Mathematical Model for Liquid Loading in Natural Gas Well Production
Chapter One
Objectives of Study
The essence of an operation venturing into the oil and gas business is to maximize profit and minimizes cost (capital and operating cost) in a safe and economic way. Thus, the aim of this study is to develop a new mathematical solution for liquid loading detection in gas well. The following objectives will be met:
- Evaluate the discrepancies in previous model
- Validating the new model with field data and existing models
- A software approach using Microsoft Visual Basic.Net framework
CHAPTER TWO
LITERATURE REVIEW
The production of a gas well stops flowing prematurely as a result of the liquid loading which has a direct financial implication and inefficient use of resources. In order to overcome this challenge, it is pertinent to identify properly the inception of liquid loading. Hence, there are several models available today for predicting the inception of liquid loading in gas well which are presented in the subsequent paragraphs.
Shu et al. (2014) developed a new comprehensive model that is based on the Barnea (1986, 1987) model. For vertical wells, the new model can better predict the inception of liquid loading than the widely used Turner et al. (1969) equation. For deviated wells, it is observed in the field and in laboratories that liquid loading starts much earlier than in vertical wells, and most liquid-loading equations are not appropriate for deviated wells. The new model takes into account the nonuniform film thickness around the circumferential position of the pipe, and, thus, it improves the prediction of liquid loading in deviated wells. The new model is validated through the use of field data in the literature and experimental data obtained at the University of Tulsa. In addition to the literature data, a new set of field data is reported and used to validate the new model, which shows a significant improvement over the droplet model as well as other film models.
Duggan (1961) was the first to develop an approach to solve the liquid loading problem; he postulated that the gas velocity at well head should not be less than 15 ft/s (4.6 m/s) at the lowest test rate. Although the approach worked in a number of cases, it was often felt to be conservative and the criterion could not be adhered to; for example, low rate producers of which the well head velocity was already close to 15 ft/s at full flow. A more refined method and approach was presented by Turner et al (1969), they were the first investigators to develop mathematical model for analyzing and predicting the minimum gas flow rate to prevent liquid loading. The two models they postulated were; the film movement model and the entrained drop movement model.
On te basis of analysis of field data, they conclude that the film movement model does not represent the controlling liquid transport mechanism. This was because the velocity predicted to sustain liquid transported as a film coating the tubing wall to the surface is high which can only be applicable to high rate producers. Since at low gas rate liquid are still transported to the surface, the conclusion to this realization was that liquid film transport mechanism cannot be valid approach to predict minimum gas velocity required to continuously transport liquid droplets to the surface.
The conclusion from Duggan (1961) was basically based on empirical data, in an attempt to make an easy guideline to operators testing the well with routine well tests. This was later found not be generally applicable by Libson et al., (1980) who found that well with as high as wellhead velocities as 16 ft/s could cease from flowing. If the symptoms of liquid are recognized at early stages, loses in gas production that may eventually cost the life of the well may be avoided. A proper analysis of the decline curve of a gas well can be informative about down-hole flow problems of the well.
Coleman et al., (1991) proposed a new look at predicting load up without the 20% increase as proposed by Turner et al in the minimum gas flow rate, known as critical rate. They also stated that liquid-gas ratios below 3.6 of liquid per twenty eight thousand cubic meter of gas have no influence in determining the onset of load-up, meaning the gas flow rate is the dominant factor. Nosseir et al., (2000) suggested a new approach for accurate prediction of loading in gas wells under different flowing conditions. Figure 2.1 & 2.2 show the result of Coleman’s data on Turner’s and Barnea’s models.
CHAPTER THREE
METHODOLOGY
This chapter presents the development of the new mathematical model for to predict the inception of liquid loading in a gas well with an assumption that both drag and buoyancy forces are predominantly acting on the gas particles. This model looks at the critical velocity and rate at which liquid loading starts accumulating. The work flow for this study is given in Figure 3.1. Also, some of the existing models for liquid loading prediction are presented to validate the new model developed in this study with a typical field data.
New model development for inception of liquid loading
There are three forces acting on a particle moving through a fluid:
- The external force, gravitational or centrifugal;
- The buoyant force, which acts parallel with the external force but in the opposite direction;
- The drag force, which appears whenever there is relative motion between the particle and the fluid and this force acts in the direction of flow exerted by the fluid.
Mathematically, the forces acting on a settling particle are:
CHAPTER FOUR
RESULT AND DISCUSSION
In this study, data from a typical XY Niger Delta field was used as a case study to validate the model developed with measured data and existing models that are widely used in the oil and gas industry today. The fluid properties obtained from three sources which were reservoir, wellhead and separator conditions given in Table 4.1.
CHAPTER FIVE
CONCLUSION AND RECOMMENDATION
Conclusion
Liquid loading occurs in gas wells when the produced gas velocity is less than the droplet critical velocity at well-head conditions. The results (Table A1) obtained from this study shows that the best region to evaluate the minimum gas velocity require to prevent the inception of liquid loading is at the wellhead conditions. Thus, the minimum flow conditions necessary to lift the accumulated liquid in the wellbore from the gas wells are provided by the gas velocity sufficient to remove the largest droplet of liquid that can exist which can be calculated using any of the models in this study.
Turner’s model was only able to match the field data after 20% adjustment to the initial model but the model developed for this study does not need any adjustment.
Furthermore, it can also be concluded that the critical gas velocity is independent of pressure and flowing area or diameter of the conduit and the gas velocity depends on density, temperature, interface tension, pressure and conduit diameter thus affecting the distribution and size of droplets.
Above all, in comparison of the minimum, maximum and standard deviation of the percentage relative errors using Turner et al, the new model gave the least of all models in all the conditions
Recommendation
- The model developed in this study can be modified to match field data as that done by Turner’s et al by increasing the origin model by 20%.
- The effect of impurities in the entrained liquid need to be investigated which could be paramount in determining the critical gas rates for low-pressure gas stripper wells.
References
- Barnea, D. (1987) A unified model for predicting flow-pattern transition for the whole range of pipe inclinations, International Journal of Multiphase Flow, Pg 13
- Belfroid, S.P.C., Schiferli, W. Alberts, G.J.N., Veeken, C.A.M. and Biezen, E. (2008), Prediction Onset and Dynamic Behavior of Liquid Loading Gas Wells, paper SPE 115567 presented at the 2008 SPE Annual Technical Conference, September 21‐24
- Coleman, S.B., Clay, H.B., McCurdy, D.G. and Norris III, H.L. (1991), A New Look at Predicting Gas‐Well Load‐Up, paper SPE 20280, JPT (March 1991)
- Duggan, J.O. (1961), Estimating Flow Rates Required to Keep Gas Wells Unloaded, Journal of Petroleum Technology, SPE 1173-1176.
- Hassan, A.R., (2007), A Basic Approach to Wellbore Two-Phase Flow Modeling, SPE 109868.
- Hinze, J.O. (1995), Fundamentals of the Hydrodynamic Mechanism of Splitting in Dispersion Processes, AIChe Jour. No. 3, 289
- Lea, James F. and Nickens, Henry V. (2004), Solving Gas‐Well Liquid‐Loading Problems, paper SPE 72092, Distinguished Author Series, JPT (April 2004)
- Libson, T. N., and Henry, J. T., (1980), Identification of and Remedial Action for Liquid Loading in Gas Wells-Intermediate Shelf Gas Play, Journal of Petroleum Technology.