# Chapter 16 Kruseman and Ridder (1970)

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Chapter 16 Kruseman and Ridder (1970)
Slug Tests Chapter 16 Kruseman and Ridder (1970) Stephanie Fulton March 25, 2014

Background Small volume of water—or alternatively a closed cylinder—is either added to or removed from the well Measure the rise and subsequent fall of water level Determine aquifer transmissivity (T or KD) or hydraulic conductivity (K) If T is high (i.e., >250 m2/d), an automatic recording device is needed No pumping, no piezometers Cheaper and faster than conventional pump tests But they are NO substitute for pump tests!!! Only measures T/K in immediate vicinity of well Can be fairly accurate

Types of Slug Tests Curve-Fitting methods (conventional methods)
Confined, fully penetrating wells: Cooper’s Method Unconfined, partially or fully penetrating wells: Bouwer and Rice Oscillation Test (more complex method) Air compressor used to lower water level, then released and oscillating water level measured with automatic recorder All methods assume exponential (i.e., instantaneous) return to equilibrium water level and inertia can be neglected Inertia effects come in to play for slug tests in highly permeable aquifers or in deep wells oscillation test Prior knowledge of storativity needed

Cooper’s Method (1967) Confined aquifer, unsteady-state flow
Instantaneous removal/injection of volume of water (V) into well of finite radius (rc) causes an instantaneous change of hydraulic head: (16.1)

Cooper’s Method (cont.)
Subsequently, head gradually returns to initial head Cooper et al. (1967) solution for the rise/fall in well head with time for a fully penetrating large-diameter well in a confined aquifer:

Cooper’s Method (cont.)
Annex 16.1 lists values for the function F(α,β) for different values of α and β given by Cooper et al. (1967) and Papadopulos (1970) These values can be presented as a family of curves (Figure 16.2)

Cooper’s Method: Assumptions
Aquifer is confined with an apparently infinite extent Homogeneous, isotropic, uniform thickness Horizontal piezometric surface Well head changes instantaneously at t0 = 0 Unsteady-state flow Rate of flow to/from well = rate at which V changes as head rises/falls Water column inertia and non-linear well losses are negligible Fully penetrating well Well storage cannot be neglected (finite well diameter)

Remarks May be difficult to find a unique match of the data to one of the family of curves If α < 10-5, an error of two orders of magnitude in α will result in <30% error in T (Papadopulos et al. 1973) Often rew (i.e., rew = rwe-skin) is not known Well radius rc influences the duration of the slug test: a smaller rc shortens the test Ramey et al. (1975) introduced a similar set of type curves based on a function F, which has the form of an inversion integral expressed in terms of 3 independent dimensionless parameters: KDt/rw2S, rc2/2rw2S and the skin factor

Uffink’s Method More complex type of slug test for “oscillation tests”
Well is sealed with inflatable packer and put under high pressure using an air line Well water forced through well screen back into the aquifer thereby lowering head in the well (e.g., ~50 cm) After a time, pressure is released and well head response to sudden change is characterized as an “exponentially damped harmonic oscillation” Response is typically measured with an automatic recorder

Uffink’s Method (cont.)
This oscillation response is given by Van der Kamp (1976) and Uffink (1984) as:

Uffink’s Method (cont.)
Damping constant, γ = ω0B (16.7) Angular frequency of oscillation, ω = ω0 1− B (16.8) Where ω0 = “damping free” frequency of head oscillation (Time-1) B = parameter defined by Eq (dimensionless)

Uffink’s Method (cont.)

Uffink’s Method (cont.)
The nomogram in Figure 16.4 (below) provides the relation between B and rc2/ω04KD for different values of α as calculated by Uffink: Figure 16.4

Uffink’s Method: Assumptions and Conditions
Assumptions are the same as with Cooper’s Method (Section 16.1), EXCEPT: Water column inertia is NOT negligible and Head change at t > t0 can be described as an “exponentially damped cyclic fluctuation” Added condition: S and skin factor are already known or can be estimated with fair accuracy

Bouwer-Rice’s Method Unconfined aquifer, steady-state flow
Methods for full or partially penetrating wells Method is based on Thiem’s equation for flow into a well following sudden removal of slug of water: The well head’s subsequent rate of rise: Figure 16.5

Bouwer-Rice’s Method Combining Eqs and 16.17, integrating, and solving for K:

Bouwer-Rice’s Method Values of Re were experimentally determined using a resistance network analog for different values of rw, d, b, and D Derived two empirical equations relating Re to the geometry and boundary condition of the system Partially penetrating wells: A and B are dimensionless parameters which are functions of d/rw Fully penetrating wells: C is a dimensionless parameter which is a function of d/rw

Bouwer-Rice’s Method

Bouwer-Rice’s Method: Assumptions and Conditions

Bouwer-Rice’s Method: Remarks