SMOOTHING METHOD AIDS GAS-INVENTORY VARIANCE TRENDING

Robert G.MasonTranscontinental Gas Pipe Line Corp. Houston

A method for determining gas-storage inventory and variance in a natural-gas storage field uses the equations developed to determine gas-in-place in a production field.

The calculations use acquired data for shut-in pressures, reservoir pore volume, and storage gas properties.

These calculations are then graphed and trends are developed.

Evaluating trends in inventory variance can be enhanced by use of a technique, described here, that "smooths" the peaks and valleys of an inventory-variance curve.

Calculations using the acquired data determine inventory for a storage field whose drive mechanism is gas expansion (that is, volumetric).

Based on gas laws and the material-balance equation, the formulas are only as accurate as the acquired data. This accuracy is limited by reservoir homogeneity, and pipeline conditions.

Although each of these limits determines shut-in time, neither allows a shut-in period long enough to acquire perfect data. To determine variance, therefore, the results must be graphed and trends observed.

When used for a dry gas, condensate, or gas-condensate reservoir, the formulas require no further modification.

Inventory in depleted oil fields can be determined in this same manner, as well. Some additional calculations, however, must be made to assess the influence of oil production on the gas-storage process.

Additional manipulation is also required for a water-drive field or aquifer; these, however, will not be discussed here.

DRY GAS RESERVOIRS

Gas reservoirs are those having no liquid hydrocarbons at reservoir temperatures and pressures. Any reservoir whose temperature is greater than that of the cricondentherm of the hydrocarbon accumulate is considered to have dry gas, and no liquid hydrocarbon accumulation will exist at any reservoir pressure.

Some liquid may be captured at the surface in separators, if the cricondentherm is high. But if the cricondentherm is low, no liquids will be recovered.

Some liquids may still be recovered through use of some extraordinary method (for example, low-temperature separation, natural gasoline recovery plant); but such gas production is still considered dry.

This type reservoir is ideal for storage because no adjustment must be made for liquid production, neither retrograde condensate nor oil. The pore volume also remains the same as determined from the production data.

OIL, GAS-OIL RESERVOIRS

Those reservoirs containing liquids at reservoir temperatures and pressures can be classified as oil reservoirs, either bubble point or retrograde condensate.

Hydrocarbon accumulation is defined by a phase diagram which depends only on the composition of the accumulation. Any reservoir whose temperature is greater than the cricondentherm will be all gas.

And, depending on the pressure, any reservoir whose temperature is less than the cricondentherm may contain such liquids as are defined by the phase envelope.

At greater than the critical temperature, retrograde condensate will be present; at less than such temperature will be the bubble point at which gas comes out of solution as opposed to oil as the precipitate.

This oil reservoir must move the liquid to the well bore for production. As some gas breaks free, more oil is left behind and a considerable amount may remain at abandonment. Additional recovery may be enhanced by flood methods, or the field may be swept by natural-gas storage operations.

This liquid occupation of, and finally production from, the pore space will change the pore volume during storage cycles. The change in pore space caused by liquid production must be accounted for during inventory verification. Liquid production is somewhat inefficient because the gas tends to bypass the oil in place and is then produced at the well bore. Because storage depends on gas cycles rather than oil production, this form of natural-gas production is desirable.

In fact, oil production in a gas-storage field, when it occurs in uneconomical quantities, is undesirable because the recovered liquid must be removed from the gas stream at the surface.

The void space created in the subsurface, because of liquid production, must be calculated to adjust the pore volume for inventory verification. This is accomplished by a method similar to that used with retrograde condensate reservoirs. It involves calculating the gas equivalent of the produced oil by use of Equation I (see accompanying equations box).

The void space created in an oil field must be considered as additional pore volume which will cause the historesis curve falsely to project an appearance of gas migration.

Calculating the gas equivalent of the produced oil allows for an adjustment of the pore volume. This in turn allows accurate calculation of reservoir inventory.

CONDENSATE, GAS RESERVOIRS

In a condensate reservoir the retrograde condensate left in the pore space at abandonment is revaporized by the high-pressure cycle of the storage. The condensate is then produced as storage gas during withdrawal and eventually replaced, during the injection cycle, by a lower BTU gas.

The pore space does not change because of the production of condensate, but the gas inventory does change. This is attributable to the new composition of the storage gas.

The gas formation volume factor and the gas deviation factor (Z) change with the gas composition and pressure. Thus, as the condensate is produced by the resulting cycles of storage, the gas inventory changes by the gas equivalent of the produced condensate.

The equation for the gas equivalent is listed as Equation 1 in units of standard cubic feet/standard barrel (scf/std. bbl). This change in inventory is very slight and can be ignored because most condensate fields have been cycled to remove the resulting liquids.

The remaining condensate, while economically useful, is quite small in volume in fields which have been cycled and has a negligible effect on inventory calculations.

INVENTORY CALCULATION DATA

Inventory calculations require accumulation of the following data:

Bottomhole pressure
Bottomhole temperature
Gas compressibility factor
Standard temperature and pressure.

The bottomhole data are of primary importance because most recurring and compounding errors occur when faulty bottomhole data are used.

These errors occur for two reasons:

1. Mechanical problems with the temperature and pressure devices

2. Failure to achieve static conditions because of a short shut-in period.

The first error can be eliminated by calculating the bottomhole pressure and eliminating the mechanical problems associated with mechanical or digital downhole pressure-sensing devices.

Bottomhole pressures calculated from surface data are accurate and repeatable, when surface pressure data are accurate. The subsurface pressures can be calculated with Equation 2.

The second error is much more difficult to eliminate because of pipeline operating conditions. Large, tight fields require long periods to stabilize, while smaller fields with high porosity and permeability usually require a shorter shut-in period.

Even these smaller fields usually demand more stabilization time than pipeline operating conditions allow.

Near stabilization can be determined by graphing shut-in time vs. pressure. The curve should asymptotically approach a point where the change in pressure nears zero. Figs. 1 and 2 illustrate this point.

CALCULATING PRESSURES, TEMPERATURES

Calculating the bottomhole pressure is an iterative process requiring an initial pressure conjecture and comparing a recorded surface pressure with a calculated surface pressure. Because the gas deviation factor (Z) changes with pressure and governs compressibility, successive trials of the computation must be completed.

Close agreement between the actual surface pressure and calculated surface pressure must be reached before the bottomhole pressure, as calculated, may be included in the inventory formula.

This agreement should be within 1 psia. Bottomhole pressures can be calculated as shown in Example 1.

Reservoir temperature can be calculated with regional gradients. But this approach may cause a deviation from the true reservoir temperature of several degrees.

Thus, the initial bottomhole temperature, as recorded at discovery, should be used for all calculations. If production drawdown of the reservoir is slow compared with the storage-cycle process, the initial reservoir temperature will probably be accurate.

Rapid injection or withdrawal of the storage inventory will change the temperature of the gas in the formation, but a return to the original temperature will occur with a proper length of shut-in period.

Any error caused by a short shut-in, causing an incorrect temperature in the formula, will be corrected by the graphical results of the calculations.

CALCULATING PORE VOLUME

The reservoir pore volume can be calculated at each shut-in period by the gas-law equation (Equation 3).

The error introduced by nonstatic conditions of the reservoir during storage cycles, however, will result in large errors being interjected and thus cause the results of the calculations to be questionable.

The pore volume used should be derived from the original production data and can be calculated with the gas law or extrapolated from the production decline curve. Both methods are based on the gas law and are accurate for inventory-calculation purposes.

The pore volume can be calculated with Equation 3 from a point on the production curve as shown in Fig. 3. Once a calculated pore volume has been selected, it should then be used during every shut-in inventory-verification study.

Although this practice may introduce a slight error, the process is comparative and any error will be relative.

Conversely, if the pore volume is calculated with each successive shut-in pressure, the error will be recurring and result in a compounding, ever-increasing deviation.

Pore volume can be calculated as shown in Example 2.

CALCULATING INVENTORY

Inventory calculated by this method depends on current reservoir conditions obtained at the time of shut-in and on the calculated pore volume. If there is an error, it will only be in the shut-in pressure and can be easily evaluated.

The inventory is calculated with Equation 4. The inventory may then be graphed on a historesis curve which is a modified P/Z vs. inventory graph. This graph may also be used to indicate any inventory variance.

The original decline curve vs. P/Z will serve as the base line and each storage-cycle pressure/inventory point will be used for investigation. Movement to the right of the base line suggests variance.

A typical historesis curve will usually have some withdrawal cycle points to the right of the base line and some injection cycle points to the left. This is a classic indication of shut-in pressures not reaching a static condition.

An example of inventory and historesis is shown in Fig. 4. Inventory can be calculated by methods of Example 3.

Inventory variance does not always mean gas is migrating from the storage field. Indeed, sometimes, minor leaks on the surface may cause an inventory variance of some magnitude.

In the past, many believed that all storage fields lost some natural gas at both surface and subsurface locations. But this is not necessarily the case because good maintenance practices can prevent gas loss.

Although some fields experience gas loss naturally, most losses can be traced to mechanical sources.

Natural phenomena can be classified as those occurrences in the subsurface reservoir where gas migration is attributable to some cause other than that directly created by man.
This natural phenomenon can be a collapse in the sealing caprock leading to gas loss, migration across a nonsealing fault, migration across a saddle when the reservoir is pressured past its sealing limits, or other causes not associated with the mechanics of drilling and well completion.
There have been cases of gas loss from reservoirs, in locations near other reservoirs, which were high pressure at discovery. Rather than being separated by sealing faults or sandpinch outs, these fields were closed by water contact. There were no problems during production except for perhaps excess water production.
When the fields were developed for storage, even though the resulting pressure was less than discovery pressure, gas migrated from field to field.
The lower pressure of the undeveloped field allowed storage gas of the developing field to migrate across a saddle and collect in the now abandoned production field.
Close observation of the pressure of the once abandoned field made it possible for an enterprising producer to collect and sell the storage gas.
Mechanical problems may be classified as those related to drilling and completion practices in the subsurface or valve, line, compressor, and connection leaks at the surface.

The subsurface losses may be caused by the collapse of the sealing zones caused by drilling and completion techniques, microannuli at the casing/cement/formation contact, casing leaks caused by corrosion or erosion processes, or collar leaks.

Surface leaks are usually obvious. Some leaks can be so small and numerous, however, that detection is difficult and losses high.

Gas loss has been known to occur in the subsurface because of cement completion problems. Such losses are generally attributable to the storage cyclic process which causes the casing to contract and expand below the packer of tubing-completed wells.

This expansion-contraction contributes to the deterioration of the cement bond resulting in possible, if not eventual, gas movement and loss. The process is detectable and a cement squeeze in the area of poor bonding will usually relieve the problem.

Most mechanical leaks can be repaired if not allowed to progress to the point of catastrophic proportions. These are controllable loss sources, while natural losses may not be governable.

SMOOTHING TECHNIQUES

An example of inventory variance is illustrated in Figs. 5 and 6 from the Fall 1986 (F86) season to the F90 season. Examples of close agreement with book inventory are seen in Figs. 5 and 6, as well, from the F81 season to the F86 season.

Fig. 6 appears similar to Fig. 5. Indeed, Fig. 6 is a plot of the average variance as depicted in Fig. 5. This (Fig. 6) is a simple method of "smoothing" the calculation results.

Smoothing indicates that the maximum and minimum peaks have been removed. This will aid the observer in developing the trends necessary to establish variances. Smoothing the curve produces visual results which illustrate stability or gas loss.

There are two methods for smoothing a curve. One is a simple mathematical averaging exercise; the other involves a polynomial quadratic equation which produces a parabolic curve.

The averaging method requires a set of inventory, calculations which are averaged from season to season. Simple mathematical averaging from season to season produces a curve with the peaks and valleys removed.

Each season is added to the previous season and averaged to replot the curve. Each peak is removed by averaging the current inventory- with the preceding inventory and plotting the results.

An instantaneous result is not possible because each new point is a result of two inventories. The curve can be used to evaluate a trend and determine the absence of inventory stability.

Redrawing the curve with a quadratic equation produces a curve which can be used to determine instantaneous results. "Instantaneous" here simply means that the inventory can be determined by referring to the curve and selecting a point at any given time.

The calculated results can then be compared to the measured inventory and Variance can be determined by the method indicated in Example 4.

The quadratic equation used is a polynomial parabolic equation generally of third degree. The inventory usually has parabolic tendencies from season to season either ascending or descending. The parabolic equation seems to produce acceptable results especially when there is a change in the trend.

The graphical examples of Figs. 5 and 6 show a Storage field which exhibited stable inventory and finally variance or loss. The parabolic quadratic equation shows the trend from stable to descending; and when the inventory is again brought under control, this equation will produce a curve from descending to stable.

The equation can also be used to predict future results assuming future events follow present tendencies. Predicting future inventories must be approached with caution because the equation eventually, tends to produce parabolic results.

CALCULATING VARIANCE

Inventory variance in a storage field can usually, if not always, be traced to periods of high gas cycling. When gas is injected and withdrawn repeatedly, causing either high pressures in the reservoir or higher velocity natural gas movement, higher levels of inventory variance can be detected. An example of this can be seen in Fig. 7.

Inventory variance, calculated from Equation 5, is not instantaneous but must be derived over a period of time. It can be used to determine close agreement with measured inventory.

The variance is derived with time comparisons and averaging. The formula used is a Variation of the gas law and is accurate within the limits of the collected data.

The errors caused by data collection will require the comparison of cyclic inventories. Example 4 shows inventory variance calculated.

This example would appear to suggest that the calculated inventory is 2.753 bcf short of the measured inventory. Indeed, the field in question is short some storage gas but probably less than is calculated here.

This example was taken during the shut-in period following a withdrawal season. The field was not stabilized because of a shut-in period of only 7 days; most fields require a longer period. The recorded shut-in pressure is therefore lower than the static pressure.

In fact, shut-in pressures after a withdrawal season will generally be lower than true stabilized pressures, while shut-in pressures after an injection season will generally exceed true stabilized pressures.

The resulting error in pressure causes an error in the calculated inventory, which is different from the true gas in place.

The calculation results must be graphed in order to establish a trend. The results must be evaluated from season to season, rather than instantaneously, to suggest any variance the resulting graph (Fig. 5) is saw-toothed, a pattern attributable to the higher than static pressures after an injection season and lower than static pressures after a withdrawal season. This cannot be eliminated because of the time limitations of shut-in; as a result, a true instantaneous inventory usually cannot be calculated.

Instead, the inventors, and variance calculations must be graphed to establish a trend with inferences made from the tendencies.

The saw-toothed line may be smoothed by calculating a trend with a polynomial regression equation and a least squares fit curve. The point of intersection with the desired time period will be the inventory variance.

Another method is to average the calculated points from season to season and plot (Fig. 6). The variance can be predicted at any given time period, remembering that the average is season to season.

A trend of this graph is probably most accurate for deducing inventory variance.

Fig. 8 will enable the examiner to see the trends developed which depict the inventory variance. This graph (Fig. 8) also illustrates field stability with respect to gas loss and the resulting instability as the field loses gas.

It is assumed that gas loss is constant throughout the period of F86 to F90. Examination of the trend line will enable the natural-gas storer to establish a write-off of gas inventory to balance the gas account.