Theis equation

A common application of a solution to Eq. [3-10b] is the prediction of time-varying drawdown in the vicinity of a well that is pumped at a constant rate. The Theis equation (Theis, 1935) was derived for confined aquifers and applies to unconfined aquifers for some period of time after a well begins to be pumped. The Theis equation can be written as... 

FIGURE 3-14 Plot of drawdown as a function of time for a well in an infinite aquifer with no recharge. Theoretically, as described by the Theis equation, drawdown increases indefinitely after pumping has begun. The graph can be extended beyond the time of the test to predict the amount of drawdown that would occur after a longer period of continuous pumping (Driscoll, 1986). 

A successful and effective groundwater control mainly depends on rehable hydrogeological modeling. In the past few decades, under the guidance of groundwater dynamics especially Thiem equation and Theis equation, some analytical models for estimating water inflow rate have been established, which could be utilized to build the... 

When competing reactions are minimized, the response of thei detector can be described by equation (3.8) (112). 

Equation (1,5-2i) is a general relacionsbip between Henry s Law end Raonlt s Law activity coefficients (or a component in a binary mixture. Pariicutar expressions for 7 are obtaiand from particular expressions for 71, which require a model forg for their determiuation see Sections 1,4-1-1.4-3. To illustrate. suppose thei gK is described by the Potter equation, Eq- (1.4-14). Then, by Eqs- (1.5-21). (1.4-15a). and (1.4- 9a), we find the ons-paramatcr expression... 

Equation (1.6-7) says that, at a given temperature, the ideal solubility or component 2 depends only on the properties of pure component 2, thei is, the solubility is tha same in all solvents. Funheresore, Eq. (1.6-7) says that the ideal solubility always rises with increasing lemparalure. These statements, especially the Erst, are not in agreameni with experiment. To correct the ideal solubility, ii is necessary to include the liquid-phase activity coefficient y2 which depends on temperature aed composition and on the natare of components 1 and 2. 

The analysis of macropore diffusion in binary or multicomponent systenis presents no particular problems since the transport properties of one compos nent are not directly affected by changes ini the concentration of the bther components. In an adsorbed phase the situation is more complex since ih addition to any possible direct effect on thei mobility, the driving force for each component (chemical potential gradient is modified, through the multi-component equilibrium isotherm, by the coiicentration levels of all components in the system. The diffusion equations for each component are therefore directly coupled through the equilibrium relationship. Because of the complexity of the problem, diffusion in a mixed adscjrbed phase has been studied tjs only a limited extent. 

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