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Reservoir connectivity is a critical issue in the process of oil-gas exploration and development. According to the theory of fluid mechanics and the achievements of many scholars, a connected reservoir coincides with a unified formation pressure system; there is a linear relationship between formation pressure and depth in normal pressure system reservoir. However, in high-permeability or multi-phase fluid reservoirs, this method has poor applicability and limitations. Through theoretical analysis and formula derivation, a new method for judging the connectivity of normal pressure reservoirs is found, that is, the inverse proportional function relationship between the pressure coefficient and the depth. In this paper, the relationship between the pressure system and the inverse proportional function has been verified. The function of the same pressure system is unique, monotonic, and has unified asymptote and symmetry axis and vice versa. Examples show that the inverse proportional function is more accurate and reliable for judging reservoir connectivity than the linear function.

The study of reservoir connectivity runs through the whole process of oilfield exploration and development. For the high drilling cost of offshore oil field, it is obviously not feasible to verify the reservoir connectivity by the multiple wells. Especially, in the exploration and reserve evaluation stage of oil and gas field, there are only one or two exploration wells in each fault block or trap, understanding the connectivity relationship of oil and gas reservoir directly affects the calculation of reserve scale, the deployment of well network. Traditionally, the linear relationship between formation pressure and depth to determine reservoir connectivity has been widely applied [

The commonly used techniques to analyze reservoir connectivity include slim layer correlation, logging curve feature correlation, reservoir geological modeling technique, and single attribute description technique, etc [

Li chuanliang (2005) elaborated the basic principle for using the linear relation of formation pressure to judge reservoir connectivity: The reduced (equivalent) pressure at any point of the same reservoir is equal, namely the pressure at different depth of a connected reservoir is located in the same straight line, and the value of the pressure conversion to the reference plane is unique [

Shaker (2001) proposed to use fluid residual pressure and sealed pressure to quantitatively and semi-quantitatively analyze the connectivity relationship of reservoirs [

E P = p p − p p hydro (1)

S C = p p d − p p u (2)

In this formula：EP is the fluid residual pressure, psi; SC is the sealing pressure, psi; the p p d and p p u are the formation pressure of overlying and underlying reservoirs of the mudstone interlayer respectively, psi; p_{p} is the original formation pressure, psi; p p hydro is hydrostatic pressure, psi.

Due to the high permeability of the reservoir and multi-phase fluid, original formation pressure at the top of the reservoir is “abnormal”, the residual pressure of the non-single-phase fluids are different (

On the basis of many scholars’ studies, this paper uses rich pressure data from wireline formation tester, uses mathematical formulas to derive, and analyzes thousands of formation pressure data from more than 50 normal pressure hydrocarbon reservoirs in Bohai Bay [

According to the theory of fluid mechanics, the original formation pressure at any point in a connected normal pressure reservoir meets the pressure equation, that is, the formation pressure and depth of a connected reservoir theoretically present a linear relationship (

H = a p b + b ⇒ p p = ( H − b ) / a (3)

Another method to study the variation of formation pressure with depth is the pressure coefficient, which is very important but often ignored. Assuming that the formation water density is constant, the following formula is derived:

p p hydro ≡ ∫ 0 h ρ w ( H ) g d h ≈ ρ w g H (4)

α p = p p / p p hydro = ( H − b ) / a ρ w g H (5)

⇒ H = − b / ( c α p − 1 ) (6)

In this formula: H is depth, m; ρ_{w} is the formation water density, g/cm^{3}; α_{p} is the pressure coefficient, dimensionless; α, b, c is constant.

The above equation is a variant of the inverse proportional function with pressure coefficient α_{p} as the independent variable and depth H as the dependent variable (

1) The Monotonicity

With the increase of reservoir burial depth, the pressure coefficient shows a monotonic decreasing trend (^{−4} Mpa^{−1}) causes decompression expansion elastic energy to be very huge [

2) The Symmetry

The inverse proportion function image is an axisymmetric graph, and the axis of symmetry is unique. For a connected reservoir, the image of its pressure coefficient and depth has a unique axis of symmetry, and two or more sets of reservoirs with different symmetry axes do not belong to the same pressure system and are not connected.

3) The Boundedness

There are two asymptotes in the inverse proportional function (α_{p} = 1/c, H = h), and the numerical distribution of pressure coefficient and reservoir height in the same reservoir is controlled by two asymptotes, and different reservoirs with inconsistent asymptotes. With the reservoir altitude becomes shallow, the pressure coefficient is monotonically increasing and approaching the fracture pressure at the top of the reservoir, and the upper limit of the altitude is also getting close to the maximum oil column thickness h. As the depth increases, the formation pressure gradually tends to hydrostatic pressure, and the lower limit of the pressure coefficient is also getting infinitely close to hydrostatic pressure coefficient 1/c (

4) The Consistency

The formation pressure at each depth of a connected reservoir can only be fitted to an inverse proportional function image, which has a uniform pressure track, and vice versa.

Under the action of gas, oil, water and other reservoir driving forces, the reservoir pressure system maintains a state of dynamic equilibrium, and the pressure coefficient presents an inverse proportional function distribution with the change of depth. Due to differences in reservoir physical properties, fluid properties and height of oil and gas columns in different reservoirs, the pressure equilibrium state will be different, and then the inverse proportion function will also be different. Therefore, the property of the inverse proportion function can be an important basis for judging the connectivity of reservoirs.

The LD21-X oilfield is located in the southern part of the Liaodong Bay, and is located in the central structural belts of southern Liaozhong Sag in the Lower Liaohe Depression of the Bohai Basin. The main hydrocarbon accumulations are the Neogene Guantao Formation IV and V oil groups (

The oil-water contact of the V oil group of Well 1 is −1619 m. 10 qualified pressure data were obtained from the oil layer of the V oil group, 5 qualified pressure data were obtained in the water layer, and the measuring depth was in the thicker reservoir section (

The mudstones of about 3.9 m thick, is developed between the IV oil group and the V oil group of Well 1. The other exploration wells prove that the mudstones are unstable in the oil field, whether the two oil groups are the same fluid system or not need further demonstration. A total of 3 qualified pressure data were obtained from the oil layer of the IV oil group, and the measuring depth was within the thicker reservoir section (

Well | Oil Group | Altitude/m | Formation pressure/psi | Formation pressure coefficient | Fluid |
---|---|---|---|---|---|

1 | IV | −1554 | 2178.1 | 0.99988 | oil |

−1556 | 2180.2 | 0.99954 | oil | ||

−1560 | 2185 | 0.99913 | oil | ||

V | −1584 | 2216.2 | 0.99802 | oil | |

−1587 | 2220.6 | 0.99808 | oil | ||

−1589 | 2222.9 | 0.99784 | oil | ||

−1602 | 2237.5 | 0.99626 | oil | ||

−1605 | 2241.4 | 0.9961 | oil | ||

−1608.5 | 2246.7 | 0.99632 | oil | ||

−1613 | 2249.8 | 0.99487 | oil | ||

−1614 | 2252.9 | 0.99561 | oil | ||

−1616 | 2254.7 | 0.99516 | oil | ||

−1618 | 2257.5 | 0.99514 | oil | ||

−1623 | 2263.5 | 0.99473 | water | ||

−1629 | 2272 | 0.9948 | water | ||

−1630 | 2273.1 | 0.99466 | water | ||

−1633 | 2277.6 | 0.99478 | water | ||

−1636 | 2281.6 | 0.99467 | water |

between the oil layer of the IV oil group and the oil layer of the V oil group is not large, and it is impossible to determine whether it is a unified pressure system. However, it can be seen from the pressure coefficient and depth profile (

According to Darcy’s law, the higher the reservoir permeability, the smaller the rate of change of formation pressure will be. Even the unconnected sand bodies are in the same layer or adjacent, the residual pressure value of the fluid will not be very different. The traditional linear relationship discriminates the connectivity of high-permeability reservoirs with high uncertainty and low accuracy. However, the law of pressure coefficient and depth is effectively improved the accuracy of the connection analysis of high permeability reservoirs.

KL3-X oilfield is located in the southern part of the Bohai Sea, and is located in the southern slope of the Huanghekou Sag. The main hydrocarbon accumulation happens in the lower Minghuazhen Formation of the Neogene [

The Well 3 drilled into 1# and 2# sand bodies, met the gas layer and the oil layer respectively, and obtained 3 and 6 qualified pressure data respectively (

Well | Sand | Altitude/m | Formation pressure/psi | Formation pressure coefficient | Fluid |
---|---|---|---|---|---|

3 | 1# | −1473.5 | 2129.1 | 1.01612 | gas |

−1475.5 | 2129.7 | 1.01503 | gas | ||

−1478.5 | 2130.3 | 1.01326 | gas | ||

2# | −1487 | 2136.6 | 1.01112 | oil | |

−1489 | 2140 | 1.01069 | oil | ||

−1492 | 2143.3 | 1.01022 | oil | ||

−1494 | 2145.6 | 1.00995 | oil | ||

−1497 | 2149.1 | 1.00957 | oil | ||

−1499 | 2151.3 | 1.00925 | oil |

According to the previous research results, the premise of using the formation pressure-depth linear relationship to distinguish the reservoir connectivity relationship is that it has the same fluid properties. Different fluid properties and different linear relationships can cause the connectivity to be inaccurately determined. The pressure coefficient-depth inverse proportional function distribution is generated by the pressure balance of gas, oil, water and other fluids. The function curvature is continuously changed by many factors such as reservoir physical properties, fluid properties and oil column height. The interference of non-single-phase fluid differences on deciding the connectivity of the sand body with the linear relationship is avoided.

1) Pressure coefficient and depth inverse proportional function are new methods for analyzing the connectivity of normal pressure oil reservoirs. Consistency of the inverse proportional function, the monotonous changes of pressure coefficient with depth, the same two asymptotes, and symmetry axes are the standards for the connection of sand bodies.

2) Compared with the linear relationship between formation pressure and depth, the pressure coefficient and the depth inverse proportional function method is more sensitive and the result is more reliable.

3) The inverse proportional function curvature of the Bohai Bay normal pressure reservoir is controlled by many factors such as reservoir physical properties, fluid properties and oil column height, which avoids the interference of reservoir high permeability and non-single-phase fluid differences on deciding the connectivity of the sand body with the linear relationship.

The authors declare no conflicts of interest regarding the publication of this paper.

Zhu, J.M., Shi, C.Y., Liu, X.L., Qian, G. and Zhang, Q.P. (2019) The Application of Pressure Coefficient in Judging Normal Pressure Reservoirs Connectivity—A Case Study of LD21-X and KL3-Xoilfield in Bohai Bay. Open Journal of Geology, 9, 295-305. https://doi.org/10.4236/ojg.2019.96020