Placement of a sufficient volume of acid in all desired zones is critical for a successful acid stimulation treatment. Particularly in thick, highly heterogeneous carbonate formations, the acid distribution is crucial for optimal stimulation results. A variety of diversion methods are applied in acidizing treatments to evenly place acid along the well, but the effectiveness of these diversion methods is generally only inferred from the rate and pressure behavior during the treatment, and is not known with any certainty. It would be extremely helpful if the acid distribution could be measured.

We developed a model to simulate the temperature behavior along the wellbore during acid injection and during the flow back period following an acid stimulation. An important phenomenon in this process is the heat generated by reaction, the key factor enabling the interpretation of the acid distribution from the temperature profile. We have developed a mathematical model that describes the coupled flow and heat transfer process. The flow system consists of a near wellbore formation with a wormhole region and a spent acid region. Wormhole propagation and the spent acid front are simulated as a function of acid injection volume (time). The thermal model includes conduction, convection, and reaction heating to seek the connection between acid volume distribution and temperature profile. The result of the thermal model showed significant temperature effects caused by reaction. During flow back, the zone that took more acid volume would have created more heating because of reaction, providing a mechanism to quantitatively determine the acid flow profile.


Acid placement is crucial for efficient acidizing treatments, especially for thick, heterogeneous carbonate formations. This is because the acid distribution could be uneven among target zones without any diversion method. Even with diversion technologies, the effectiveness of these diversion methods cannot be determined with any certainty if we do not know the acid distribution. It would be extremely helpful to know the acid distribution during acidizing treatments. With the acid distribution known, acidizing treatments could be evaluated and optimized.

Because of the development of DTS, continuous and accurate temperature measurement along the wellbore is possible, which provide a method to measure the acid distribution during acidizing treatments. Some research has been conducted to determine the injected fluid distribution from temperature data.

Glasbergen et al. (2007) and Clanton et al. (2006) developed a numerical model to obtain the fluid distribution based on the wellbore temperature data measured by distributed temperature sensors. By tracking the movement of a fluid with a different temperature from the original fluid, they measured the velocity of the slug and consequently the leakoff profile of acid. This acid injection profile could be considered as the initial profile because once the slug passes a particular layer, the acid will change the layer properties and the injection profile could vary. This phenomenon was not simulated by this model. An analytical solution has been presented by Gao and Jalali (2005) based on a wellbore temperature model to interpret distributed temperature data in horizontal wells, from which they could create an estimated initial injection profile. The method is valid for horizontal wells and also based on a fluid slug in the wellbore having a different temperature from the original fluid.

Johnson et al. (2006) and Wang et al. (2008) developed models to interpret distributed temperature data for gas reservoirs and oil reservoirs during production. The method they used applies a wellbore thermal model with Joule-Thomson effects.

Their method could not be applied here because we are considering an acid injection profiling problem with reaction heat in the formation.

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