Are decline rates really exponential? Evidence from the UK Continental Shelf.

Understanding of oil and gas production decline rates is important in order to predict future behaviour and give policy guidelines. Most studies propose exponential and/or hyperbolic decline rates. Econometric techniques are extensively used in the present study to establish that logistic decline

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INTRODUCTION

Decline curve analysis has been used extensively to study the historical behaviour of oil and gas production and to predict future trends. The present analysis focuses on production decline rates and is distinct from reserves depletion analysis which has received much attention in the literature especially by geologists. The two variables are different by definition. Depletion starts with first production, while decline rates are measured relative to peak production.

Oil and gas field production generally go through the broad phases of growth, plateau, and decline. The growth phase is the build-up to the plateau while the decline phase encapsulates production beyond this level. In this study, the threshold of production decline starts immediately after peak production, and its terminal point occurs when production ceases at the economic cut-off point. The decline rate examined is the net rate after incorporating the effects of incremental investments.

Accurate prediction of the production decline rate is important not only to successful investment decision-making but to the determination of national petroleum policies including appropriate incentives for further development and exploration. Inaccurate projections can result in sub-optimal policies being pursued.

2. SELECTING AN APPROPRIATE MATHEMATICAL MODEL

It is recognized that the uncertainties concerning the intertemporal behaviour of reservoir pressure, other subsurface characteristics, and market behaviour greatly complicate the task of measuring and predicting the production decline phenomenon. A two-pronged approach based on the imperative to reduce forecast errors exists in the literature to handle these problems. Firstly, over many years, reservoir engineers and economists have proposed several decline models and used curve-fitting techniques to model reservoir characteristics and predict future production. The list of respected names who have popularized this approach includes Arps (1945,1956), Hubbert (1956, 1962, 1967), Slider (1968), Stright (1983), Ikoku (1985), Luther (1985), Rowland and Lin (1985), Spivey (1986), Chen (1991), Cleveland and Kaufmann (1991), Hannesson (1998), and Moroney (2002). Arps and Hubbert's respective families of hyperbolic and exponential decline models, include the harmonic, linear, reciprocal time, reciprocal time-rate, inverse square root of time, and Kopatov's equation. The linearized and logarithmic versions of Arps' equation further developed respectively by Spivey, Luther and others have conventionally been adopted by reservoir engineers to characterize field decline rates, under varying physical and geological environments. Secondly, once a best-fit has been obtained detailed residual analyses, using standard econometric techniques can be applied to reduce forecast errors occasioned by uncertainties in the physical and market conditions. Chen (1990) demonstrated one way in which this can be done.

The plethora of work on decline rates has overlooked the logistic curve which, it is suggested, is more attuned to real-world hydrocarbon production and rectifies some of the questionable features of the linear, exponential and hyperbolic models. A dubious feature of note is the implied monotonicity of the decline rates, which bears no explicit relationship to field life, and ignores the field-life prolongation effects of technological improvements. Instead of a constant-percentage or absolute decline empirical evidence presented here points in the direction of a non-uniform production decline rate, typically high (linear or exponential) to begin with, but slowing as the falling reservoir performance is augmented, and finally reaching a steady-state rate as the field nears economic cut-off. It is the proposition of the present paper that the symmetric logistic growth model best describes the real-life time-varying decline rates.

The symmetric logistic growth model is described as:

[D.sub.1t] = K/[1 + [be.sup.(-at+[[epsilon].sub.1])]] (1)

where:

[D.sub.1t] = Current relative-to-peak production decline rate

K = asymptotic or steady state relative production decline

t = time t = 0,1,2,.........T

a, b, K are estimable parameters

[[epsilon].sub.t] = error term

Equation (1) states that the relative-to-peak production decline rate in the current period is a non-monotonic function of time (t), with the shape and location of the associated curve depending on the estimable parameters a, b, and K. The disturbance term captures the effects of measurement errors, and is assumed to be white noise. The curve is bounded, with the lower bound occurring at the onset of production decline (i.e. when t = 0, [D.sub.1t] = (K/1+b)), and as t increases towards the end of the field life at time T, the upper bound is reached at K. The boundedness property of the logistic curve makes it intuitively appealing. Production will progressively diverge from the peak level until it reaches the point of its maximum divergence at the end of the field life or economic cut-off which occurs at K. Thus, as a concept, K is common to all producing fields and plays a key role in determining the floor and ceiling of the relative-to-peak production decline rate. Depending on whether geological deposits or economic reserves are being considered K can either be a fixed static or dynamic variable. Consideration of reserves as being economic transforms K into a dynamic concept. In that case the complexity of the dynamics of oil and gas production, discovery, and production decline rates makes it difficult to know ex ante the real value of K, given its dependence on economic cut-off, which is dynamically determined by a combination of changing cost and market conditions.

Differentiating equation (1) with respect to time yields:

[[d[D.sub.1t]]/[dt]] = [a/K][D.sub.1t](K - [D.sub.1t]) (2)

According to equation (2) the marginal (annualized) rate of production decline per unit of time is proportional to the current level of relative decline ([D.sub.1t]) and (K-[D.sub.1t]). Since K is the asymptote, (K-[D.sub.1t]) can be interpreted as the remaining field life or the 'distance' that the current level of relative decline rate has to travel to reach its economic cut-off (i.e. when K - [D.sub.1t] = 0). In general, the longer the 'distance' to reach a field's economic cut-off the higher the annualized decline rate. Other things being equal, relatively new fields with a longer 'distance' to travel to economic cut-off, would exhibit higher decline rates, while older fields nearing economic cut-off would exhibit lower decline rates. The decreasing rate of production decline is governed by a mixture of geological and economic factors. The average reservoir pressure drops after peak production, but as more knowledge is gained about the reservoir characteristics, enhanced recovery investments are instigated and the production decline rate decelerates (see Ikoku (1985), Hannesson (1998) and IEA (2003)). Using numerical examples, a graphical illustration of the relationships between post-peak production field life, relative and marginal production decline rates is presented in Fig. 1.

[FIGURE 1 OMITTED]

3. ESTIMATING DECLINE RATES

The first step in minimizing field decline misforecasts is to specify and estimate a decline model that best captures the field's production profile. In order to determine the appropriate model for the UKCS, a number of curves including the compound, cubic, exponential, growth, inverse, linear, logarithmic, logistic, power, quadratic and S-curve were fitted to the data, to establish which would provide the best fit. However, since these curves are either the linear, exponential or logistic curves by other names or belong to the same family of curves as these three, the comparative results presented in this study refer only to the linear, exponential, and logistic curves. Consistent with the model selection technique outlined above, the model with the highest R-square statistic was adjudged the best-regressed model, capable of better explaining historical trends and producing useful predictions of future production decline rates.

The data on annual oil and gas production, investment, and operating costs in the UKCS were obtained from a database validated by the field operators. This database holds detailed information on 248 sanctioned fields, covering the period since first production in 1967. However, the time series data on 13 fields were too short for any meaningful statistical analysis and were, therefore, dropped from the analysis.

The full results of the curve-fitting exercise for all the individual fields can be obtained from the corresponding author. Summaries of the results are in Table 1.

[FIGURE 2 OMITTED]

In general, the R-square statistics of the logistic, exponential and linear models were reasonably high in the individual field estimation results (1). However, it is clear from Table 1 that the logistic equation best describes the decline rates in the majority of cases. When classified by vintage (2) the relative superiority of the logistic decline model is confirmed. The vast majority of fields in each vintage exhibit logistic decline rates. Exponential decline rates had best fits only among the 1980's and 1990's fields. Accordingly, the logistic decline rate is adopted for detailed analysis in this study.

In order to demonstrate the implications for production and investment planning of using the correct decline rate, the Forties and Audrey fields were chosen as case studies. The Forties oilfield was discovered in 1970 while the Audrey gas field was discovered in 1976. Respectively, production in the two fields commenced in 1975 and 1988, peaking correspondingly in 1980 and 1990.

[FIGURE 3 OMITTED]

Figs. 2 and 3 show the relative goodness-of-fit of the three models from the year of decline commencement. It is seen that the logistic decline model is by far the best predictor of production in the two fields. In the Forties field, the logistic model very closely mirrored both the initial steep decline in production and the gentler decline rate thereafter. The logistic curve is also seen to perform more accurately in the Audrey field, which exhibits considerable production irregularities. Both the linear and exponential decline models perform relatively poorly, failing especially to mimic the turning points or non-monotonicity of decline rates. The seriousness of this shortcoming can best be appreciated when it is recalled that Adelman (1990) and others have shown that depletion/decline rates are the decision variable when determining field marginal investment requirements. Also, Stright (1983) has pointed out that using a decline curve which does not properly describe a reservoir's flow system may lead to inaccurate forecasts of production rates and recoverable reserves. Erroneously ascribing exponential or linear decline to a field or region whose decline rates are better characterized by a logistic decline is misleading and partly explains the misforecasts in the literature predicting imminent production decline, since the eighties, in the UKCS, with the attendant consequences for investment and government policies (see, for example, PIU (2001), and BP (2001)) (3).

4. SIMPLE AND COMPLEX LOGISTIC DECLINE RATES

A further attraction of the logistic model is its ability to characterize complex decline processes. Meyer (1994) distinguished between simple and complex logistic growth processes. Complex logistic decline rate occurs when a radical shift in the initial conditions significantly alters the momentum of the initial decline trend, creating a new pattern of logistic decline, which may overlap or occur sequentially relative to the original decline pattern. In general, the overlapping or sequential logistic decline patterns slow down the rate of decline. The combination of two or more sequential or overlapping logistic decline rates into one continuous S-shape curve defines the so-called bi-logistic (or complex) curve.

The equation of the bi-logistic curve is a concatenation of two or more single logistic curves. That is,

[D.sub.2t] = [[K.sub.1]/[1 + [b.sub.1][e.sup.[-a.sub.1][t.sub.1]]]] + [[K.sub.2]/[1 + [b.sub.2][e.sup.[-a.sub.2][t.sub.2]]]] + .............. + [[K.sub.n]/[1 + [b.sub.2][e.sup.[-a.sub.n][t.sub.n]]]] (3)

where, in addition to previous definitions,

[D.sub.2t] = Complex current relative production decline,

the subscripts 1,2,.....n on the RHS refer to the phases of the logistic decline process.

Equation (3) describes a complex logistic decline as consisting of one through n-decline phases.

The logic of the bi-logistic decline concept can readily be applied to oil and gas production. Over the life of a field, successive introduction of new technologies, designed to enhance recovery, can be expected to generate a series of overlapping or sequential decline rates relative to the one that existed earlier. The bi-logistic concept was used to analyze the decline rates of UKCS fields.

A best-fit test was conducted by fitting each field's observed decline rate to models of single and bi-logistic declines. Comparisons were made of the relative magnitudes of the adjusted R-squares of the two regressions. The model with the higher adjusted R-square was adjudged the best-regressed and better descriptor of the type of logistic decline. The parameters a, b, and K were fitted non-linearly through a series of iterations using the Levenberg-Marquardt method (4). The regression results are summarized and briefly discussed below.

In order to demonstrate how fitting data to the single and bi-logistic models can help determine more accurately the type of decline process underway, the Forties field was used as an example. The R-square in the simple logistic regression was 0.972 whereas it is 0.996 in the bi-logistic regression. Furthermore, comparing the regression residuals of the single and bi-logistic fits of the Forties field in Fig. 4, it is obvious that the latter fit contains less residual errors, providing evidence that the field has experienced a complex logistic decline.

[FIGURE 4 OMITTED]

Overall, about 69% of UKCS fields showed evidence of complex production decline rates while the remaining 31% appear to have simple logistic decline rates.

The preponderance of bi-logistic decline processes is consistent with the work by Watkins (2002) on reserves appreciation in the North Sea. While noting that the characteristics of the North Sea are not markedly different from any other offshore hydrocarbon province in the world, Watkins established that there have been about 9 billion barrels of oil reserves appreciation in the UKCS from initial start-ups to 1996. Clearly, such increases in reserves appreciation will alter the production decline rates in those fields, and be manifested in complex logistic decline rates.

5. MEAN ANNUAL PRODUCTION DECLINE RATES

A graphical comparison of the production decline rates produced by the three models--exponential, linear and logistic--is presented in Fig. 5. Significantly, the estimated decline rates of the three models, apart from the differences in magnitudes, share several common features. Firstly, the older field vintages exhibit lower annual mean decline rates. Secondly, the annual mean field production decline rates have fluctuated, but have generally increased through time, reaching a peak in the fields whose production decline commenced in 2000. This trend has potentially important consequences for the behaviour of total UKCS production. An increasing proportion of total output emanates from fields of recent vintage. Thus in 2000 no less than 47% of oil output came from fields which commenced production since 1995 (DTI (2001)). Total hydrocarbon production peaked in 1999. The average annual decline rate since then has been just over 3%. On current trends in decline rates by field vintage the overall pace of production fall will increase.

[FIGURE 5 OMITTED]

6. KEY RELATIONSHIPS

Production decline rates are determined by the interplay of a number of qualitative and quantitative influencing factors. The qualitative factors include field vintage, location (Central, Northern, or Southern North Seas, the Irish Sea or West of Scotland), reservoir age (Carboniferous, Permian, Triassic, Jurassic Cretaceous, or Tertiary), and resource type (oil, gas or condensate), while the quantitative influencing factors include field life, reserves, water depth, and investments. Field vintage, reserves, and field life all have statistically-significant effects on decline rates in the UKCS (5). Building on these findings, the present study focuses on detailed analyses of the effects on decline rates of incremental investments, and the interplay of field vintages and reserves on the one hand, and field vintages and post-peak investment on the other.

6.1 Field vintage effects in the presence of reserves

In order to investigate the combined effect of the interplay of field vintage and reserves on decline rates, two ANCOVA (analysis of co-variance) models were specified and estimated under different assumptions to test for vintage effects. Specifically, the assumptions underlying the ANCOVA models are as follows:

(i) Benchmark vintage: The oldest field vintage labeled Vintage 5 (pre-1970 fields) was selected as the bench mark category,

(ii) uniform slope: Even though production decline rates of the various vintages may start at different levels, once started the rate of change of decline with respect to the size of reserves is the same, or, alternatively,

(iii) differentiated slope: Both the starting points of decline rates and sensitivity to the size of reserves differ among the various vintages.

The estimated regression result for the uniform slope case is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7) (6)

[R.sub.adjusted.sup.2] = 0.0830 [F.sub.5,212] = 4.937

where:

D[R.sub.i] = Production decline rate of the ith vintage field (i = 1, 2,......5).

[R.sub.i] = Proved initially-recoverable reserves of the ith vintage field.

[V.sub.1] = 1 if vintage = 1

= 0 otherwise

[V.sub.2] = 1 if vintage = 2

= 0 otherwise

[V.sub.3] = 1 if vintage = 3

= 0 otherwise

[V.sub.4] = 1 if vintage = 4

= 0 otherwise

The estimated regression result for the differentiated slope case is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

[R.sub.adjusted.sup.2] = 0.1030 [F.sub.9,208] = 3.779

where, in addition to previous definitions,

[V.sub.i][R.sub.i] = Interactive effect of vintage i and associated proved reserves

[FIGURE 6 OMITTED]

The adjusted R-squares of both regressions are rather low but the Fstatistics are significant. It is noteworthy that even though only marginal, the (2%) higher adjusted R-square of the differentiated-slope model implies that one can not reject the hypothesis that there are vintage effects in the extent to which availability of reserves can help to reduce decline rates. The question of the direction of the effect arises.

The intercepts and slopes of the two models are illuminating. The comparative implied annual mean decline rates (computed from the differentiated intercepts of the two models) are presented graphically in Fig. 6. The chart reveals that (a) individually, the decline rates in newer fields start at higher levels than in older fields in the uniform and differentiated models, and (b), comparatively, allowing for vintage effects, the newer vintages exhibit higher decline rates than otherwise, implying that the uniform reaction assumption understates the true decline rates. The reverse is the case with the older vintages.

The estimated uniform and differentiated slope co-efficients of the two models are presented below in Table 4.

The results in Table 4 indicate that, while the marginal effect of field vintage on production decline rate is the same across the vintages in the uniform case, the effect increases inversely with the age of the fields in the differentiated slope case. That is, the availability of reserves in newer fields would ameliorate the decline process to a greater extent than in the older fields. (7)

6.2 Vintage effects in the presence of post-peak field Investments

As before, two ANCOVA models distinguished by the assumptions made concerning their slope coefficients were specified and estimated, with post-peak production investment (8) replacing reserves in an attempt to determine the vintage effects on decline rates in fields endowed with post-peak investment.

The estimated regression result under the uniform slope assumption is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9) (9)

[R.sub.adjusted.sup.2] = 0.1910 [F.sub.5,185] = 9.968

where in addition to previous definitions:

[I.sub.i] = Post-peak field development investment of fields of the ith vintage (i=1,2,....5).

[V.sub.1] = 1 if vintage = 1

= 0 otherwise

[V.sub.2] = 1 if vintage = 2

= 0 otherwise

[V.sub.3] = 1 if vintage = 3

= 0 otherwise

[V.sub.4] = 1 if vintage = 4

= 0 otherwise

The estimated regression result under the differentiated slope assumption is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

[R.sub.adjusted.sup.2] = 0.2510 [F.sub.9,181] = 8.082

where, in addition to previous definitions:

[V.sub.i][I.sub.i] = Interactive effect of vintage i and associated post-peak investment

The comparative results of the two models are summarized in Table 5 and Fig. 7.

[FIGURE 7 OMITTED]

A study of Table 5 reveals similarities with Table 4, indicating a similar pattern in the interactive effects of vintage and post-peak investment on decline rates on the one hand, and the interactive effects of vintage and recoverable reserves on the other.

6.3 Effects of Incremental Investment on Decline Rates

In the field database some operators distinguished 'incremental' investments defined explicitly as capital outlays in enhanced oil recovery (EOR) schemes and in-fill development wells, targeted at enhancing recoverable reserves (10). This is different from all post-production peak investment (11) considered above. 54 fields were identified by operators as attracting such specific incremental investments. The investigation of the effects of incremental investment on decline rates was conducted within two analytical frameworks.

6.3.1 Inter-field/cross section analysis

The following ANCOVA linear model was specified and estimated to test the hypothesis of zero incremental investment effect. Reserves were included as an explanatory variable in equation (11) because of their already-established centrality to production and production decline rates

D[R.sub.k] = [a.sub.0] + [a.sub.1][V.sub.k] + [a.sub.2][R.sub.k] + [a.sub.3]([V.sub.K] X [R.sub.K]) + [e.sub.k] (11)

where:

D[R.sub.k] = mean annual production decline rate of group k fields

[V.sub.k] = dummy variable assuming:

= 1, if a field has incremental investment

= 0, otherwise

[R.sub.k] = Proved reserves of group k fields

([V.sub.K] X [R.sub.K]) = interaction effects of reserves and incremental investment of the kth group

[a.sub.0], [a.sub.1], [a.sub.2], [a.sub.3] = estimable parameter coefficients

[e.sub.k] = disturbance team (white noise assumptions)

The regression result is summarized as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

[R.sub.2]adjusted = 0.0728 Significance F = 0.0002

The regression result in equation (12) above provides evidence that a negative relationship exists between proved reserves and decline rates. This relationship is statistically significant (t = -3.5683). The interactive effects of incremental investment and reserves on decline rates are positive and statistically significant (t = 2.5596). Overall, the joint influence of the three explanatory variables is statistically significant as reflected in the low value of the significance F statistic (=0.0002), even though the R-square is relatively low. The statistical significance of the differential intercept (t = -2.7196) and differential slope (t = 2.5596) supports the hypothesis that the decline rates of the two groups are statistically different, with the rate being higher in the fields without incremental investment.

6.3.2 Intra-field/time series analysis

Using time series data an investigation was conducted into whether additional investment makes any difference to the decline rates in the pre- and post-incremental investment periods in each field.

In order to conduct this investigation, the dataset for each field was divided into pre- and post-incremental investment periods. A linear model of the following form was assumed, estimated, and tested:

[D.sub.jt] = [b.sub.0] + [b.sub.1][U.sub.jt] + [b.sub.2][Y.sub.jt] + [b.sub.3]([U.sub.jt] X [Y.sub.jt]) + [e.sub.jt] (13)

where:

[D.sub.jt] = production decline rate of the jth field at time t

[U.sub.l] = dummy variable assuming:

= 1 in the pre-incremental investment period

= 0, in the post-incremental investment period

[Y.sub.it] = remaining proved reserves of the jth field at time t

([U.sub.jt] X [Y.sub.jt]) = interaction of time period and proved remaining reserves of the jth field

[b.sub.0], [b.sub.1], [b.sub.2], [b.sub.3] = estimable parameter coefficents

[e.sub.jt] = disturbance term

The regression results are summarized in Appendix 1. The results provide evidence that in the vast majority of cases the differential intercepts and slopes are statistically significant, implying that, not only are the mean annual decline rates in the pre- and post-incremental investment periods different, but the responsiveness of decline rates to changes in remaining reserves is radically different in the two periods. Further, the post-incremental investment decline rates are lower than in the pre-investment period, suggesting that incremental investment does temper decline rates.

6.3.3 Decline rate decelerators

Granted that there are appreciable reductions in decline rates in the post-incremental investment period, the next stage was to identify the major factors influencing the amelioration of them. Several experiments were run to test the statistical significance of the individual influences of the following variables: (a) field vintage, (b) field location (SNS or the Rest of the UKCS), (c) resource type (oil, gas or condensate), (d) size of reserves, (e) geological vintage, (f) water depth, (g) total (or size of) incremental investment, and (h) field life.

Of the eight possible determinants of the deceleration in decline rates induced by incremental investment, only two--field vintage and field life--were found to have statistically significant degrees of influence (12). Two conclusions can be drawn from these results. Firstly, regardless of location, resource-type, size of reserves, geological vintage, water depth and the size of incremental investment, it is the incidence of incremental investment in a field that would normally slow down the decline rate. The statistical insignificance of the size of incremental investment is consistent with the principle that one cannot indefinitely reduce decline rates by increasing the amount of incremental investment.

Secondly, combining this result with an earlier result which established the dependence of field life on field vintage, it can be concluded that under ceteris paribus assumptions (including the assumption of rational producer behaviour), incremental investments in fields of more recent vintages which have shorter field lives (13) are likelier to achieve larger moderations to decline rates, subject to the availability of economically-recoverable reserves, as follows:

Table 6. Potential moderations in mean annual decline rates arising from
incremental investments

Field vintage  Potential reduction in decline rate

Pre-1970s                  0.05%
1970s fields               7.02%
1980s fields              13.20%
1990s fields              16.33%
2000s fields              17.77%

This result seems plausible in the light of Watkins' (2002) finding that reserves appreciation occur over a long period of time from 3 sources as follows:

a. reservoir development and performance providing new information;

b. recalibration of field engineering and geological models in the light of new knowledge; and,

c. investment in, and application of, new technology.

The scope of older fields to benefit from the aforementioned sources has probably been greater with the third source, as they have had sufficient time to exploit the opportunities offered by (a) and (b). Even then, the ability of the older fields to maximally exploit new technology is constrained by existing infrastructure, well, and production designs. By contrast, although the incidence of the inception of enhanced recovery techniques at production start-up is more prevalent among the newer fields, (which limits future gains in reserves appreciation via this route) it is plausible that these fields still have scope to enhance reserves by raising their recoverable reserves and hence ameliorate their production decline rates through (a) and (b) above.

7. CONCLUSIONS

The present study has attempted to define and measure production decline rates in the UKCS and to establish the important relationships which influence these rates. The study measures a field's production decline relative to its peak production. A curve-fitting exercise was conducted to test which of linear, exponential, and logistic models best fitted the data. It was found that the logistic model was the best-regressed model in the great majority of cases. Further, the study demonstrated that UKCS fields have witnessed both simple and complex logistic decline processes, with the majority of fields experiencing the latter process. Using the Forties and Audrey fields as examples, the study demonstrated that the accuracy of oil and gas production forecasts crucially depends on choosing the appropriate decline rate model. Production forecasts based on either a linear or exponential decline rate when the true rate is logistic would produce quite inaccurate predictions.

The effects of field reserves and incremental investment on production decline rates were investigated. The estimated differentiated intercepts and slope coefficients established that, while the availability of reserves would generally lead to lower absolute annual mean decline rates, the rate of change of decline rates varies among the five field vintages identified in the study, with the deceleration rate being highest among the more recent vintages. However, in absolute terms, the newer fields have relatively higher mean annual decline rates, probably on account of their relatively smaller reserves. This poses a challenge and an opportunity for the industry. The danger is that as the older fields approach economic cut-off increasing reliance on the newer fields raises the overall production decline rate thus accelerating the onset of maturity of the province (see DTI (2001)). Therein lies the challenge.

The investigation of the effects of post-peak and specific incremental investment in EOR and in-fill drilling established that both forms of investment significantly reduce production decline rates. Given the vital importance of recoverable reserves and their enhancement an investment-friendly operating environment needs to be sustained to minimize the decline rates of UKCS fields.

APPENDIX 1 Results Of Testing The Effects Of Incremental Investment On
Production Decline Rates

                                           SLOPE CO-EFFICIENTS
                                           (unit change with respect to
FIELDNAME        MEAN ANNUAL DECLINE RATE  proved remaining reserves)

                 Pre-          Post-         Pre-          Post-
                 investment    investment    investment    investment
                 (%)           (%)

Alba             14.04          3.77         -0.06          0.08
Andrew           17.49          3.00         -0.13          0.09
Arbroath         10.13          2.18         -0.09          0.10
Arkwright        11.08          2.13         -0.56          0.19
Auk               1.17          0.37          0.00          0.11
Barque            9.12          0.94         -0.07          0.01
Beryl            10.53          1.46         -0.02          0.05
Brae South        5.94          0.33         -0.01          0.10
Brent             4.38          0.60          0.00          0.01
Bruce            17.13          2.24         -0.25          0.17
Claymore          3.30          0.54         -0.01          0.02
Clyde             4.63          0.84          0.00          0.16
Cormorant
  North & South   4.74          0.62         -0.01          0.06
Cyrus            25.42          0.45         -2.22         52.91
Douglas          11.48          2.06         -0.11          0.11
Dunlin            3.73          0.23          0.01          0.21
Dunlin
  South-West     24.08          3.61         -3.83          4.98
Eider             8.15          0.12         -0.06          0.97
Everest          18.70          1.03         -0.24          0.48
Forties           4.96          0.55          0.00          0.01
Gannet A         14.43          2.80         -0.15          0.28
Gannet C         12.06          3.60         -0.18          0.15
Gannet D         30.64          7.12         -1.00          0.04
Gannet G         66.23          5.20         -9.27          0.49
Gawain           12.74         10.52         -0.39          0.37
Harding           6.16          3.59         -0.03          0.03
Heather           3.67          1.07          0.00          0.14
Keith            -6.68          3.99          0.00          0.78
Ketch            11.77          2.14         -0.18          0.08
Leman             3.16          0.40          0.00          0.01
Lomond           14.57          2.55         -0.18          0.37
Machar           19.17          5.74         -0.16         -0.01
Marnock          26.42          0.79         -0.37          0.38
Merlin           17.98          1.96         -0.79          2.70
Miller           22.21          2.19         -0.12          0.44
Montrose          3.15          0.05          0.04          0.78
Nelson           13.30          0.66         -0.03          0.06
Nevis South       3.20          5.03         -0.06          0.35
Osprey            9.43          1.76         -0.09          0.44
Pelican          22.56          1.44         -0.48          1.78
Pierce           39.78          5.23         -0.58          0.16
Piper             3.92          0.43          0.00          0.01
Saltire          19.24          1.40         -0.22          0.68
Schooner         12.41          1.57         -0.21          0.26
Sean North       31.54          1.67         -1.77          0.08
Tartan            2.98          0.30          0.01          0.18
Tern             11.56          1.62         -0.05          0.22
Thelma           26.54          4.05         -0.79          1.46

                 GOODNESS-OF-FIT
FIELDNAME        MEASURES
                                    differentiated  differentiated
                                    intercept       slope
                 adjusted R-square  (t statistic)   (t statistic)

Alba             0.30                1.32            -2.54
Andrew           0.75                3.98            -6.16
Arbroath         0.72                5.77            -7.30
Arkwright        0.61                3.94            -4.88
Auk              0.33                3.61            -3.22
Barque           0.79                7.75            -8.78
Beryl            0.93               15.90           -17.01
Brae South       0.71                7.48            -5.87
Brent            0.76                8.16            -6.59
Bruce            0.90                2.11            -5.71
Claymore         0.72                8.95            -5.04
Clyde            0.52                3.60            -0.10
Cormorant
  North & South  0.61                6.04            -3.63
Cyrus            0.94               10.79            -5.64
Douglas          0.68                4.90            -6.02
Dunlin           0.43                2.98            -0.93
Dunlin
  South-West     0.73                5.94            -5.19
Eider            0.71                6.30            -1.13
Everest          0.93               10.94           -16.30
Forties          0.68                8.02            -2.55
Gannet A         0.83                6.30            -7.05
Gannet C         0.50                3.20            -3.77
Gannet D         0.15                0.87            -1.08
Gannet G         0.71                3.29            -4.18
Gawain           0.39                0.31            -1.07
Harding          0.62                0.48            -1.82
Heather          0.44                3.93            -2.34
Keith            0.56                0.00             0.00
Ketch            0.51                2.81            -3.59
Leman            0.72                9.86            -5.13
Lomond           0.47                2.24            -4.37
Machar           0.19                1.01            -1.18
Marnock          0.86                5.23            -7.66
Merlin           0.71                5.63            -3.38
Miller           0.82                6.86            -4.65
Montrose         0.33                2.25            -0.10
Nelson           0.87                8.67           -10.33
Nevis South      0.40               -0.09            -0.08
Osprey           0.63                5.61            -2.85
Pelican          0.96               16.30           -17.88
Pierce           0.59                2.38            -3.07
Piper            0.39                3.40            -0.78
Saltire          0.73                7.87            -3.03
Schooner         0.88               11.50           -12.10
Sean North       0.49                2.67            -2.83
Tartan           0.64                4.28            -1.33
Tern             0.91               12.06           -11.37
Thelma           0.84                6.78            -7.20

APPENDIX 2

Tests of significance of factors influencing a deceleration of decline rates

The following is a summary of the one-way ANOVA results of testing the significance of decline rates-reducing effects of:

Variable                           F    Sig. F         Remarks

Field vintage                    2.729  0.055          Significant
Field location (14)              0.379  0.769          Not significant
Resource type                    0.269  0.765          Not significant
Reserves size                           not available
Reservoir age                    0.939  0.466          Not significant
Field location (15)              0.056  0.814          Not significant
Size of incremental investment   0.165  0.686          Not significant
Field life                      11.283  0.002          Significant

Table 1. Best-fit models by field vintage

Field         Best-fit models (% of cases)   Total
Vintage       Logistic  Linear  Exponential

Pre-1970      66.67     33.33   0.0          100.00
1970s         77.78     22.22   0.0          100.00
1980s         63.46     26.92   9.62         100.00
1990s         65.25     29.08   5.67         100.00
2000s         81.82     18.18   0.0          100.00
All vintages  67.26     26.99   5.75         100.00

Table 4. Marginal interaction effects of vintage and reserves on decline
rates

Field          Estimated Slope Coefficients
Vintage     Uniform             Differentiated

Pre-1970    -0.0033             -0.0001
1970s       -0.0033             -0.0002
1980s       -0.0033             -0.0048
1990s       -0.0033             -0.0171
2000s       -0.0033             -0.0230

Table 5: Marginal interaction effects of vintage and post-peak
investment on decline rates

Field       Estimated Slope Coefficients
Vintage     Uniform     Differentiated

Pre-1970    -0.0376     -0.0109
1970s       -0.0376     -0.0107
1980s       -0.0376     -0.0140
1990s       -0.0376     -0.0235
2000s       -0.0376     -0.0201

ACKNOWLEDGMENT

We are grateful to two anonymous referees and the Editor for their incisive comments which helped to improve the paper.

1. The detailed results are reported in Kemp and Kasim (2002).

2. A field's vintage is determined by its year of first production. Five categories, representing 5 decades since oil and gas production commenced in the UKCS, were selected. They are:

(a) Pre-1970 fields

(b) 1970s fields

(c) 1980s fields

(d) 1990s fields

(e) 2000s fields

3. In 2001, PIU noted that 'Over the last 20 years predictions of imminent decline of oil production in the North Sea have been common.' But, as noted by BP in the same year ' ... production has risen every year for the last ten years, which nobody would have dared to predict ten years ago'.

4. The non-linear regression was conducted using Loglet, a specialized computer program developed at the Rockefeller University, USA. The program is based on the Levenberg-Marquardt iterative least-square method for fitting non-linear models to data. The detailed regression results may be obtained from the corresponding author.

5. The results of one-way ANOVA tests of the influence of the qualitative factors on decline rates, using the 3 decline models are summarized below:

One-Way ANOVA Test Results

                    F-statistic                       Sig. F statistic
Variable            logistic     exponential  linear  logistic

Field vintage       5.531        7.274        8.799   0.0
Reservoir age       0.389        1.517        1.366   0.885
Field location (5)  0.449        1.066        0.460   0.773
Resource Type       1.681        0.087        0.312   0.189

Variable            exponential  linear

Field vintage       0.0          0.0
Reservoir age       0.174        0.238
Field location (5)  0.374        0.765
Resource Type       0.917        0.732

Clearly, regardless of the decline model chosen (linear, exponential or logistic) and/or location of the producing field, field vintage appears to be the only factor with statistically significant effects on production decline rates in the UKCS.

The individual influence of the quantitative variables (field life, reserves and water depth) on decline rates were also tested in separate bivariate regression runs. The results are summarized below:

Summary of comparative regression results

Explanatory                                        ANOVA
variable     t-statistic         R2 adjusted       (sig. F statistic)

Field         -6.75 (logistic)   0.17 (logistic)   0.00 (logistic)
life          -9.70 (expo)       0.30 (expo)       0.00 (expo)
             -12.55 (linear)     0.42 (linear)     0.00 (linear)
Water          0.06 (logistic)  -0.01 (logistic)   0.95 (logistic)
depth          0.73 (expo)      -0.00 (expo)       0.47 (expo)
               0.21 (linear)    -0.01 (linear)     0.84 (linear)
Reserves      -3.17 (logistic)   0.04 (logistic)   0.00 (logistic)
              -3.28 (expo)       0.04 (expo)       0.01 (expo)
              -4.18 (linear)     0.07 (linear)     0.00 (linear)

Explanatory  Pearson
variable     correlation

Field        -0.42 (logistic)
life         -0.55 (expo)
             -0.65 (linear)
Water         0.00 (logistic)
depth         0.05 (expo)
              0.01 (linear)
Reserves     -0.21 (logistic)
             -0.22 (expo)
             -0.27 (linear)

Reserves and field life appear to decelerate decline rates in a statistically significant manner while water depth appears to weakly accelerate decline rates (the perverse sign of the adjusted R-square in the water depth regression implies that this particular result must be treated with caution).

6. The t-statistics are in brackets in this and subsequent estimation results.

7. A recent study (Toole and Grist (2003)) found that the recovery factors for oil fields in the UKCS averaged 45%, while for dry gas fields it was around 75%. Significant variations were also found. Substantial scope for further increased recovery remained.

8. Defined to include all field-related investment incurred after peak production.

9. The t-statistics are in the brackets.

10. It is acknowledged that other operators may not always have specifically identified such production-enhancing investments.

11. Includes capital outlays not specifically targeted at reserves enhancement such as safety.

12. See Appendix 2.

13. A bivariate regression of field life on field vintage was performed. One-way ANOVA results predicted that the mean field life of the various vintages are as follows:

           Vintage          Differential               Mean
Vintage    legend           intercept     t-statistic  field life

Vintage 5  Pre-1970 fields   48.667       10.980       48.67
Vintage 4  1970s fields     -38.128       -8.145       33.67 years
Vintage 3  1980s fields     -35.034       -7.825       20.36 years
Vintage 2  1990s fields     -28.315       -6.218       13.64 years
Vintage 1  2000s fields     -15.000       -3.133       10.54 years

14. 6-area classification--i.e. Central, Northern and Southern North Seas, Irish Sea, Moray Firth and West of Scotland

15. 2-area classification i.e. SNS and the Rest of UKCS

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Alex G. Kemp and A.S. Kasim*

* Department of Economics, University of Aberdeen, Dunbar Street, Aberdeen AB24 3QY, Tel: +44 (0) 1224 272168, Fax: +44 (0) 1224 272181, E-mail: a.g.kemp@abdn.ac.uk