We present analytical solutions for primary production, producer infills and early response to waterflood in a low permeability, compressible, layered reservoir filled with oil, water and gas. The sample calculations are for the California Diatomites, but the equations apply to other tight rock systems. Primary oil recovery from rows of hydrofractured wells in a low permeability reservoir is described by linear transient flow of oil, water and gas with the concomitant pressure decline. During primary, it may be desirable to drill infill wells to accelerate oil production. At some later time, the infill wells may be converted into waterflood injectors for pressure support and incremental oil recovery. In this paper, we analyze the pressure response and fluid flow rates due to the original wells and infill wells drilled halfway between the original wells, and - finally - due to water injection at the infill wells. All of the formation and fluid properties are described by a single hydraulic diffusivity, a, assumed to be independent of time and production or injection. We solve the one-dimensional pressure diffusion equation analytically using pressure boundary conditions at the original and infill wells and use superposition to account for the water injection. We give solutions for the pressure in the formation and discuss how to calculate oil, water and gas rates and cumulatives as functions of time at both the original wells and infill wells. Finally, we present a computational example of oil production from a stack of seven diatomite layers with different properties and show the effects of infill wells and water injection on the total oil production. We show that results of this analytical solution and a compositional numerical simulation for primary production in the diatomite agree well. Our analysis can predict the onset of pressure depletion and quantify how long to produce from the infill wells before injecting water. It shows that producing from the infill well for a few years significantly increases the production from the field and can minimize the lost production at the infill well due to conversion to a waterflood injector. Our analysis also generates very reliable, well-by-well, field-wise forecasts of fluid production and water injection.