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Following is a brief description of the range of volume calculation techniques used. This discussion uses a grid-based system, although similar procedures could apply to triangulated or other systems. The discussion assumes that volumes are calculated within a bounding area (polygon).

Following is a brief description of the range of volume calculation techniques used. This discussion uses a grid-based system, although similar procedures could apply to triangulated or other systems. The discussion assumes that volumes are calculated within a bounding area (polygon).

[[file:using-and-improving-surface-models-built-by-computer_fig18.png|thumb|{{figure number|18}}The cell is centered on the grid node and lies either inside or outside the polygon. The cell's area is multiplied by its z value (thickness) and that volume is added to volumes for all other cells inside the polygon.]]

[[file:using-and-improving-surface-models-built-by-computer_fig18.png|thumb|left|{{figure number|18}}The cell is centered on the grid node and lies either inside or outside the polygon. The cell's area is multiplied by its z value (thickness) and that volume is added to volumes for all other cells inside the polygon.]]

====Volume by point count====

====Volume by point count====

Grid nodes will fall either inside or outside the polygon of interest. Statistics can be generated for the nodes that fall inside the polygon. Those statistics and the following equation are used to determine volume:

Grid nodes will fall either inside or outside the polygon of interest. Statistics can be generated for the nodes that fall inside the polygon. Those statistics and the following equation are used to determine volume:

<disp-quote>Number of nodes × Average value × ''x''-grid increment × ''y''-grid increment = Volume inside the polygon

<math>\text{Number of nodes } \times \text{ Average value } \times~x \text{-grid increment } \times~y \text{-grid increment} = \text{Volume inside the polygon}</math>

</disp-quote>This approach assumes that each grid cell extends from a base up to a flat top, which is the grid node's value, and that the node is in the center of the cell. If the center of the cell is inside the polygon, it is counted; if it is outside, it is not ([[:file:using-and-improving-surface-models-built-by-computer_fig18.png|Figure 18]]).

This approach assumes that each grid cell extends from a base up to a flat top, which is the grid node's value, and that the node is in the center of the cell. If the center of the cell is inside the polygon, it is counted; if it is outside, it is not ([[:file:using-and-improving-surface-models-built-by-computer_fig18.png|Figure 18]]).

[[file:using-and-improving-surface-models-built-by-computer_fig19.png|left|thumb|{{figure number|19}}The cell's corners are defined by grid nodes. The top is defined by two or more planes passing through the node z values and lie inside the polygon. The prism of volume under each plane is calculated and added to volumes for all other prisms inside the polygon.]]

[[file:using-and-improving-surface-models-built-by-computer_fig19.png|left|thumb|{{figure number|19}}The cell's corners are defined by grid nodes. The top is defined by two or more planes passing through the node z values and lie inside the polygon. The prism of volume under each plane is calculated and added to volumes for all other prisms inside the polygon.]]

====Volume by simple plane fits====

====Volume by simple plane fits====

Grid nodes occupy corners of grid cells, and a line is drawn diagonally across a cell dividing it into two triangles. The value at each corner of the triangle is known; therefore, a flat plane can be fit through these points. The base above which volumes are to be calculated is also a plane, and its value is known. Since the dimensions of the sides of the triangular prism are known from the grid increments, all of the information needed to calculate the prism's volume is available. The volume of all triangle prisms totally inside the polygon are calculated and summed. Any prisms partially within the polygon are subdivided into smaller prisms with the values at the corners of the smaller prisms linearly interpolated from the three original triangle corners. The volumes of these partial values are calculated, summed, and added to the volume of prisms totally within the polygon ([[file:using-and-improving-surface-models-built-by-computer_fig19.png|Figure 19]]).

Grid nodes occupy corners of grid cells, and a line is drawn diagonally across a cell dividing it into two triangles. The value at each corner of the triangle is known; therefore, a flat plane can be fit through these points. The base above which volumes are to be calculated is also a plane, and its value is known. Since the dimensions of the sides of the triangular prism are known from the grid increments, all of the information needed to calculate the prism's volume is available. The volume of all triangle prisms totally inside the polygon are calculated and summed. Any prisms partially within the polygon are subdivided into smaller prisms with the values at the corners of the smaller prisms linearly interpolated from the three original triangle corners. The volumes of these partial values are calculated, summed, and added to the volume of prisms totally within the polygon ([[:file:using-and-improving-surface-models-built-by-computer_fig19.png|Figure 19]]).

[[file:using-and-improving-surface-models-built-by-computer_fig20.png|thumb|{{figure number|20}}A mathematical surface is fit to the grid cell. Calculus is used to integrate the volume under the curve, inside the grid cell, and inside the polygon. All cell volumes inside the polygon are added together.]]

[[file:using-and-improving-surface-models-built-by-computer_fig20.png|thumb|{{figure number|20}}A mathematical surface is fit to the grid cell. Calculus is used to integrate the volume under the curve, inside the grid cell, and inside the polygon. All cell volumes inside the polygon are added together.]]

Political boundaries, [[porosity]] cutoffs, or other types of constraints must also be incorporated into the calculation. In some systems, these are incorporated into the model before going into the volumetrics program. In others, they are handeled automatically by the program.

Political boundaries, [[porosity]] cutoffs, or other types of constraints must also be incorporated into the calculation. In some systems, these are incorporated into the model before going into the volumetrics program. In others, they are handeled automatically by the program.

[[file:using-and-improving-surface-models-built-by-computer_fig21.png|left|thumb|{{figure number|21}}Thickness Is normally defined by grids representing the top and base of reservoir and the fluid contact(s).]]

 

 

 

[[file:using-and-improving-surface-models-built-by-computer_fig21.png|thumb|{{figure number|21}}Thickness Is normally defined by grids representing the top and base of reservoir and the fluid contact(s).]]

[[file:using-and-improving-surface-models-built-by-computer_fig22.png|thumb|{{figure number|22}}The gross hydrocarbon rock thickness is progressively reduced by net to gross ratio, average porosity, and oil saturation, until only the thickness of pores filled with hydrocarbon remains.]]

[[file:using-and-improving-surface-models-built-by-computer_fig22.png|thumb|{{figure number|22}}The gross hydrocarbon rock thickness is progressively reduced by net to gross ratio, average porosity, and oil saturation, until only the thickness of pores filled with hydrocarbon remains.]]

===Modeling and volume calculation in a thickness domain===

<def-item><term>HPT =</term> <def>hydrocarbon pore thickness, which is a surface model representing the thickness of hydrocarbons. This is integrated over the area of interest to determine hydrocarbon pore volume (HPV).

</def></def-item><def-item><term>GR =</term> <def>gross hydrocarbon rock thickness, which is a surface model representing total thickness of the interval containing hydrocarbons.

A typical goal when preparing models for input to a volumetrics program is to create one model that represents the thickness of hydrocarbons ([[:file:using-and-improving-surface-models-built-by-computer_fig21.png|Figures 21]] and [[:file:using-and-improving-surface-models-built-by-computer_fig22.png|22]]). This is done by solving the following equation:

</def></def-item><def-item><term>N: G =</term> <def>net to gross ratio, which is a model or constant representing the ratio of porous (pay) rock thickness to gross rock thickness.

:<math>\mbox{HPT} = \mbox{GR} \times \mbox{N:G} \times \mbox{PR} \times (1 - \mbox{SW})</math> where

</def></def-item><def-item><term>PR =</term> <def>average porosity, which is a model or constant representing the average porosity of the porous rock.

HPT = hydrocarbon pore thickness, which is a surface model representing the thickness of hydrocarbons. This is integrated over the area of interest to determine hydrocarbon pore volume (HPV). <br>

GR = gross hydrocarbon rock thickness, which is a surface model representing total thickness of the interval containing hydrocarbons. <br>

N:G = net to gross ratio, which is a model or constant representing the ratio of porous (pay) rock thickness to gross rock thickness. <br>

PR = average porosity, which is a model or constant representing the average porosity of the porous rock. <br>

</def></def-item><def-item><term>SW =</term> <def>water saturation, which is a model or constant representing the average water saturation.

There are many considerations when building each of these surface models.

</def></def-item>

[[file:using-and-improving-surface-models-built-by-computer_fig23.png|thumb|left|{{figure number|23}}The envelope technique is used to define one grid for the top of reservoir and another for the base of the reservoir. These are subtracted to create the gross hydrocarbon rock thickness.]]

 

There are many considerations when building each of these surface models.

====Building the GR model====

====Building the GR model====

To build a surface model for the gross hydrocarbon rock thickness (GR), we envelope the volume of interest by building one surface model for its top and another for its base. These surface models should cross where the volume goes to zero.

To build a surface model for the gross hydrocarbon rock thickness (GR), we envelope the volume of interest by building one surface model for its top and another for its base. These surface models should cross where the volume goes to zero.

The top of volume model is built by comparing all surface models that define part of the top of volume envelope (top-E), creating a single model that is the minimum of their values. Next, compare all surface models that define part of the base of volume envelope (base-E) and create a single model that is the maximum of their values (Figure 23).

The top of volume model is built by comparing all surface models that define part of the top of volume envelope (top-E), creating a single model that is the minimum of their values. Next, compare all surface models that define part of the base of volume envelope (base-E) and create a single model that is the maximum of their values ([[:file:using-and-improving-surface-models-built-by-computer_fig23.png|Figure 23]]).

[[file:using-and-improving-surface-models-built-by-computer_fig23.png|thumb|{{figure number|23}}The envelope technique is used to define one grid for the top of reservoir and another for the base of the reservoir. These are subtracted to create the gross hydrocarbon rock thickness.]]

Once constructed, the base of volume model is subtracted from the top of volume model, creating the gross rock thickness model. This model is positive where thickness exists and either zero or negative where it does not. The negatives in this case are desired as they allow clear definition of the reservoir edge (zero line).

Once constructed, the base of volume model is subtracted from the top of volume model, creating the gross rock thickness model. This model is positive where thickness exists and either zero or negative where it does not. The negatives in this case are desired as they allow clear definition of the reservoir edge (zero line).

[[file:using-and-improving-surface-models-built-by-computer_fig24.png|thumb|{{figure number|24}}Incomplete data for net and porosity due to partial penetrations, truncations, baselaps, and so on create problems when building models of these and related variables.]]

====Other variables for volumetrics====

====Other variables for volumetrics====

Often porosity and water saturation (and sometimes net to gross ratio) are input as constants representing the average value over the area of interest. Otherwise the variables are entered as surface models. Creating these surface models is complex and can be done in many ways. One of the most common is to digitize a hand-drawn map and build a model. Another is to build a model from well data. During model construction and use, certain issues must be considered:

Often porosity and water saturation (and sometimes net to gross ratio) are input as constants representing the average value over the area of interest. Otherwise the variables are entered as surface models. Creating these surface models is complex and can be done in many ways. One of the most common is to digitize a hand-drawn map and build a model. Another is to build a model from well data. During model construction and use, certain issues must be considered:

* Incomplete information caused by partial penetration, eroded top, faulting, and so on is often encountered. When this happens, the value of net to gross ratio or any other parameter being modeled will only represent the portion of the rock unit present. Figure 24 demonstrates this problem for a partially penetrating well. The N: G for the middle well is 0.875 (or 3.5/4), while for the left and right wells, which fully penetrate the unit, the N: G is 0.55. Clearly the partial unit value does not correctly represent the “true” unit value. If the missing portion was pay, then the N: G would be 0.95 [(3.5 + 6)/10]. If the missing portion was nonpay, then the N: G would be 0.35 (3.5/10). The true N: G lies somewhere between these two limits. Special techniques must be used to model incomplete data (<xref ref-type="bibr" rid="pt08r11">Jones et al., 1986</xref>).

* Incomplete information caused by partial penetration, eroded top, faulting, and so on is often encountered. When this happens, the value of net to gross ratio or any other parameter being modeled will only represent the portion of the rock unit present. [[:file:using-and-improving-surface-models-built-by-computer_fig24.png|Figure 24]] demonstrates this problem for a partially penetrating well. The N: G for the middle well is 0.875 (or 3.5/4), while for the left and right wells, which fully penetrate the unit, the N: G is 0.55. Clearly the partial unit value does not correctly represent the “true” unit value. If the missing portion was pay, then the N: G would be 0.95 [(3.5 + 6)/10]. If the missing portion was nonpay, then the N: G would be 0.35 (3.5/10). The true N: G lies somewhere between these two limits. Special techniques must be used to model incomplete data (<xref ref-type="bibr" rid="pt08r11">Jones et al., 1986</xref>).

* Modeling water saturation using standard algorithms and well data generally does not produce acceptable results. This is because the amount of water in the oil or gas portion of the reservoir is dependent upon porosity, [[permeability]], height above fluid contact, and other factors. Generally several engineering functions (J-curves) that relate porosity, height above fluid contact, and water saturation are used to convert structure top, structure base, fluid contact, and porosity models to a water saturation model (<xref ref-type="bibr" rid="pt08r9">Hamilton and Jones, 1992</xref>). The resulting model can be adjusted to honor the existing water saturation data at wells.

* Modeling water saturation using standard algorithms and well data generally does not produce acceptable results. This is because the amount of water in the oil or gas portion of the reservoir is dependent upon porosity, [[permeability]], height above fluid contact, and other factors. Generally several engineering functions (J-curves) that relate porosity, height above fluid contact, and water saturation are used to convert structure top, structure base, fluid contact, and porosity models to a water saturation model (<xref ref-type="bibr" rid="pt08r9">Hamilton and Jones, 1992</xref>). The resulting model can be adjusted to honor the existing water saturation data at wells.

* Net to gross and sometimes average porosity can change rapidly in the area extending from the point where the base of reservoir encounters the fluid contact to the reservoir edge (wedge zone). If the vertical distribution of net rock is not homogeneous throughout the reservoir, then these variables may change significantly in the wedge zone relative to values where the reservoir is full thickness. Often these changes are ignored. Sometimes the reservoir is separated into subzones, with a full suite of volumetric models constructed for each subzone. Three-dimensional modeling of net and porosity is a more precise solution.

* Net to gross and sometimes average porosity can change rapidly in the area extending from the point where the base of reservoir encounters the fluid contact to the reservoir edge (wedge zone). If the vertical distribution of net rock is not homogeneous throughout the reservoir, then these variables may change significantly in the wedge zone relative to values where the reservoir is full thickness. Often these changes are ignored. Sometimes the reservoir is separated into subzones, with a full suite of volumetric models constructed for each subzone. Three-dimensional modeling of net and porosity is a more precise solution.

* If more than one of the four models input to the HPT equation contain negative values, then additional incorrect volumes could result. This is because these models are multiplied together, and if two have negative values at the same location, the resulting value will be positive, creating a volume where no volume should exist. A commonly used safety measure is to clip porosity, water saturation, and net-to-gross models to a minimum value of zero, eliminating the problem. Zeros in the model often produce a very jagged zero line contour. However, that is preferred rather than significant volume errors. There are techniques for correcting these jagged zero contour lines.

* If more than one of the four models input to the HPT equation contain negative values, then additional incorrect volumes could result. This is because these models are multiplied together, and if two have negative values at the same location, the resulting value will be positive, creating a volume where no volume should exist. A commonly used safety measure is to clip porosity, water saturation, and net-to-gross models to a minimum value of zero, eliminating the problem. Zeros in the model often produce a very jagged zero line contour. However, that is preferred rather than significant volume errors. There are techniques for correcting these jagged zero contour lines.

===Modeling and volume calculation in a structure domain===

===Modeling and volume calculation in a structure domain===