A Model of Reservoir Permeability Evolution during Oil Production

Abstract

In this paper, we present a mathematical model to predict the evolution of rock permeability depending on effective pressure during oil production. The model is based on the use of the results of well testing data from wells operating in the oil fields of the Perm–Solikamsk region in the north of the Volgo Ural oil and gas province. Dependences of the change in flow characteristics in the reservoir on the effective pressure were established. We performed a comparative assessment using permeability and effective pressure data that were normalized to dimensionless forms of k/ko and P/Po. The factors and their influence on the nature of the change in permeability from the reservoir pressure were determined. Depending on the type of rock, its composition, initial permeability, and bedding conditions, we determined the limits of variation of the constants in empirical equations describing the change in the permeability of rocks from the effective pressure. The mathematical model we developed enables the prediction of the change in permeability of rocks during oil production from reservoirs on the basis of reservoir properties such as initial permeability, initial reservoir pressure, average bedding depth, net-to-gross ratio, and initial effective rock pressure.

Cyclic confining pressure and rock permeability: Mechanical compaction or fines migration

“…The transport properties of porous and fractured rocks decrease during cyclic loading. With each subsequent cycle it does not recover to the initial values and this phenomenon is also known as a permeability hysteresis [ [1] , [2] , [3] , [4] , [5] , [6] ]. According to the classical poromechanics theory, the apparent permeability degradation and hysteresis occur as a result of mechanical compaction by plastic deformations, and microcracks closure [ [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] , [41] , [42] , [43] ] which agrees well with rock mechanics [ [44] , [45] , [46] , [47] , [48] , [49] , [50] , [51] , [52] , [53] , [54] , [55] ].…”

“…With each subsequent cycle it does not recover to the initial values and this phenomenon is also known as a permeability hysteresis [ [1] , [2] , [3] , [4] , [5] , [6] ]. According to the classical poromechanics theory, the apparent permeability degradation and hysteresis occur as a result of mechanical compaction by plastic deformations, and microcracks closure [ [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] , [41] , [42] , [43] ] which agrees well with rock mechanics [ [44] , [45] , [46] , [47] , [48] , [49] , [50] , [51] , [52] , [53] , [54] , [55] ]. In addition, during compaction, crushing of mineral grains can occur within the rocks as a result of which a certain amount of detrital material can form [ 56 ] with a size from a few microns (colloids) to tens of microns (fines) which is especially typical for higher loads.…”

“…The need to determine the role of colloids and fines on permeability is due to the fact that various theories and models of permeability are built on the basis of experimental studies. But [ 7 , 42 ], did not take into account the migration of colloids and fines. Only a few theoretical [ 78 , 79 ] and experimental [ 80 , 81 ] works discuss the influence of load and colloids on permeability of porous media while these phenomena are studied separately in sufficient detail [ 6 , 64 , [82] , [83] , [84] , [85] , [86] , [87] , [88] , [89] , [90] , [91] , [92] , [93] , [94] , [95] , [96] , [97] , [98] , [99] , [100] , [101] , [102] , [103] , [104] ].…”

Predicting the permeability of the near-bottomhole zone during wave impact

“…Numerous fractures form in the rock [2-4], dividing the crystalline core into smaller blocks [5][6][7]. Under prolonged impact of low frequency and high amplitude, plastic deformation of rocks is possible [8,9]. At low amplitudes rock strength and modulus of deformation decrease exponentially with increasing loading cycles [10].…”