Determining Rate Profile in Gas Wells from Pressure and Temperature Depth Distributions
Authors: Barrett E. , Abbasy I. , Wu C.-R. , You Z. , Bedrikovetsky P. 
Published: May 2016

Abstract
Gas flow profile along the wellbore is an important piece of information for reservoir and production management purposes, since it provides flow contribution from each producing interval along the wellbore, which is critical for optimizing well performance and maximizing recovery of reserves. Traditional methods are expensive, particularly in high temperature wells and involve running production logsging tools (PLT's) along with flowmeters. Deployment of production logging tools into a well can be operationally difficult and typically requires flow to be suspended temporarily to allow the tools to be run in hole. This can have a negative impact on the quality of data collected, potentially making it un-representative of normal producing conditions. A simple and effective method of the gas rate prediction from temperature and pressure data is discussed in this paper. Solving the inverse problem allows determination of the flow rate and thermal conductivity of the formation by matching the gas pressure and temperature distributions with measured profiles. The results of field data treatment show good agreement with the model prediction and are consistent with flowmeter (PLT) data. Besides, the approximate estimate from direct averaging using the measured data shows good accuracy of rate and thermal conductivity prediction.

Introduction
There have been plenty of papers in the literature on the depth distributions of pressure, temperature and flow rate along the wellbore. Regarding the pressure and temperature profiles, continuous measurement in a complex well can be obtained accurately and inexpensively, which is owed to the use of distributed pressure sensors (DPSs) and distributed temperature sensors (DTSs), an application of advanced technology of fiber optics.
Although the accurate production profiling is essential for completion and production performance evaluation and reservoir characterization, the direct flowmetering for the rate distribution along the well is still difficult and costly, especially for multiphase-flowing wells and complex well trajectories [1,2]. At present the spinner and wireline logging are used in the industry to make certain measurements and construct the flow profile across a series of producing intervals. Temperature and pressure logs can usually be acquired with less operational complications and at a relatively lower cost in most wells, however without a flowmeter, the industry has struggled to convert this data into a representative and unique description of flow contribution along the wellbore.
A number of researchers have reported their work on the rate estimation from measured temperature and pressure profiles [3–5]. However, the models aiming at flow profiling involving multiphase-flow or coupled reservoir-well flow are either complicated for engineering applications or dependent on additional information, e.g. reservoir properties.
This paper proposes an effective inverse problem solver derived from the first principles, to predict rate profile using the gas pressure and temperature data. This technique offers tremendous advantage where high temperature production logging is either unavailable or prohibitively expensive. A fast and explicit method based on measured well temperature and pressure profiles to estimate the flow rate and an extra parameter ? formation thermal conductivity is also presented. The initial values of rate and thermal conductivity for iterative minimization algorithm have been obtained by averaging the values directly calculated from the measured pressure and temperature profiles. The initial values as the approximate estimates are shown to provide the final solution with good accuracy.