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# Planimeter. Petroleum engineer Essay

Objective / aim

To analyze particle size distribution of a given sediment using a sieve shaker.

Theory

Petroleum reservoirs have the ability to contain precious hydrocarbons in the microscopic pores under geological formations and to transmit the fluids under certain driving forces.

One of the core roles and responsibilities of a reservoir engineer is to make a good estimation of the hydrocarbons in place in a reservoir. That is, he must be able to determine the Oil Initially In Place (OIIP) and the Gas Initially In Place (GIIP). Many factors have to be carefully considered and the one discussed in this lab is the Bulk Rock Volume and how it is acquired.

Bulk rock volume is really the gross rock volume of rock above any hydrocarbon-water contact. It can be determined by mapping and correlating contour maps of the given area. The net-to-gross ratio is then calculated to determine the proportion of the area that contains reservoir rocks. The bulk rock volume multiplied by the net-to-gross ratio gives the net rock volume of the reservoir.

Next, the net rock volume multiplied by porosity gives the total hydrocarbon pore volume. The summation of these volumes will give the OIIP and GIIP for a given exploration prospect and will allow explorers and commercial analysts to determine whether a prospect is financially viable.

The methods most commonly used are volumetric methods, material balances methods and decline curve methods. This lab discusses the volumetric method using a planimeter. This is a drafting instrument used to measure the area of a graphically represented planar region. The region being measured may have an irregular shape, making this instrument versatile.

A planimeter measures the area of a plane figure as a mechanically coupled pointer traverses the perimeter of the figure. Swiss mathematician Jakob Amsler-Laffon built the first modern planimeter in 1854, but since then many versions have been manufactured and are even used on Android phones today. Its use is not limited to measuring bulk rock volume of reservoirs; its other uses include measuring for road repairing, roofing and range finder applications.

In petroleum engineering, planimeters are primarily used for the purpose of calculating the bulk rock volume of a potential reservoir to determine if it contains commercially viable quantities of hydrocarbons.

The planimeter readings are input into the following equations:- •The Trapeziodal Rule which states that
Bulk Rock Volume = h/2[A1 + 2A2 + 2A3 + 2A4 + 2A5] + [TMAX/2]A5

And

•Simpsons Rule which states that
Bulk Rock Volume = h/3 [A1 + 4A2 + 2A3 + 4A4 + A5] + [TMAX/2]A5

Ensuring that the correct unit is used for each variable, the unit for bulk rock volume is acft.

PROCEDURE

RESULTS

Perimeter (ins)Area (ins2)
13.7214.05
Contour 212.3111.26
Contour 310.277.77
Contour 48.335.05
Contour 55.402.05

CALCULATIONS

These calculations are shown in the table below:

Perimeter (ins)Area
(ins2)Area
(acres)
Contour 1 (A1)13.7214.052.23 x 10-6
Contour 2 (A2)12.3111.261.79 x 10-6
Contour 3 (A3)10.277.771.24 x x 10-6
Contour 4 (A4)8.335.058.03 x 10-7
Contour 5 (A5)5.402.053.26 x 10-7

The following data was also given:
T max= 7ft
h= 10ft

To calculate the average bulk reservoir volume (BRV) the following were used: 1. Trapezoidal Rule:
BRV = h/2[A1 + 2A2 + 2A3 + 2A4 + A5] + Tmax/2]*A5

2. Simpsons Rule:
BRV= h/3 [A1 + 4A2 + 2A3 + 4A4 + A5] + [Tmax/2]*A5

Hence the following values were calculated:
1. Using the Trapezoidal Rule, the bulk rock volume was calculated to be 5.24 X 10-5 acft

and
2. Using Simpsons Rule, the bulk rock volume was calculated to be 5.26 x 10-5 acft

DISCUSSION

The data was input into the two formulas and the bulk rock volume was calculated using both the Trapezoidal Rule and Simpson’s Rule. The layer volume was calculated by computing the average area of the layer from the top and bottom layer and then multiplying the average area by the layer thickness of the ispoach map.

Because isopach maps always have smaller contour areas as the thickness increases, these rules, though accurate, always slightly overestimate the reservoir volume.

The difference in the two results for the bulk rock volume calculations were about 0.02 x10-5 acft. While this difference may appear to be a minor one, it would actually be quite significant to a reservoir engineer and will have to be taken into account in a practical environment as it may greatly affect forecasting figures.

One reason for this difference is the fact that the number of intervals used in this fractured reservoir was 3, which is an odd number. When using the Simpson’s Rule an even number of intervals should be used to increase the accuracy of the calculation.

One source of error is attributed to the fact that the planimeter must be moved freehand over the contours and any slight jerking movement could affect the accuracy of the reading.

After the discovery of commercially viable quantities of hydrocarbons, many decisions have to take place to ensure its safe and cost-efficiently recovery. The life of a well can be broken down into 5 stages: planning, drilling, completion, production and abandonment.

During the planning stage, engineers decide where and how to drill holes using complex equipment. The drilling phase encompasses the use of pipes, cements, casing and careful calculations to ensure that all equipment and materials are properly placed. Completion is the stage where the well is enabled to produce the hydrocarbon.

After this, the production stage is initiated. This stage focuses on extracting the hydrocarbons in a controlled way without damaging the formation. Production wells are drilled and completed in strategic positions. 3D seismic is usually available by this stage to target wells precisely for optimal recovery. Sometimes Enhanced Oil Recovery methods such as the use of steam injection and pumps are used to extract more hydrocarbons or to redevelop abandoned fields.

Finally, when a well is deemed to be no longer finallcially viable, it is abandoned in a safe manner. Cement plugs are placed and tested across any open hydrocarbon-bearing formations, casing shoes and freshwater aquifers.

CONCLUSION

The area of a reservoir structure from a given structure contour map was determined using a planimeter.

The volume of this reservoir was calculated to be:

•5.24 X 10-5 acft (using the Trapezoidal Rule)

And

•5.26 x 10-5 acft (using Simpsons Rule)

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