Modified Inverse-Injectivity Method for Stimulation Evaluation Proves Effective
Authors: Carpenter Chris 
Published: June 2020

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 200135, “A Comprehensive Method for Diverter-Performance Evaluation During Stimulation of Long-Interval Heterogeneous Reservoirs: A Case Study” by A.F. Safari and H. Panjalizadeh, Mehran Engineering and Well Services Company; M. Pournik, SPE, The University of Texas Rio Grande Valley; and H. Jafari and A. Zangeneh, Mehran Engineering and Well Services Company, prepared for the 2020 SPE Conference at Oman Petroleum and Energy Show, Muscat, Oman, 14-16 September. The paper has not been peer reviewed.
Assessment of diversion performance is key to determining success of stimulation. Doubts remain, however, regarding the evaluation of diversion effectiveness. As diverter enters the formation, a hump in the surface pressure curve usually is expected. It then can be interpreted as supporting evidence for diversion. This, however, is a simplification of the fluid-diversion process. Such a hump may not be observed during a diversion stage even when the process is effective. In the complete paper, the inverse-injectivity method of evaluating matrix-stimulation performance is modified and validated with real data of two matrix-acidizing operations in a gas-condensate field.
South Pars Gas Field
In 1971, an enormous gas reservoir, the North Dome Field, was found in the Qatar Dome structure of the Persian Gulf. In the years since, surveys have highlighted the existence of abundant amounts of gas and condensate accumulations in a huge dome. This single gas-bearing structure is delineated by the geographical borders between Iran and Qatar in the Persian Gulf. According to one recent estimate, almost 19% of the world’s gas rests in this vast basin.
The field includes two independent gas-bearing formations, Kangan (Triassic) and Upper Dalan (Permian). Each formation is divided into layers separated by impermeable barriers, namely K1, K2, K3, and K4. The K1 and K3 layers mostly are formed of dolomites and anhydrites. Layers K2 and K4 possess better reservoir specifications (i.e., highly permeable and porous, consisting of limestone and dolomite). An anhydrite-composed layer, the Nar Member, separates Layer K4 from the underlying K5 layer, which has nonsatisfactory reservoir qualities.
Methodology
In this study, the inverse injectivity and its integral and derivative plot are coupled with results of production logs to evaluate diverter-system performance in two real acidizing operations performed in the South Pars field. What makes this work different is the complexity of the treated reservoir in terms of the number of layers (four distinct formations), formation heterogeneity, and long perforation intervals (an approximately 1,000-ft net interval).
The productivity index is a measure of the well’s production potential and is defined as a ratio of the total liquid surface rate to the pressure drop at the midpoint of the producing interval. Because the direction of flow in this case is in a direction opposite that of production, this parameter is considered as the reverse of the productivity index and is called inverse injectivity.
In this study, a program is written to calculate modified inverse injectivity during two real matrix stimulations performed in the field. The equations used in this method are provided in the complete paper.