Tracer technology is an effective way to verify the connectivity of oil and water wells in water flooding oilfields. In recent years, a series of field experiments have been conducted around the world to form a relatively complete theoretical system. The basic principle of tracer technology is referring to the dynamic and static data of the test well group and the test scheme which adds tracer into the injection wells and takes samples from the surrounding production wells, performs tracer analysis in the laboratory and obtains the tracer content then draw the tracer production curve of the production wells. According to the curve of see tracer concentration in wells around, the information such as the direction and speed of the injected fluid can be further confirmed, and the connectivity between oil and water wells can be visually given.

The well A24 in the S oilfield verified the connectivity between oil-water through tracer technology. According to the changes in the concentrations of the surrounding wells, it can be seen that the well A24 is in communication with surrounding wells.

After seeing the tracer in wells, with the extension of production time, concentration changes gradually from the local concentration to peak, and then reduced to the local concentration, showing a normal distribution. The process mainly shows the tracer flows out from the injection end to the exit end and the concentration changes as the change of the number of flow lines from the injection end to the exit end.

Based on the existing tracer test data, the connectivity between oil and water wells can be visually presented. At the same time, according to the tracer flow theory, through the technological innovation and using tracer theory combined with programming methods to achieve tracer flow law described. According to the change of the number on flow lines in different oil wells, the extent of oil well affected by injection well can be determined, and the water flooding coefficient can be quantitatively given. Further analysis is made on the flooding of oil wells effect by injection wells, the remaining oil concentration area can be determined, and the direction of potential is clarified.

Based on the theory of tracer [14] [15] and the theory of percolation, the establishment of oil-water two-phase flow equation, tracer concentration diffusion equation, wellbore output concentration variation equation and the water front law equation are established, as shown in Formulas (1)-(5).

The two-phase oil-water continuity equation is established, as shown in Equation (1):

∇ ⋅ [ k k r o B o μ o ( ∇ p o − ρ o g ∇ D ) ] − q o ρ o s c = ∂ ∂ t ( ϕ s o B o ) ∇ ⋅ [ k k r w B w μ w ( ∇ p w − ρ w g ∇ D ) ] − q w ρ w s c = ∂ ∂ t ( ϕ s w B w ) (1)

In Formula (1):

K: permeability; K_ro, K_rw: relative water-oil permeability; B_o, B_w: oil-water volume coefficient; μ_o, μ_w: oil-water viscosity; ρ_o, ρ_w: oil-water density; ρ_osc, ρ_wsc: oil-water surface standard density; P_o, P_w: oil-water pressure; Φ: porosity; S_o, S_w: oil-water saturation; q_o, q_w: flow rate of oil recovery, flow rate of water recovery; g: gravity; D: calibration height; ∇ ⋅ : degree of diffusion; ∇ : degree of Gradient.

Tracer concentration diffusion equation, as shown in Formula (2):

Z ∂ 2 c ∂ x 2 − u ∂ c ∂ x = ∂ c ∂ t (2)

Defined conditions: c ( x , t ) = c 0 , x = 0 c ( x , t ) = 0 , x = ∞ c ( x , t ) = 0 , t = 0

In formula:

Z: effective mixing coefficient; C: tracer concentration; X: one-dimensional length; U: seepage velocity; T: time.

Combined with the solution conditions, the concentration relationship formula is achieved, as shown in Formula (3):

c ( x , t ) c 0 = 1 2 e r f c ( x − u t 2 Z t ) (3)

c₀: injection concentration; erfc(x): error function.

The wellbore concentration is the result of the mixing effect of the concentration produced on each streamline. Calculated formula as shown in Formula (4):

c ( t ) = ∫ c 0 ( t − τ ( ψ ) ) q ( ψ ) d ψ / ∫ q ( ψ ) d ψ (4)

In formula:

c(t): output concentration of wellbore at a certain time; c 0 ( t − τ ( ψ ) ) : the output concentration corresponding to the wellbore position at the corresponding time on a certain streamline; q ( ψ ) : the amount of fluid contribution on the streamline; ∫ d ( ψ ) : streamlined integration.

Tracer flows along the streamline, first-seeing point is in the position of water flooding front edge, and then flow into the wellbore to output, according to the law of flow, a water-front flow equation is established, as shown in Formula (5):

x f − x 0 = f ′ w ( S w f ) ϕ A ∫ 0 t q ( t ) d t (5)

In formula:

x_f: the leading edge in the two-phase seepage zone; x₀: original oil-water interface position; φ: porosity; A: seepage flow area; S_wf: water saturation of leading edge; q(t): the flow in time t.

According to the Formulas (1)-(5), combining the tracer information in Well A24 and the surrounding tracer information, the wave propagation factor of oil wells in Well A24 is calculated, as shown in Table 1.

According to Table 1, it can be seen that well A16 has the lowest spread factor which affected least by the well A24, it shows that the remaining oil around Well A16 is enriched, that means the direction around A16 well is the main potential direction.

The fault of S sand body is well developed and the lateral distribution of sand body is small. There is remaining oil in the fault zone and the imperfect part of local well pattern. The longer the oil field is developed, the more refined the oil needs to be finely portrayed.

According to the mirror reflection method in seepage theory [16] , the mirror reflection law of oil and water wells near the fault can be obtained. According to the potential superposition principle, any potential field distribution can be calculated. Take the S oilfield one-injecting well with four oil wells pattern as an example, the formula for any potential is shown in Equation (6).

Φ M = 1 2π ( q h 1 ln r 1 + q h 2 ln r 2 − q h 3 ln r 3 + q h 4 ln r 4 + q h 5 ln r 5 ) + C = q h 1 2π ln r 1 r 2 β 1 r 4 β 3 r 5 β 4 r 3 β 2 + C (6)

The distribution of any potential field at the boundary is shown in Equation (7).

Φ e = 1 2π ( q h 1 ln r e + q h 2 ln r e − q h 3 ln r e + q h 4 ln r e + q h 5 ln r e ) + C = q h 1 2 π ln r e 1 + β 1 − β 2 + β 3 + β 4 + C (7)

Formulas (6) and (7) are superposed to obtain pressure field formula at any point, as shown in Formula (8).

P M = P e − q 1 μ 2 π K h ln r e 1 + β 1 − β 2 + β 3 + β 4 r 3 β 2 r 1 r 2 β 1 r 4 β 3 r 5 β 4 (8)

In formula:

Φ_M, Φ_e: potential field for any point M to the boundary; r₁ - r₅: distance from well 1 to well 5 to point M; r_e: the boundary point distance from well 1 to well 5; q_h1 - q_h5: thickness production or injection volume from well 1 to well 5; C: integral constant.

Among:

β 1 = q h 2 q h 1 , β 2 = q h 3 q h 1 , β 3 = q h 4 q h 1 , β 4 = q h 5 q h 1

By using Equations (6)-(8), the flow field in the sand body can be obtained by applying programming calculation, as shown in Figure 1.

It can be seen from Figure 1 that in the area near the fault and the imperfect well pattern, streamline did not affect or spread to a lesser extent. According to

the scope of the flow line, combined with the reserves calculation parameters, you can get the residual oil well near the fault and the imperfect area of the well. The remaining oil near the fault refers to the remaining oil near the fault, the imperfect remaining oil refers to the remaining oil of no wells in the well network in the sand body and the remaining oil in the area without the flow line. According to this method, the sand body of S oilfield is analyzed to calculate the remaining oil reserves in the fault zone and the imperfect area, as shown in Table 2.

According to Table 2, the remaining oil reserves in the main sand body of S oilfield are 214.00 × 10⁴ m³, which has the potential for excavation.

Based on the study in Section 3.1, the residual oil enrichment around Well A16 can be judged according to the different water flooding and coefficient of oil well. According to the study of 3.2, it can be known that remaining oil exists near the fault and in the imperfect well pattern. According to the results of the study, the numerical simulation results are revised and recalculated to obtain the remaining oil saturation map in accordance with the law of dynamic change, as shown in Figure 2. As can be seen from Figure 2, there is a large amount of remaining oil in the area near the well A16, in the imperfect area and near the fault. Through the study of this paper, a variety of methods to verify each other to achieve the remaining refined oil refinement, while the remaining oil reserves can be quantified characterization, tapping the potential for the adjustment of wells to provide confidence. Through the mutual verification of multiple methods, the research on remaining oil refinement can be realized. At the same

time, the remaining oil reserves can be quantitatively characterized, which can provide confidence for potential through adjustment wells.

This research has provided technical guidance for the implementation of horizontal adjustment wells called A3H and A33H in Nm0-19 and NmII-5+6 sub-layers of S oilfield respectively, and put into production in 2013. The production of the two wells is shown in Table 3.

It can be seen from Table 3 that the two adjustment wells have been put into operation to increase the daily oil production of 116 m³/d, increase the recoverable reserves to 20.00 × 10⁴ m³.

After putting into operation, the production effect of adjustment wells is better. Through production measurement, we can get production parameters such as daily oil production and water cut of adjustment wells. Take A33H as an example, the initial water content of the well is low at only 5%, and the daily oil yield after the production is 60 m³/d and the production is stable, as shown in Figure 3. The production of two adjustment wells is compared with the old oil well, as shown in Table 4.

In Bohai, the production parameters of each oil well will be measured every day. According to the measurement data, we can evaluate the production capacity and running dynamics of the oil well, and carry out appropriate adjustment measures to improve the effect of oil field development. It can be seen from Table 4 that the initial production capacity, water cut and oil production are better than the produced well indicators which further confirms the reliability of the study method. Refinement of remaining oil description of the study can further improve the initial production capacity, the initial calculation of water and oil yield indicators accuracy of adjustment wells, so as to provide a favorable guarantee for the implementation of the adjustment well.

Through the production of two adjustment wells, it can be seen that the method has some reliability. According to this method, four adjustment wells have been studied according to the control of low-yield wells and shut-in wells in the oilfield: side-drills A16S1 with shut-down well A16, side-drills A7H1 with low-production wells A7M, drill A29 for well A29H1 and well A34 in the remaining oil-rich zone near the fault. The four adjustment wells are put into production in 2016. Initial daily increase production is 211 m³/d, the four adjustment wells are expected to accumulate 23.82 × 10⁴ m³.

Through the research in this paper, the remaining oil is described finely. In the oilfield, six adjustment wells have been studied. Six adjustment wells forecast to have accumulated oil accumulation of 43.82 × 10⁴ m³. Improving oil recovery at the same time saving low-yield wells and shutting down the wells will achieve the purpose of reducing costs and increasing efficiency.