The oil production predicted by means of the conventional water-drive characteristic curve is typically affected by large deviations with respect to the actual value when the so-called high water-cut stage is entered. In order to solve this problem, a new characteristic relationship between the relative permeability ratio and the average water saturation is proposed. By comparing the outcomes of different matching methods, it is verified that it can well reflect the variation characteristics of the relative permeability ratio curve. Combining the new formula with a reservoir engineering method, two new formulas are derived for the water flooding characteristic curve in the high water-cut stage. Their practicability is verified by using the production data of Mawangmiao and Xijiakou blocks. The results show that the error between the predicted cumulative oil production and production data of the two new water drive characteristic curves is less than the error between the B-type water drive characteristic curve and the other two water drive characteristic curves. It is concluded that the two new characteristic curves can be used to estimate more accurately the recoverable reserves, the final recovery and to estimate the effects of water flooding.

Calculating the formulas for the traditional water flooding characteristic curves A and B is straightforward, as is understanding the physical significance of the essential quantities [

In theory, the characteristic curve of the water drive will curve towards the period of maximum water cut. Because the linear representation relationship between the oil-water relative permeability ratio and water saturation in the semi-logarithmic coordinate used to generate the standard water drive characteristic curve is no longer established after the high water cut period begins [

Based on Liu’s [

The following formula is used to establish the traditional water flooding characteristic curves of A and B:

The linear representation in semi-logarithmic coordinates is given by

Numerous researchers [_{rw}/_{ro} and _{w} exists only when _{w} is near the center of the oil-water two-phase infiltration zone (single well or Oilfield block production to medium-high water cut period). Non-exponential bending, on the other hand, will occur during the early and late stages of production in waterflooding oil fields. As a result, this formula does not apply to periods of low, high, or ultra-high water cut. Now,

As illustrated in _{w} is near 0.55 and concave after inversions. At this point

The experimental data for oil-water permeability in multiple blocks of the JH oilfield are analyzed to select core permeability data samples from multiple main production wells in the block. It encompasses the three most frequently encountered types of oil-water permeability curves in waterflood oil fields: linear water phase, concave water phase, and concave water phase. It generates a normalized oil-water relative permeability ratio curve that can be used to characterize the physical properties of oilfield blocks. By conducting matching analyses and conducting research on the inverted portion of the relative permeability ratio curve in the later period, as well as conducting literature searches. This article proposes a new characterization relation that more accurately describes the characteristics of the relative permeability ratio curve’s latter section:

Then:

Note: According to the literature [

Determination method of

Calculate the bending part of the back section of the normalized oil-water relative permeability ratio curve for the North District, North fault block, Zhouji, and the remaining three blocks of the JH oilfield using the

Oilfield block | Matching method | Matching expression | Correlation coefficient |
---|---|---|---|

North District Block | The proposed New method matching | 0.9958 | |

Exponential function matching | 0.987 | ||

Quadratic polynomial matching | 0.989 | ||

Logarithmic function matching | 0.9188 | ||

Power function matching | 0.99 | ||

North fault block | The proposed New method matching | 0.9975 | |

Exponential function matching | 0.9893 | ||

Quadratic polynomial matching | 0.9926 | ||

Logarithmic function matching | 0.9296 | ||

Power function matching | 0.992 | ||

Zhouji Block | The proposed New method matching | 0.9985 | |

Exponential function matching | 0.9979 | ||

Quadratic polynomial matching | 0.9945 | ||

Logarithmic function matching | 0.9385 | ||

Power function matching | 0.9982 |

To precisely meet the demand for dynamic and recoverable production prediction during the later stages of oilfield water injection development. In this paper, the new _{rw}/_{ro}-_{w} expression expressed by

Without regard for gravity or capillary force, the water-oil ratio

Replace

Take the logarithm on both sides of the formula, and obtain:

When the formation pressure of the water injection reservoir remains stable, the geological recovery

The preceding formula can be rewritten:

Replace

Namely:

In

Determination method of ^{R}

The literature [_{we} at the outlet can be substituted for one another. Thus,

The characterization relationship of normalized water saturation _{wd} is as follows:

According to _{we} at the outlet can be expressed:

The ultimate displacement efficiency _{d} can be expressed:

The _{om} of movable oil reserves is defined:

Replace

From

Replace

In _{1} are all constants, _{1} is as follows:

_{p}_{om} curve during the ultra-high water cut period. In a semi-logarithmic coordinate system, the relationship between the water-oil ratio and the degree of recoverable reserve recovery in the ultra-high water cut stage is exponential.

The characteristic curve of water flooding often takes one of three shapes in semi-logarithmic coordinates: linear, up-ward, or down-ward. After entering the era of high water cut, a huge number of water flooding oil field lg

Let ^{x},

B | C | y = A + B^{.}C^{x} Monotonicity |
y = A + B^{.}C^{x} Variety |
Curve form of new water drive characteristic curve | Water flooding development effect |
---|---|---|---|---|---|

B > 0 | C > 1 | + | Increase | Increase | Bad |

0 < C < 1 | − | Decrease | Contrary to the actual production law in the high (extra-high) water cut period | ||

B < 0 | C > 1 | − | Increase | ||

0 < C < 1 | + | Decrease | Decrease | Good |

If ^{x}

As shown in

The representation form of the ^{.}_{1}^{x}_{1}^{x}_{1}.

The application study and research of novel water floodings characteristic curve formulae such as

The actual development data of the Mawangmiao block in the JH oilfield is shown in

Year | Oil production/(10^{4}t) |
Water production/(10^{4}t) |
Water cut/(%) |
---|---|---|---|

1997 | 64.0106 | 28.0915 | 60.99 |

1998 | 84.9558 | 49.2754 | 64.49 |

1999 | 95.2643 | 71.2725 | 72.97 |

2000 | 103.2098 | 96.6344 | 82.86 |

2001 | 109.6502 | 120.7104 | 80.97 |

2002 | 114.5946 | 141.4029 | 81.57 |

2003 | 119.0356 | 161.6573 | 82.33 |

2004 | 123.0937 | 182.3774 | 83.39 |

2005 | 127.0176 | 206.6122 | 85.62 |

2006 | 131.1561 | 235.1154 | 87.54 |

2007 | 135.2873 | 262.7347 | 87.86 |

2008 | 139.0466 | 289.0695 | 88.13 |

2009 | 142.5075 | 312.2262 | 87.46 |

2010 | 145.9045 | 335.7224 | 88.12 |

2011 | 149.2040 | 360.6798 | 88.28 |

2012 | 152.4399 | 382.5383 | 87.08 |

2013 | 155.8199 | 400.7271 | 84.59 |

2014 | 158.9086 | 417.6396 | 84.61 |

2015 | 161.8207 | 434.1212 | 84.27 |

This block has geological reserves of 891.6531 T * 10^{4} t. The association between lg

At the moment, the characteristic curve of B-type water flooding is being utilized to match linear data points with a moisture content of 72.97 percent to 87.54 percent (1999–2006) before the MaWangMiao block measures (

Fan [

Indoor displacement experiments were conducted utilizing natural cores from a number of the MawangMiao block’s primary producing wells. The phase permeability curve obtained was normalized. The MawangMiao oil-water relative permeability curve has been normalized. This block has a 34.25 percent interstitial oil saturation and a 30.07 percent irreducible brine saturation. When the aforementioned data is entered into _{d} is determined to be 0.5102.

As seen in

Curve characteristic water flooding type | Matching expression | Matching segment R^{2} |
Year | Actual tired oil production/(10^{4}t) |
Predict oil production/(10^{4}t) |
Prediction Error/(%) |
---|---|---|---|---|---|---|

B- type water flooding characteristic curve | lg |
0.9977 | 2013 | 155.8199 | 145.8908 | 6.37 |

2014 | 158.9086 | 146.7988 | 7.62 | |||

2015 | 161.8207 | 147.6580 | 8.75 | |||

Fan’s water flooding characteristic curve | 0.9822 | 2013 | 155.8199 | 151.4218 | 2.82 | |

2014 | 158.9086 | 151.6539 | 4.57 | |||

2015 | 161.8207 | 151.9196 | 6.12 | |||

New water flooding characteristic curve | lg^{−9})^{R} |
0.9988 | 2013 | 155.8199 | 154.3721 | 0.93 |

2014 | 158.9086 | 156.2702 | 1.66 | |||

2015 | 161.8207 | 158.1470 | 2.27 |

The prediction findings for the oilfield’s actual production data indicate that the relative error between the expected and actual values of the new water flooding characteristic curve is modest. Both of these values are less than the forecast error for the other two water flooding characteristic curves in the same year, indicating that the latter is better appropriate for production. As a result, the new water flooding characteristic curve described by

The actual production data of the Xijiakou block in the JH oilfield is shown in

Year | Oil production/(10^{4}t) |
Water production/(10^{4}t) |
Water cut/(%) |
---|---|---|---|

1970 | 0.0141 | 0.0373 | 0.00 |

1971 | 0.6185 | 0.1822 | 16.24 |

1972 | 2.2099 | 0.5568 | 26.07 |

1973 | 8.5031 | 4.5346 | 45.71 |

1974 | 13.0247 | 9.1875 | 54.42 |

1975 | 17.7416 | 14.6492 | 59.25 |

1976 | 22.6109 | 22.1738 | 61.22 |

1977 | 27.5463 | 30.0291 | 59.47 |

1978 | 33.5526 | 39.5405 | 64.69 |

1979 | 38.8682 | 49.3127 | 66.62 |

1980 | 43.2180 | 58.0710 | 69.38 |

1981 | 47.6060 | 68.1303 | 73.81 |

1982 | 51.3535 | 79.8211 | 80.56 |

1983 | 54.9434 | 97.9786 | 85.49 |

1984 | 58.4884 | 121.9963 | 88.62 |

1985 | 62.2282 | 147.0592 | 88.01 |

1986 | 65.4894 | 172.9952 | 90.94 |

1987 | 68.4424 | 202.0792 | 91.64 |

1988 | 71.0067 | 232.9041 | 93.15 |

1989 | 72.7523 | 260.1738 | 94.68 |

1990 | 73.9845 | 282.5666 | 95.19 |

1991 | 74.9111 | 303.7571 | 96.94 |

1992 | 75.8036 | 324.7709 | 95.74 |

1993 | 76.6336 | 347.1723 | 96.52 |

1994 | 77.4706 | 372.0487 | 96.68 |

1995 | 78.3822 | 398.5919 | 96.74 |

1996 | 79.4587 | 430.2855 | 96.82 |

1997 | 80.4705 | 462.6117 | 97.07 |

1998 | 81.4470 | 498.4272 | 97.51 |

This block has a geological resource of 373.4947 * 10^{4}t, and the indoor displacement experiment is being conducted utilizing natural cores from many major production wells in the Xijiakou block. The phase permeability curve produced is normalized. According to the normalized relative permeability curve of Xijiakou oil-water, this block has a 24.5 percent interstitial oil saturation and a 30.5 percent irreducible brine saturation. When the following data is replaced into ^{4} t.

From the data in _{p}_{om} is drawn. When cumulative oil production reaches 72.7523 * 10^{4} t and the comprehensive water cut reaches 94.68 percent, the real lg_{p}_{om} curve goes upward. At the moment, the characteristic curve of B-type water flooding is utilized to match the linear data points to the 73.81 percent−94.68 percent (1981–1989) moisture content of the Xijiakou block (

Wang provided the following formula for the typical curve of water flooding during an ultra-high water cut period:

As seen in

Curve characteristic water flooding type | Matching expression | Matching segment R^{2} |
Year | Actual tired oil production/(10^{4}t) |
Predict oil production/(10^{4}t) |
Prediction Error/(%) |
---|---|---|---|---|---|---|

B-type water flooding characteristic curve | lg |
0.9968 | 1994 | 77.4706 | 81.3857 | 5.10 |

1995 | 78.3822 | 82.9398 | 6.05 | |||

1996 | 79.4587 | 84.6475 | 7.13 | |||

1997 | 80.4705 | 86.2714 | 8.19 | |||

1998 | 81.4470 | 87.9692 | 9.33 | |||

Wang’s water drive characteristic curve | 0.9902 | 1994 | 77.4706 | 78.3025 | 1.07 | |

1995 | 78.3822 | 79.4341 | 1.34 | |||

1996 | 79.4587 | 80.6684 | 1.52 | |||

1997 | 80.4705 | 81.8334 | 1.69 | |||

1998 | 81.4470 | 83.0426 | 1.96 | |||

New water drive characteristic curve | 0.9998 | 1994 | 77.4706 | 77.43565 | 0.05 | |

1995 | 78.3822 | 78.20739 | 0.22 | |||

1996 | 79.4587 | 79.01201 | 0.56 | |||

1997 | 80.4705 | 79.73909 | 0.91 | |||

1998 | 81.4470 | 80.46338 | 1.21 |

The prediction results for the oilfield’s actual production data indicate that the relative error between the expected and actual values of the new water flooding characteristic curve is modest. Both of these values are less than the forecast error for the other two water flooding characteristic curves in the same year, indicating that the latter is better appropriate for production. As a result, the revised water flooding characteristic curve given by

The recoverable reserves are projected using the matching formulas for three water flooding characteristic curves in _{w }=_{ }98 percent and ^{4} t. The percentage of recovery is 33.88 percent. Wang’s water flooding characteristic curve predicts recoverable reserves of 118.4704 * 10^{4} t. The percentage of recovery is 31.72 percent. The updated water flooding characteristic curve predicts that the recoverable reserves during the ultra-high water cut phase will be 94.6165 * 10^{4} t. The percentage of recovery is 25.33 percent. The prediction error variation law for the three curves in

When the water saturation is high, the new oil-water relative permeability ratio’s characterization formula may more accurately depict the relative permeability ratio’s change rule as a function of the water saturation. The new formula for the relative permeability ratio is determined. Two novel water flooding characteristic curve formulae are developed and used for the high water cut period and the high water cut period, respectively.

The form of the new characteristic curve for water flooding is dependent on the values of the matching parameters _{1}. _{1} values may be used to determine the influence of water flooding development. When _{1}) > 1, the characteristic curve of the new water flooding exhibits an upward tendency, indicating that the water flooding has a negligible influence on development. When _{1}) > 1, the new water flooding characteristic curve exhibits a downward bend, indicating a favorable influence on waterflooding development.

Two novel water flooding characteristic curves show a strong correlation with data from oilfield production during the high water cut and ultra-high water cut periods. Correlation coefficients for the corresponding curved section are 0.9988 and 0.9998. The association is quite high, which may represent the changing rule for the distinctive curve of conventional water flooding after upward or downward bending throughout the latter stages of water injection development.

Using two novel water flooding characteristic curves, we can forecast the cumulative oil production in the real JH oilfield block during high and ultra-high water cut phases. The percentage error between expected and actual oil production is smaller than the forecast error for

Water-oil ratio;

_{w}

Water production, t/day;

_{o}

Oil production, t/day;

_{rw}, K

_{ro}

Relative permeability of water phase and oil phase;

_{w}, μ

_{o}

Water, oil viscosity, mPa⋅s;

_{w}, B

_{o}

Water and oil volume coefficient, m^{3}/m^{3};

Constants influenced by reservoir and fluid properties;

_{1}

Constants;

_{w}

Water saturation, %;

Average water saturation, %;

_{we}

Outlet end water saturation;

_{wd}

Normalized water saturation, %;

_{wc}

Irreducible brine saturation;

_{or}

Interstitial-oil saturation;

_{w}, γ

_{o}

The relative density of water and oil;

The degree of geological reserves recovery;

Geological reserves, 10^{4}t;

_{p}

Accumulated oil production, 10^{4}t;

_{om}

Movable oil reserves, 10^{4}t;

_{d}

Ultimate oil displacement efficiency;

Matching parameters.

_{2}hyperbranched copolymers for enhanced oil recovery in low-mid permeability reservoirs