Subsidence and gas production: an empirical relation



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Subsidence and gas production: an empirical relation

Adriaan P.E.M. Houtenbos



Geodetic Consultant

Summary


The effectiveness of the recently introduced ‘hand on the tap’ production control mechanism relies on the predictability of the subsidence response to production. Recurring patterns of measured subsidence deviating in magnitude and timing from that predicted triggered an examination of the issue. Three hypotheses on the character of the relationship between production and subsidence over time were tested against measured subsidence. Assuming a pulse of production generates a pulse of subsidence, either immediately or after a certain delay fails to reproduce the measured subsidence. The hypothesis, that a pulse of production initiates lasting subsidence at a rate dampening out over time, is on the other hand found to provide an excellent match with measured subsidence. The difference between this gradual response and the commonly assumed direct response is found accountable for significant underestimation of future subsidence derived by inversion of subsidence measurements. While ignoring this empirical relation will pose a serious threat to successful testing of the ‘hand on the tap’ control mechanism, accounting for it holds the promise of a significantly more reliable subsidence prediction with much smaller margins of uncertainty.

Introduction


Recently a ‘hand on the tap’ production strategy was introduced as a method to keep the environmental impact of production related subsidence in check. In this strategy the production rate is adjusted as necessary to keep the subsidence below an environmentally safe limit. For the strategy to work a given percentage change in production rate should produce a reasonably immediate and quantifiable change in subsidence rate. This article examines the immediacy and predictability of the subsidence response to changes in the production rate.
In the public debate it is often assumed that cumulative subsidence is directly proportional to cumulative production. Under this hypothesis the current subsidence rate is directly proportionally to the current production rate. This response hypothesis will be referred to as the ‘direct’ response.

Subsidence often appears to react late to changes in gas production rates. This has given rise to the assumption of a ‘delayed’ response amongst groups of professionals. This hypothesis presumes proportionality between the current subsidence rate and the production rate some constant period earlier.



Finally, the observation that production rate changes by a factor 2 or more often produce much smaller changes in subsidence rates resulted in the hypothesis of a ‘gradual’ response. This assumes that a unit production pulse initiates subsidence that starts immediately but dampens out in time producing a fixed volume of subsidence over an infinitely long time.
The three hypothesized models for the subsidence response to production are tested against measured subsidence in two real life cases.

Response hypotheses


The characteristics of the three hypotheses are summarized in figure 1. All 3 models imply a fixed volume of subsidence per unit of gas produced. The models differ in the time at which the subsidence occurs and the period over which the full response accumulates. A production pulse results immediately or after a fixed time delay in a subsidence pulse under the ‘direct’ and ‘delayed’ hypotheses respectively. In the ‘gradual’ case a production pulse generates a dampened subsidence response. A simple exponential damping function is assumed.


Figure 1: Response hypotheses

Subsidence versus production


The three hypothesized models of the subsidence response to production are tested against measured subsidence in two real life cases. Time is expressed in years since the start of production. Both production and subsidence are assessed in a volumetric terms. Yearly production and cumulative production are expressed as a percentage of the foreseen ultimate cumulative production volume. Subsidence is expressed as a percentage of the ultimate cumulative subsidence volume expected under the best fit, i.e. ‘gradual’, hypothesis.
In the first case the production rate abruptly increased by a factor 5, while the measured subsidence rate increased to 3 times the original value. The second case is more common. Production quickly builds up to a maximum rate, then slowly decreases to a rate at which production no longer pays. While the production rate over the years 2 to 6 is more than three times that over the years 14 to 19, the subsidence rate remains virtually constant.
The parameters i.e. scale (a) and delay/damping period (b), of the three hypothesized relations between production and subsidence are resolved by a weighted least squares adjustment of the response against measured subsidence:

Case 1: Production rate increase


Figure 2 shows the production history for case 1.



Figure 2: Case 1 production
The best fit of the response hypotheses to measured subsidence is shown in figure 3.



Figure 3: Case 1 response fit

Case 2: Production rate decrease


Figure 4 shows production history for case 2.



Figure 4: Case 2 production
The best fit of the response hypotheses to measured subsidence is shown in figure 5.



Figure 5: Case 2 response fit

Discussion


The results of the least squares fit of the response assumptions to the measured subsidence are tabulated in the top right of figures 3 and 5. The compatibility of the hypothesis with the measured subsidence is indicated by the standard deviation of the fit. The direct and delayed response hypotheses pass the statistical test only marginally in the first case and are squarely rejected in the second. The gradual response hypothesis fits the measurements 33% and 214% better than the second best alternative in case 1 and 2 respectively. Although the distinction is not as sharp in case 1 as in case 2, the conclusion that the gradual response hypothesis predicts the subsidence response to production significantly better than either the direct or delayed response hypothesis, is inescapable.

The total volume of subsidence eventually materializing per unit of production is roughly 3 times as much in case 1 as in case 2, 0.752 versus 0.276 m3 of subsidence per 1000 m3 of production for the most likely, gradual response scenario. The direct response assumption underestimates ultimately materializing subsidence volume by some 34%, while the delayed response assumption underestimates it by 23%. The direct and delayed response assumptions will on the other hand overestimate the immediate effect of production rate changes on the rate of subsidence.

For the delayed response in case 1 and 2 a time shift of 0.8 and 1.4 years is computed between production and associated subsidence. The damping constant (1/b) of the gradual response is the reciprocal of the damping period (b). A value of 5.3 and 4.3 years respectively emerged from the least squares fit of the delayed response model to measured subsidence. Only some 13% of the subsidence initiated by production in a given year is realized and measurable by the end of that year. The rest will follow later.

The brown lines in figures 3 and 5 represent the petrophysical prediction, the solid/dashed parts show the periods for which measurements were/were not available for calibration purposes. Both cases fit in a trend of petrophysical overestimation of volumetric subsidence. Petrophysically predicted vertical displacement subsidence usually agrees well with geodetically measured vertical subsidence at the time at which the prediction is made. The predictions in figures 3 and 5 also follow typical patterns in mimicking the direct response to production rather than the gradual response for the period that calibration values are available.


These findings raise the question what is to be expected if the ‘hand on the tap’ mechanism is operated assuming a direct subsidence response to production, while it is in fact – as the measurements indicate - gradual. The effects will be examined using a typical, hypothetical case (figure 6). Production spans a 30 year period. Each volume of production is assumed to initiate a fixed amount of subsidence that will be realized gradually over time from the moment of production. The damping constant is taken equal to that derived for case two (4.2 years). As a result realized subsidence (figure 6, yellow line) will be less than initiated subsidence (solid blue line). This initiated subsidence will only be realized in the fullness of time. Hence, comparison of measured (= realized) subsidence at a certain moment in time with cumulative production at the same time will structurally underestimate the scale of the eventual subsidence. The factor with which the eventual subsidence will be underestimated will asymptotically decrease from infinity at the start of production to 1 after the end of production. Figure 7 shows three successive predictions of vertical displacement subsidence made for case 2. It exhibits a decreasing pattern of underestimation of ultimate subsidence similar to that analytically derived (figure 6), lending further support to the gradual response hypothesis. In each of the years 5, 12 and 17 ultimate subsidence was predicted. These predictions underestimated the current best estimate of ultimate subsidence by a factor 2.0, 1.3 and 1.0 respectively. If forecasts assumed a direct response, while actual subsidence evolved according to a gradual response hypothesis, underestimation factors of 2.2, 1.3 and 1.2 can be expected. Note also that successive predictions deviate increasingly from the measurements in the early stages of production, suggesting a systematic flaw in prediction modeling.



Figure 6: Production, initiated and realized subsidence



Figure 7: Underestimation assuming direct response
In the hypothetical case considered here the scale of the expected subsidence is presumed equal to that measured in a field with comparable geological and petrophysical parameters that is already 6 years in production. As this scale is derived by inversion of measured subsidence after 6 years and comparison (via the pressure drop) with the associated cumulative production it will be underestimated by a factor 2.1 (realized/initiated subsidence in figure 6). The length of the production period has been chosen such that the expected subsidence rate (under the direct response hypothesis) remains a safe margin of 25% under the environmentally safe limit (figure 8). Unaware of actual subsidence rate (solid blue line), the subsidence is expected to behave as petrophysically predicted by comparison with similar producing fields and assuming a direct response (solid purple line). .



Figure 8: Predicted and actual subsidence, before and after intervention
If measurement noise and benchmark instability over such short periods permit, a substantial (20%) overrun of measured over predicted subsidence will be discovered in year 4. Still assuming a direct response, the production rate will be scaled back by 20%, expecting a more or less immediate decrease of the subsidence rate by 20% (dashed purple line), back to levels that are expected to remain 25% clear of the environmentally safe limit. In reality the system will however react gradually (dashed blue line). The subsidence initiated by the early production, but not yet materialized will take over control from the ‘hand on the tap’ operators and drive the rate through the safe limit. As public opinion will allow just one chance to prove the effectiveness of the ‘hand on the tap’ control mechanism, such failure to recognize and account for the indirectness of the subsidence response to production is likely to inflict massive damage on the public trust, without which all operations come to full stop.

Such damage is however entirely avoidable. Adopting the gradual response hypothesis in the calibration of the subsidence scale for producing reference fields by inversion of measured subsidence results a significantly more reliable and precise results, as indicated by the case histories. Applying the scale and damping period thus derived, in predicting the subsidence response to future production, is a prudent approach promising tighter control over the scale of its environmental impact.


Finally, the effects of different production schedules are investigated. Ignoring possible operational constraints on the production schedule, figure 9 shows the characteristics of the schedule affording maximum control over the associated subsidence rate. The standard (blue) and the alternative (purple) production schedule produce the same volume of gas over the 30 year period. Assuming a gradual response the alternative schedule will results in a lower, flatter, and more directly controllable subsidence rate.



Figure 9: Subsidence rates and production schedules

Conclusions and recommendations


  1. Many case histories exhibit the tell-tale signs of a more indirect subsidence response to production than commonly assumed, slowly gathering speed after the start of production and reacting late and disproportional to changes in the production rate.

  2. The hypothesized gradual response fits the case histories significantly better than both the commonly assumed direct response and the delayed response. The current subsidence rate is a function of the current production rate under the direct response hypothesis, of the production rate a fixed period ago under the delayed response hypothesis and of the entire production rate history under the gradual response hypothesis.

  3. Failure to recognize the gradual nature of subsidence response to production, in deriving its scale by inversion of measured subsidence, leads to serious underestimation. In the early stages of production, underestimation by a factor 2 or more must be expected. This constitutes a significant threat to a successful first real life test of the ‘hand on the tap’ control mechanism.

  4. Recognizing the empirically derived gradual nature of the response in scheduling ‘hand on the tap’ production holds a promise of more reliable subsidence prediction with significantly smaller margins of uncertainty.

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