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"Modeling of reservoir temperature transients, and parameter estimation constrained to a reservoir temperature model" by Obinna Duru

The Alternating Conditional Expectations (ACE) technique was applied to temperature and rate signals from Permanent Downhole Gauges (PDGs) to establish the existence of a functional relationship between them.

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Performing energy, mass and momentum balances, reservoir temperature transient models were developed for singleand multiphase uids, as functions of formation parameters, uid properties, and changes in rate and pressure. The pressure field in oil and gas bearing formations are usually nonstationary.

This gives rise to pressure-temperature eects appearing as temperature changes in the porous medium when the pressure field is nonstationary. The magnitudes of these effects depend on the properties of the formation, geometry, time and other factors and result in a reservoir temperature distribution that is changing in both space and time.

In addition to establishing a representative model for the temperature distribution in the reservoir, reservoir and properties could be estimated in an inverse optimization problem.

Permanent downhole gauges (PDGs) provide a continuous source of downhole pressure, temperature and sometimes rate data. Until recently, the measured temperature data have been largely ignored. However, a close observation of the temperature measurements reveals that the temperature responds to changes in rate and pressure, which implies that the temperature data may be a source of reservoir information.

Numerical solution schemes as well as the semianalytical scheme - Operator Splitting and Time Stepping (OSATS) were used to solve the models, and the solutions closely reproduced the temperature profiles seen in real measured data. By matching the models to different temperature transient histories obtained from PDGs, reservoir parameters namely porosity and saturation and uid Joule-Thomson coecient could be estimated. The signiffcant contributions of this work include a method which:

 Utilizes temperature data measured by PDGs.

 Provides a way to estimate porosity and potentially saturation.

 May provide a less expensive substitute for downhole rate measurement.

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