**Trap capacity history**

In a proper model of entrapment of HC charge by a trap, the geochemical history of HC charge is usually modeled with the help of programs, such as BASINMOD, TEMISPACK, etc, or the GAEATOOLS program GEOHIST. Such programs usually provide a full history of the amounts of oil and gas charge as a function of geologic time. If we want to confront such charges with the trap in a realistic manner we also need the history of the depth of the trap and its trap capacity. This "trap history" is the subject of this program.

The best way to obtain a trap history is to construct a number of structural maps from the seismic information, translated to depth. The next best thing is to work with a paleostructural section, thus in 2-D only. This may show the main periods of growth of the trap and the depths of the culmination at the various points of the geological history.

The work involved in the paleostructural mapping may be prohibitive, or the data may not be accessable. In such a case, a simple approach may be useful, as implemented in this program. The discussion will be based on a structural trap, e.g. anticline with a target formation at some depth, of which we know the age.

From a seismic section (in depth terms) or from two wells where formation tops have been recorded, a comparison can be made between the depths of corresponding horizons. The basic idea is that the tops at the culmination were subsiding generally less than the tops downflank. The program works out the paleo depths of the tops in a well A on a flank and a well C at the culmination. Depth differences at points in history are normalized to a percentage of the present depth difference. Knowing the ages of the formation tops in million years allows a plot of such percentage depth difference versus time. It is recommended to select a thrid well "B", also downflank at the other side of the culmination from A. This will improve control.

This rather simple idea of guessing paleostructural development of a trap is maily aimed at the **similar type of folding** that is the result of vertical movements: salt pillows, basement blocks, growth fault structures, but not compressional type folds (see the discussion of parallel folds below).

Although we have mentioned depths to various stratigraphic tops, the input is in terms of **interval thicknesses**. On good reason is that this makes it easier to describe periods of erosion. Another important reason is that in dipping formations the present depth difference is not a correct indicator of the paleodepth, whch should, of course, be the interval thickness. If dip is known, the following correction should be applied to the apparent thickness (= present day depth difference in a vertical well):

where *d* is average dip of the interval where the well penetrated it. Note that at the bottom of the interval, in case of parallel folding, the dip is larger than at the top while in similar folding the dip is larger also, but due to the vertical closure growth.

The obvious output of this analysis is the list of paleodepths of the culmination of the trap at the "target reservoir level" which is usually taken as the lowest interval in the analysis. Less obvious is the importance of the depth difference between A and C. This has to be translated into a rough indicator of trap capacity. Now by comparing well/section A with C, we obtain some measure of **vertical closure** history.

In a trap that has a reservoir thickness exceeding the vertical closure, the trap capacity is almost proportional to the vertical closure, at least within the range of normal trap geometries. The assumption that the trap capacity (Bulk Reservoir Volume or BRV) is more or less proportional to the vertical closure only holds when the gross reservoir thickness exceeds the vertical closure. When during the growth of the trap, the vertical closure exceeds the gross reservoir thickness, the vertical closure should have a much reduced effect. This problem is analysed for the case of the simple "spherical segment" trap model, assuming a similar folding rather than a parallel folding. The similar fold for a spherical segment trap is shown below:

Note that at any point the vertical distance between top and base reservoir is equal to **g**, the gross reservoir thickness. In other words, a 'copy' of the top reservoir is shifted down vertically over a distance **g**. The radii of curvature for top and base reservoir are equal, but have centers that are also a vertical distance of **g** apart. The BRV is the subtraction of the BTV for the top reservoir and the BTV for the base reservoir, both are segments of a sphere. To calculate these volumes we need the radii **r _{t}** and

The Bulk Trap Volume V is equal to the BRV when the gross reservoir exceeds h:

where:

**V ** = Bulk Trap Volume

**h ** = Vertical closure

**w ** = Width of trap

**l ** = Length of trap

This relationship can be shown for a fairly steep trap where the width and length of the trap are equal to 20 times the vertical closure.

This shows that the relationship is practically linear, even up to the half sphere condition that corresponds to the vertical closure of 10 units.

Now the effect of the gross reservoir has to be taken into account. This is calculated by the substraction of a similar segment of a sphere, but with a height equal to the vertical closure minus the gross reservoir thickness. This works out to:

where **g** = Gross Reservoir Thickness.

Say that Length (**l**) and Width (**w**) are 20 units. If we study the effect on BRV of various values for **g** between **1** and 20 units there is a slight growth of the BRV with increasing closure, but this growth is considerably less than when **g > h**. As long as **g > h**, each increase in **h** adds an elliptic area at the base to the BRV. However, when **g < h**, only an elliptic ring ("donut") is added instead of a full elliptic area:

The implementation in TRAPHIST involves the new entries **g**, **h** as single estimates in meters, or feet. The **w** and ** l** are entered as km but the program makes meters of these.The growth of **h** is worked out already, because we assume that the input **h** corresponds to the 100% value of growth (present day). It is assumed that **G, w** and **l** are constants during the trap history. This is the assumption that the synclinal axes remain approximately where they are. Hence the full formulas are used to calculate a pseudo trap capacity with the spherical model. This in turn is worked back into percentages.

In parallel folding the apparent interval thickness is greater downflank than at the culmination. But true thicknesses are the same all over the fold. In a simple conceptual model of parallel folding we have a number of parallel horizontal layers that at some tectonic compression phase forms a parallel fold. In contrast with the similar folding for which TrapHist was designed, the width (and maybe the length) of the structure changes at the same time as the vertical closure changes. Therefore we do not believe that this program should be applied to a parallel fold type trap unless deformed later in a 'similar' folding phase.

When a parallel fold is buried and affected by vertical movements after the compressional tectonic phase the horizontal dimensions obtained during the compressional phase would remain more or less the same, but vertical closure may grow further. To allow analysis of such a situation, the program allows a parallel fold option. Here we analyse the parallel spherical model giving formulas to estimate trapcapacity as a function of vertical closure.

The situation is as shown below:

The gross reservoir thickness is **g**. The radius of the sphere forming the top reservoir is **R _{t}**. Then the smaller radius of the inner sphere forming the base reservoir is

and, substituting:

In these calculations we have to make sure that **g >= h** because any excess reservoir would be below the spillpoint.

Again Pythagoras in the smaller triangle:

which simplifies to:

Using the formula for the volume of a spherical segment of which the top surface is zero we obtain:

and writing **r _{b}** in terms of the length and width variables:

The input consists of **title** information that will identify the job and serves as labels for the output graph. Two or three wells or well prognoses can be used for input. Their names are entered in boxes for Well A, B and C. The well "C" should be the structurally highest position, at least for the top target reservoir.

The data for the formations/stratigraphic **intervals** are entered in the first five columns of the input sheet.

You can move around the input grid by the arrow keys or by the mouse. Simple editing, such as cut, copy and paste is available. If more than one cell has to be moved or deleted, select a range by holding the Shift Key down and either dragging the mouse or using the arrow keys to enlarge the range. The F2 key is for editing a cell entry. After editing cell contents, press Enter to fix the changes and to quit the 'edit mode'.

The headings of the input columns have a yellow background. In these columns data can be typed. The columns to the right, with a gray background, are for intermediate and final results. It is not possible to type in such columns. In column 1 the interval name is an optional input, but useful as a record. Column 2 contains the **Top interval age** in million years b.p. Note that the first line in the table is representing the present (age = 0). Further lines are in order of increasing age (so-called "driller's sequence"). Having the name of the time-stratigraphic unit, the menu item 'Edit/Age in my' can be used to insert the million years age of the base of that interval in the age input column. This facility can also be activated by a right mouse button click in the age column. If the cursor is not in the input age column, nothing will happen. The age table in this program is a combination from various sources. The best and complete reference is from Haq & van Eysinga, (1994).

The **thicknesses** are entered in columns 3, 4 and 5 for "wells" A, B and C. The reservoir under study is itself not entered, because the interest lies in analysing how the top of the reservoir was deformed in geological history. The youngest interval is in this case the present with a base age of zero years, and, obviously it does not have any thickness. This first input line is required for the calculation and is automatically provided. Note that thickness taken from depth differences may be overestimated. If the dip is appreciable the true thickness is the apparent thickness times the cosine of the dip, provided the well is vertical.

**Erosion intervals** are represented by a *negative thickness* followed below by an equal positive thickness. In other words we can only erode what was first deposited.

Contrary to the GEOHIST program, this TRAPHIST program does not have a decompaction option. It was thought that the simple approach used here in estimating the trap growth curve would not justify such a sophistication.

The upper-right corner of the input form shows the inputs that refer to the trap description. This input is optional, but helps to get a more realistic modeling of the trap capacity history, if the data are provided. The first thing to do is to decide on the type of folding, i.e. similar or parallelsimilar folding. Click on the appropriate 'option button' . Then describe the trap under study in a simple way by estimating the width and length of the trap in km, and the closure and gross reservoir in the length units you have chosen with the Customize menu item. If the trap description is given, the results are calculated using them, otherwise the trap capacity history is assuming that the paleo-trapcapacity is proportional to the vertical paleo-closure.

The output consists in the first place of a **table** that combines the input data on the left and the calculations on the right.

Another output is the **graph** showing one or two curves, for the pairs A-C and B-C. If based on three wells, the curves hardly ever coincide. It is recommended to interpolate in between the two curves, which is done in the column "Mean AB-C" of the output table. The Y axis is in terms of percentage relative to the trap capacity of today. Note that sometimes the paleo-trap capacity was larger than today. Some tilting of a trap might cause this while the geometry of the top reservoir might still remain approximately the same.

And an example from the North Sea, showing a fast growth due to fault movements.

GAEA (1995) Internal research report.

Gaea (2000) 'Gaeapas 2.0 User's manual'Gradstein, F.M., J.G.Ogg & A. Smith et al.(2004) "A Geological Timescale 2004". www.stratigraphy.org

Haq, B.U. & W.B. van Eysinga (1994) 'Geological Time Table'.Fourth revised, enlarged and updated edition, from Elseviers Science b.v., P.O.bax 211, 1000 AE, Amsterdam, Netherlands. (This is a wall chart that is very useful and at the same time very decorative!).(This scale has been used in this program but possibly superceded by Gradstein et al, 2004).

Maher, C.E., H.R.H.Schmitt & S.C.H. Green (1992) "Piper Field - UK, Outer Moray Firth Basin, North Sea" Treatise of Petroleum Geology, Atlas of Oil and Gas Fields, Structural Traps, v. 6, p.85-107.

Merriam, D.F. (2005) "Origin and development of plains-type folds in the mid-continent (United States) during the late Paleozoic".", Bull. A.A.P.G., v. 89, No. 1, pp. 101-118.