Let us discuss the two reasons related to reduction and ultimate reversal in temperature rise with time. The primary reason is that our model accounts for fluid heat loss to the overburden and under-burden formations. This heat loss increases with increased fluid temperature. Figure 5 shows the estimated fluid temperature using the rigorous model (solid lines) compared to that estimated assuming no heat loss (everything else remaining the same) to the formation (dashed lines). Note that the maximum temperature after 400 days of flow period is about 10 F higher when heat loss to the formation is not accounted for compared to when it is. Further analyses of ignoring fluid heat loss to the formation are discussed later.
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The proposed analytical solution also improves wellbore fluid and heat flow modeling because of more realistic temperature evaluation at sandface. The bottomhole flowing-fluid temperature derived from the analytical model can be coupled with wellbore heat transfer model to allow prediction of flowing-fluid temperature along the wellbore. Accurate flowing-fluid temperature profile along the wellbore is also desirable for well design and production optimization, as well as for pressure transient analysis (Onur and Cinar 2016). An accurate estimation of the reservoir fluid temperature from the analytical formulations can yield a better estimation of well productivity index, which is useful in production optimization and well development planning.
The advantage of this analytical model over other analytical solutions for reservoir temperature estimation is that heat transfer from/to overburden and under-burden formations \(\dotQ\) is included. While the derivation of the analytical solution neglects property variation, the use of the solution allows for property changes with pressure and temperature. We have shown that \(\dotQ\) is crucial in the estimation of flowing-fluid temperature in a reservoir, especially at long producing times when the reservoir fluid is heated significantly, and the reservoir fluid temperature is very different from that in its surroundings.
An important assumption in our model is that conductive heat flow for our problem is negligible. App and Yoshioka (2013) has shown that the effect of formation thermal conductivity can be represented by the Peclet number. Relating fluid velocity u to production rate q, App and Yoshikawa expressed P e as follows:
Similarly, for our highest production rate of 6200 STB/D, P e = 36.3. Therefore, for the cases considered in this study, omitting thermal conductivity of the formation does not introduce any significant error. We note that for most deepwater assets, economic production rates are expected to be high enough to result in correspondingly high Peclet numbers. As a consequence, the underlying assumptions made while deriving the analytical formulation of this coupled fluid and heat flow problem appear reasonable.
Abstract:CO2 fracturing has unparalleled advantages in the reservoir reform which can significantly improve oil and gas recovery in unconventional oil and gas resources. The wellbore flow behavior is one of the fundamental issues of CO2 fracturing. A model of flow and heat transfer in the wellbore is developed in this paper, and wellbore temperature and pressure are coupled using an iterative method. The model is validated by measured data from the field. Wellbore pressure, temperature, CO2 properties, and phase state along depth are observed and a sensitivity study is conducted to analyze the controlling factors for CO2 fracturing. Results show that displacement is the key factor affecting CO2 flow behavior in the wellbore and injection temperature has greater influence on CO2 flow behavior than injection pressure and geothermal gradient; however, excess injection temperature brings enormous cost in wellbore pressure. CO2 phase state is related to working parameters and it tends to stay in liquid state under higher displacement, which is matched with field tests. This study can help optimize the working parameters of CO2 fracturing.Keywords: Carbon dioxide fracturing; Wellbore flow model; Heat transfer; Phase state; Sensitivity analyses
A comprehensive coupled wellbore/reservoir simulator was developed to study the behavior of single-phase oil flow in the wellbore. The wellbore is modeled numerically where mass, momentum, and energy of the fluid are conserved, while the reservoir fluid flow is treated analytically. Energy transport occurs through tubulars, cement sheaths, and the formation by conduction. However, both conductive and convective heat-transport mechanisms are operative for the annular fluid. Heat losses through seawater and air are also modeled for a well producing in an offshore environment.
A sensitivity study shows that heat loss through seawater becomes significant for long submerged tubulars (> 2,000 ft), but is marginal for shorter pipes because of the fluid's short residence time. Further, a deviated well loses more heat to formation than its vertical counterpart for the same reason. Of the major variables, thermal conductivity of the annular fluid plays a key role in heat retention and, therefore, the wellhead temperature (WHT). We have identified the phenomenon of thermal storage. This storage behavior is associated with heat absorption or desorption by cement sheaths and tubulars and is reflected as the time taken to attain equilibrium WHT for a given flow rate. A longer storage period occurs at low flow rates because of lower associated fluid enthalpy.
Both the droplet-flow reversal and liquid-film-flow reversal have been postulated to be the underlying mechanism for liquid loading. Both mechanisms are predominantly premised on diagnosing the problem at the wellhead-flow conditions. This study explores the deliquefication issue in a gas well by fluid- and heat-flow modeling of the entire wellbore for a variety of flow situations in gas and gas/condensate reservoirs.
PROSPER is capable of modelling thermal profiles in wellbores using multiple methods, ranging from a constant rate of heat transfer (Rough Approximation) through to a detailed and rigorous full energy balance (Enthalpy Balance) that considers the forced and free convection, conduction and radiation heat transfer mechanisms. The latter considers a detailed materials specification, and to aid with this PROSPER has been furnished with a database of common casing, tubing, cement and mud descriptions with their associated heat transfer properties. Users can also take advantage of a hybrid thermal calculation technique that was developed by Petex (Improved Approximation). This allows for Joules-Thomson effects to be captured in the well, while at the same time enabling multiple heat transfer coefficients with depth to be used.
Dimensionless groups are useful in arriving at key basic relations among system variables that are valid for various fluids under various operating conditions. Dimensionless groups can be divided into two types: (a) Dimensionless groups based on empirical considerations, and (b) Dimensionless groups based on fundamental considerations. The first type has been derived empirically, often on the basis of experimental data. This type has been proposed in literature on the basis of extensive data analysis. The extension to other systems requires rigorous validation, often requiring modifications of constants or exponents. The convection number (Co), and the boiling number (Kf) are examples of this type. Although the Lockhart-Martinelli parameter (X) is derived from fundamental considerations of the gas and the liquid phase friction pressure gradients, it is used extensively as an empirical dimensionless group in correlating experimental results on pressure drop, void fraction, as well as heat transfer coefficients.
It should be noted that using of dimensionless groups is important in obtaining some correlations for different parameters in two-phase flow. For example, Kutateladze (1948) combined the critical heat flux (CHF) with other parameters through dimensional analysis to obtain a dimensionless group. Also, Stephan and Abdelsalam (1980) utilized eight dimensionless groups in developing a comprehensive correlation for saturated pool boiling heat transfer.
This dimensionless number was introduced by Shah (1982) in correlating flow boiling data. It was not based on any fundamental considerations. For example, based on more than 10 000 experimental data points for various fluids, including water, refrigerants, and cryogents, Kandlikar (1990) proposed a generalized heat transfer correlation for convective boiling in both vertical and horizontal tubes. One of the dimensionless numbers used in his correlation was the convection number (Co).
And represents the ratio of gravitational and viscous force scales. The Galileo number (Ga) is an important number in two-phase gas-liquid flow in determining the motion of a bubble/droplet under the action of gravity in the gravity-driven viscous flow. For instance, Haraguchi et al. (1994) expressed the condensation heat transfer coefficient in terms of Nusselt number as a combination of forced convection condensation and gravity controlled convection condensation terms. They expressed the gravity controlled convection condensation term as a function of the Galileo number (Gal).
In this dimensionless number, heat flux (q) is non-dimensionalized with mass flux (G) and latent heat (hlg). It is based on empirical considerations. It can be used in empirical treatment of flow boiling because it combines two important flow parameters, q and G. It is used as one of the parameters for correlating the flow boiling heat transfer in both macro-scale and micro-scale. For example, Lazarek and Black (1982) proposed the nondimensional correlation for the flow boiling Nusselt number for their heat transfer experiments on R-113 as a function of the all-liquid Reynolds number (Relo), and the Boiling number (Kf). Also, Tran et al. (1996) obtained a correlation for the heat transfer coefficient in their experiments on R-12 and R-113 as a function of the all-liquid Weber number (Welo), the Boiling number (Kf), and the liquid to vapor density ratio (l/g) to account for variations in fluid properties 2ff7e9595c
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