# Step-Drawdown Tests

by Glenn M. Duffield, President, HydroSOLVE, Inc.

### Well Loss Equation

Jacob (1947) proposed the following drawdown equation that accounts for linear and nonlinear head losses in the pumping well:

sw=B(re,t)Q+CQ2

where B is the linear head-loss coefficient [T/L2] and C is the nonlinear well-loss coefficient [T2/L5].

Rorabaugh (1953) modified Jacob's equation to account for variations in the nonlinear well-loss term:

sw=B(re,t)Q+CQP

where P is the order of nonlinear well losses. According to Rorabaugh (1953), the value of P can assume values ranging from 1.5 to 3.5 depending on the value of Q, but many researchers accept the value of P=2 as proposed by Jacob (1947).

The linear head-loss coefficient B is a function of the effective or equivalent radius of the well and time. The equivalent well radius is defined as the radial distance from the well at which the theoretical drawdown equals the drawdown immediately outside the well screen. The linear head-loss coefficient consists of two components:

B(re,t)=B1(rw,t)+B2

where B1 is the linear aquifer-loss coefficient [T/L2] and B2 is the linear well-loss coefficient [T/L2]. The linear aquifer-loss coefficient B1 is a function of the radius of the well and time. Ramey (1982) defines the linear well-loss coefficient B2 in terms of a dimensionless wellbore skin factor as follows:

sw=B2·2πT

#### Nonlinear Well Loss Coefficient, C

Walton (1962) reported the following relationships between the nonlinear well loss coefficient (C) and well condition based on field experience.

 Well Loss Coefficient Well Condition (sec2/ft5) (min2/m5) <5 <0.5 properly designed and developed 5 to 10 0.5 to 1 mild deterioration 10 to 40 1 to 4 severe deterioration or clogging >40 >4 difficult to restore well to original capacity

#### Well Efficiency

The efficiency of a pumping well, which expresses the relationship between theoretical and actual drawdown in the well, is computed as follows (Kruseman and de Ridder 1994):

Ew=(theoretical drawdown/actual drawdown)·100%

Ew=[B1Q/((B1+B2)Q+CQP)]·100%