## I. INTRODUCTION

Offshore platforms especially wellhead platforms have test facilities and xoffloading facilities. These facilities to obtain composition and performance of well. This data will forecast the lifecycle stages of well. According to ISO 16530 delineates the stages of the lifecycle into six lifecycle phases, Basis of design, design, construction, operational, intervention, and abandonment.

The average life span of an oil or natural gas well is up to 20 or 30 years. However, new technologies are being developed to find new ways to extend the life span. The life span of a well is based on the active years the well is in production. ‘Active’ is one of the six main life cycle classifications of a well.

Offloading and test separator has several typical designs. One of the different designs of test separators is using MPFM. If the wellhead platform The offloading activities involve KO drum to collect the liquid during offloading process.

This article will try to estimate the liquid of estimated tubing volume well by using available instrument measurement on the KO Drum Vessel. This article will be focused on KO drum as offloading vessel. This article will limit only 2 phase vessels.

## II. OFFLOADING

Offloading a Well is a technique in which borehole pressure is reduced from a borehole in order to cause the suction of hydrocarbon fluids into the wellbore from perforations made in the casing. This is made possible by the creation of a partial vacuum by the removal of air so as to force the hydrocarbons into the vacant space, thereby initiating a flow of liquids from a well.

Offloading could be perform via Test Separator Vessel or Knock Out (KO) Drum.

Individual performance of well reservoir in wellhead platform is tested either using Multiphase Flow Meter (MPFM) or Test Separator. Therefore, test separator is part of offloading process besides as well individual test.

The test system on the platform will consist of a test manifold and an MPFM/Test Separator. Flow from each well can be diverted from the production manifold to the test manifold by changing the position of the On-Off valves located upstream of the production and test manifolds.

Incase MPFM is utilize to simultaneously measure the flow rate of each phase of fluid coming from a well., KO drum is used as part of Offloading process where it capture liquid if the wellhead platform utilize MPFM.

The test manifold will be utilized during both test and offloading; during test, the fluid will be sent to the MPFM and then to the Export Trunkline, while during offloading the fluid will be sent to the Vent/Flare.

## III. VOLUME VESSEL BASIC THEORY

**III.1. ELLIPSOIDAL HEAD**

For pressure over 10bar, ellipsoidal heads are often used. This is also called a 2:1 elliptical head. The shape of this head is more economical because the height of the head is just a quarter of the diameter. Its radius varies between the major and minor axis.

**III.2. HEMISPHERICAL HEAD**

A hemispherical head is the strongest shape; capable of resisting about twice the pressure of a tori spherical head of the same thickness. A sphere is an ideal shape for a head, because the pressure in the vessel is divided equally across the surface of the head. The radius (R) of the head equals the radius of the cylindrical part of the vessel.

**III.3 TORISPHERICAL HEAD**

A tori spherical shape, which is extensively used as the end closure for a large variety of cylindrical pressure vessels. These heads have a dish with a fixed radius (CR), the size of which depends on the type of torispherical head. The transition between the cylinder and the dish is called the knuckle. The knuckle has a toroidal shape.

The complexity of volume cylinder calculation depends on the plane layout cylinder. The horizontal plane position will be more complicated than the vertical plane.

The volume of a vertical cylinder is an area of the circle multiply by the height cylinder.

Cylinder Volume = pi() x ID^{2}/4 x h, where pi()=3.14 ………………………(1)

In the example, there is no shape of the head. If the head appears whether elliptical or hemispherical. Then the volume is added to the cylinder volume.

The horizontal will be different from the vertical. The horizontal cylinder will depend on the segment circular

It will give a totally different equation if the cylinder arrangement is horizontal. When the position is horizontal the volume of liquid will depend on the segmented circle. So the volume of the horizontal cylinder = segment circle x length of the cylinder.

Total heads volume (Hemispherical) = 2 x pi() x ID^{3}/12 ……………………..(2)

or

Total Heads Volume (Elliptical) = 2xpi()xID^{3}/22.8 ………………………………(3)

Zc/Ze = h/ID ………………………………………………………………………………………(4)

Angle in radians = 2 x Atan(h/sqrt(2x(h x ID/2) – h^{2}) …………………………(5)

f(Ze)=(angle-sin(angle) x cos(angle))/pi( ) ……………………………………………..(6)

f(Zc)= (Zc/Ze)^{2} x (3-2 x(Zc/Ze)) …………………………………………………………(7)

Area, m2 = f(Zc) x pi() x ID^{2}/4 ………………………………………………………….. (8)

Partial Volume Cylinder, m^{3} = f(Zc) x tangent to tangent (L) ……………….(9)

Partial Volume Heads, m^{3} = f(Ze) x Total Heads Volume/2 ……………….(10)

Total Volume (horizontal) Cylinder=

Partial Volume Cylinder + Partial Volume Heads………………………………….(11)

In programming Unity PRO XL it looks like:

## IV. CALCULATION LIQUID of WELL

During the offloading, the amount of liquid of a specific well could be determined by the following equation general mass balance.

Based on the general mass balance

(V_{in} – V_{out})/dt = dV/dt

V_{in}/dt = dV/dt + V_{out}/dt

V_{out}/dt is measured by a Coriolis flowmeter using a totalizer.

dV/dt is displacement volume.

dt is period of start offloading and stop offloading

As the configuration above, there are several cases to calculate the volume of liquid in the vessel. It depends on the instrument sensor available on the vessel KO drum.

There are two ways to calculate

- Manual Calculation

The manual calculation is performed by observation and data record. Data gathered will be further input into a spreadsheet.

The volumetric flow rate of inlet liquid could be calculated manually on a spreadsheet or automatically by the operation team.

- Automated using PLC

The automated calculation is using program PLC, by pressing start and stop push button on HMI.

## IV. 1 Volumetric Flow Rate Outlet

The interval time could be determined from level LAL as start pump and LAH as stop pump.

Using totalizer from Coriolis flowmeter. This method usually accesses by an operator on the display of the Coriolis menu. It requires operator intervention.

Before starting the totalizer it should be reset. The additional feature start-stop totalizer from the control room or local HMI (platform) is not giving major advance since activity offloading requires a standby operator. Start and stop automatically will give a better estimation of period offloading.

Instead of using analogue 4-2-mA to retrieve volumetric flow rate, the Coriolis should use serial (RS-485) connection as slave and master to the PLC. PLC could send command start and stop.

If creating a connection requires a cost, the totalizer could be created on the PLC program.

The other schematic could be as bellow

If the flowrate as seen above. Totalizer is created on the PLC program. Most of PLC have function totalizer on the libraries.

The method is same, start and stop totalizer is control by liquid level.

## IV. 2 Displacement Volume of Vessel KO Drum

Displacemnt Volume is calculated using level measurement – Average height liquid in certain interval time.

- Pump is start automatically in low level
- Pump is stop automatically in high level.

By conversion of volume, volume displacement as stated in equation …(11)

The equation could be put on the PLC in order to synchronize the start totalizer on outlet vessel KO drum.

## IV.3 Volumetric Flowrate Inlet as Volume Tubing

Since volumetric flowrate and displacement volumetric flowrate have been determined, they can both be programmed in PLC.

Volumetric flowrate inlet represents the amount of liquid (volume tubing)in a certain well during offloading.

V_{in}/dt = dV/dt + V_{out}/dt

Vin = ( Total Volume (horizontal) Cylinder + Totalizer recorded) x period offloading (period of start and stop offloading)

## V. Reference

https://wumbo.net/formula/volume-of-cylinder/

https://petrowiki.spe.org/Well_integrity_lifecycle

https://www.mathsisfun.com/geometry/cylinder-horizontal-volume.html