Determining Matrix Treatment Performance From Downhole Pressure And Temperature Distribution: A Model
Authors: Tardy Philippe Michel Jacques , Chang Frank Fakuen , Qiu Xiangdong 
Published: March 2015

Abstract
Distributed temperature sensing (DTS) is a fiber-optic technology that provides continuous temperature profiles along the length of a wellbore. Inside a coiled tubing (CT), installed as a retrievable or permanent cable, the DTS can be used to monitor the temperature evolution during a matrix treatment. This evolution, in turn, yields some indications about the fluid placement performance. So far, interpretation of such DTS traces has mostly been qualitative. This work presents a mathematical model that can be used to predict and interpret DTS data and other downhole measurements such as pressure, to quantify the intake profile of the treatment fluid along the wellbore. A recent field case of a matrix acidizing treatment is presented as an example.

Introduction
Poor zonal coverage during chemical treatments usually means poor later performance of the well, and ultimately, loss of production and reduced access to reserves. One of the keys to improving the quality of such jobs is the ability to assess treatment efficiency before the treatment is pumped and to learn lessons from previous operations. The method described here enables the prediction and determination of zonal coverage and contributes to maximizing the value of chemical treatments.
The 1990s saw the beginning of fiber optics deployment to log temperatures along the full length of the well, at highfrequency time and space intervals, and without hardware movement, thus allowing engineers to pinpoint the time and position of temperature changes as they occur (Karaman, et al., 1996) (Brown, et al., 2002) (Brown, 2008). In (Brown, et al., 2000), DTS is shown to enable detection of flow behind casing, cross-flow during shut-in, and water breakthrough. In (Clancy, et al., 2002), cold fluid slugs are pumped downhole and tracked along the wellbore with DTS to infer production profile along long laterals and from each lateral. In (Brown, 2006), DTS data are shown to allow the monitoring of the zones pressure and GOR when combined with a near-wellbore thermal model. In (Sierra, et al., 2008) and (Glasbergen, et al., 2009), the use of DTS is proposed to monitor fluid placement in real time during injection. The analysis of DTS logs acquired during a postinjection shut-in has also been performed to estimate acid placement (Garzon, et al., 2010), and in real time (Cantaloube, et al., 2010). More recently, (Tardy, et al., 2011) proposed a quantitative methodology to transform DTS logs acquired during a postinjection shut-in into a zonal coverage log.
The scope of this work is to provide some models that are necessary to quantitatively assess how the observed downhole temperature changes relate to the fluid injection profile along the section of the well connected to the reservoir. While thermal models have long been studied and developed for oilfield applications (Prats, 1986) (Hill, 1990) (Maubeuge, et al., 1994) (Kaviany, 1999) (Hasan, et al., 2002), little attention has been paid to the specificity of matrix treatments, in particular with acids in carbonates. Recently, (Tan, et al., 2009) proposed a model to study temperature profiles during matrix acidzing of carbonate formations. Though this model shows some interesting temperature profiles specific to matrix acidizing, it does not elaborate on the complex wellbore heat transfer mechanisms, it ignores the effect of the acid-induced dissolution channels on the heat transfer between injected fluid and the formation and models the exothermic reaction in standard conditions only.
The model presented here encompasses an extensive set of relevant physical phenomena occurring in the matrix and in the wellbore (and in the CT if used) and data on the acid-rock exothermic reaction. With such a model, one can predict the temperature changes for a given situation and decipher the links between zonal coverage and temeparture profiles.