This chapter looks at the changes that over time affect the geochemical properties of a system or a set of systems, such as the mantle, the crust, or the ocean, when subjected to disturbances whether caused naturally or by human activity. The essential concepts utilized – residence time and forcing – are taken from chemical engineering. Viewing system Earth as a chemical factory composed of reactors, valves, sources, and sinks, has proved to be a simple and robust model. The theory goes by various names, with the “box model” probably the most widely used. We will first set out the principles by describing the behavior of a system with a single reservoir and then go on to generalize the approach.

Single-reservoir dynamics

Let us begin by considering a lake (Fig. 6.1) containing a mass of water M that we will take to be constant. A river flows through the lake with a rate of flow Q, which we will express in kilograms per year; Q is therefore the same upstream and downstream. We are interested in the balance of a chemical species in the lake. A chemical element i introduced upstream with a concentration Ci in is either lost through the lake outlet or entrained into sediments. The sedimentation rate P is also expressed in kilograms per year. The lake itself is considered homogeneous, being well mixed by turbulent flow and by convection.