Aida Aslanova

Department of Petroleum Engineering

Baku Higher Oil School

Yeni Salyan Highway 3rd km, 25, Sabail district, Bibiheybat settlemen, Baku, Azerbaijan, AZ 1010

[email protected]

Jalil Jalilov

Learner of Landau School

6 Gulbala Aliyev St, Baku, Azerbaijan, AZ 1010

[email protected]

Currently, the development of low-permeable hydrocarbon reservoirs is becoming an increasingly urgent task, and therefore, the study of the laws of fluid movement in subcapillary pores and microcracks is a crucial scientific and technical problem.

Despite a large number of experimental and theoretical works, there are some issues in this area that require further researches.

According to the results of some experimental studies, a viscous liquid during flow in low-permeable reservoirs exhibits an anomalous non-Newtonian character, accompanied by a violation of the linearity of the filtration process, and, consequently, Darcy’s law [1-4].

It is established [4] that starting from a certain critical size of the opening of the crack, the flow of a Newtonian fluid (water, viscous oil) becomes non-Newtonian, with the manifestation of an initial pressure gradient and flow locking.

However, to date there is no consensus on the mechanism of these phenomena, although there are different approaches to explain the abnormal hydrodynamic behavior of liquids during flow in a low-permeable porous medium and microcracks.

The work [5] is one of the first steps to study the influence of the electrokinetic potential of the flow on the hydraulic characteristics of real liquid systems, in which it was revealed that various thermohydrodynamic effects in heterogeneous liquid systems are largely determined by the electrokinetic factor, by regulating which it is possible to significantly change the rheophysical state of the system.

The rheophysical peculiarities of water flow in microchannel was considered experimentally. 

The experimental setup mainly consisted of a microchannel model, a high-pressure balloon, and a thermostat. Tap water was used as the working fluid. The microchannel model with a length of 30cm and a width of 4cm was formed by two parallel smooth steel plates with a thickness of 1.8 cm.

Microcracks of a given opening (h) were obtained by installing non-wettable gaskets of the corresponding micron thickness between the plates. The experiments were carried out at various values of h in the range of 20÷50 μm.

To ensure the isothermality of the process, the model was placed in a thermobath connected to an ultrathermostat. To determine the pressure drop at the inlet and outlet of the model, model pressure gauges were installed with an error of 0.2-0.35%. The mass flow rate of the liquid was determined on electronic scales with an accuracy of 0.001 mg.

 Upon reaching a steady flow regime, the flow curves for water were plotted at different values of the crack opening. Fig. 1 shows the flow curves obtained from experiments at five values of the opening of the crack h – 20μm, 30μm, 40 μm, 45 μm and 50 μm, at a constant temperature T = 300C.

Fig. 1 Flow curves 1 –20 μm, 2 – 30 μm, 3 –40 μm, 4 – 45 μm, 5 – 50 μm

As can be seen, for the crack with h=30μm, the water flow curve is linear and corresponds to the Newtonian model. However, at lower values of h, the flow becomes nonlinear – water behaves like a non-Newtonian fluid with some initial pressure gradient ΔP0 typical for Bingham fluids, which is consistent with the results of previous studies [4]. With a decrease in the opening of the crack, starting from the threshold value h = 45 μm, the nonlinear nature of the water increases, the effect of locking the flow is manifested, which is maximally expressed at the lowest value of the gap (h =20μm) in the considered range.

In the observed transformation of a Newtonian system into a non-Newtonian one, strengthening of rheological nonlinearity, enhancing of hydraulic resistance in thin slits, the role of the electrokinetic factor, in particular, the stream potential, is unconditional. According to Coehn rule [6], double electric layer (DEL) is formed at the contact boundary between liqud and solid surface with a certain electrokinetic potential. The distribution of DEL is rather blurry and the thickness of diffusion layer might be several microns. The electrostatic field created by the DEL affects the character of the flow around the boundary zone. For channels with sufficiently large opening thicknesses, this effect can be insignificant. However, for microchannels, the situation becomes principally different – electrokinetic potential creates additional hydraulic resistance.

In the experiments, the streaming potential Δφ was measured with a microvoltmeter (CHY 20 Multimeter) using platinum electrodes at the input and output of the model. The measurement error did not exceed 0.8%.

When plotting the flow curves, for each individual case, measurements of the streaming potential Δφ were simultaneously carried out. The values of Δφ, with a pressure difference of ΔР = 1atm, for different values the crack opening h, are shown in Fig. 2.

Fig.2. The dependence of the stream potential Δφ on the magnitude of the opening of the crack (h).

It is established that the value of Δφ significantly depends on the opening h and increases with decreasing of the gap. So, for values of h – 50μm, 45μm, 40μm, 30μm and 20μm, at ΔP=1atm, the average values of Δφ, respectively, are equal to 1910mV, 2190mV, 2680mV, 2975mV and 3360mV. With decreasing of h, the stream potential Δφ increases and reaches its highest value at the smallest thickness. (Fig.2).

The obtained results indicate that the hydraulic characteristics of the water flow in microcracks significantly depend on the degree of electrokinetic factor of the flow and by its corresponding variation the flow parameters can be significantly changed. 

Authors are gratefull to Professor Fuad Veliyev for setting of the task and discussing of obtained results. 


  1. Feng Wenguang, Giaeli Ge. The problem of non-Darcy flow at low velocity non fixed single medium, dual medium. Petroleum exploration and development. – 1985. – № 1.
  2.  Chen Yongming, Juan Zhou, Experimental demonstration of the non-Darcy phenomenon during low velocity flow through porous media. Journal of Chongqing University (Natural science edition). -2000. – № 1.
  3.  Prada A., Civan F. Modification of Darcy’s law for the threshold pressure gradient. Journal of petroleum science and engineering. -1999. – № 22 (4). – P. 237-240.
  4. Mamedova M.A., Gurbanov R.S. Investigation of the Rheology of Fluids in Fracture and Pore Channels and determination of Their Opening. Journal of Engineering Physics and Thermophysics: Volume 88. Issue 4 (2015), Page 815-824)
  5. Veliyev F.H. Study of electrification of hydraulic flows. Thematic collection of scientific papers AZINEFTEKHIM. Baku, 1984, 110p(in Russian).
  6. Leonard B.Loeb B., Static Electrification, Springer-Verlag, Berlin, 1958.

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