Conductive heat transfer is studied in the complex geometries encountered with partial buried and fully buried pipes. Both geometries can be simplified with conformal mapping. Since Laplace''s equation is preserved, an analytical steady state solution is obtained. Closed form solutions are also proposed that are practical for engineering applications. Transient heat transfer is considered when the conduction in the pipe wall is much higher than in the soil.
In an offshore subsea environment, pipeline embedment into the seafloor is a reasonably common phenomenon. Resulting from the action of currents, sediment deposition, wave action or settling, embedment of a pipeline can significantly impact the thermal description of the pipeline system in steady state and transient situations. Incorrect modelling of such situations at the design stage can impact both production availability and pipeline integrity of the production system. Until recently no robust analytical solutions for the situation of partially or shallowly buried pipe have existed, and therefore engineering judgement has been used along with appropriate margins to ensure conservative designs. This is true for both steady state and transient applications, but the transient scenarios have received even less attention in the literature with little or no analytical work being done. This is surprising since even in the steady state case the result of such conservatism can lead to practical implications such as poor thermal performance of cooling spools, overly conservative designs, uncontrolled lateral bucking of pipelines, accelerated top of line corrosion rates and many other design related issues. In the transient realm the implications may be even greater with erroneous prediction of cooldown times, pipeline thermal response or operational philosophies. While the context discussed here is appropriate for the oil and gas industry the issue itself is the same across the entire engineering domain.
Terrain or severe slugging has been observed operationally in a 5-mile long subsea oil tie-back when certain wells or combination of wells are flowed back to the platform through the test line. The flowlines have a downward incline to the base of the riser that enhances terrain or severe slugging. Under operating conditions with slugging, the tuned flow management tool failed to predict any slugging. Additionally, according to multiphase flow analysis with a commercial transient simulator during design studies, slugging was not predicted except for significantly lower flowrates and higher water cuts. Recent rigorous modelling highlighted significant differences to the resulted slugging predictions depending on the modelling approach and different versions of the tested simulator, OLGA®. Also the commercial transient simulator LedaFlow® was tested yielding similar results to OLGA® with same input parameters. Some slugging mitigation methods shown through modelling to mitigate slugging have been tested in the field without success. While the more rigorous modelling achieved better agreement with operating data, still poor accuracy was achieved. The inability to properly capture multiphase flow characteristics during the design phase of the project has led to an under-designed system and significant process upsets.
The accurate prediction of multiphase flow phenomena has been the topic of research for many years. Even though steady state conditions can usually be predicted with good accuracy, significant efforts are still being expended to model transient flow phenomena, such as various slug types and transient operating conditions, such as shut-downs, blowdowns, restarts, and ramp-ups. Accurate steady state and transient flow assurance analyses during early design phases are paramount to the further engineering of a subsea oil or gas project. Slugging inherently creates significant issues in the topsides process train due to large fluctuations in operating conditions.
Experiments for air-water flow with and without added foamers were performed in a 50 mm diameter 12 m long vertical pipe at ambient pressure. It was observed that adding foamers to water will lead to a lower pressure drop at superficial gas velocities below the transition limit from annular flow to churn annular flow (which is around 15 m/s) and at superficial liquid velocities between 0.5 and 2 cm/s. Visualisation of the flow with a high speed camera indicates that the decrease in the pressure drop is due to the more regular nature of the flow when the water is foaming: churning of the flow is suppressed by the foam. This is confirmed by the decrease of the pressure oscillations in the presence of foamers. These experiments give insight into why and how liquid loading in gas wells is prevented by the addition of foamers.
In a gas well, both liquids – in the form of water and gas condensate – and gas are produced. If the reservoir pressure is high, the gas velocity in the well tubing is sufficient to drag the liquids to the surface. However, near the end of field life when the reservoir pressure has depleted, the gas velocity becomes too low to transport the liquids through the well. The minimum gas velocity required to lift the liquids is called the critical velocity. When the gas velocity becomes lower than the critical velocity, liquid will start accumulating at the bottom of the well. This will generate a large hydrostatic pressure in the well, which severely limits the gas production. This process is called liquid loading (1). Most foamers used in gas wells foam only the water (2), but there also exist some condensate foamers (3). In this work, only a water-based foamer has been considered.