Linear transient flow solution for primary oil recovery with infill and conversion to water injection

Eric Zwahlen*, Tad W. Patzek

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this paper, we analyze the effects of primary production, producer infills and repressurization by water injection 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 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. We analyze the pressure response and fluid flow rates for the original wells and infill wells drilled halfway between the original wells, and - finally - from water injection at the infill wells. All of the formation and fluid properties are described by a single hydraulic diffusivity assumed to be independent of time and production or injection. We solve the onedimensional 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, oil, water and gas rates and cumulatives at both the original wells and infill wells as functions of time. Finally, we present a computational example of oil production from a stack of seven independent diatomite layers with different properties and show the effects of infill wells and water injection on the total oil production. We show that a single-layer analytical solution and a 1-D 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. We show 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 because of conversion to a waterflood injector.

Original languageEnglish (US)
Pages (from-to)297-330
Number of pages34
JournalIn Situ
Issue number4
StatePublished - 1997
Externally publishedYes

ASJC Scopus subject areas

  • General Chemical Engineering
  • Fuel Technology
  • Geotechnical Engineering and Engineering Geology
  • Energy Engineering and Power Technology


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