Most of old onshore oilfields in China have entered into the late development stage with high water cut and the continuous production decline of individual wells. After water flooding, the economic benefits of the application effect by changing the development mode and enhancing the recovery is close to zero. With the development mode of “secondary and tertiary recovery combination”, the production adjustment can be realized by combining the secondary recovery based on the overall infill of water flooding well pattern with the well pattern deployment of tertiary recovery based on the conversion of development mode. Through coordinated optimization and step-by-step implementation, the highest ultimate recovery and the maximum comprehensive benefit in the whole life cycle of the oilfield can be obtained^{[1,2,3,4,5,6,7]}. At present, chemical flooding is the most mature tertiary oil recovery technology in China, and the medium and high permeability reservoir by chemical flooding after water flooding is the main operation type of the “secondary and tertiary recovery combination” project^{[8,9,10,11,12,13]}.

The “secondary and tertiary recovery combination” project based on chemical combination flooding (STRC) often involves infill adjustment of well pattern^{[4, 7]} in order to establish an efficient injection-production pressure system, and ensure high injection-production fluid volume and oil production rate. Predicating accurately the annual production changes of the chemical combination flooding of STRC is of great significance for improving the design quality of the development plan, determining the investment in productivity construction and ensuring the benefits of the project.

At present, researches on the production effect of chemical combination flooding primarily rely on laboratory experiments and reservoir numerical simulation^{[5, 14]}. The reservoir numerical simulation method can predict the production of STRC. However, it is difficult to accurately quantify and characterize the complex flooding mechanisms, such as emulsification, fluid-rock interaction, etc., which will affect its reliability to a certain extent, particularly for oil reservoirs with low permeability. In addition, numerical simulation technology is high in requirements and time-consuming, which is not convenient for on-site personnel to use. Practical reservoir engineering methods predicting the production of STRC can be roughly divided into three categories. First, combined with the physical parameters of the actual block, a large number of numerical simulations of orthogonal schemes are carried out, and then the statistical analysis method is used to make mathematical statistical analysis on the simulation results to determine the practical formula for calculating the reasonable water injection amount. Then, according to the injection-production balance of well group and the formation coefficient, the fluid production of each layer of an individual well is calculated by splitting^[14,15]. This method requires a large number of numerical simulation calculations, and is time-consuming. In the second type, the production variation characteristics of chemical flooding projects that have been performed are statistically analyzed, and quantitative relationships between the production variation with reservoir conditions, conversion timing and types of chemical flooding technology are established^[16]. This method is an empirical reference method and has obvious limitations when applied to new areas. In the third type, first of all, the reservoir engineering method is used to calculate the injection volume, and then according to the injection-production balance, factors such as reasonable injection rate, injection-production relationship, well pattern and spacing, etc., are comprehensively considered to calculate the fluid production of chemical flooding wells, but this method can’t predict future production^[17].

In this study, according to the basic principles of reservoir engineering, combined with the major mechanisms of oil recovery enhancement of chemical combination flooding, the overall production prediction method framework of STRC has been established on the basis of the actual experience of oilfield development and the production performance prediction method of modified water flooding in sandstone reservoirs^[18]. The reservoir engineering method forecasting the production index is proposed for the “secondary and tertiary recovery combination” project converted to composite chemical flooding after completion of water flooding. The reliability of this method is verified by two alkali-free SP flooding projects in Jin 16 of Liaohe Oilfield and Gangxi 3 area of Dagang Oilfield, Bohai Bay Basin, East China.

STRC often involves well pattern infill adjustment, such as infilling the water flooding well pattern with a well spacing of about 300 m to about 150 m, to establish an efficient injection-production pressure system to ensure high enough fluid volume for injection-production well. When using the reservoir engineering method to predict the production of STRC, it is necessary to make clear about the production of the old water flooding well pattern before infilling, the production at the water flooding stage of the new STRC well pattern after infilling, and increased production after the conversion to chemical flooding on the basis of water flooding.

The annual production of the old water flooding well pattern before infilling is equal to the product of the number of oil wells and the annual production of individual well of the old water flooding well pattern, that is:

The production at the water flooding stage of the new STRC well pattern after infilling is equal to the product of the number of oil wells in the new well pattern and the annual production of single water flooding well, that is:

The ratio of the number of production wells of the new STRC well pattern to the number of production wells of the old water flooding well pattern is recorded as r_well3/2, that is:

The ratio of production of single water flooding well of new and old well pattern is recorded as λ_o, that is:

For sandstone reservoirs, the individual well production q_ow2+3 of the new well pattern is often lower than the individual well production q_owold of the old well pattern. While for a conglomerate reservoir, the individual water flooding well production of the new pattern is often higher than that of the old well pattern (Table 1).

The overall production of STRC can be expressed as the increasing multiple of the production based on the production in the water flooding stage, that is:

Substituting Eqs. (1)-(4) into Eq. (5), and the following formula is obtained after sorting, that is:

In the above formula, the number of production wells and individual well production during water flooding in old well pattern, the ratio of the number of production wells of the new and old well pattern, and the individual well production ratio of water flooding in the new and old well patterns are known. Only the production increasing multiple of chemical flooding is unknown. To predict the overall production of the chemical-flooding of STRC, the first step is to determine the production increasing multiple of chemical flooding.

The oil reservoir converted to chemical combination flooding is regarded as a new oil reservoir. The geological reserves of the new oil reservoir are equal to the remaining geological reserves at the time of flooding conversion. The sweep efficiency of water flooding is defined as the ratio of the recovery factor to oil displacement efficiency of the water flooding, that is:

The correction factor η of sweep volume of chemical combination flooding is defined as the sweep efficiency ratio of the conventional water flooding to that of chemical combination flooding, that is:

For this new reservoir, the recovery of chemical combination flooding is equal to the product of oil displacement efficiency of the chemical composite system and its sweep efficiency, that is:

The relationship between the recovery of chemical combination flooding based on the remaining geological reserves at the time of flooding conversion and the recovery of chemical combination flooding based on the original geological reserves is:

Combining Eqs. (7)-(10), the recovery of chemical combination flooding based on original geological reserves is obtained:

It can be seen from the derivation process that the above formula is applicable to the calculation of recovery factor of any part of the reservoir. Although the timing of chemical flooding conversion affects the effect of chemical combination flooding in heterogeneous reservoirs, the remaining oil saturation or oil displacement efficiency when the same system is displaced to the limit water cut of 98% is little affected by the timing of injection (for example, the oil displacement efficiency of the first member of the Paleogene Kongdian Formation in Dagang Oilfield is 66.5% by direct polymer-surfactant (SP) flooding, and the oil displacement efficiency of SP flooding conversion at the water cut of 80% and 95.8% are 66.1% and 67.2% respectively, there are very little differences among the three cases). The remaining oil saturation can be regarded as a fixed value. The oil displacement efficiency of the new reservoir based on the remaining oil saturation at the time of flooding conversion is:

Assuming that instead of converting to the chemical combination flooding, water flooding is continued, the water flooding efficiency of the new reservoir based on the remaining oil saturation is:

The reservoir can be divided into a series of grids G_i, and the chemical combination flooding stage can also be divided into a series of time steps Δt_i. If the injected fluid in Δt_i can completely sweep the grid G_i, the increment of reservoir recovery degree during this time is approximately equal to the recovery of the corresponding grid G_i, that is:

If instead of chemical flooding, water flooding is continued in the new well pattern, the recovery degree of the water flooding stage based on the remaining geological reserves in Δt_i is:

Combining Eqs. (11), (14) and (15), the following formula is obtained:

According to the aforementioned definition of the oil production rate, both sides of Eq. (16) are multiplied by the original geological reserves N_o (N_o=V_pS_oiB_oρ_o), and the following formula is obtained after sorting:

The oil rate enlargement factor F_ChemW of chemical combination flooding can be defined as the ratio of the production of chemical combination flooding to the production of conventional water flooding in the same period (Eq. 18), the production of composite chemical flooding can be obtained by combining the water flooding decline law of the new STRC well pattern and the oil rate enlargement factor of chemical combination flooding.

Since the remaining oil saturation of chemical combination flooding and water flooding can be regarded as the fixed values. Substituting Eqs. (12) and (13) into Eq. (18), the following formula is obtained:

For water flooding reservoirs in old oilfields, during the long oilfield development process, there are hydrodynamic time-cumulative effects such as layered water injection, profile control and displacement control, periodic water injection, and injection-production pressure adjustment. According to oilfield development experience and theoretical research, the water flooding sweep efficiency of conventional well pattern in medium-high permeability reservoirs can be close to 0.900^{[19,20,21,22,23,24]}. For example, the sweep efficiency of water flooding in Gangxi 3 area is 0.880, while the sweep efficiency of water flooding in Jin 16 high-extra-high permeability reservoir is as high as 0.947. During the practice of oilfield development, infill wells with water cut and production similar to those wells at the beginning of oilfield development are few, indicating that injected water almost sweeps the entire reservoir. The actual sweep efficiency can be expressed as:

The weight ω (0<ω<1.0) reflects the distribution uniformity of the remaining oil. The more uniform the distribution, the greater the ω is.

The theoretical sweep efficiency is equal to the ratio of the recovery of conventional water flooding based on the original geological reserves to the initial oil displacement efficiency of water flooding, that is:

For the water flooding oil reservoirs in old oilfields that are about to convert to chemical compound flooding, the remaining oil is “highly dispersed and relatively rich” on the whole^[19]. It can be considered that the remaining oil is generally uniform in distribution, so it is recommended that:

The recovery degree of water flooding swept area is obviously higher than the overall recovery degree of the reservoir. The relationship between the recovery degree of the actual swept area and the overall recovery degree of the reservoir can be obtained according to the material balance, that is:

The average well spacing of the new STRC well pattern is usually 100-200 m, which is generally smaller than the distribution width of sand body (Table 2). No matter for water flooding or chemical combination flooding, the small well spacing can ensure the high flooding efficiency of the new well pattern, resulting in high reserves producing degree and sweep efficiency.

The STRC infilling well pattern can further strengthen the control on sand body. The overall infilling of well pattern can generally make the recovery factor of water flooding increase by 2%-6%. The oil displacement efficiency of water flooding is estimated at 50%, and the sweep efficiency of water flooding will increase by 0.04-0.12. The sweep efficiency of water flooding of the infilling well pattern can be as high as 0.92-0.98^{[25,26,27,28,29,30,31]}. Therefore, it can be considered that the sweep efficiency of chemical combination flooding of the new well pattern is approximately equal to that of water flooding, that is, the correction factor of sweep volume:

Combining Eqs. (20)-(24), the engineering calculation formulas for the oil rate enlargement factor of chemical combination flooding are obtained after sorting:

In the above formulas, the initial oil displacement efficiency of water flooding and initial oil displacement efficiency of chemical combination flooding can be obtained through core displacement experiments under the original oil saturation; the recovery degree at the time of flooding conversion is the ratio of the cumulative production of target reservoir to its original geological reserves.

Based on the Eq. (25), the curve of the oil rate enlargement factor of chemical combination flooding with the ratio of recovery degree at the time of flooding conversion to the initial oil displacement efficiency of water flooding was drawn (Fig. 1). It can be seen that the oil rate enlargement factor of chemical combination flooding increases uniformly with the increase of the ratio (R₁) of the initial oil displacement efficiency of the chemical combination flooding to that of water flooding, and it increases rapidly with the increase of the ratio (R₂) of the recovery degree at the time of flooding conversion to the initial oil displacement efficiency of water flooding. The highest oil rate enlargement factor of chemical flooding exceeds 7.0, indicating that the selected area is very important for improving stimulation effect of chemical combination flooding.

On the basis of the reorganization of well pattern and reconstruction of surface injection system, the industrial test of polymer-surfactant combination flooding was carried out in the west 8-9-3 well block of the No.3 fault block in Gangxi 3 area. At the first phase of the project, standard reverse five-spot well pattern was adopted (7 injection wells and 14 production wells). The injection layers were NmⅢ-2-1 and NmⅢ-3-1, with geological reserves of 80×10⁴ t. The designed injection slug was 0.4 PV (pore volume) and composed of front slug, main slug and protection slug, and the injection rate was 0.12 PV/a. The chemical flooding started in August 2013, the daily oil production at the water flooding stage was 20 t, and the daily oil production in the peak period of the SP flooding stage was 74 t with the effect better than the designed plan, and the recovery factor expected to increase by 17%. The oil displacement efficiency of the polymer-surfactant flooding in this test area is 54.1%, the oil displacement efficiency of water flooding is 42.4%, and the recovery degree before flooding conversion was 37.2%. The average daily oil production of water flooding was about 20.5 t in the year before the flooding conversion of new STRC well pattern. Substituting the data into Eq. (25), the oil rate enlargement factor of chemical combination flooding was calculated at 3.25, and the average production during the one-year peak period of SP flooding was 70.6 t/d. The predicted production of the development plan was 76.7 t/d, the actual production was 77.2 t/d, and the relative error of this method is -8.52% (Fig. 2), indicating the prediction result is basically reliable.

In the SP flooding test in Jin 16 Block, reverse five-spot well pattern (with 24 injection wells and 35 production wells) at injection-production well spacing of 150 m is used. The production layer is the Xinglongtai high-extra- high permeability reservoir (the flooding was carried out first in XingⅡ4_7-8 (the 7th and 8th sublayers of the 4th sand layer, oil layer Ⅱ in Xinglongtai oil layer of Paleogene Shahejie Formation), and then in XingⅡ3_5-6 (the 5th and 6th sublayers of the 3rd sand layer, oil layer Ⅱ in Xinglongtai oil layer of Paleogene Shahejie Formation)), with geological reserves of 298×10⁴ t. The flooding designed consisted of front slug, main slug, auxiliary slug and protection slug. The concentration and size of the slug were adjusted twice according to the actual production performance. The current scheme design has a total slug size of 1.3 PV, and an injection rate of 0.15 PV/a. The front slug injection started in April 2011, and the injection of main slug started in December 2011. The secondary slug displacement started in May 2018. The daily oil production rose to a peak of 353 t, the comprehensive water cut dropped significantly. The effect is better than the scheme design, and the recovery factor is expected to increase by 19%.

The oil displacement efficiency of the SP system of this reservoir is 56.7%, the oil displacement efficiency of the water flooding is 47.8%, and the recovery degree before flooding conversion is 45.3%. The average daily oil production of water flooding was about 76.1 t in the year before the conversion to the new STRC well pattern. Substituting the data into Eq. (25), the oil rate enlargement factor of chemical combination flooding in Jin 16 Block was calculated at 4.56, and the average production during the one-year peak period of SP flooding was 367.8 t/d. The predicted production of the development plan was 413.0 t/d, and the actual production was 330.5 t/d. The result from this method has an error of about 11.3% (Fig. 3), with higher accuracy than the development plan.

The peak production of chemical combination flooding depends on the oil rate enlargement factor of chemical combination flooding and the production of water flooding at the time of flooding conversion. The oil rate enlargement factor of chemical combination flooding increases uniformly with the increase of the ratio of the initial oil displacement efficiency of chemical combination flooding to that of water flooding, and increases rapidly with the increase of the ratio of the recovery degree at the time of flooding conversion to the oil displacement efficiency of water flooding. Chemical combination flooding works better in enhancing production in the reservoir with high recovery degree.

Compared with the production data of on-site tests, the results from the production calculation method for STRC reservoirs have a relative error of about ±10%. The prediction accuracy can meet the requirements of reservoir engineering.

B_o—volume coefficient of crude oil, dimensionless;

E_DChemi—initial oil displacement efficiency of chemical combination flooding (direct chemical flooding in original oil reservoir), %;

E_DChemn—oil displacement efficiency of chemical system of new reservoir based on the remaining oil saturation at the time of flooding conversion, %;

E_Dwi—initial oil displacement efficiency of water flooding (in original reservoir), %;

E_Dwn—oil displacement efficiency of water flooding of new reservoir based on remaining oil saturation, %;

E_RChem—recovery of chemical combination flooding based on original geological reserves, %;

E_RChemn—recovery of chemical combination flooding of new reservoir, %;

E_Rw—recovery of water flooding based on original geological reserves, %;

E_Rwn—recovery of water flooding based on geological reserves of new reservoir, %;

E_V0—theoretical sweep efficiency, %;

E_VChem—sweep efficiency of chemical combination flooding, dimensionless;

E_Vw—sweep efficiency of water flooding of new reservoir, dimensionless;

F_ChemW—oil rate enlargement factor of chemical combination flooding, dimensionless;

gradF_Chemw, gradient vector length of oil rate enlargement factor of chemical combination flooding, di-mensionless;

G_i—grid;

n_o2+3—number of oil wells in new well pattern;

n_oold—number of oil wells of old well pattern;

N_o—original geological reserves of reservoir, t;

q_ow2+3—individual well production of new well pattern, t/d;

q_owold—individual well production of old well pattern, t/d;

Q_ow2+3—annual production of STRC new well pattern of water flooding or production of water flooding in the same period (that is, production of water flooding of new well pattern when it is not converted into chemical flooding), t/a;

Q_owold—annual production of old water flooding well pattern, t/a;

Q_oChem2+3—production level of STRC (that is, production level of chemical combination flooding of new well pattern), t/a;

r_well3/2—ratio of number of production wells of new STRC well pattern to that of old water flooding well pattern, dimensionless;

R₁—ratio of initial oil displacement efficiency of chemical combination flooding to that of water flooding, %;

R₂—ratio of recovery degree at the time of flooding conversion to initial oil displacement efficiency of water flooding, %;

R_Chem—chemical combination flooding based on original geological re-serves, %;

ΔR_Chem—recovery degree of chemical combination flooding based on original geological reserves, %;

ΔR_wn—recovery degree of water flooding based on geological reserves of new reservoir, %;

R_e0—total recovery degree of reservoir based on original geological reserves at the time of flooding conversion, %;

R_ews—recovery degree based on original oil saturation before flooding conversion, %;

R_vwn—recovery rate of water flooding based on remaining geological reserves at the time of flooding conversion, %;

R_vChem—recovery rate of chemical combination flooding based on remaining geological reserves at the time of flooding conversion, %;

R_wn, recovery rate of water flooding based on remaining geological reserves at the time of flooding conversion, %;

S_oi—original oil saturation, %;

S_o—remaining oil saturation at the time of flooding conversion, %;

V_p—pore volume of reservoir, m³;

Δt_i—length of time step, a;

η—correction factor of swept volume of chemical combination flooding, dimensionless;

λ_o—ratio of individual well production level of water flooding of new and old well patterns, dimensionless;

ρ_o—surface density of crude oil, 10³ kg/m³;

ω—weight value reflecting distribution uniformity of remaining oil, dimensionless.