# Determination Of Flowing Bottom-Hole Pressure From Well-Head Data

## Abstract

The number of gas injection or exploitation projects is on fast increase with growing energy needs and environmental problems. Of these projects, the calculation and the control of wellhead pressure or bottom-hole pressure in wellbores are usually key steps. However, methods used to predict wellhead and bottom-hole pressure are multifarious, making the program writing and practical application inconvenient. In this study, a unified formula derived from the differential equations of one-dimensional steady pipe flow and applicable in both injection wells and production wells was presented for calculation of both wellhead pressure and bottom-hole pressure.

The recalculation with a traditional numerical method of the same equations corroborated well the accuracy of the unified formula, and the positive- reverse checking calculation verified its reliability. Basic data from Shenhua CCS project were used for studying the influence of injected gas temperature, geothermal gradient and flow rate on wellbore pressure by applying the unified formula. The results can provide a technical guidance for practical operation.

## Table of Content

### Preliminary Page(s)

- Title page
- Approval page
- Dedication
- Acknowledgement
- Abstract
- List of table

### Chapter One

#### Introduction

- 1.1 Background Of Study
- 1.1.1 What Is Bottom Hole Flowing Pressure
- 1.1.2 Typical Flow Regimes
- 1.1.3 Vertical Multiphase flow
- 1.2 Statement Of The Problem
- 1.3 Aim And Objectives

### Chapter Two

#### Literature Review

- 2.1 Introduction
- 2.2 Determination Of Bottom-Hole Pressures

### Chapter Three

#### Methodology

- 3.1 Research Design
- 3.2 Basic equations and calculation method
- 3.3 Unified formula

### Chapter Four

#### Results And Discussion

- 4.1 Reliability Demonstration
- 4.2 Comparison with numerical method
- 4.3 Positive-reverse checking calculation
- 4.4 Influential Factors
- 4.5 Flow initial temperature and geothermal gradient
- 4.6 Flow rate

### Chapter Five

#### Summary And Conclusion

- 5.1 Summary
- 5.2 Conclusion
- References

## Chapter One

### Introduction

#### 1.1 Background Of Study

Interpretation of data from Well test analysis has been based on the implicit assumption that the reservoir is a homogeneous single layer. However, the real petroleum reservoir, is a composition of layers with unique interlayer characteristics. The individual layers are usually separated from each other by an interface which could be either permeable or impermeable. Pressure behavior in this kind of vertically heterogeneous system is not necessarily like that of a single layered system and seldom reveals more than the average properties of the entire system. It is against this backdrop that this study became necessary.

Well completion in such systems would be more instructive, enabling better reservoir and production engineering practice if detailed layer information is available at it prime. The petroleum industry is however interested in accurately calculating the pressure losses that occur for multiphase flow in the tubing and pipelines. Accurate predictions of pressure losses in pipes would enable proper design. Also, pressure determination in a production system in the petroleum industry is very important as it helps in the effective production of oil and gas from the reservoir but of all, the most important is the determination of flowing bottom-hole pressure as its knowledge helps in the determination of so many parameters needed for efficient production and also to avert early depletion of the reservoir. Its knowledge can also be used to prevent formation damage which could be caused by early sand production in the reservoir. Surface pressures often can be converted to bottom-hole values if adequate information is available about the wellbore system.

##### 1.1.1 What Is Bottom Hole Flowing Pressure

The pressure at the bottom of a working oil, water, or gas well (the Great Soviet Encyclopedia, 1979). The pressure measured in a well at or near the depth of the producing formation. For well-test purposes, it is often desirable to refer the pressure to a datum level chosen at a reference depth by calculating the pressure that would occur if the pressure measurement were made at the datum level rather than at the actual depth of the gauge (Schlumberger oilfield glossary). A knowledge of this pressure is fundamental in determining the most efficient methods of recovery and the most efficient lifting procedure, yet there is less information about these pressures than about any other part of the general problem of producing oil (Millikan and Sidwell, 1930).

As earlier said, the bottom-hole pressure can be determined from surface pressures like the well head pressure if adequate information is available about the production system which can be easily gotten from well testing operations (Economides, 1979). Since the well head pressure and parameters are easily gotten from pressure transient analysis whose success depends on the accurate measurement or estimation of bottom-hole pressure (Omohimoria and Ayodele, 2013), it is therefore desirable and necessary to obtain the bottom-hole pressure from these data. This will be carried out in order to further highlight the advantages which is associated with having adequate knowledge about the bottom-hole pressure of a reservoir.

##### 1.1.2 Typical Flow Regimes

At certain position and time in the reservoir different flow behaviors are usually encountered in the reservoir. This gives rise to different flow regimes. Flow regimes are usually classified according to the rate of change of pressure with respect to time and position.

###### Steady state

During steady-state flow, the pressure does not change with time. This is observed for example when a constant pressure effect, such as resulting from a gas cap or some types of water drive, ensures a pressure maintenance in the producing formation. Pressure usually will changes from one point to the other in the reservoir algebraicallyâ€¦1.1

###### Pseudo steady state

The pseudo steady state regime characterizes a closed system response. With a constant rate production, the drop of pressure becomes constant for each unit of timeâ€¦ 1.2

Where k is a constant. In practice, this can be reached more easily than the steady state.

###### Transient state

Transient responses are observed before constant pressure or closed boundary effects are reached. The pressure variation with time is a function of the well geometry and the reservoir properties, such as permeability and heterogeneity. It can be expressed mathematically asâ€¦â€¦â€¦ 1.3

Usually, well test interpretation focuses on the transient pressure response. Near wellbore conditions are seen first and later, when the drainage area expands, the pressure response is characteristic of the reservoir properties until boundary effects are seen at late time (then the flow regime changes to pseudo steady or steady state). The applications of the steady-state flow to describe the flow behavior of several types of fluid in different reservoir geometries are presented below. These include:

- Linear flow of incompressible fluids
- Linear flow of slightly compressible fluids
- Linear flow of compressible fluids
- Radial flow of incompressible fluids
- Radial flow of slightly compressible fluids
- Radial flow of compressible fluids
- Multiphase flow

##### 1.1.3 Vertical Multiphase flow

Much has been written in the literature regarding the multiphase flow of fluids in pipe. This problem is much more complex than the single-phase flow problem because there is the simultaneous flow of both liquid (oil or condensate and water) and vapor (gas). The mechanical energy equation is the basis for methods to estimate the pressure drop under multiphase flow; however, the problem is in determining the appropriate velocity, friction factor, and density to be used for the multiphase mixture in the calculation. In addition, the problem is further complicated as the velocities, fluid properties, and the fraction of vapor to liquid change as the fluid flows to the surface due to pressure changes.

Many researchers have proposed methods to estimate pressure drops in multiphase flow. Each method is based on a combination of theoretical, experimental, and field observations, which has led some researchers to relate the pressure-drop calculations to flow patterns. Flow patterns or flow regimes relate to the distribution of each fluid phase inside the pipe. This implies that a pressure calculation is dependent on the predicted flow pattern. There are four flow patterns in the simplest classification of flow regimes:

- Bubble flow
- Slug / Plug flow
- Churn flow
- Annular-mist flow

###### Bubble:

This type of flow was noted to occur at very low gas velocities. This type of flow is characterized by bubbles of gas moving along the upper part of pipe at approximately the same velocity as the liquid.

###### Slug / Plug Flow:

In this type of flow, the flow of liquid is basically restricted due to the amount of gases which evolve from the liquid phase and collage to form slug-like gas pockets. Like the bubbly flow, the liquid phase is the continuous phase but in this case, the gas phase overrides the liquid phase.

###### Churn Flow / Semi-Annular:

It is characterized by secondary currents set up by the velocity gradients in the liquid causing the liquids to climb the tube walls and, aided by waves, to coalesce at the top. The amount of liquid in the bottom of the tube was greater than at top and walls, hence the name semi-annular.

###### Annular:

This type of flow is characterized by liquid flowing in a thin film around the entire inside face of the pipe, the gas flowing at a high velocity as a central core. The liquid is flowing in a continuous annular rings, hence the name annular flow.

#### 1.2 Statement Of The Problem

A calculation method for predicting Bottom Hole Pressure (BHP) based on easily obtainable wellhead parameter has been the preferred method in the oil and gas industry. But the predictive capability of the existing correlations is a thing of concern to the oil industry operators. This is due to the inability of the existing models and correlations to account for the presence of sand particles in the flow stream; also, the requirement for the well to be shut-in for BHP predictions is counterproductive.

#### 1.3 Aim And Objectives

The aim of the project is to determine the flowing bottom-hole pressure of a vertical well from surface pressure and well parameters. This will be done by the modification of the general energy equation considering only the frictional pressure term. The modified equation (derived model) will be validated with a well data which will be gotten from a company.

The objectives of determining the flowing bottom-hole pressure of a well from well head pressure and well head data include the following:

- Efficient interpretation of the behavior of the underground system.
- Determination of BHP helps in provision of important information for efficient production, avert early depletion and early sand production in the reservoir.
- Determination of the most efficient methods of recovery and the most efficient lifting procedures.
- Determination of pressure losses in pipes and tubing for proper design of Artificial Lift Systems – Gas Lift, ESPâ€™s etc.
- Production Optimization – Identification of production bottlenecks, Gaslift optimization, and completion designs.

## Chapter Five

### Summary And Conclusion

#### 5.1 Summary

The fundamental differential equations of one dimensional pipe flow was studied in depth, based on which the equation of motion of gas was transformed to an ordinary differential equation about pressure considering the flow rate at any position of pipe is constant. Then, finite difference method was applied to solve the ordinary differential equation and four different formulas for node pressure were obtained according to corresponding calculation condition. Further, two sign variables were introduced to integrate them to a unified formula. A comparison with the traditional numerical method of solving ordinary differential equation was conducted, which validated the reliability of this new unified formula. And a positive-reverse checking calculation proves its correctness in relevant respect.

Basic data from Shenhua CCS project was used for influential factors studies. The wellbore pressure profiles of both injection and production wells under different flow initial temperatures and geothermal gradients were plotted. In order to analyze the influence of flow rate on wellhead and bottom-hole pressure calculation, the calculated pressures were plotted with increasing flow rate in both injection and production wells. The results can provide technical guidance for operation and site selection.

#### 5.2 Conclusion

The superiority of the unified formula is that it applies to calculate both wellhead pressure and bottom- hole pressure of both injection and production well, which greatly facilitates program writing and practical application. Besides, its derivation does not neglect acceleration term in equation of motion like previous methods, so it can apply to occasions where acceleration term is important. Moreover, the finite difference method used in derivation has specialties of little calculation and simplicity compared to traditional numeral methods. At the same time, the unified formula can be generalized to multiphase flow, horizontal and deviated wells.

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