Oil and gas fields result from complex sequences of events spanning geologic time scales. The three most fundamental steps in the process are generation of the hydrocarbons (oil and gas) in a source rock, migration of the hydrocarbons from the source rock to a more permeable formation, and trapping of the hydrocarbons by a low-permeability seal. More information about these steps can be found in Petroleum: a primer for Kansas. We will provide brief summaries here.
Typical hydrocarbon source rocks are shales that are rich in organic matter, generally formed from sediment that was deposited in stagnant, oxygen-deprived water bodies such as lagoons. The low oxygen conditions in these settings allow for preservation of organic material. Over the millenia, these sediments are buried by younger material and are subject to increasing temperature and pressure as the depth of burial increases. The organic material is gradually "cooked" to form hydrocarbons. Although shales usually have high porosity, they generally have fairly low permeability because the pores are not connected in a way that allows fluid to flow through them readily. However, over time the hydrocarbons may be expelled from the source rock and move into more permeable formations.
The general direction of hydrocarbon migration is up. This is because oil and gas are less dense than water, the fluid that fills almost all the pore space in rocks below the water table, and are also insoluble in water. Therefore, oil and gas tend to migrate up the stratigraphic section until they reach a "seal" -- typically a low-permeability formation. To be effective, the geometry of this seal has to form a "trap" -- prohibiting further upward movement. Although there are a number of kinds of traps in the subsurface, the only kind that is present in Small County is an anticline, a dome-shaped structure that is generally formed by compressional tectonic forces. If the anticline is of sufficient height, then a hydrocarbon column may develop in the permeable formation below the seal. If gas is present, it will typically be in a pocket at the peak of the structure, since it is more buoyant than oil:
Although the picture above shows distinct regions in which the pore space is saturated solely with oil or water, in reality the saturations of these fluids will vary as a function of the height above the free water level -- a level below which the pore space is completely occupied by water. Because there is no gas present in Small County, we are looking at a situation in which oil saturation increases and water saturation decreases as a function of height above the free water level, or "column height":
So, in the Small County exercise, you are looking for anticlines of sufficient height to be promising prospects for trapping oil. The primary tools for finding these prospects are maps of the elevations of the tops of the permeable intervals that might contain oil (the Quivira Dolomite, Westport Limestone, Morn Sandstone, and Sawyer Sandstone).