Absolute open flow potential (q_AOF) and dynamic reserves (G) are the key parameters representing well/reservoir deliverability and rate maintenance capability, and they are the basis for well production proration, well spacing determination and field depleting rate optimization^[1,2,3,4].

Absolute open flow potential (q_AOF), defined as the rate when a well is flowing at zero bottom hole pressure (gauge pressure)^{[1-2, 5]}, is the foundation for well production proration and is usually determined through deliverability test. Besides reservoir pressure and deliverability coefficient (Kh), q_AOF is also dominated by stimulation and completion. So, in gas field development, such measures as horizontal drilling, acidizing or fracturing are usually utilized to enhance well deliverability. q_AOF varies for different type of gas reservoirs due to different geology and completion condition.

Dynamic reserves (G) are described as the drainage gas volume (under original condition) during well/reservoir pressure depletion. It is a key parameter to evaluate the active or drained quantity of volumetric reserves during production and is also the basis for field development planning, infill drilling and recovery factor estimation^[6,7,8]. How much the volumetric reserves will be drained is affected by many aspects, such as reservoir transmissibility, heterogeneity, well spacing and aquifer encroachment. Normally, field development is planned based on volumetric reserves and optimized during production when there are enough data to give a proper evaluation G. With the increasing geology complexity of gas reservoirs, the reservoir fluids get more difficult to produce, and the discrepancy between dynamic reserves and volumetric reserves becomes more significant^[9]. Literature reviews show that current domestic and foreign large gas field development studies focus on development principle and exploitation mode^{[10,11,12,13,14,15]}, and few literatures discuss the quantitative correlations among the key development index such as deliverability, dynamic reserves and the like.

Under the principle that large gas fields should be produced at fixed annual capacity to reach certain plateau production while meet the requirement of maximum profits, what are the correlations among key development index such as deliverability and dynamic reserves for developed gas fields, and how to apply them to guide new gas fields development are the purpose of this study. Based on performance data of over 600 production wells from 32 various type large gas fields in China, the correlation between per-well average dynamic reserves and average Initial Absolute Open Flow Potential of each field is established in log-log plot, and its connotation is further discussed through theoretical development. The correlation diagram can be used as analogue in new gas field development planning to evaluate the minimum dynamic reserves which meet the requirement of stable and profitable production, and facilitate well pattern arrangement. It also provides a rapid and convenient methodology to appraise the development effects and infill drilling potential for developed gas fields.

The 32 developed large gas fields mentioned in this paper, cover almost all the types of developed gas reservoirs in China (Table 1), including 6 low-permeability and tight reservoirs such as Sulige and Xujiahe, 15 porous gas reservoirs like Sebei and Kela, and 11 fracture-porous (vuggy) reservoirs such as Dabei and Keshen. The total OGIP of these 32 gas fields amount to 9.48×10¹² m³ with summed plateau annual production 1 200×10⁸ m³.

With performance data, initial AOFP and dynamic reserves are calculated for over 600 production wells from the 32 various type large gas fields. Results showed that, (1) for those fields with high permeable, large extent and good internal communication reservoirs, well dynamic reserves are correlated positively with initial AOFP, and (2) for such type of gas reservoirs as low-permeability and tight gas reservoirs and volcanic reservoirs, variations in lithology and reservoir property result in poor reservoir extent and communication, which leads to limited well drainage area, and the correlation between well dynamic reserves and initial AOFP becomes unpredictable. And there is no objective necessary that those two parameters should be dependent on each other in such type of reservoirs (Fig. 1).

For each of these 32 fields, $\bar{G}$ and $\bar{q}_{IAOF}$ are calculated with arithmetic mean methods among producing wells, which can eliminate heterogeneity among wells in individual field and can represent the predominant feature of each field resulted from distinct reservoir property and development approach. The average data from 32 fields are plotted in log-log diagram, and the $\bar{G}$ vs. $\bar{q}_{IAOF}$ plot shows a highly dependent linear trend (Fig. 2). In the diagram, the data are distributed along a narrow band, with line A indicating data regression trend (R²=0.863 7), line B and C being the upper and lower limit of the band respectively. The regression line A can be expressed with the following equation:

Line A denotes the overall average level of $\bar{G}$ vs. $\bar{q}_{IAOF}$ trend for developed large gas fields in China in current technology and economy situation; line B represents the upper limit trend for gas fields with higher $\bar{G}$ values and longer term stable production capacity; line C signifies the lower limit trend of gas field which shows higher $\bar{q}_{IAOF}$ but lower $\bar{G}$, implying the poor stable maintenance capacity.

The quantitative relationship between $\bar{G}$ and $\bar{q}_{IAOF}$ can be developed mathematically based on the definition of well proration and recovery rate.

Based on definition, the average initial AOFP ($\bar{q}_{IAOF}$) for each field can be written as:

And the per-well average dynamic reserves ($\bar{G}$) for each field can be expressed as:

The average daily proration (q_g) can be formulated with power function of $\bar{q}_{IAOF}$ as follows ^[1,4]:

Allowing for facility maintenance and surveillance, we take 330 days as the annual opening time for individual well, and the relationship between q_g and well annual production (G_pw) is:

The field annual production (G_p), dynamic reserves recovery rate (v) and field dynamic reserves (G_t) can be correlated together with the following equation:

Substitute Eq. 5 into Eq. 6, the relationship among v, q_g and $\bar{G}$ are then established as follows:

The $\bar{G}$ vs. $\bar{q}_{IAOF}$ correlation can be developed by substituting Eq. 4 into Eq. 7:

Taking logarithm for both sides of Eq. 8, we get:

Eq. 9 indicates that log-log linear relationship exists between $\bar{G}$ and $\bar{q}_{IAOF}$, with constant m as the slope and interception dependent on proration coefficient (α) and v. This equation interpreted the theoretical background for the linear trend of $\bar{G}$ vs. $\bar{q}_{IAOF}$ from 32 fields data in Fig. 2. In Eq. 9, α and v are determined based on development technical policy when a field is put on production, so Fig. 2 implicates the compatibility between $\bar{G}$ and $\bar{q}_{IAOF}$ attained through development optimization to reach the balance among annual flow capacity, maximum profits and certain production plateau, that is, to match productivity with long term rate maintenance capacity. To further interpret the practical meaning represented by Fig. 2 and Eq. 9, the dynamic reserves recovery rates and proration coefficients for gas fields will be discussed below.

Field Development Management Guiding Principles regulate that large gas fields should maintain 10-15 years of plateau production period, and to meet this plateau production requirement, the recovery rate of gas field should be controlled in certain scope. Based on the types of gas fields which data are shown in Fig. 2, dynamic reserves recovery rates (v) for these large gas fields are analyzed and are shown in Fig. 3. Statistics show that there is certain difference in v values among different types of gas fields, but all varied within certain limits: (1) for low-permeability and tight gas fields, the average v value is 4.6%. The tight reservoir with the lack of natural fractures results in poor gas mobility, which leads to low recovery rate; (2) the mean v value for porous gas fields reaches to 6.6%. This type of gas field exhibits medium to high permeability, and with fair pore-throat configuration, the matrix processes high mobility and connectivity, therefore, the dynamic reserves recovery rate is higher; (3) fracture-porous (vuggy) fields show 5.1% in mean v value. Both matrix porosity and permeability in this group of fields are very low, but with the development of natural fractures, the reservoirs present good communication and high dynamic permeability, and to inhibit water invasion, the recovery rate is between those in low-permeability and tight fields and porous fields.

In conventional gas development, the fields’ stable production usually achieved through the stable production of individual well, so proper proration of individual well is crucial. In field development plan design and development optimization, proper individual well production will be determined to meet the requirements of stable production, completion limitations, and uniform depletion. For comparison, the proration ratio (q_g/q_IAOF) is often used to weight the proration level. Fig. 4 illustrates the proration ratios for the three groups of fields.

It can be concluded that there is certain difference among proration ratios in different types of gas fields due to the variation in geology and initial AOFP. The low-permeability and tight gas fields also show a low proration ratio, 0.12 on average (1/8 q_IAOF ), and 0.17 and 0.21 for porous and fracture-porous (vuggy) fields respectively. Proration ratio reflects the well’s long term stable flow maintenance capacity under high flow rates, and it implicates the compatibility between $\bar{q}_{IAOF}$ and $\bar{G}$.

In this paper, $\bar{q}_{IAOF}$/$\bar{G}$ is defined to evaluate the compatibility between $\bar{q}_{IAOF}$ and$\bar{G}$, and the statistics shown in Fig. 5 implies that, with the increasing of $\bar{q}_{IAOF}$/$\bar{G}$, the proration ratio decreases notably, which means poor plateau maintenance capacity at high flow rates, as is the case with low-permeability and tight gas fields. In porous and fracture-porous (vuggy) fields, the higher permeability and better connectivity result in larger well drainage area and higher well dynamic reserves. Compared with low-permeability and tight gas fields, the $\bar{q}_{IAOF}$/$\bar{G}$ in those two types of fields are low, but the proration ratios are high.

Based on Eq. 4, the relationship between proration ratio and proration coefficient (α) can be expressed as:

Define b as the proration ratio, that is:

Combine Eq. 10 and Eq. 11, the correlation b and a can be formulated as:

Based on the regression m value in Eq. 1, we can see that when the $\bar{q}_{IAOF}$ ranges from (1-1 000)×10⁴ m³/d, the values of $\bar{q}_{\text{IAOF}}^{\ \ \text{1}-m}$ show limited variation. And the proration ratio, b, also varied in a limited range, around 1/6-1/3 (as shown in Fig. 5). Therefore, a can be seen as a constant with limited fluctuation. Dynamic reserves recovery rates vary for different type of fields, but at a fixed interval. Consequently, the interception term a/ν in Eq. 9 changes in a minimal scope and can roughly be taken as a constant. This explains the presence of narrow band linear trend of 32 fields data in Fig. 2 (constant slope, and interception varies in limited scope).

The correlation diagram can be used as analogue in new gas field development planning to evaluate the dynamic reserves and to define the lower limit for commercial development, which facilitate well pattern arrangement. It also provides a rapid and convenient methodology to appraise the development effects and infill drilling potential for developed gas fields.

The Sinian gas reservoir in Gaoshi#1 well group area in Gaoshiti-Moxi Block of central Sichuan Basin is a widely spread^[16], fracture solution porosity reservoir. Dominated by fracture, deposition, and karst, strong heterogeneity exists in reservoir property and deliverability. Before development plan design, deliverability tests were conducted in 15 wells and pressure transient tests interpretation show composite reservoir flow behavior for most of the wells, and dynamics analysis indicate limited well drainage area. For this type of low porosity, strong heterogeneity and widely spread carbonate gas reservoir, performance data are limited in field appraisal period, so, it is hard to give an accurate prediction of producing reserves which meet the requirement of stable and profitable production.

The $\bar{q}_{IAOF}$ of 15 wells in Gaoshi#1 well group area is about 125×10⁴ m³/d which corresponding to a $\bar{G}$ value of 11.4×10⁸ m³ calculated with the established correlation (Fig. 2, Eq. 1). It means in this fields, to achieve stable and profitable production, the lower limit for mean well dynamic reserves must be no less than 11.4×10⁸ m³. After the implementation of field development plan, well dynamic reserves are calculated for 5 of the 15 wells with nearly 2 years of production history data, and results showed that the dynamic reserves for each well ranges between (3-30)×10⁸ m³, with 11.55×10⁸ m³ in average (Table 2), which proves that with the improvement in preferred drilling sites identification and productivity enhancement, the field has reached the level of commercial production.

For a developed gas field, the development effects can be appraised by analogy with the $\bar{G}$ vs. $\bar{q}_{IAOF}$ diagram (Fig. 6): (1) calculate $\bar{G}$ and $\bar{q}_{IAOF}$ with performance data, and then plot the $\bar{G}$ vs. $\bar{q}_{IAOF}$ data in Fig. 6, if the data falls on the line A, it indicates that the development mode and approach can both fully implement well’s productivity potential and meet commercial production standards; (2) the presence of field data below line A (for example point D in Fig. 6) corresponds to higher well deliverability, but lower dynamics reserves. In connecting reservoirs, this indicates a dense well placement without infill drilling potential. But in poor communicated lentic clasolite reservoirs, volcanic reservoirs and the like, it means optimization should be focused on well dynamic reserves enhancement; (3) the occurrence of field data above line A (for example point E in Fig. 6) reveals higher well dynamic reserves and infill drilling^{[17,18,19,20,21,22,23]} can be implemented to increase field annual yields.

The major pay zone in Su#20 block of central Sulige Gas field is the lower Shihezi Formation of mid Permian reservoir occurred in braided channel delta deposits environments. The reservoir is composed of low porosity and extremely low permeability lentic sands, with average porosity 8.95%, average permeability (0.06-2.00)×10^-3µm². The poor reservoir continuity connectivity confines the well drainage area and results in very low well dynamic reserves. The Su#20 block was on stream in 2006 with vertical and horizontal production wells. More than 30 wells’ performance data were analyzed, with predicated $\bar{G}$ value of 0.304×10⁸ m³, and $\bar{q}_{IAOF}$ value 16.93×10⁴ m³/d (Table 3). In the $\bar{G}$ vs. $\bar{q}_{IAOF}$ diagram (Fig. 6), the field data falls on point F below line A, indicating very low well dynamic reserves. Although in such kind of fields, infill drilling is usually taken as effective ways to produce the non-depleted reserves, to reach the development effects of other kinds of fields, it is recommended that further technology innovation should focus on the improvement of individual well drainage area to increase well dynamic reserves.

The per-well average dynamic reserves ($\bar{G}$) and average Initial Absolute Open Flow Potential ($\bar{q}_{IAOF}$) from 32 large gas fields in China present highly correlated linear trend in log-log plot, with slope related to proration index (m) and interception dependent on proration coefficient (a) and dynamic reserves recovery rate (ν). The dependence between $\bar{G}$ and $\bar{q}_{IAOF}$ reflects the compatibility between well deliverability and long-term stable flow capacity attained through development optimization to reach the balance among annual flow capacity, maximum profits and certain production plateau.

The $\bar{G}$ vs. $\bar{q}_{IAOF}$ correlation diagram can be used in the early stage of field development to evaluate the dynamic reserves needed to achieve commercial production, which provide a time saving and effective way to determine development index. It can also serve as an analogue to appraise field development effects and infill drilling potential evaluation for developed fields.

The data in the $\bar{G}$ vs. $\bar{q}_{IAOF}$ correlation diagram are from 32 developed gas fields in China, which almost covered all the types of gas fields currently developed in China, therefore, the diagram has universal applicability as analogue to evaluate the development of both conventional and unconventional gas fields.

a—proration coefficient, dimensionless;

b—proration proportion, dimensionless;

G—well dynamic reserves, 10⁸ m³;

$\bar{G}$—per-well average dynamic reserves, 10⁸ m³;

G_p—field annual gas production, 10⁸ m³;

G_pw—well annual gas production, 10⁸ m³;

G_t—field dynamic reserves, 10⁸ m³;

i—well number;

m—proration index, dimensionless;

n—total well counts;

q_g—average proration, 10⁴ m³/d;

q_IAOF—well Initial Absolute Open Flow Potential, 10⁴ m³/d;

$\bar{q}_{IAOF}$—arithmetic average well Initial Absolute Open Flow Potential, 10⁴ m³/d;

ν—dynamic reserves recovery rate, %.