Model for Transient Temperature and Pressure Behavior in Commingled Vertical Wells

Abstract

Multilayer transient testing is designed for determining individual layer properties (permeability and skin) for multiple layers commingled in a well. Traditional multilayer transient testing requires a combination of rate profiles from production log and transient rate and pressure measurements acquired at multiple surface rates. This method can be time consuming and may involve significant errors depending on the accuracy of the transient flow rate measurements. Today, many wells are equipped with downhole sensors that provide distributed or multipoint temperature measurements along the wellbore. Using these data to determine formation properties can minimize time and disturbances in well production. This paper presents a forward model to investigate the possibility of evaluating formation properties from transient temperature and pressure measurements. The model couples wellbore and reservoir models for simulating transient temperature and pressure for single-phase flow. The wellbore model was developed based on mass, momentum, and energy balance. The reservoir model consists of a reservoir thermal model and a pressure/flow-rate transient model. Besides heat conduction and convection, it considers viscous heating and temperature variation due to fluid and rock expansion/compression. Wellbore and reservoir models are solved numerically to predict transient temperature and pressure behavior. Comprehensive experiments reveal the sensitivities of transient temperature to individual layer permeability and skin values in multilayer systems. The results indicate that there are two main mechanisms governing wellbore transient temperature behavior; formation heating/cooling and wellbore fluid mixing at entry points, and that permeability and skin affect transient temperature and pressure differently. Examples in the paper show that the transient temperature response can distinguish between low permeability and high skin factor as reasons for low productivity in any layer. Additionally, this work revealed that the transient temperature behavior is sensitive to the radius of the damaged zone, suggesting for the first time a mechanism to quantify the damaged radius. The observations show promise of using transient temperature and pressure to determine multilayer formation properties. Introduction Multilayer formation properties are necessary information for reservoir development. Distinct layers in multilayer reservoirs usually have different thickness, porosity, permeability, and skin factor that tend to cause differential depletion during reservoir development. Therefore, multilayer reservoir characterization has been attracting interest for many years. Since the first rigorous mathematical model derived by Lefkovits in 1961, there have been numerous studies of the behavior of multilayer reservoirs. A complete literature review of the analytical model developed between the 1960s and the 1980s can be found in Ehlig-Economides (1987a). This study showed that individual layer properties in multilayer reservoirs cannot be determined from conventional drawdown or buildup tests. Kuchuk et al. (1986) introduced a quantitative modeling and testing technique combining stabilized rate profiles with transient rate and pressure measurements described briefly in Ehlig-Economides (1987b) as "layered reservoir testing". The layered reservoir testing" models have been enhanced by some authors (Kuchuk et al., 1991; Spath, 1994; Larsen, 1999; Prats, 1999), and the testing method has proven effective during the past two decades. However, a series of step-wise surface rate changes are still required during the test, with the production logging tool stationed above each layer to be characterized to record the transient rate variations during each rate step. This method is time consuming and may involve significant errors depending on the accuracy of the transient flow rate measurements.

Sustaining Production by Managing Annular-Pressure Buildup

“…Rate validation in integrated-asset modeling is a case in point. In contrast, temperature measurements have not found routine usage, but are gaining increased attention in connection with transientpressure testing (Sui et al 2008;Duru and Horne 2008;Izgec et al 2007;Hasan et al 2005;Kabir et al 1996), downhole flow profiling Nath et al 2007;Johnson et al 2006;Ouyang and Belanger 2006), and flow-rate estimation (Izgec et al 2009;Kabir et al 2008). This paper shows that both pressure and temperature responses at the tubinghead and annuli are strongly related to flow rates and that these measured values can be used to alert the operator of possible APB.…”

Temperature Transient Analysis for Characterization of Multilayer Reservoirs with Crossflow

“…Several recent studies attempted to investigate the potential of analyzing temperature measurements to characterize multilayer reservoirs. Sui et al (2008) presented a numerical model to evaluate the individual layer permeability and skin from transient temperature measurements of a commingled production well penetrating a multilayer gas reservoir. Under the condition of no layers communication, they found that the temperature response is sensitive to the damaged zone radius and permeability.…”

Novel Analytical Methods of Temperature Interpretation in Horizontal Wells

“…They relied on classical wellbore physical models 24,25,26 or on computational flow dynamics 27 . A recent model of a flowing compressible reservoir was used to show that the (simulated) temperature response could give detailed information on the near-wellbore structure 28 .…”

“…The analysis tools developed for this work required research on mathematical and numerical temperature description for wellbores 32,33 and flowing reservoirs 28,34,35,36 . The complexity of the supporting equations dictated that reservoir temperature models were solved for either the steady-state 34 or pseudo-steady-state 36 situations (with reservoir heat transfer coefficients (HTC) taken from other studies).…”