To date, several mathematical models, empirical correlations and physical mechanisms have been developed within TUHFP. These models range from predicting hydrate flow properties, hydrate slurry flow patterns, hydrate displacement in jumper/riser geometry to hydrate plug dissociation using THIs or DEH.
4-Layer Flow Model
The model may be used to predict friction pressure losses in horizontal and near horizontal flowlines. Also the model predicts thicknesses of the different layers – gas, solid and liquid, moving bed and stationary bed. The model is based on solid-liquid-gas flow under stratified or dispersed conditions. In the model, each phase is treated separately and continuity and momentum equations for each phase/layer are solved. Three possible flow patterns for the solids distribution in the liquid phase are considered: heterogeneous flow, flow with moving bed and flow with stationary bed. Moreover, a modification to the viscosity of the liquid phase using the Camargo and Palermo (2002) model is included. Inputs for the model are the fluid properties, pipe geometry, fluid velocities, solids concentration and either the aggregates diameter or the adhesive force used in the Camargo and Palermo model to predict the aggregates diameter. These two latter parameters are used to tune the model to the experimental data.
2-D DEH Model
In an effort to develop a new model that can integrate the capabilities and eliminate the shortcomings of existing dissociation models, a FORTRAN-based one-dimensional (radial) and a pseudo two-dimensional (radial and axial) model were developed for this work. The developed model can simulate the hydrate dissociation phenomenon with emphasis on estimation of pressure buildup before (due to thermal expansion) and during hydrate dissociation under quiescent conditions. Simulation results were qualitatively (1-D and pseudo 2-D model) and quantitatively (1-D model) compared with existing models and data available in the literature. This model may serve as a tool to simulate possible worst-case scenarios and to evaluate the magnitude of risk perceived with hydrate dissociation by DEH for a given flowline under given field conditions. While the 1-D simulations are used for sensitivity studies and estimation of hydrate dissociation period, which can be useful in devising remediation strategies, a working 2-D model can help estimate the risk involved in hydrate remediation by DEH.
Inhibitor Dissociation Models
The purpose of this model is to predict the plug dissociation time with the inhibitors without any fitting parameters. To date, two dissociation models are complete, one for liquid inhibitors and another for gaseous inhibitors. The two inhibitors considered so far are nitrogen and MEG. Both dissociation models employ Fourier’s law of conduction in the radial direction to solve for the temperature profile along the pipe radius and convective mass transfer equations in the axial direction for multi-component systems to estimate the inhibitor concentration profile along the plug length. An Excel VBA code is available as well. The two models were linked with the thermodynamic software PVTsim 19.0 to obtain the hydrate properties and a dissociation temperature look-up table. Sensitivity analyses were performed for both models to check if the models predict the results as they should. The model results were compared to experimental data and the model-predicted dissociation times are about 0.8 to 2.2 times the experimental dissociation times. These models can serve as tools to the field engineers in devising a plug remediation strategy.
Transient Hydrate Displacement Model
Efforts in this area have led to the development of 1-D (OLGA), 2-D and 3-D (CFD) models. Simulations using 1D transient multiphase flow simulator OLGA were conducted to evaluate its capacity to predict the thermodynamic inhibitor dispersion by using the inhibitor tracking module. Large discrepancy between OLGA simulation results and experimental data exits for low injection rate cases. 2D CFD simulations in FLUENT ® 6.3.26 help optimize the amount and flowrates of chemicals required as well as to optimize the location of the injection ports. The results are presented for the miscible displacement of THI in the jumper configurations. Comparisons were made between the simulation results and experimental data from full fresh water loading jumper displacement tests with MEG and methanol. Both 2D and 3D CFD simulations provide reasonable prediction for THI distribution along the jumper after displacement test, except that neither was able to reproduce methanol overriding water phase at both low spots. Results obtained by Star-CCM+ 3D generally gave better agreement with the results from the experiment.
Slurry Stability Map and Deposition Velocity Model
This model is used to generate a “stability flow map” for slurries showing the different flow regimes of the solids under the given flow conditions. The boundaries on the map are predicted using a set of critical deposition velocity models based on slurry rheology and slurry transporting conditions. The critical deposition model utilizes a more robust generalized 2-parameter rheology model to account for any given slurry rheology. The “stability flow map” demarcates the different flow patterns that may be observed at different mixture velocity and rheology. On this map, the homogeneous slurries are predicted at low rheology and high mixture velocity whereas heterogeneous slurries (with a concentration gradient) predicted at high rheology (yield stress effects). Sensitivity analysis was conducted on critical Reynolds number, particle density, carrier fluid density, generalized flow behavior index, and pipe diameter. It was observed that increase in shear thinning behavior, particle density, pipe diameter, and particle diameter led to a decrease in the laminar region and an increased unstable region. The model showed good performance when tested on glass and stainless steel beads test data available in open literature. The model was tested on hydrate slurries generated with additives at The University of Tulsa and the flow regime predictions were in good agreement with observations.
2-Layer Slurry Transport Model
A comprehensive mechanistic model was developed for hydrate slurry transportation in horizontal and near horizontal pipelines. Multiphase models are usually developed by solving the conservation equations together with the corresponding closure relationships. This model also takes into account the complex slurry rheology and particle concentration gradient effects. The liquid phase was modified to account for the presence of hydrates. Due to density differences, the slurry is assumed to be carried at the bottom and the gas (if present) at the top. The slurry constitutes the hydrate solids, water and oil (if present). The generalized two-parameter rheological model was used. A new friction factor for the dispersed slurries was developed accounting for complex rheology systems. The friction factor for flow systems with solid concentration gradient was determined experimentally and correlated to hydrate volume fraction. Over the past decade, extensive experimental work has been done at The University of Tulsa to investigate hydrate transportability. This huge database was used to evaluate the performance of the model. The evaluation, based on comparison between the measured and predicted pressure drops, demonstrated that the overall performance of this model is better than other models that do not account for rheology changes and particles concentration gradient.
