From the microscopic scale, the growth trend of crude oil production can be predicted by the production composition curve model; From the macro scale, there are many forecasting models that can be used to predict the growth trend of crude oil production, including trend extrapolation model, elastic coefficient forecasting model, regression analysis forecasting model, time forecasting model, optimal combination comparison forecasting model, Delphi model, Hubert model and so on.
Figure 2.4 curve of reserve growth function of 48 States in the United States.
Fig. 2.5 Prediction Process of Reserve Growth of USGS
2.5.2. 1 yield composition model
The growth trend of crude oil production in oil reservoir can be predicted by production composition curve method, and the initial annual output can be calculated by the following formula:
Initial annual output = proven reserves × oil production rate × proven reserves utilization rate (2.5)
In the formula, analogy method, empirical method and expert evaluation method are mainly used to estimate oil production speed, stable production period, decline rate and utilization rate of proven reserves. The law of output decline is generally calculated by hyperbolic decline method, harmonic decline method and exponential decline method.
The annual output during the stable production period can be predicted by three methods:
(1) According to the oil test results, stable production, production pressure difference, perforation thickness, etc. And the effective thickness of the target, or according to the analogy between oil and gas reservoirs and reservoir physical properties, the average daily output of a single well in the stable production period is obtained:
Stable annual output = average daily output of stable single well × number of production wells× 330 (2.6)
(2) According to the analogy of oil and gas reservoir and reservoir physical properties, the production speed in stable production period is obtained:
Annual output in stable period = mining speed in stable period × finally proven reserves (2.7)
(3) According to the analogy of oil and gas reservoir and reservoir physical properties, the estimated productivity after completion can be regarded as the annual output in the stable production period.
2.5.2.2 trend extrapolation prediction model
When crude oil production shows a certain upward or downward trend with time, and there is no obvious seasonal fluctuation, and a suitable function curve can be found to reflect this trend, a trend model y=f(t) with time t as the independent variable and time series value y as the dependent variable can be established. When there is reason to believe that this trend can continue into the future, the future value of the time series at the corresponding time can be obtained by giving the required value of the variable t. This is the trend extrapolation method.
The principle is as follows:
Let the trend extrapolation model become
The sum of squares of prediction error is
The partial derivatives of model parameters are obtained and made zero, and the equation is constructed.
Comparative study on the history of oil production and consumption between China and the United States
Where bi is the i-th parameter in the model, the calculated model parameters can be predicted by substituting the sum of known data.
There are two hypothetical conditions for applying trend extrapolation method: ① assuming that the output has not changed by leaps and bounds; (2) It is assumed that the factors affecting output growth remain unchanged or change little. Choosing a suitable trend model is an important part of applying trend extrapolation method, and graphic recognition method and difference method are two basic methods to choose trend model.
Trend extrapolation method can be subdivided into linear trend prediction method and nonlinear trend prediction method (including logarithmic trend prediction method, quadratic curve trend prediction method and exponential curve trend prediction method, etc.). ), periodic fluctuation trend model prediction method, growth curve trend prediction method, etc.
The advantages of trend extrapolation method are: only historical data is needed, and the amount of data required is less; The disadvantage is that if the crude oil output changes, it will cause a big error.
2.5.2.3 elastic coefficient prediction model
The growth of many products is closely related to economic growth, and the demand for oil and natural gas increases with the growth of national economy. The elastic coefficient method links the two, first predicts the elastic coefficient (β), and then obtains the demand growth rate according to the predicted GDP growth rate, namely:
Elasticity coefficient (β) = demand growth rate /GDP growth rate (2.9)
In the formula, the determination of β should be considered from the following aspects:
(1) Simulation based on historical data. Simulating the existing historical data, establishing a mathematical model, and then extrapolating according to the changing trend of historical development, and combining with the future development trend of products, modifying on the basis of extrapolation, so as to get the β of the future year, which is set as β 1, mainly reflecting the influence of economic inertia on the future.
(2) according to the final use of the product. The demand development of oil and gas production depends on the expansion of its application field and the improvement of its application level. Each application field and industry has its own development plan, so this part reflects the role of planning in development. For a product, it can be considered that the beta value of the product is equal to the weighted average of its various end uses. The weight is determined according to the proportion of each use and the analysis and judgment of the development speed. The beta value is set to beta2.
(3) The range of the development prospect of new uses is 0 ~ 0.5, and it is set as β3. According to the application status of products, the possibility of developing new uses in the future and the competition intensity of new uses.
(4) The range of product substitution possibility is -0.5 ~ 0, and it is set as β4. According to the competition intensity between substitute products and forecast products.
(5) If there is no industry development planning data, the β value obtained by comprehensive analysis and judgment of experts is introduced and set as β5. Finally: β5=[(β 1+β2)/2]+β3+β4, or β5=[(β 1+β2+β3)/3]+β4.
Compared with the traditional mathematical statistical model forecasting method, this method is less disturbed by historical fluctuation factors, and can reflect the influence of government regulation, macroeconomics, scientific and technological progress and other factors on the market to some extent.
The elastic coefficient method is the ratio of the average growth rate of crude oil production to GDP, and the total oil consumption at the end of the planning period is obtained according to the GDP growth rate combined with the elastic coefficient. Elastic coefficient method is to determine the relative speed of crude oil production development and national economic development from a macro perspective, and it is an important parameter to measure national economic development and oil production demand.
The advantage of this method is simple and easy to calculate. The disadvantage is that a lot of detailed research work is needed.
2.5.2.4 regression analysis prediction model
Regression prediction is to establish a mathematical model that can be used for mathematical analysis according to the historical data of crude oil production. Using the regression analysis method in mathematical statistics, the observed data of variables are statistically analyzed, so as to predict the future output.
The main task of regression analysis is to find the regression equation according to the N groups of observation values of dependent variable Y and independent variable x 1, x2, …, xp:
Comparative study on the history of oil production and consumption between China and the United States
Where bi (I = 0, 1, …, p) is the regression coefficient.
Regression models generally include univariate linear regression, multivariate linear regression, nonlinear regression and other regression prediction models. Among them, linear regression can generally be used to predict short-term and medium-term output, which has the advantage of high prediction accuracy, but the disadvantage is that it is difficult to make detailed statistics on the total industrial and agricultural output value at the planning level. Regression analysis can only calculate the comprehensive oil production level, but not the specific production and development level of each oilfield, so it is impossible to make specific production and construction planning.
2.5.2.5 time series prediction model
The time series forecasting model attempts to establish a mathematical model based on the historical data of crude oil production. On the one hand, this mathematical model is used to describe the statistical regularity of the changing process of crude oil production as a random variable; On the other hand, on the basis of this mathematical model, the mathematical expression of crude oil production prediction is established to predict the future crude oil production.
Time series models mainly include autoregressive AR(p), moving average MA(q) and autoregressive moving average process ARMA(p, Q). The advantages of these methods are: less historical data and less workload; The disadvantage is that it does not consider the factors of crude oil production change, only devotes to data fitting, and does not deal with regularity enough, and is only suitable for short-term prediction of uniform crude oil production change.
The autoregressive integrated moving average process (ARIMA) is an improved model of ARMA, which takes into account both the dependence on time series and the interference of random fluctuations, and has a high accuracy in forecasting the short-term trend of crude oil production. It is one of the methods widely used internationally in recent years.
The basic idea of ARIMA model is to regard the data sequence formed by the predicted object over time as a random sequence, which is approximately described by a certain mathematical model. Once this model is identified, the future value can be predicted from the past and present values of the time series.
Comparative forecasting model of 2.5.2.6 optimal combination
The optimal combination has two meanings: one is to choose the appropriate weighted average from the results obtained by several forecasting methods; The second is to compare several forecasting methods and choose the forecasting model with the best fitting degree or the smallest standard deviation for forecasting. For the combined forecasting method, it must also be noted that when a single forecasting model can not completely and correctly describe the changing law of forecasting quantity, combined forecasting plays a role. It is entirely possible that a model that can fully reflect the actual development law can predict better than the combination forecasting method.
The advantages of this method are: the information of multiple single prediction models is well combined, and the influence information considered is more comprehensive, which can effectively improve the prediction effect; The disadvantage is that the weight is difficult to determine, and all the factors that will play a role in the future cannot be included in the model, which limits the improvement of prediction accuracy to some extent.
2.5.2.7 Delphi forecasting model
Delphi model, also known as expert evaluation prediction model. At the end of 1950s, RAND Corporation of the United States first proposed the investigation and planning method with Delphi as the code name. In this method, the survey organizer formulates a questionnaire and conducts a consultation survey according to the prescribed procedures. After several rounds of repetition, experts' opinions were solicited and analyzed repeatedly, so that their opinions gradually tended to be consistent, thus increasing the reliability of the conclusion.
The advantages of Delphi method are collectivity, anonymity, objectivity and statistical analysis. Its shortcomings mainly lie in: ① intuition. Delphi method is basically an intuitive forecasting method, which is largely restricted by experts' personal ideas, knowledge and experience. ② Lack of strict textual research. Because the result of discussion is not the result of heated debate at the meeting, their arguments are often insufficient, which may exclude the correct opinions of a few people.
Aiming at the weakness of Delphi method, a derivative Delphi method was produced later. Its working feature is the combination of anonymous consultation and face-to-face discussion, which improves the limitations of Delphi method and greatly improves the work efficiency and planning quality.
Delphi method is based on experts' subjective judgment, especially suitable for planning lacking objective materials and data. It is a beneficial extension of system analysis method in the field of viewpoint and value judgment, which breaks through the limitation of traditional quantitative analysis and opens up a new road for more scientific planning. Delphi method provides planners with the possibility of multi-scheme selection, because it can evaluate all kinds of "possible" and "expected" prospects in the future development.
2.5.2.8 harbert forecasting model.
1956, American geophysicist M.K.Hubbert obtained the famous Hubbert model according to the dynamic curve characteristics of recoverable reserves and production in 48 States in the United States, and assumed that the curve between production and development time was bell-shaped, which was a special case of Logistic model [63]. Hubert predicted that American oil production would peak in the early 1970s, and the final development results also showed that American oil production really peaked in 1970, which made many scientists accept Hubert's view and use this model to predict oil and gas production in the basin.
The equation of Hubert model can be expressed as
Comparative study on the history of oil production and consumption between China and the United States
Where CP is the cumulative output; U is the predicted final recoverable resources; Tm is the inflection point, that is, the time when the output peak appears; B is a constant.
Hubert model assumes that the growth process of oil and gas production is a symmetrical bell curve, so the peak production predicted by Hubert model can be derived from equation (2. 1 1).
Comparative study on the history of oil production and consumption between China and the United States
At present, Hubert model still attracts many scholars to conduct in-depth research. 1998, according to Hubert model [64], Campell and Laherrere predicted that the global crude oil production would peak and begin to decline 20 10 years ago. In 2000, Fattah and Startzman improved the bell curve of Hubert's prediction of oil production, and put forward a multi-stage Hubert mathematical model [65]. Albert A.Bartlett published an article in 2000, which tested and analyzed the sensitivity of Hubert model to predict the crude oil production in the United States and the world [66]. In 2004, Imam and others published an article in the American Journal of Oil and Gas, pointing out that the global conventional natural gas production will reach its peak in the second decade of 2 1 century, and will gradually decrease thereafter. According to the natural gas production data from 1970-2002, the output trend of 46 major natural gas producing countries in the world before 2050 is predicted by using the multi-stage Hubert model: the peak of global natural gas production will appear in 20 19, when the annual natural gas production will reach 2.5 trillion cubic meters; The final output of global natural gas is 260 trillion cubic meters, and 72% of natural gas remains to be exploited [67].
Although the Hubert model has accurately predicted that the peak of crude oil production in the United States is 1970, the crude oil production is affected by many factors such as crude oil physical properties, politics and economy, and the geological, crude oil physical properties, politics and economy factors that have great influence on oil and gas well production are not considered in the Hubert model. Therefore, the forecasting process obtained by bell curve can only roughly reflect the growth trend of output, but can not accurately reflect it.