This paper presents a practical and useful analysis technique for effectively accomplishing a rigorous superposition-in-time (convolution) analysis of the transient drawdown performance of oil and gas wells that does not require that the flowing pressures (wellhead or bottom hole) be known for every flow rate data point in the production history. If at least one flowing pressure point is available at any point in time during the production history of the well, a unique analysis of the production data for the evaluation of the reservoir effective permeability, well drainage area, and well parameters such as unfractured well radial flow steady-state skin effect, fractured well effective fracture half-length and average fracture conductivity, or horizontal well effective length in the pay zone may be obtained. Even if no flowing pressures are available at all during the production history of the well, estimates of these well and reservoir parameters can still be obtained with reasonable accuracy using the analysis techniques presented in this paper.

The general evaluation procedures presented in this paper are applicable for all well types, including flowing wells and wells with artificial lift systems (i.e., conventional beam pumping units and electrical submersible pumps (ESP)). The theoretical basis for a rate-transient analysis of the production performance of a vertically fractured well is presented in detail in this paper. Application of the proposed general analysis procedure to other well types (unfractured vertical/slanted wells, horizontal wells, etc.) may also be found in a similar manner as presented in this paper. The theoretical basis for a pressure-transient based solution for a vertically fractured well is also available in the references.

In the relatively short period of time that this new analysis technique has been available, it has radically changed the way that engineers may now rigorously analyze the production performance of oil and gas wells to evaluate the well and reservoir properties from the well's production performance, as well as greatly expanding the number and types of wells that can now be considered. The new analysis techniques presented in this paper therefore represent a step-change in the petroleum industry's technical capabilities for the analysis of the production performance of oil and gas wells over that which existed prior to this work.


One of the most common problems encountered by a production or reservoir engineer when analyzing an oil or gas well's production history to evaluate the formation and completion system properties (by inversion of the production history record of the well), is the lack of a complete data record with which to employ a conventional convolution analysis. The variable that is most commonly not recorded that is required for a conventional convolution analysis of the production history of the well is the well flowing pressure. An analysis technique is presented in the following sections of this paper that will remove this limitation in a convolution analysis of the production data record of a vertically fractured well. Similar analysis techniques have also been developed for other types of wells1.

The flow rates of the hydrocarbon phases (oil and gas) of a well are generally known with a reasonably high degree of accuracy, since the oil and gas production directly correspond to revenue for the operator and royalty owners. Custody transfers also dictate that the production of these fluids be monitored as accurately as possible. The exception to this general statement is the case where the production of several wells are processed at a single separation facility and the actual production of any single well in the system may be estimated from the combined system production with periodic tests of the individual wells in the system.

Often known with a much lower degree of certainty is the water production from the well, since this variable generally represents an operating cost of the well, it is commonly not recorded or reported with a great deal of precision. Often the most reliable way of ascertaining a representative water production history for a producing well is through the use of run tickets for the loads of water transported to disposal wells.

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