Research Methods of Main Parameter Sensitivity Differences in China’s Dynamic Oil and Gas Reserve Estimation under SEC Standards

Abstract

International oil and gas companies listed in New York must publish the information of oil and gas reserves under the SEC (United States Securities and Exchange Commission) standards every year. For greatly improving the SEC reserve, the SEC reserve value and the SEC reserve substitution rate, in this article not only the SEC reserve equations have been determined but also the SEC reserve value models have been established. The SEC reserve value models have been verified as correct. Based on these models, the multivariate function calculus method, the multivariate function limit method and the function recurrence method have been adopted to research parameter sensitivity differences rules, parameter adjustment directions, parameter adjustment degrees and SEC reserve parameter linkage adjustment rules. The research is significant, because there are great differences between SEC standards and China’s in reserve management mode, reserve estimation method system and financial management system. It is just these differences that cause the frequent adjustment of SEC reserve parameters during the process of SEC reserve submissions each year. As a result, this article reaches some conclusions. Above all, the article has clarified the parameter quantitative conditions that lead to the sensitivity between the SEC reserve and the initial production to begin stronger and weaker than the sensitivity between the SEC reserve and the price in production exponential, hyperbolic and harmonic decline types. Furthermore, the article has clarified the parameter quantitative conditions that lead to the sensitivity between the SEC reserve value and the initial production to begin stronger and weaker than the sensitivity between the SEC reserve value and the price in common production exponential decline types. Moreover, the article has clarified reserve parameter linkage adjustment rules and found the most significant parameter whose least adjustment will cause the largest reserve increase. In addition, the function calculus method adopted to disclose reserve parameter sensitivity rules will expand the parameter sensitivity analysis method that took the previous statistical mapping method as the main analysis method.

1. Introduction

International oil and gas companies listed in New York must publish the information of oil and gas reserves under SEC (United States Securities and Exchange Commission) standards every year [1]. According to the new regulations in the “Modernization of oil and gas report” issued by SEC in 2008, both the physical SEC reserve volume and the SEC reserve value have become the necessary provisions for the publication of listed reserve assets information [2].

There are two main reasons that cause great differences in the geological parameters, development parameters and economic parameters between American professional estimation companies and domestic oil companies. For one thing, there are great differences between SEC standards and China’s in reserve management mode, reserve estimation method system and financial management system [3,4,5,6,7,8,9,10,11,12]. For another, SEC commits professional oil estimation companies to estimate domestic reserves with American professional estimation software [13]. As a result, the SEC reserve substitution rate was smaller than the previous year’s, often when some domestic listed oil companies were in an increasing production period with great development investment. Obviously, the reserve estimation results were inconsistent with the actual production situation. Therefore, in general, for greatly improving the SEC reserve, the SEC reserve value and the SEC reserve substitution rate, the parameter sensitivity difference rules, parameter adjustment directions and reserve parameter linkage adjustment rules have become significant.

According to the petroleum development theory, the petroleum geology theory and the petroleum technical economics theory, not only the SEC reserve equations have been determined but also the parameter models of the SEC reserve value have been established. The multivariate function calculus method, the multivariate function limit method and the function recurrence method have been adopted to clarify the parameter quantitative parameter conditions that cause the sensitivity between the SEC reserve and the initial production to begin stronger and weaker than the sensitivity between the SEC reserve and the oil price in production exponential, hyperbolic and harmonic decline types. Furthermore, the research conclusions will clarify the direction, the range and the rules of SEC reserve parameter linkage adjustments. In general, these conclusions will contribute to optimize the decisions of increasing production and contribute to improving the SEC reserve, the SEC reserve value and the SEC reserve substitution rate greatly. Moreover, the function calculus method adopted to disclose the reserve parameter sensitivity rules will expand the parameter sensitivity analysis method system that took the previous statistical mapping method as the main analysis method.

2. SEC Reserve Estimation Method

According to the reservoir development status, the SEC reserve estimation can be divided into two kinds: the SEC proved developed reserve estimation and the SEC proved undeveloped reserve estimation [14].

Based on the new regulations in the “Modernization of oil and gas report” issued by SEC in 2008, both the physical reserve quantity and the reserve value have become the necessary provisions for the reserve information publication [2].

Since domestic oil and gas companies were listed in New York more than 20 years ago, the reservoir Arps production decline curve method [15] and the financial net present value method have been constantly adopted to estimate the SEC dynamic reserve with the American professional reserve estimation software [16,17,18].

3. SEC Dynamic Reserve Estimation Model Research

3.1. SEC Dynamic Reserve Equations

According to the Arps production decline curve method, the production decline types are mainly divided into exponential, harmonic and hyperbolic decline types. SEC dynamic reserve equations below indicate the relationship between production and cumulative production [8,16,19,20]:

$$\mathrm{Exponential}\mathrm{decline}\mathrm{type}:{\mathrm{N}}_{\mathrm{e}}=\frac{{\mathrm{q}}_{\mathrm{i}}-{\mathrm{q}}_{\mathrm{el}}}{\mathrm{d}}$$

(1)

$$\mathrm{Hyperbolic}\mathrm{decline}\mathrm{type}:{\mathrm{N}}_{\mathrm{e}}=\frac{{\mathrm{q}}_{\mathrm{i}}{}^{\mathrm{n}}}{\left(1-\mathrm{n}\right){\mathrm{d}}_{\mathrm{i}}}\left[{\mathrm{q}}_{\mathrm{i}}{}^{\left(1-\mathrm{n}\right)}-{\mathrm{q}}_{\mathrm{el}}{\mathrm{l}}^{\left(1-\mathrm{n}\right)}\right]$$

(2)

$$\mathrm{Harmonic}\mathrm{decline}\mathrm{type}:{\mathrm{N}}_{\mathrm{e}}=\frac{{\mathrm{q}}_{\mathrm{i}}}{{\mathrm{d}}_{\mathrm{i}}}{\ln }^{\frac{{\mathrm{q}}_{\mathrm{i}}}{{\mathrm{q}}_{\mathrm{el}}}}$$

(3)

• N_e—SEC reserve, barrel;
• q_i—initial production monthly, barrel/month;
• d—decline rate monthly, %;
• d_i—initial decline rate monthly, %;
• q_el—economic limit production, barrel/month.

3.2. Modeling SEC Dynamic Reserve Value

SEC dynamic reserve estimation methods mainly concern the Arps production decline curve method and the net present value method (NPV). The financial NPV method is the best indicator for economic estimations of oil and gas resources [21,22].

According to SEC standards, the variable cost method is adopted as the financial accounting method of operation cost. Within the economic producing life, the fixed operation cost and unit variable operation cost per barrel of the initial estimation base year are taken as the fixed operation cost and unit variable operation cost of the remaining years [3].

In Formulas (1)–(3), adopting the economic limit production will obtain the remaining economic recoverable reserve. The economic limit production can determine the cut-off point of the estimation production sequence, the cut-off point of the cash flow and the economic producing life. Adopting the variable cost method and the profit and loss balance method will obtain the formula of the economic limit production of each month [23]:

Profit = economic limit production × oil price − fixed operating cost
− variable operating cost − taxes − special oil gain levy = 0.

Therefore, the economic limit production of each month expressed as:

$$\begin{array}{cc}{\mathrm{q}}_{\mathrm{el}}& =\frac{{\mathrm{C}}_{\mathrm{fm}}}{\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{tax}}\right)-{\mathrm{C}}_{\mathrm{vu}}-\mathrm{sogl}}\\ & =\frac{{\mathrm{C}}_{\mathrm{L}}{\mathrm{rQ}}_{\mathrm{L}}}{12\left[\mathrm{P}\left(1-{\mathrm{ht}}_1-{\mathrm{ht}}_1{\mathrm{t}}_3-{\mathrm{ht}}_1{\mathrm{t}}_4-{\mathrm{t}}_5\right){\mathrm{Q}}_{\mathrm{L}}+{\mathrm{C}}_{\mathrm{L}}\mathrm{r}-{\mathrm{C}}_{\mathrm{L}}-{\mathrm{Q}}_{\mathrm{L}}{\mathrm{S}}_{\mathrm{ogl}}\right]}\end{array}$$

(4)

q_el—economic limit production, barrel/month; C_fm—fixed operating cost per month, $/month; C_VU—unit variable operating cost, $/barrel; P—oil price, $/barrel; t_{compound_tax}—comprehensive taxes, concern value-added tax, urban construction tax, education surtax, resource tax; t₁—value-added tax rate; t₂—income tax rate; t₃—product of urban construction tax rate and value-added tax rate; t₄—product of education surtax rate and value-added tax rate; t₅—resource tax rate; r—fixed cost proportion; C_L—total operating of estimation year, $; h—appropriate proportion of operating income; Q_L—total production of estimation year, barrel; S_ogl—special oil income levy, $/barrel.

3.2.1. Modeling SEC Reserve Value of Exponential Decline Type

Adopting the SEC financial variable cost method, the financial profit and loss balance method, the financial NPV method, the Arps production decline curve method, combined with economic limit production without development investment, the SEC reserve value model of the exponential decline type is established as follows:

$$\begin{array}{l}{\mathrm{NPV}}_{\mathrm{SEC}\mathrm{dynamic}\mathrm{reserve}\mathrm{value}}\\ ={\displaystyle \sum _{\mathrm{j}=1}^{\left[\mathrm{T}\right]}}\left\{\begin{array}{c}\left[\mathrm{P}\times \left(1-{\mathrm{ht}}_1-{\mathrm{ht}}_3-{\mathrm{ht}}_4-{\mathrm{t}}_5\right)-{\mathrm{C}}_{\mathrm{vu}}-\mathrm{Sogl}\right]\\ \times \frac{{\mathrm{q}}_{\mathrm{i}}\times {\mathrm{e}}^{-\left[12\times \left(\mathrm{j}-1\right)\times \mathrm{d}\right]}-{\mathrm{q}}_{\mathrm{i}}\times {\mathrm{e}}^{-\left[12\times \left(\mathrm{j}-1\right)\times \mathrm{d}\right]}\times {\mathrm{e}}^{-\left(11\times \mathrm{d}\right)}}{\mathrm{d}}\\ -12\times {\mathrm{C}}_{\mathrm{fm}}\end{array}\right\}\times \left(1-{\mathrm{t}}_2\right)\times {\left(1+\mathrm{i}\right)}^{-\mathrm{j}}\\ +\left\{\left[\mathrm{P}\times \left(1-{\mathrm{ht}}_1-{\mathrm{ht}}_3-{\mathrm{ht}}_4-{\mathrm{t}}_5\right)-{\mathrm{C}}_{\mathrm{vu}}-\mathrm{Sogl}\right]\times \frac{{\mathrm{q}}_{\mathrm{i}}\times {\mathrm{e}}^{-\left(12\times \mathrm{j}\times \mathrm{d}\right)}-{\mathrm{q}}_{\mathrm{el}}}{\mathrm{d}}-\mathrm{V}\times {\mathrm{C}}_{\mathrm{fm}}\right\}\\ \times \left(1-{\mathrm{t}}_2\right)\times {\left(1+\mathrm{i}\right)}^{-\left(\left[\mathrm{T}\right]+1\right)}+{\mathrm{S}}_{\mathrm{residual}\mathrm{value}\mathrm{of}\mathrm{fixed}\mathrm{assets}}\end{array}$$

(5)

NPV_{SEC-dynamic-reserve-value}—SEC dynamic reserve value, $; qi—initial production, barrel/month; q_el—economic limit production, barrel/month; C_fm—fixed operating cost per month, $/month; C_VU—unit variable operating cost, $/barrel; P—oil price, $/barrel; d—decline rate monthly, %; t_{compound tax}—comprehensive taxes, concern value-added tax, urban construction tax, education surtax, resource tax; t₁—value-added tax rate; t₂—income tax rate; t₃—product of urban construction tax rate and value-added tax rate; t₄—product of education surtax rate and value-added tax rate; t₅—resource tax rate; r—fixed cost proportion; C_L—total operating of estimation year, $; h—appropriate proportion of operating income; Q_L—total production of estimation year, barrel; S_ogl—special oil income levy, $/barrel; T—economic producing life, years; [T]—integer part of T, years; i—discount rate, %; j—ordinal of producing years; V—producing months of last year, months; S_{residual value of fixed assets}—residual value of fixed assets, $.

In Formula (5), the economic producing life T can be expressed as:

$$\mathrm{T}=\frac{{\ln }^{\mathrm{qi}}-{\ln }^{\mathrm{qel}}}{\mathrm{d}}-\mathrm{M}$$

(6)

T—economic producing life, years; M—decimal part of T, years. In Formula (6), when the economic producing life T is an integer, M is a decimal part.

Substitute Formula (4) and Formula (6) into Formula (5) to achieve the SEC reserve value model of exponential decline type:

$$\begin{array}{l}{\mathrm{NPV}}_{\mathrm{SEC}\mathrm{dynamic}\mathrm{reserve}\mathrm{value}}\\ ={\displaystyle \sum _{\mathrm{j}=1}^{\left[\mathrm{T}\right]}}\left\{\begin{array}{c}\left[\mathrm{P}\times \left(1-{\mathrm{ht}}_1-{\mathrm{ht}}_3-{\mathrm{ht}}_4-{\mathrm{t}}_5\right)-{\mathrm{C}}_{\mathrm{vu}}-\mathrm{Sogl}\right]\\ \times \frac{{\mathrm{q}}_{\mathrm{i}}\times {\mathrm{e}}^{-12\left(\mathrm{j}-1\right)\mathrm{d}}-{\mathrm{q}}_{\mathrm{i}}\times {\mathrm{e}}^{-12\left(\mathrm{j}-1\right)\mathrm{d}}\times {\mathrm{e}}^{-11\mathrm{d}}}{\mathrm{d}}-12\times {\mathrm{C}}_{\mathrm{fm}}\end{array}\right\}\times \left(1-{\mathrm{t}}_2\right)\times {\left(1+\mathrm{i}\right)}^{-\mathrm{j}}\\ +\left\{\begin{array}{c}\left[\mathrm{P}\times \left(1-{\mathrm{ht}}_1-{\mathrm{ht}}_3-{\mathrm{ht}}_4-{\mathrm{t}}_5\right)-{\mathrm{C}}_{\mathrm{vu}}-\mathrm{Sogl}\right]\\ \times \frac{{\mathrm{q}}_{\mathrm{i}}\times {\mathrm{e}}^{-12\times \mathrm{j}\times \mathrm{d}}-{\mathrm{q}}_{\mathrm{el}}}{\mathrm{d}}-\mathrm{V}\times {\mathrm{C}}_{\mathrm{fm}}\end{array}\right\}\times \left(1-{\mathrm{t}}_2\right)\times {\left(1+\mathrm{i}\right)}^{-\left\{\frac{{\ln }^{{\mathrm{q}}_{\mathrm{i}}}-{\ln }^{{\mathrm{q}}_{\mathrm{el}}}}{\mathrm{d}}-\mathrm{M}+1\right\}}\\ +{\mathrm{S}}_{\mathrm{residual}\mathrm{value}\mathrm{of}\mathrm{fixed}\mathrm{assets}}\end{array}$$

(7)

NPV_{SEC-dynamic-reserve-value}—SEC dynamic reserve value, $; qi—initial production, barrel/month; q_el—economic limit production, barrel/month; C_fm—fixed operating cost per month, $/month; C_VU—unit variable operating cost, $/barrel; P—oil price, $/barrel; d—decline rate monthly, %; t_{compound tax}—comprehensive taxes, concern value-added tax, urban construction tax, education surtax, resource tax; t₁—value-added tax rate; t₂—income tax rate; t₃—product of urban construction tax rate and value-added tax rate; t₄—product of education surtax rate and value-added tax rate; t₅—resource tax rate; r—fixed cost proportion; C_L—total operating of estimation year, $; h—appropriate proportion of operating income; Q_L—total production of estimation year, barrel; S_ogl—special oil income levy, $/barrel; T—economic producing life, years; [T]—integer part of T, years; i—discount rate, %; j—ordinal of producing years; V—producing months of last year, months; S_{residual value of fixed assets}—residual value of fixed assets, $.

3.2.2. Modeling SEC Reserve Value of Hyperbolic Decline Type

Adopting the SEC financial variable cost method, the financial profit and loss balance method, the financial NPV method and the Arps production decline curve method, combined with economic limit production without development investment, the SEC reserve value model of hyperbolic decline type is established as follows:

$$\begin{array}{l}{\mathrm{NPV}}_{\mathrm{SEC}\mathrm{dynamic}\mathrm{reserve}\mathrm{value}}\\ ={\displaystyle \sum _{\mathrm{j}=1}^{\left[\mathrm{T}\right]}}\begin{array}{c}\left\{\begin{array}{c}\frac{{\mathrm{q}}_{\mathrm{i}}\times \left\{1+{\mathrm{a}}_{\mathrm{i}}\mathrm{n}\times \left[12\left(\mathrm{j}-1\right)\right]\right\}}{{\mathrm{a}}_{\mathrm{i}}\left(1-\mathrm{n}\right)\times {\left\{1+{\mathrm{a}}_{\mathrm{i}}\mathrm{n}\left[12\left(\mathrm{j}-1\right)\right]\right\}}^{\frac{1}{\mathrm{n}}}}\times \left\{1-{\left\{1+\frac{12{\mathrm{a}}_{\mathrm{i}}\mathrm{n}}{1+{\mathrm{a}}_{\mathrm{i}}\mathrm{n}\left[12\left(\mathrm{j}-1\right)\right]}\right\}}^{\frac{\mathrm{n}-1}{\mathrm{n}}}\right\}\times \\ \left[\mathrm{P}\times \left(1-{\mathrm{ht}}_1-{\mathrm{ht}}_3-{\mathrm{ht}}_4-{\mathrm{t}}_5\right)-{\mathrm{C}}_{\mathrm{vu}}-\mathrm{Sogl}\right]-12\times {\mathrm{C}}_{\mathrm{fm}}\end{array}\right\}\times \end{array}\\ \left(1-{\mathrm{t}}_2\right)\times {\left(1+\mathrm{i}\right)}^{-\mathrm{j}}\\ +\left\{\begin{array}{c}\frac{{\mathrm{q}}_{\mathrm{i}}\times \left[1+{\mathrm{a}}_{\mathrm{i}}\mathrm{n}\times 12\times \left[\mathrm{T}\right]\right]}{{\mathrm{a}}_{\mathrm{i}}\left(1-\mathrm{n}\right)\times {\left[1+{\mathrm{a}}_{\mathrm{i}}\mathrm{n}\left(12\times \left[\mathrm{T}\right]\right)\right]}^{\frac{1}{\mathrm{n}}}}\times \left\{1-{\left[1+\frac{{\mathrm{a}}_{\mathrm{i}}\mathrm{nv}}{1+{\mathrm{a}}_{\mathrm{i}}\mathrm{n}\left(12\times \left[\mathrm{T}\right]\right)}\right]}^{\frac{\mathrm{n}-1}{\mathrm{n}}}\right\}\times \\ \left[\mathrm{P}\left(1-\mathrm{h}{\mathrm{t}}_1-\mathrm{h}{\mathrm{t}}_3-\mathrm{h}{\mathrm{t}}_4-{\mathrm{t}}_5\right)-{\mathrm{C}}_{\mathrm{vu}}-\mathrm{Sogl}\right]-\mathrm{v}\times {\mathrm{C}}_{\mathrm{fm}}\end{array}\right\}\\ \times \left(1-{\mathrm{t}}_2\right)\times {\left(1+\mathrm{i}\right)}^{-(\left[\mathrm{T}\right]+1)}+{\mathrm{S}}_{\mathrm{residual}\mathrm{value}\mathrm{of}\mathrm{fixed}\mathrm{assets}}\end{array}$$

(8)

NPV_{SEC-dynamic-reserve-value}—SEC dynamic reserve value, $; qi—initial production, barrel/month; q_el—economic limit production, barrel/month; C_fm—fixed operating cost per month, $/month; C_VU—unit variable operating cost, $/barrel; P—oil price, $/barrel; a_i—initial decline rate monthly, %; t_{compound tax}—comprehensive taxes, concern value-added tax, urban construction tax, education surtax, resource tax; t₁—value-added tax rate; t₂—income tax rate; t₃—product of urban construction tax rate and value-added tax rate; t₄—product of education surtax rate and value-added tax rate; t₅—resource tax rate; r—fixed cost proportion; C_L—total operating of estimation year, $; h—appropriate proportion of operating income; Q_L—total production of estimation year, barrel; S_ogl—special oil income levy, $/barrel; T—economic producing life, years; [T]—integer part of T, years; i—discount rate, %; j—ordinal of producing years; n—production decline curve index; V—producing months of last year, months; S_{residual value of fixed assets}—residual value of fixed assets, $.

3.2.3. Modeling SEC Reserve Value of Harmonic Decline Type

Equally, adopting the SEC financial variable cost method, the financial profit and loss balance method, the financial NPV method and the Arps production decline curve method, combined with economic limit production without development investment, the SEC reserve value model of harmonic decline type is established as follows:

$$\begin{array}{l}{\mathrm{NPV}}_{\mathrm{SEC}\mathrm{dynamic}\mathrm{reserve}\mathrm{value}}\\ ={\displaystyle \sum _{\mathrm{j}=1}^{\left[\mathrm{T}\right]}}\left\{\left\{\begin{array}{c}\frac{{\mathrm{q}}_{\mathrm{i}}}{{\mathrm{a}}_{\mathrm{i}}}\times {\ln }^{\left(1+\frac{12\times {\mathrm{a}}_{\mathrm{i}}}{1+{\mathrm{a}}_{\mathrm{i}}\times \left[12\times \left(\mathrm{j}-1\right)\right]}\right)}\\ \times \left[\mathrm{P}\left(1-{\mathrm{ht}}_1-{\mathrm{ht}}_3-{\mathrm{ht}}_4-{\mathrm{t}}_5\right)-{\mathrm{C}}_{\mathrm{vu}}-\mathrm{Sogl}\right]-12{\mathrm{C}}_{\mathrm{fm}}\end{array}\right\}\times \left(1-{\mathrm{t}}_2\right)\times {\left(1+\mathrm{i}\right)}^{-\mathrm{j}}\right\}\\ +\left\{\begin{array}{c}\frac{{\mathrm{q}}_{\mathrm{i}}}{{\mathrm{a}}_{\mathrm{i}}}\times {\ln }^{\left(1+\frac{\mathrm{v}\times {\mathrm{a}}_{\mathrm{i}}}{1+{\mathrm{a}}_{\mathrm{i}}\times 12\times \left[\mathrm{T}\right]}\right)}\\ \times \left[\mathrm{P}\left(1-{\mathrm{ht}}_1-{\mathrm{ht}}_3-{\mathrm{ht}}_4-{\mathrm{t}}_5\right)-{\mathrm{C}}_{\mathrm{vu}}-\mathrm{Sogl}\right]-\mathrm{v}\times {\mathrm{C}}_{\mathrm{fm}}\end{array}\right\}\times \left(1-{\mathrm{t}}_2\right)\times {\left(1+\mathrm{i}\right)}^{-\left[\mathrm{T}\right]+1}\\ +{\mathrm{S}}_{\mathrm{residual}\mathrm{value}\mathrm{of}\mathrm{fixed}\mathrm{assets}}\end{array}$$

(9)

NPV_{SEC-dynamic-reserve-value}—SEC dynamic reserve value, $; qi—initial production, barrel/month; q_el—economic limit production, barrel/month; C_fm—fixed operating cost per month, $/month; C_vu—unit variable operating cost, $/barrel; P—oil price, $/barrel; a_i—initial decline rate monthly, %; t_{compound tax}—comprehensive taxes, concern value-added tax, urban construction tax, education surtax, resource tax; t₁—value-added tax rate; t₂—income tax rate; t₃—product of urban construction tax rate and value-added tax rate; t₄—product of education surtax rate and value-added tax rate; t₅—resource tax rate; r—fixed cost proportion; C_L—total operating of estimation year, $; h—appropriate proportion of operating income; Q_L—total production of estimation year, barrel; S_ogl—special oil income levy, $/barrel; T—economic producing life, years; [T]—integer part of T, years; i—discount rate, %; j—ordinal of producing years; V—producing months of last year, months; S_{residual value of fixed assets}—residual value of fixed assets, $.

3.3. Verification of SEC Reserve Value Model

Taking the production data of a fault block oilfield in one particular basin in the east of China as an example, the SEC dynamic reserve value models will be verified with China’s current fiscal and taxation system. According to the verification results, the new models have been verified as correct with an extremely high fit degree, as shown in Figure 1, Figure 2, Figure 3, Figure 4, Figure 5 and Figure 6. With world economic integration, nearly every country is building the use paid mineral resource tax and fee system, which takes the royalty mechanism or the similar royalty mechanism as the main body [24].

The basic estimation data of the reservoir have been shown in

Table 1. Verification data of SEC reserve value model of exponential decline type.

Parameters	Unit	Parameter Data
Oil price	$/barrel	47	48	50
SEC reserve value (production value)	$ × 104	1102	1177	1344
SEC reserve value (simulated value)	$ × 104	1104	1188	1338
Present valuefirst year (simulation data)	$ × 104	671	716	787
Present value second year (simulation data)	$ × 104	318	344	387
Present value third year (simulation data)	$ × 104	107	118	142
Present value fourth year (simulation data)	$ × 104	8	10	22
Economic life	Months	40	41	43
Decline rate	%	3.90	3.90	3.90
Month fixed cost	$/month	285,714	285,714	285,714
Unit variable cost	$/barrel	6.6	6.6	6.6
Initial production	Barrel/month	58,418	58,418	58,418
V	Months	4	5	7

,

Table 2. Verification data of SEC reserve value model of hyperbolic decline type.

Parameters	Unit	Parameter Data
Oil price	$/barrel	47	48	50
SEC reserve value (production data)	$ × 104	321	347	410
SEC reserve value (simulation data)	$ × 104	324	356	434
First year present value j = 1(simulation data)	$ × 104	283	305	354
Second year present value [T] = 2(simulation data)	$ × 104	41	52	80
Initial production	Barrel/month	58,418	58,418	58,418
Initial decline rate	%	16.2	16.2	16.2
Hyperbolic decline index n	Dimensionless	0.7	0.7	0.7
Unit variable cost	$/barrel	7.7	7.7	7.7
Month fixed cost	$ × 104/month	33	33	33
v	Months	4	5	7
Economic life	Months	16	17	19

and

Table 3. Verification data of SEC reserve value model of harmonic decline type.

Parameters	Unit	Parameter data
Oil price	$/barrel	47	48	50
SEC reserve value (production data)	$ × 104	268	295	353
SEC reserve value (simulation data)	$ × 104	245	268	324
First year present value j = 1(simulation data)	$ × 104	239	259	304
Second year present value [T] = 2(simulation)	$ × 104	6	10	20
Initial production	Barrel/month	58,418	58,418	58,418
Initial decline rate	%	22.0	22.0	22.0
Unit variable cost	$/barrel	7.7	7.7	7.7
Month fixed cost	$ × 104/month	33	33	33
v	Months	4	5	7
Economic life	Months	16	17	19

. As follows are the basic situations of development: (1) The average depth is around 2000–4000 m. (2) The development stage is in the middle-to-late stage of producing. Having taken some measures, such as optimizing well pattern, fracturing acidizing, injecting water, etc., the production has indicated an obvious decline tendency. (3) The rock component types are mainly feldspar powder-fine sandstone and calcite carbonate rocks. (4) Stratum with strong heterogeneity, the range of porosity 10–20% and the range of penetration rate 30–100 × 10⁻³ um². (5) Distributed 112 wells total. (6) Exchange rate is 7. (7) Ton–barrel coefficient is 7.274. (8) Value-added tax rate is 17%, income tax rate is 25%, resource tax rate is 1%. (9) Urban construction tax is 7%, education surcharge is 3%.

4. SEC Reserve Parameter Sensitivity Differences

4.1. Initial Production Sensitivity

4.1.1. Initial Production Sensitivity in Exponential Decline Type

According to Formula (1), when the production decline rate is a certain data, the partial differentiable function from the SEC reserve to initial production will determine the sensitivity rule between the SEC reserve and the initial production:

$$\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}=\frac{1}{\mathrm{d}}$$

(10)

N_e—SEC reserve, barrel; q_i—initial production, barrel/month; d—decline rate monthly, %.

Therefore, the exponential decline type, according to Formula (10), can obtain the sensitivity rule between the SEC reserve and the initial production; the smaller the production decline rate, the stronger the sensitivity between the SEC reserve and the initial production.

4.1.2. Initial Production Sensitivity in Hyperbolic and Harmonic Decline Types

The sensitivity rules between the SEC reserve and the initial production in hyperbolic and harmonic decline types are the same: (1) the higher the initial production, the stronger the sensitivity between the SEC reserve and the initial production; (2) the higher the oil price, the stronger the sensitivity between the SEC reserve and the initial production, as shown in Formulas (11) and (12).

(1) According to Formula (2), when the initial production decline rate of the hyperbolic decline type is a certain data, the partial differentiable function from the SEC reserve to the initial production will determine the sensitivity rule between the SEC reserve and the initial production:

$$\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}=\frac{1}{{\mathrm{d}}_{\mathrm{i}}\left(1-\mathrm{n}\right)}-\frac{\mathrm{n}\times {\left({\mathrm{q}}_{\mathrm{i}}\right)}^{\left(\mathrm{n}-1\right)}}{{\mathrm{d}}_{\mathrm{i}}\left(1-\mathrm{n}\right)}\times {\left[\frac{{\mathrm{C}}_{\mathrm{fm}}}{\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-\mathrm{Cvu}-{\mathrm{S}}_{\mathrm{ogl}}}\right]}^{\left(1-\mathrm{n}\right)}$$

(11)

N_e—SEC reserve, barrel; q_i—initial production, barrel/month; n—production decline curve index; C_fm—fixed operating cost per month, $/month; C_vu—unit variable operating cost, $/barrel; d_i—initial decline rate monthly, %; t_{compound tax}—comprehensive taxes, concern value-added tax, urban construction tax, education surtax, resource tax; S_ogl—special oil income levy, $/barrel.

(2) According to Formula (3), when the initial production decline rate of the harmonic decline type is a certain data, the partial differentiable function from the SEC reserve to the initial production will determine the sensitivity rule between the SEC reserve and the initial production:

$$\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}=\frac{1}{{\mathrm{d}}_{\mathrm{i}}}\times {\ln }^{{\mathrm{Q}}_{\mathrm{i}}}-\frac{1}{{\mathrm{d}}_{\mathrm{i}}}\times {\ln }^{\mathrm{qel}}+\frac{1}{{\mathrm{d}}_{\mathrm{i}}}$$

(12)

N_e—SEC reserve, barrel; q_i—initial production, barrel/month; d_i—initial decline rate monthly, %; q_el—economic limit production, barrel/month.

4.2. Oil Price Sensitivity

4.2.1. Oil Price Sensitivity in Exponential Decline Type

According to Formula (1), the partial differentiable function from the SEC reserve to the oil price will determine the sensitivity rule between the SEC reserve and the oil price:

$$\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{P}\right)}=\frac{{\mathrm{C}}_{\mathrm{fm}}}{12\mathrm{d}{\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-\mathrm{sogl}\right]}^2}=\frac{{\mathrm{q}}_{\mathrm{el}}}{12\mathrm{d}\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]}$$

(13)

N_e—SEC reserve, barrel; q_el—economic limit production, barrel/month; C_fm—fixed operating cost per month, $/month; C_vu—unit variable operating cost, $/barrel; P—oil price, $/barrel; S_ogl—special oil income levy, $/barrel.

Therefore, the exponential decline type, according to Formula (13), can obtain the sensitivity rule between the SEC reserve and the oil price: (1)the higher the oil price, the more the sensitivity between the SEC reserve and the oil price will decrease; (2)the smaller the production decline rate, the stronger the sensitivity between the SEC reserve and the oil price.

4.2.2. Oil Price Sensitivity in Hyperbolic and Harmonic Decline Types

The sensitivity rules between the SEC reserve and the oil price in hyperbolic and harmonic decline types are the same: (1) the higher the initial production, the stronger the sensitivity between the SEC reserve and the oil price; (2) the higher oil price, the more the sensitivity between the SEC reserve and the oil price will decrease; (3) the smaller the initial decline rate, the stronger the sensitivity between the SEC reserve and the oil price, as shown in Formulas (14) and (15).

(1) According to Formula (2), the partial differentiable function from the SEC reserve to the oil price will determine the sensitivity rule between the SEC reserve and the oil price:

$$\begin{array}{c}\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{P}\right)}=\frac{{\mathrm{q}}_{\mathrm{el}}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)}{{12}^{\left(1-\mathrm{n}\right)}{\mathrm{d}}_{\mathrm{i}}\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-\mathrm{Cvu}-{\mathrm{S}}_{\mathrm{ogl}}\right]}{\left(\frac{{\mathrm{q}}_{\mathrm{i}}}{{\mathrm{q}}_{\mathrm{el}}}\right)}^{\mathrm{n}}\\ =\frac{{\left({\mathrm{q}}_{\mathrm{i}}\right)}^{\mathrm{n}}{\left({\mathrm{C}}_{\mathrm{fm}}\right)}^{\left(1-\mathrm{n}\right)}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)}{{12}^{\left(1-\mathrm{n}\right)}{\mathrm{d}}_{\mathrm{i}}{\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-\mathrm{Cvu}-{\mathrm{S}}_{\mathrm{ogl}}\right]}^{\left(2-\mathrm{n}\right)}}\end{array}$$

(14)

N_e—SEC reserve, barrel; P—oil price, $/barrel; q_el—economic limit production, barrel/month; q_i—initial production, barrel/month; d_i—initial decline rate monthly, %; C_fm—fixed operating cost per month, $/month; C_vu—unit variable operating cost, $/barrel; n—production decline curve index; S_ogl—special oil income levy, $/barrel.

(2) According to Equation (3), the partial differentiable function from the SEC reserve to the oil price will determine the sensitivity rule between the SEC reserve and the oil price:

$$\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{P}\right)}=\frac{{\mathrm{q}}_{\mathrm{i}}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)}{{\mathrm{d}}_{\mathrm{i}}\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-\mathrm{Cvu}-{\mathrm{S}}_{\mathrm{ogl}}\right]}$$

(15)

N_e—SEC reserve, barrel; P—oil price, $/barrel; d_i—initial decline rate monthly, %; C_vu—unit variable operating cost, $/barrel; S_ogl—special oil income levy, $/barrel.

4.3. SEC Reserve Parameter Sensitivity Differences

4.3.1. Parameter Sensitivity Differences in Exponential Decline Type

Comparing Formula (10) with Formula (13) can obtain sensitivity differences between the reserve sensitivity caused by the initial production change and the reserve sensitivity caused by the oil price change. According to Formulas (10) and (13), based on the mathematic limit theory, the following conclusion can be obtained:

(1)

When: ${\mathrm{q}}_{\mathrm{el}}<\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-\mathrm{sogl}\right]$, in case of high oil price, exist rules:

$$\frac{1}{\mathrm{d}}>\frac{{\mathrm{q}}_{\mathrm{el}}}{12\mathrm{d}\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-\mathrm{sogl}\right]},\mathrm{at}\mathrm{this}\mathrm{point},\left|\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{qi}\right)}\right|>\left|\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{p}\right)}\right|.$$

(16)

Thus, the following conclusion is achieved: the sensitivity between the SEC reserve and the initial production is stronger than the sensitivity between the SEC reserve and the oil price.

(2)

When: ${\mathrm{q}}_{\mathrm{el}}>\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-\mathrm{sogl}\right]$, in case of low oil price, exist rules:

$$\frac{1}{\mathrm{d}}<\frac{{\mathrm{q}}_{\mathrm{el}}}{12\mathrm{d}\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-\mathrm{sogl}\right]},\mathrm{at}\mathrm{this}\mathrm{point},\left|\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{qi}\right)}\right|<\left|\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{p}\right)}\right|.$$

(17)

Thus, the following conclusion is achieved: the sensitivity between the SEC reserve and the initial production is weaker than the sensitivity between the SEC reserve and the oil price.

4.3.2. Parameter Sensitivity Differences in Hyperbolic Decline Type

Comparing Formula (11) with Formula (14) can obtain differences between the reserve sensitivity caused by the initial production change and the reserve sensitivity caused by the oil price change. According to Formulas (11) and (14), formulas can be obtained as follows:

$$\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}/\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{P}\right)}=\frac{{12}^{\left(1-\mathrm{n}\right)}\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-\mathrm{Cvu}-\mathrm{sogl}\right]}{{\mathrm{q}}_{\mathrm{i}}\times \left(1-\mathrm{n}\right)\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)}\times \left[\frac{{\left(\mathrm{qi}\right)}^{\left(1-\mathrm{n}\right)}}{{\left(\mathrm{qel}\right)}^{\left(1-\mathrm{n}\right)}}-\mathrm{n}\right]$$

(18)

(1)

According to Formula (18), when:

$\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-\mathrm{Cvu}-\mathrm{sogl}\right]>{\mathrm{q}}_{\mathrm{i}}\times \frac{\left(1-\mathrm{n}\right)\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)}{{12}^{\left(1-\mathrm{n}\right)}\left[{\left(\frac{\mathrm{qi}}{\mathrm{qel}}\right)}^{\left(1-\mathrm{n}\right)}-\mathrm{n}\right]}$, in case of high oil price, sensitivity rules exist: $\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}>\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{P}\right)}$.

Thus, the following conclusion is achieved: the sensitivity between the SEC reserve and the initial production is stronger than the sensitivity between the SEC reserve and the oil price.

(2)

According to Formula (18), when:

$\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-\mathrm{Cvu}-\mathrm{sogl}\right]<{\mathrm{q}}_{\mathrm{i}}\times \frac{\left(1-\mathrm{n}\right)\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)}{{12}^{\left(1-\mathrm{n}\right)}\left[{\left(\frac{\mathrm{qi}}{\mathrm{qel}}\right)}^{\left(1-\mathrm{n}\right)}-\mathrm{n}\right]}$, in case of low oil price, sensitivity rules exist:$\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}<\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{P}\right)}$.

Thus, the following conclusion can be reached: the sensitivity between the SEC reserve and the initial production is weaker than the sensitivity between the SEC reserve and the oil price.

4.3.3. Parameter Sensitivity Differences in Harmonic Decline Type

Comparing Formula (12) with Formula (15) can obtain differences between the reserve sensitivity caused by the initial production change and the reserve sensitivity caused by the oil price change. According to Formulas (12) and (15), the following formulas can be obtained:

$$\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}/\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{P}\right)}=\frac{{\mathrm{C}}_{\mathrm{fm}}\times {\ln }^{\frac{{\mathrm{Q}}_{\mathrm{i}}}{\mathrm{qel}}}}{{\mathrm{q}}_{\mathrm{i}}\times \mathrm{qel}\times \left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)}$$

(19)

(1)

According to Formula (19), when: ${\mathrm{C}}_{\mathrm{fm}}>\frac{{\mathrm{q}}_{\mathrm{i}}\times \mathrm{qel}\times \left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)}{\mathrm{lnqi}-\mathrm{lnqel}}$, in case of high oil price, sensitivity rulesexist: $\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}>\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{P}\right)}$.

Thus, the following conclusion can be reached: the sensitivity between the SEC reserve and the initial production is stronger than the sensitivity between the SEC reserve and the oil price.

(2)

According to Formula (19), when: ${\mathrm{C}}_{\mathrm{fm}}<\frac{{\mathrm{q}}_{\mathrm{i}}\times \mathrm{qel}\times \left(1-\mathrm{compound}\mathrm{taxes}\right)}{\mathrm{lnqi}-\mathrm{lnqel}}$, in case of low oil price, sensitivity rulesexist: $\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}<\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{P}\right)}$.

Thus, the following conclusion can be reached: the sensitivity between the SEC reserve and the initial production is weaker than the sensitivity between the SEC reserve and the oil price.

5. SEC Reserve Value Parameter Sensitivity Differences

Formulas (1)–(3) are continuous differentiable functions, so Formulas (7)–(9) can be transformed into a piecewise differentiable function model:

$$\begin{array}{ll}{\mathrm{NPV}}_1& ={\displaystyle \sum _{\mathrm{j}=1}^{\left[\mathrm{T}\right]}}\left\{\left[\mathrm{P}\times \left(1-{\mathrm{ht}}_1-{\mathrm{ht}}_3-{\mathrm{ht}}_4-{\mathrm{t}}_5\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]\times {\mathrm{Q}}_{\mathrm{j}}-12\times {\mathrm{C}}_{\mathrm{fm}}\right\}\\ & \times \left(1-{\mathrm{t}}_2\right)\times {\left(1+\mathrm{i}\right)}^{-\mathrm{j}}+\left\{\begin{array}{c}\left[\mathrm{P}\times \left(1-{\mathrm{ht}}_1-{\mathrm{ht}}_3-{\mathrm{ht}}_4-{\mathrm{t}}_5\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]\\ \times {\mathrm{Q}}_{\left(\left[\mathrm{T}\right]+1\right)}-\mathrm{V}\times {\mathrm{C}}_{\mathrm{fm}}\end{array}\right\}\\ & \times \left(1-{\mathrm{t}}_2\right)\times {\left(1+\mathrm{i}\right)}^{-\left(\left[\mathrm{T}\right]+1\right)}+{\mathrm{S}}_{\mathrm{residual}\mathrm{value}\mathrm{of}\mathrm{fixed}\mathrm{assets}}\end{array}$$

(20)

NPV₁—SEC dynamic reserve value, $; Q_j—annual production, barrel/year; Q_([T]+1)—last year production, barrel/year; C_fm—fixed operating cost per month, $/month; C_vu—unit variable operating cost, $/barrel; P—oil price, $/barrel; t₁—value-added tax rate; t₂—income tax rate; t₃—product of urban construction tax rate and value-added tax rate; t₄—product of education surtax rate and value-added tax rate; t₅—resource tax rate; r—fixed cost proportion; h—appropriate proportion of operating income; S_ogl—special oil income levy, $/barrel; T—economic producing life, years; [T]—integer part of T, years; i—discount rate, %; j—ordinal of producing years; V—producing months of last year, months; S_{residual value of fixed assets}—residual value of fixed assets, $.

According to the calculus theory, in Formula (20), the partial differentiable functions from NPV1to parameters can determine the sensitivity rule between the SEC reserve value and the main parameters. For analyzing not only the sensitivity rule between the SEC reserve value and the initial production, but also the sensitivity rule between the SEC reserve value and the price, based on the Arps production decline curve theory, the continuous differentiable functions from NPV1 to main parameters can be transformed into functions of dispersed points. The transformation method of the production of dispersed points is a kind of mathematic recursion method [16]. Acting on SEC’s prudence principle, the production exponential decline type is often adopted in SEC reserve estimations. Thus, the SEC reserve value mainly researches the parameter sensitivity differences rules in the production exponential decline type.

5.1. Initial Production Sensitivity

According to Formulas (7) and (20), the partial differentiable function from the SEC reserve value to the initial production can determine the sensitivity rule between the SEC reserve value and the initial production.

$$\begin{array}{l}{\frac{\partial \left({\mathrm{NPV}}_1\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}}_{\mathrm{shape}-\mathrm{dispersed}-\mathrm{point}}\\ ={\displaystyle \sum _{\mathrm{j}=1}^{\left[\mathrm{T}\right]}}\left\{\begin{array}{c}\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]\\ \times \frac{{\mathrm{e}}^{-\left[12\left(\mathrm{j}-1\right)\mathrm{d}\right]}-{\mathrm{e}}^{-\left[12\left(\mathrm{j}-1\right)\mathrm{d}\right]}\times {\mathrm{e}}^{-11\mathrm{d}}}{\mathrm{d}}\end{array}\right\}\times \left(1-{\mathrm{t}}_2\right)\times {\left(1+\mathrm{i}\right)}^{-\mathrm{j}}\\ +\left[\frac{{\mathrm{e}}^{-\left(12\times \mathrm{j}\times \mathrm{d}\right)}}{\mathrm{d}}\times {\left(1+\mathrm{i}\right)}^{-\left(\left[\mathrm{T}\right]+1\right)}-\frac{{\mathrm{e}}^{-\left(12\times \mathrm{j}\times \mathrm{d}\right)}\times {\ln }^{\left(1+\mathrm{i}\right)}}{{\mathrm{d}}^2}\times {\left(1+\mathrm{i}\right)}^{-\left(\left[\mathrm{T}\right]+1\right)}\right]\\ \times \left\{\left[\mathrm{P}\times \left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]\times \left(1-{\mathrm{t}}_2\right)\right\}\\ +\left[\mathrm{P}\times \left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]\times \frac{{\mathrm{q}}_{\mathrm{el}}}{\mathrm{d}}\times \left(1-{\mathrm{t}}_2\right)\times \frac{{\ln }^{\left(1+\mathrm{i}\right)}}{{\mathrm{q}}_{\mathrm{i}}\times \mathrm{d}}\times {\left(1+\mathrm{i}\right)}^{-\left(\left[\mathrm{T}\right]+1\right)}\\ +\left(\mathrm{T}-\left[\mathrm{T}\right]\right)\times {\mathrm{C}}_{\mathrm{fm}}\times \left(1-{\mathrm{t}}_2\right)\times \frac{{\ln }^{\left(1+\mathrm{i}\right)}}{{\mathrm{q}}_{\mathrm{i}}\times \mathrm{d}}\times {\left(1+\mathrm{i}\right)}^{-\left(\left[\mathrm{T}\right]+1\right)}+\acute{\left[\mathrm{T}\right]\times }{\mathrm{C}}_{\mathrm{L}}\mathrm{r}\left(1-{\mathrm{t}}_2\right){\left(1+\mathrm{i}\right)}^{-\left(\left[\mathrm{T}\right]+1\right)}-\frac{1}{\mathrm{d}\times \mathrm{qi}}\end{array}$$

(21)

NPV₁—SEC dynamic reserve value, $; q_j—initial production, barrel/month; P—oil price, $/barrel; t_{compound tax}—comprehensive taxes, concern value-added tax, urban construction tax, education surtax, resource tax; C_vu—unit variable operating cost, $/barrel; d—decline rate monthly, %; q_el—economic limit production, barrel/month; r—fixed cost proportion; S_ogl—special oil income levy, $/barrel; T—economic producing life, years; [T]—integer part of T, years; i—discount rate, %; j—ordinal of producing years; C_L—total operating of estimation year, $.

According to Formula (21), formulas can be obtained as follows: ${\frac{\partial \left[\mathrm{NPV}\left(1\right)\right]}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}}_{\mathrm{shape}-\mathrm{dispersed}-\mathrm{p}\mathrm{o}\mathrm{i}\mathrm{n}\mathrm{t}}>0$. Thus, the partial differentiable function from the SEC reserve value to the initial production is a kind of monotonic increase function.

5.2. Oil Price Sensitivity

According to Formulas (7) and (20), the partial differentiable function from the SEC reserve value to the oil price can determine the sensitivity rule between the SEC reserve value and the oil price; it is described in Formula (22).

According to Formula (22), the following formulas can be obtained: ${\frac{\partial \left[\mathrm{NPV}\left(1\right)\right]}{\partial \left(\mathrm{P}\right)}}_{\mathrm{shape}-\mathrm{dispersed}-\mathrm{p}\mathrm{o}\mathrm{i}\mathrm{n}\mathrm{t}}>0$. Thus, the partial differentiable function from the SEC reserve value to the oil price is a kind of monotonic increase function.

$$\begin{array}{l}{\frac{\partial \left({\mathrm{NPV}}_1\right)}{\partial \left(\mathrm{P}\right)}}_{\mathrm{shape}-\mathrm{dispersed}-\mathrm{point}}\\ ={\displaystyle \sum _{\mathrm{j}=1}^{\left[\mathrm{T}\right]}}\left\{\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)\times {\mathrm{q}}_{\mathrm{i}}\times \frac{{\mathrm{e}}^{-\left[12\left(\mathrm{j}-1\right)\mathrm{d}\right]}-{\mathrm{e}}^{-\left[12\left(\mathrm{j}-1\right)\mathrm{d}\right]}\times {\mathrm{e}}^{-\left(11\mathrm{d}\right)}}{\mathrm{d}}\right\}\times \left(1-{\mathrm{t}}_2\right)\times {\left(1+\mathrm{i}\right)}^{-\mathrm{j}}\\ +\frac{{\mathrm{q}}_{\mathrm{i}}\times {\mathrm{e}}^{-\left(12\times \mathrm{j}\times \mathrm{d}\right)}}{\mathrm{d}}\times \left(1-{\mathrm{t}}_2\right)\times \left\{\begin{array}{c}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)\times {\left(1+\mathrm{i}\right)}^{-\left\{\frac{{\ln }^{\mathrm{qi}-{\ln }^{\mathrm{qel}}}}{\mathrm{d}}-\mathrm{M}+1\right\}}\\ -\left[\mathrm{P}\times \left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]\times {\left(1+\mathrm{i}\right)}^{-\left\{\frac{{\ln }^{\mathrm{qi}-{\ln }^{\mathrm{qel}}}}{\mathrm{d}}-\mathrm{M}+1\right\}}\\ \times \frac{\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)\times {\mathrm{Q}}_{\mathrm{L}}\times {\ln }^{\left(1+\mathrm{i}\right)}}{\mathrm{d}\times \left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right){\mathrm{Q}}_{\mathrm{L}}+{\mathrm{C}}_{\mathrm{L}}\mathrm{r}-{\mathrm{C}}_{\mathrm{L}}-{\mathrm{Q}}_{\mathrm{L}}\times {\mathrm{S}}_{\mathrm{ogl}}\right]}\end{array}\right\}\\ -\left\{\begin{array}{c}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)\left(1-{\mathrm{t}}_2\right)\times \frac{\mathrm{qel}}{\mathrm{d}}\times {\left(1+\mathrm{i}\right)}^{-\left\{\frac{{\ln }^{\mathrm{qi}}-{\ln }^{\mathrm{qel}}}{\mathrm{d}}-\mathrm{M}+1\right\}}\\ -\left(1-{\mathrm{t}}_2\right)\left[\mathrm{P}\times \left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]\times {\left(1+\mathrm{i}\right)}^{-\left\{\frac{{\ln }^{\mathrm{qi}-{\ln }^{\mathrm{qel}}}}{\mathrm{d}}-\mathrm{M}+1\right\}}\\ \times \frac{\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right){\mathrm{C}}_{\mathrm{L}}{\mathrm{rQ}}_{\mathrm{L}}{}^2}{\mathrm{d}{\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right){\mathrm{Q}}_{\mathrm{L}}+{\mathrm{C}}_{\mathrm{L}}\mathrm{r}-{\mathrm{C}}_{\mathrm{L}}-{\mathrm{Q}}_{\mathrm{L}}\times {\mathrm{S}}_{\mathrm{ogl}}\right]}^2}\\ -\left(1-{\mathrm{t}}_2\right)\left[\mathrm{P}\times \left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]\times \frac{\mathrm{qel}}{\mathrm{d}}\times {\left(1+\mathrm{i}\right)}^{-\left\{\frac{{\ln }^{\mathrm{qi}-{\ln }^{\mathrm{qel}}}}{\mathrm{d}}-\mathrm{M}+1\right\}}\\ \times \frac{\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)\times {\mathrm{Q}}_{\mathrm{L}}\times {\ln }^{\left(1+\mathrm{i}\right)}}{\mathrm{d}\times \left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right){\mathrm{Q}}_{\mathrm{L}}+{\mathrm{C}}_{\mathrm{L}}\mathrm{r}-{\mathrm{C}}_{\mathrm{L}}-{\mathrm{Q}}_{\mathrm{L}}\times {\mathrm{S}}_{\mathrm{ogl}}\right]}\end{array}\right\}\\ +\left(\mathrm{T}-\left[\mathrm{T}\right]\right)\times {\mathrm{C}}_{\mathrm{fm}}\times \left(1-{\mathrm{t}}_2\right)\times {\left(1+\mathrm{i}\right)}^{-\left\{\frac{{\ln }^{\mathrm{qi}-{\ln }^{\mathrm{qel}}}}{\mathrm{d}}-\mathrm{M}+1\right\}}\times \frac{\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)\times {\mathrm{Q}}_{\mathrm{L}}\times {\ln }^{\left(1+\mathrm{i}\right)}}{\mathrm{d}\times \left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right){\mathrm{Q}}_{\mathrm{L}}+{\mathrm{C}}_{\mathrm{L}}\mathrm{r}-{\mathrm{C}}_{\mathrm{L}}-{\mathrm{Q}}_{\mathrm{L}}\times {\mathrm{S}}_{\mathrm{ogl}}\right]}\\ +12\acute{\left[\mathrm{T}\right]}-\frac{\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right){\mathrm{Q}}_{\mathrm{L}}-{\mathrm{C}}_{\mathrm{L}}\right]\times \ln \left(1+\mathrm{i}\right)\left(1-{\mathrm{t}}_2\right)\times {\left(1+\mathrm{i}\right)}^{-\left[\mathrm{T}+1\right]}}{12\times 12\mathrm{d}\left[{\mathrm{C}}_{\mathrm{L}}\mathrm{r}+\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right){\mathrm{Q}}_{\mathrm{L}}-{\mathrm{C}}_{\mathrm{L}}-{\mathrm{Q}}_{\mathrm{L}}\times {\mathrm{S}}_{\mathrm{ogl}}\right]}\end{array}$$

(22)

NPV₁—SEC dynamic reserve value, $; P—oil price, $/barrel; q_j—initial production, barrel/month; t _{compound tax}—comprehensive taxes, concern value-added tax, urban construction tax, education surtax, resource tax; C_vu—unit variable operating cost, $/barrel; d—decline rate monthly, %; Q_L—total production of estimation year, barrel; q_el—economic limit production, barrel/month; r—fixed cost proportion; S_ogl—special oil income levy, $/barrel; T—economic producing life, years; [T]—integer part of T, years; i—discount rate, %; j—ordinal of producing years; C_L—total operating of estimation year, $.

5.3. SEC Reserve Value Parameter Sensitivity Differences

Comparing Formula (21) with Formula (22), can obtain sensitivity differences between the reserve value sensitivity caused by the initial production change and the reserve value sensitivity caused by the oil price change. According to Formulas (21) and (22), because the first term of the polynomial is the main numerical term and the other terms are smaller numerical terms, the limit data of Formulas (21) and (22) can be determined; thus, obtaining the following conclusion:

(1)

When $\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]>\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)\times {\mathrm{q}}_{\mathrm{i}}$, in case of high oil price, ${\frac{\partial \left({\mathrm{NPV}}_1\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}}_{\mathrm{shape}-\mathrm{dispersed}-\mathrm{point}}>{\frac{\partial \left({\mathrm{NPV}}_1\right)}{\partial \left(\mathrm{P}\right)}}_{\mathrm{shape}-\mathrm{dispersed}-\mathrm{point}}$.

Thus, the following conclusion can be reached: the sensitivity between the SEC reserve value and the initial production is stronger than the sensitivity between the SEC reserve value and the oil price.

(2)

When $\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]<\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)\times {\mathrm{q}}_{\mathrm{i}}$, in case of high oil price, ${\frac{\partial \left({\mathrm{NPV}}_1\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}}_{\mathrm{shape}-\mathrm{dispersed}-\mathrm{point}}<{\frac{\partial \left({\mathrm{NPV}}_1\right)}{\partial \left(\mathrm{P}\right)}}_{\mathrm{shape}-\mathrm{dispersed}-\mathrm{point}}$.

Thus, the following conclusion can be reached: the sensitivity between the SEC reserve value and the initial production is weaker than the sensitivity between the SEC reserve value and the oil price.

6. Example Analysis of Parameter Sensitivity Differences

According to the SEC prudence principle, the production exponential decline type is often adopted in SEC reserve estimations. Taking the production data of the fault-block reservoir in the east of China as an example to analyze parameter sensitivity differences rules, the oil price changes frequently. The oil price frequent change is mainly affected by the balance between economic supply and demand, exchange rate inflation, geopolitics and crises or oil strategy.

The basic development situations are as follows: (1) the average depth is around 3000 m; (2) the development layer system belongs to the east third member of the Eogene of Dong Ying formation, the deposition is controlled by two north–south direction boundaries caused by a large Dong Ying formation fault, the deposition is the main oil supply fault and controls the reservoir’s formation; (3) six oil wells and two water wells are distributed; (4) the reservoir has strong heterogeneity, good permeability and an average penetration rate 177 × 10⁻³ um²; (5) most of the oil layers are 2–4 m medium thickness oil layers; (6) the development stage is in the middle-to-late stage of producing; (7) through water injection development, fracture and acidification measures, tertiary oil recovery and other stimulation measures, the production statuses have indicated a gentle decline tendency; (8) crude oil density 0.8166 g/cm³, unit variable cost is $6 per barrel, the annual operation cost is $2,418,459, the exchange rate is 7.05; (9) the ton–barrel coefficient is 7.7, the value-added tax rate is 17% the income tax rate is 25%, the urban construction tax rate is 7%, the resource tax rate is 1% and the education surcharge tax rate is 3%.

6.1. Example Analysis of SEC Reserve Parameter Sensitivity Differences

(1)

When: ${\mathrm{q}}_{\mathrm{el}}<\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]$, in case of high oil price, sensitivity rules exist:

$$\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}>\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{P}\right)},$$

The example data of the result are shown in

Table 4. SEC reserve parameter sensitivity differences.

Parameters	Unit	Sensitivity between SEC Reserve and Initial Production
SEC reserve	barrel	388,018	413,475	440,333	468,998	500,009
SEC Reserve increment	barrel	/	25,456	26,858	28,665	31,011
Initial production	barrel/month	15,847	16,678	17,556	18,434	19,358
Incrementrange of adjacent initial production	%	5	5	5	5	5
Decline rate	%	3.3	3.3	3.3	3.3	3.3
Economic limit production	barrel/month	3265	3265	3265	3265	3265
Oil price	$/barrel	57	57	57	57	57
Parameters	Unit	Sensitivity between SEC reserve and price
SEC reserve	barrel	395,326	419,404	440,332	446,754	452,760
SEC reserve increment	barrel	/	24,078	20,929	6422	6006
Oil price	$/barrel	52	54	57	59.9	62.8
Incrementrange of adjacent price	%	5	5	5	5	5
Initial production	barrel/month	17,556	17,556	17,556	17,556	17,556
Economic limit production	barrel/month	3634	3465	3266	3088	2926

and Figure 7.

According to Figure 7, it is obviously indicated that the sensitivity between the SEC reserve and the initial production is stronger than the sensitivity between the SEC reserve and the oil price.

(2)

When: $\mathrm{qel}>\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]$, in case of low oil price, sensitivity rules exist:

$$\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}<\frac{\partial \left({\mathrm{N}}_{\mathrm{e}}\right)}{\partial \left(\mathrm{P}\right)},$$

The example data of the result are shown in

Table 5. SEC reserve parameter sensitivity differences.

Parameters	Unit	Sensitivity between SEC Reserve and Initial Production
SEC reserve	barrel	80,080	105,351	131,947	158,551	186,563
SEC reserves increment	barrel	/	25,271	26,596	26,604	28,013
Oil price	$/barrel	20	20	20	20	20
Initial production	barrel/month	15,839	16,678	17,556	18,433	19,358
Increment range of adjacent initial production	%	5	5	5	5	5
Decline rate	%	3.30%	3.30%	3.30%	3.30%	3.30%
Economic limit production	barrels/month	13,183	13,183	13,183	13,183	13,183
Parameters	Unit	Sensitivity between SEC reserve and price
SEC reserve	barrel	55,710	96,119	131,948	162,339	192,030
SEC reserves increment	barrel	/	40,410	35,828	30,392	29,689
oil price	$/barrel	18.05	19	20	21	22.05
Increment range of adjacent initial production	%	5	5	5	5	5
Initial production	barrel/month	17,556	17,556	17,556	17,556	17,556
Economic limit production	barrel/month	15,716	14,384	13,198	12,196	11,296

and Figure 8.

According to Figure 8, it is obviously indicated that the sensitivity between the SEC reserve and the initial production is weaker than the sensitivity between the SEC reserve and the oil price.

6.2. Example Analysis of SEC Reserve Value Parameter Sensitivity Differences

(1)

$\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]>\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right){\mathrm{q}}_{\mathrm{i}}$

Then: ${\frac{\partial \left({\mathrm{NPV}}_1\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}}_{\mathrm{shape}-\mathrm{dispersed}-\mathrm{point}}>{\frac{\partial \left({\mathrm{NPV}}_1\right)}{\partial \left(\mathrm{P}\right)}}_{\mathrm{shape}-\mathrm{dispersed}-\mathrm{point}}$

The example data of the result are shown in

Table 6. SEC reserve value parameter sensitivity difference.

Parameters	Unit	Sensitivity between SEC Reserve Value and Initial Production
SEC reserve value	$ × 104	903	968	1039	1113	1192
SEC reserve value increment	$ × 104	/	66	71	74	78
Oil price	$/barrel	67.2	67.2	67.2	67.2	67.2
Initial production	barrel/month	17,556	18,434	19,358	20,320	21,329
Increment range of adjacentinitial production	%	5	5	5	5	5
Decline rate	%	3.3	3.3%	3.3%	3.3%	3.3%
Economic limit output	barrel/month	2741	2741	2741	2741	2741
Parameters	Unit	Sensitivity between reserve value and price
SEC reserve value	$ × 104	903	948	998	1063	1135
SEC reserve value increment	$ × 104	/	45	50	66	71
Oil price	$/barrel	67.2	70.6	74.1	77.8	81.7
Increment range of adjacent price	%	5	5	5	5	5
Initial production	barrel/month	17,556	17,556	17,556	17,556	17,556
Economic limit production	barrel/month	2741	2626	2541	2433	2356

and Figure 9.

According to Figure 9, it is obviously indicated that the sensitivity between the SEC reserve value and the initial production is stronger than the sensitivity between the SEC reserve and the oil price.

(2)

$\left[\mathrm{P}\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right)-{\mathrm{C}}_{\mathrm{vu}}-{\mathrm{S}}_{\mathrm{ogl}}\right]<\left(1-{\mathrm{t}}_{\mathrm{compound}\mathrm{taxes}}\right){\mathrm{q}}_{\mathrm{i}}$

Then: ${\frac{\partial \left({\mathrm{NPV}}_1\right)}{\partial \left({\mathrm{q}}_{\mathrm{i}}\right)}}_{\mathrm{shape}-\mathrm{dispersed}-\mathrm{point}}<{\frac{\partial \left({\mathrm{NPV}}_1\right)}{\partial \left(\mathrm{P}\right)}}_{\mathrm{shape}-\mathrm{dispersed}-\mathrm{point}}$

The example data of the result are shown in

Table 7. SEC reserve value parameter sensitivity differences.

Parameters	Unit	Sensitivity between SEC Reserve Value and Initial Production
SEC reserve value	$ × 104	617	670	726	786	848
SEC reserve value increment	$ × 104	/	53	56	60	63
Oil price	$/barrel	63.99	63.99	63.99	63.99	63.99
Initial production	barrel/month	14,299	15,053	15,844	16,678	17,556
Increment range of adjacent initial production	%	5	5	5	5	5
Decline rate	%	3.3	3.3	3.3	3.3	3.3
Economic limit production	barrel/month	2826	2826	2826	2826	2826
Parameters	Unit	Sensitivity between reserve value and price
SEC reserve value	$ × 104	522	613	700	777	848
SEC reserve value increment	$ × 104	/	91	87	77	72
Oil price	$/barrel	52.16	54.9	57.76	60.8	63.99
Increment range of adjacent price	%	5%	5%	5%	5%	5%
Initial production	barrel/month	17,556	17,556	17,556	17,556	17,556
Economic limit production	barrel/month	3623	3412	3217	3026	2826

and Figure 10.

According to Figure 10, it is obviously indicated that the sensitivity between the SEC reserve and the initial production is weaker than the sensitivity between the SEC reserve and the oil price.

7. Conclusions

In practice, it is quite difficult to adjust any one of the SEC reserve parameters a little higher when the domestic SEC reserves have been submitted to the American professional estimation company committed by the SEC. For greatly improving the SEC reserve, the SEC reserve value and the SEC reserve substitution rate, through quantitative research, this paper has disclosed reserve parameter sensitivity differences rules, reserve parameter adjustment directions, parameter adjustment degrees and reserve parameter linkage adjustment rules. Moreover, the greatest benefit from the identified reserve parameter sensitivity differences rules will find which reserve parameter is the most significant parameter whose least adjustment will cause the largest reserve increase.

Furthermore, this paper has discovered the quantitative parameter conditions that lead to the sensitivity between the SEC reserve and the initial production to begin stronger and weaker than the sensitivity between the SEC reserve and the price in the production exponential, hyperbolic and harmonic decline types. Meanwhile, this paper has discovered the parameter quantitative conditions that lead to the sensitivity between the SEC reserve value and the initial production to begin stronger and weaker than the sensitivity between the SEC reserve value and the price in the common production exponential decline type.

In addition, the function calculus method adopted to disclose the reserve parameter sensitivity rules will expand the parameter sensitivity analysis method system that took the previous statistical mapping method as the main analysis method.