Laboratory and Theoretical Modeling of Diverting Agent Behavior
Authors: Hill A.D. , Galloway P.J. 
Published: December 2007

Summary
Diverting agents composed of finely ground, oil-soluble resin particles were tested in the laboratory and modeled with a numerical simulator to determine their effectiveness in matrix stimulation treatments. First, the diverting agents were characterized with linear coreflood tests, and then experiments were performed in a physical wellbore model scaled to a typical well completion. A numerical simulator was developed to predict the effect of diverting agent on injected fluid distribution. This paper describes the laboratory and mathematical models paper describes the laboratory and mathematical models of diverting agent behavior and the results obtained with these models.
Among the conclusions drawn from this study are:the finely ground, oil-soluble-resin diverting agents are effective for matrix diversion;diverting agent added continuously to treating fluid equalizes the flow to all zones; anddiverting agent injected in small stages ahead of treating fluids can cause a highly skewed distribution of injected fluid.

Introduction
A diverting agent is a material (usually a particulate solid) used with a stimulation treatment to distribute the treatment more uniformly throughout the zones in the well. It is intended to plug high-conductivity areas temporarily so that more stimulating fluid is placed in the lower permeability zones. Diverting agents are either added continuously to the acid solution or injected in stages between stages of acid. Both matrix acidizing and fracturing treatments involve use of diverting agents.
Diverting agents have been used since shortly after the introduction of acidizing. Materials ranging from mothballs and oyster shells to the modem polymer resins have been used. Diverting agents have been evaluated by measuring their ability to reduce flow into cores or sandpacks. King and Hollingsworth tested diverting agents by measuring flow rate through a sandpack as a function of volume of diverting agent solution injected at a constant pressure. They concluded that organic resins are the best diverting agents.
We evaluated diverting agents in the laboratory in linear coreflood experiments. A solution containing diverting agent was injected into Berea core at a constant rate, and the pressure drop across the face of the core was measured as a function of time. An organic-resin diverting agent caused a rapid pressure increase as it built up on the sandface.
We also conducted wellbore model experiments to simulate actual treatments more closely and to check the numerical simulation of diverting agent behavior. Three cores with different permeabilities were attached to a scale model of a wellbore, and diverting agent solution was injected into the wellbore (Fig. 1). The experiments showed that diverting agent equalized flow to all cores, despite the differing permeabilities. The mathematical model of diverting agent behavior provided a good match of wellbore model results.
The effect of diverting agents on the distribution of injected fluid in actual treatments was simulated with a numerical fluid placement model, which uses the data on pressure drop vs. volume injected from the coreflood pressure drop vs. volume injected from the coreflood experiments to determine the added resistance to flow caused by diverting agents. This model also considers other effects that influence fluid placement in a well treatment, including viscous fluid injection and gravity segregation in the wellbore, 3 and can simulate multiple-sequence treatments in multizone reservoirs. Model simulations show that diverting agent added continuously to stimulation fluid will equalize flow to all reservoir layers. Diverting agent added in small stages can lead to uneven distributions of injected fluid and can affect a treatment adversely.

Experimental Evaluation of Diverting Agents
The primary method of testing diverting agents was injection of a solution containing diverting agent into linear core plugs and measuring the pressure drop across the face of the core. Berea sandstone core plugs (i in. × 3 in. [ 1.54 cm × 7.62 cm]) were mounted in a core holder that had a space in its injection end to allow for diverting agent buildup. The pressure drop was measured across the first 1/2 in. [1.27 cm] of the core and across the remaining 2 1/2 in. [6.35 cm]. Fig. 2 shows the experimental apparatus. The primary measurement was the pressure drop across the face of the core, deltap face, vs. the pressure drop across the face of the core, deltap face, vs. the volume injected at a constant rate. We also measured the pressure drop across the back of the core to check for pressure drop across the back of the core to check for penetration of diverting agent into the core. penetration of diverting agent into the core. Experiments were run at a constant rate using a Ruska pump. In most experiments, the rate was approximately pump. In most experiments, the rate was approximately 3 mL/min [3 cm /min] because this was the calculated rate per perforation in a typical well completion. The experiments began with injection of 3% NaCl brine at several rates to obtain a brine permeability for the core. After a stable pressure drop was obtained at the rate of 3 mL/min [3 cm /min], the fluid was switched to 3% NaCl brine containing the diverting agent being tested.
JPT
P. 1157