Well losses vs Aquifer Losses

The components of observed drawdown in a pumping well was first described by Jacob (1947), and the test was refined independently by Hantush (1964) and Bierschenk (1963) as consisting of two related components,
s = BQ + CQ2,
where s is drawdown (units of length e.g., m), Q is the pumping rate (units of volume flowrate e.g., m³/day), B is the aquifer loss coefficient (which increases with time — as predicted by the Theis solution) and C is the well loss coefficient (which is constant for a given flow rate).
The first term of the equation (BQ) describes the linear component of the drawdown; i.e., the part in which doubling the pumping rate doubles the drawdown.

The second term (CQ2) describes what is often called the 'well losses'; the non-linear component of the drawdown. To quantify this it is necessary to pump the well at several different flow rates (commonly called steps). Rorabaugh (1953) added to this analysis by making the exponent an arbitrary power (usually between 1.5 and 3.5).

To analyze this equation, both sides are divided by the discharge rate (Q), leaving s / Q on the left side, which is commonly referred to as specific drawdown. The right hand side of the equation becomes that of a straight line. Plotting the specific drawdown after a set amount of time (Δt) since the beginning of each step of the test (since drawdown will continue to increase with time) versus pumping rate should produce a straight line.

\frac{s}{Q} = B + CQ

Fitting a straight line through the observed data, the slope of the best fit line will be C (well losses) and the intercept of this line with Q = 0 will be B (aquifer losses). This process is fitting an idealized model to real world data, and seeing what parameters in the model make it fit reality best. The assumption is then made that these fitted parameters best represent reality (given the assumptions that went into the model are true).