the zone of fresh and brackish water extending downward into the confining unit. Results of the flow-rate analysis indicated that the flow rate should reach equilibrium after about 1 week because the Upper Floridan aquifer received recharge from the Boulder Zone through the intervening middle confining unit. The well modifications probably only decreased the rate of flow by 18 to 19 percent. A sensitivity analysis indicated that variation in the roughness coefficient of a degree that could represent severe deterioration of the well casing decreased the estimated flow rate by about 17.5 percent. Another sensitivity analysis indicated that installation of 80 feet of 8-inch liner had only a slight effect on the flow rate. The flow-rate inconsistency was not fully resolved by the analysis, but could be explained as a combination of the result of well modification, deterioration of the condition of the well, and other factors not amenable to analysis (inaccuracy in one or more of the flow-rate measurements or greater than estimated losses through the casing). The transmissivity of the source aquifer was estimated to be 11,125 feet squared per day at the well site. Besides the construction of a generalized model of the Floridan aquifer system, the most significant result of the analysis was the demonstration of a simulation approach for accurately showing the relation between aquifer characteristics and the rate of flow from artesian wells. However, this approach requires considerably more analytical effort and data describing aquifer properties than does application of the constant drawdown formula.