# Volumetrics

Volumetrics is a static measurement based on a geologic model that uses geometry to describe the volume of hydrocarbons in the reservoir. Volumetrics, volumetric estimation, is currently the only way that is available to assess hydrocarbons-in-place prior to drilling. The purpose of calculating a volumetric estimation is to evaluate a reservoir and calculate the potential reserves of the reservoir in question. Once drilling has started pressure and production data is collected giving a greater insight into the volume that needs to be evaluated. To conduct volumetric estimation geoscientists must use any data they have collected such as cores, logs, seismic and other surveys to:

- Determine the depositional environment
- Identify structural features
- Identify traps
- Determine fluid interactions

## Contents

##### Purpose of Volumetric Calculations:

The data collected is used to:

- Estimate the volume of subsurface rock that contains hydrocarbons.
- Determine the weighted average of the effective porosity.
- Obtain a water resistivity value and calculate water saturation.
- Estimate if the reservoir is economical.

Volumetrics is an integration of geological, fluid and the modeled relationships. An overview of the interactions between the different variables is displayed in the flow chart below:

^{[1]}

## Equations:

There are a number of equations that can be derived for a volumetric calculation of a reservoir. Since calculating a reservoirs volume is dependent on the reservoir properties such as volume, porosity and fluid saturation there are a number of different equations. There are original hydrocarbon-in-place calculations that are specifically for absorbed gas in shale reservoirs, coalbed methane reservoirs, and many more scenarios. Below are the general equations for original oil-in-place and original gas-in-place.

### Original Oil-In-Place:^{[2]}

Original Oil-in-place refers to the total volume of oil stored in a reservoir prior to production.

#### Metric Calculation:

##### Variables:

- Rock Volume (m
^{3}) = 10^{4}* A * h - A = Drainage Area, Units: Hectares (1 ha = 10
^{4}m^{2}) - h = Net Pay thickness, Units: Meters
- ∅ = Porosity which is the fraction of a rock volume that is void space that is available to store fluids.
- S
_{w}= Water Saturation which is the volume fraction of the porosity that is filled with interstitial water. - B
_{oi}= Oil formation volume factor, which is a factor for the change in the oil volume between the reservoir conditions and the standard conditions at the surface. Typically this is given with respect to a specific pressure. Units: pressure, p, bbl/STB - 1/B
_{oi}= Shrinkage, which is the volume change that the oil undergoes when brought to the surface. This is due to solution gas that is escaping out of the oil.

#### Imperial Calculation:

##### Variables:

- Rock Volume (acre-feet) = A * h
- A = Drainage Area, Units: Acres
- h = Net Pay thickness, Units: Feet
- ∅ = Porosity which is the fraction of a rock volume that is void space that is available to store fluids.
- S
_{w}= Water Saturation which is the volume fraction of the porosity that is filled with interstitial water. - B
_{oi}= Oil formation volume factor, which is a factor for the change in the oil volume between the reservoir conditions and the standard conditions at the surface. Typically this is given with respect to a specific pressure. Units: pressure, bbl/STB - 1/B
_{oi}= Shrinkage, which is the volume change that the oil undergoes when brought to the surface. This is due to solution gas that is escaping out of the oil.

### Original Gas-In-Place:^{[2]}

Original Gas-in-place refers to the total volume of gas stored in a reservoir prior to production.

#### Metric Calculation:

##### Variables:

- Rock Volume (m
^{3}) = 10^{4}* A * h - A = Drainage Area, Units: Hectares (1 ha = 10
^{4}m^{2}) - h = Net Pay thickness, Units: Meters
- ∅ = Porosity which is the fraction of a rock volume that is void space that is available to store fluids.
- S
_{w}= Water Saturation which is the volume fraction of the porosity that is filled with interstitial water. - T
_{s}= Base Temperature at standard conditions which is °Kelvin (273° +15°C) - P
_{s}= Base Pressure at standard conditions of 101.35 kPaa - T
_{i}= Formation Temperature in °Kelvin (273° + °C at the formation depth) - P
_{i}= Initial Reservoir pressure, Units: kPa - Z
_{i}= Compressibility at P_{i}and T_{i}

#### Imperial Calculation:

##### Variables:

- Rock Volume (acre-feet) = A * h
- A = Drainage Area, Units: acres (1 acre = 43,560 sq.ft)
- h = Net Pay thickness, Units: Feet
- S
_{w}= Water Saturation which is the volume fraction of the porosity that is filled with interstitial water. - T
_{s}= Base Temperature at standard conditions which is °Rankine (460° + 60°F) - P
_{s}= Base Pressure at standard conditions of 14.65 psia - T
_{i}= Formation Temperature in °Rankine (460° + °F at the formation depth) - P
_{i}= Initial Reservoir pressure, Units: psia - Z
_{i}= Compressibility at P_{i}and T_{i}

## Explanation of Variables:

### Rock Volume Calculations:

Rock volume calculations are used to obtain the rock volume of the reservoir in question. The reservoir volumes can be calculated using computerized means with geophysical processing software and by using net pay isopach maps and planimetering, measuring the area of a plane, by hand. In order to calculate volumes from the net pay isopach maps the areas between the contours are determined to allow for the determination of the volume of the reservoir rock. The volumes can be calculated using different mathematical area formulas.

### Net Pay:

Net pay is the portion of the reservoir that hydrocarbons can be produced economically with respect to the determined production method. This is determined by applying cut-off values that are determined due to the interactions between porosity, permeability, and water saturation, which are derived from well logs or offset well log information.

### Porosity:

Porosity values are determined as an average value over the entire reservoir or as a weighted average if multiple wells are available for a given area.

### Water Saturation:

Water saturation is the fraction of the pore space in a volume that is filled with water in the formation. The water saturation values are determined by taking an average value over the entire reservoir or by taking an average weighted thickness of the water saturation.

### Formation Volume Factor:

The formation volume factor is the ratio of the volume of hydrocarbons at in-situ, or at reservoir level, compared to the hydrocarbons at surface reservoir pressure and temperature. The formation volume factor is derived from the fluid composition, reservoir pressure (if known), temperature and depth. These values are usually estimated by offset wells.

## Limitations:

Volumetric estimates provide a static measure of the initial hydrocarbons in place. This means that the accuracy of these measurements are heavily dependent on the amount of data the geoscientist has available to them. In the early stages of development, the data of a potential reservoir is limited and the volumetric estimate is based on the accuracy of the parameters of:

- Gross Rock Volume
- Reservoir Geometry and Trapping
- Pore Volume
- Permeability
- Fluid Contacts

As the stages of exploration continue and drilling begins the accuracy of the volumetric estimation increases. The data collected during drilling gives a better representation of the properties downhole increasing the accuracy of the estimation. The uncertainty calculation with respect to volumetric calculations and is dependent on the limitations of each parameter in the equation is known as the Monte Carlo Analysis.

## Recovery Factor:

Volumetrics is a measurement based on a geologic model that uses geometry to describe the volume of hydrocarbons in the reservoir. Once the original hydrocarbons-in-place are calculated to further determine the economic feasibility and risk assessment of the reservoir the hydrocarbons-in-place is multiplied by a recovery factor. Given the volume of a reservoir is the product of the porosity and the hydrocarbon saturation, and if the area and thickness of the reservoir is larger there is the potential for larger oil and gas accumulation.^{[3]}

The recovery factor is dependent on the drive mechanisms which is the way in which the hydrocarbons will be produced. There are adopted values that the hydrocarbons-in-place are multiplied by to determine the estimated recovery of the reservoir. Typically there are limits to these recovery factors in respect to optimism from a poor producing reservoir to a high producing one.

## References:

- ↑ Pan, J. G.S., 2000, Integrated 3D seismic inversion and volume visualization for reservoir characterization and reserve estimation: SEG Technical Program Expanded Abstracts, January 2000, 1489-1492. https://doi.org/10.1190/1.1815688
- ↑
^{2.0}^{2.1}Dean, L., 2008, Volumetric Estimation in R., Mireault, and L. Dean, Reservoir Engineering for Geologists: Canadian Society of Petroleum Geologists Reservoir Magazine, 2011-14, accessed October 20, 2017: http://large.stanford.edu/courses/2013/ph240/zaydullin2/docs/fekete.pdf - ↑ Nwankwo, C. N., Ohankwere-Eze, M., and J. O. Ebeniro, 2015, Hydrocarbon reservoir volume estimation using 3-D seismic and well log data over an X-fields, Niger Delta Nigeria: Journal of Petroleum Exploration and Production Technology, v5, 4, 453-462, accessed October 20, 2017; http://rdcu.be/x3Dt