Ecology and Economics of Oil Production

Investigation of a Centrifugal Pump’s Thermal Behavior

Mathematical description of a pump’s thermodynamic condition for the purposes of assessing the pump’s temperature and determining its dependency on the ESP unit’s operating parameters leads to the solution of a nonlinear thermal-conductivity equation under boundary conditions of the 2nd and 4th kind [1, 2, 3, 4], since in the processes taking place inside the ESP, the heat source (dissipation of mechanical energy) is nonlinear (relationship between the friction coefficient and the temperature of mating surfaces, etc.); the change in the heat-absorption capacity of the liquid-gas mixture (oil) under high pressure and with complicated chemical composition has not been studied; the “temperature-pressure” function of oil saturated with VHC is underexplored. The transfer of heat from the metal mating surfaces to the fluid and from the fluid to the metal pump housing is a complicated process (in the first place, because of the sophisticated shape of the labyrinths in the pump’s working elements and the complicated dependency of the physical and chemical properties of the liquid-gas mixture); however, it is expected that this is a convection process, since other heat-transfer techniques, like mass transfer or radiant interchange, produce a minor effect; so at first approximation, this process can be ignored [5, 6]. Due to the substantial difference between the heat conductivity of the oil-gas and the fluid, we may assume that each pump section transfers a small amount of heat to the surrounding fluid and further to the production string, i.e. that the pump stays in a kind of “thermostat.” Thus, the amount of heat generated in the centrifugal pump’s working elements is partly spent on heating of the fluid and the metal parts of the pump and partly transferred to the other assemblies of the ESP unit [2, 3, 4, 7, 8, 9, 10, 11, 12, 13, 14]. The temperature rise of the pump (∆Tw) may be expressed by the formula (1) as follows:

$$ \Delta T _ {w} = T _ {w} - T _ {f} = \frac {\phi}{1 - \phi} \frac {q _ {0} P _ {b} P _ {p} R _ {2}}{2 (1 - B)} h \Gamma_ {a} P _ {a r} \left\{\frac {1}{\alpha} + \frac {\delta_ {t g}}{\lambda_ {g b}} \right\} $$ (1) where: Tw: temperature inside the pump housing, Tf: temperature of the liquid-gas mixture on the intake side, R2: radius of the pump’s cylindrical housing (0.05 m), Pb: bubble-point pressure (MPa), Гa: reservoir gas-oil ratio (m3/m3), h: pump head (MPa) with free gas φ in the mixture (fraction), δtg: thickness of gas bubbles on the pump surface (about 0.002-5 m), В: water content in the production stream, in fractions (less than 0.98), λgb: gas blanket heat conductivity on the pump’s housing surface (W/(m*K)), α: convection heat- transfer coefficient (W/(m2*K)) in the labyrinths of pump elements with respect to the liquid-gas mixture, q0: heat- source power density per one running pump (W/m3), Pat: atmospheric pressure (MPa), Ptp: the pressure at the inlet of the pump, (MPa).

Analysis of the Obtained Mathematical Expression

The obtained mathematical expression (1) enables us to determine the centrifugal pump’s suction pressure [1, 2], which in turn allows for investigation of the pump’s potential conditions. The phenomena of “automatic relaxation oscillation” and of “heat shock” leading to the centrifugal pump’s sudden failure have been discovered.

Salt deposition in oil-production equipment is a rather- common yet poorly-explored phenomenon. This is because of the established opinion among experts that salt deposition is mainly caused by the supersaturation of the formation fluid (water) by a particular component of dissolved substances [6, 12]. However, both oil-production practice and the available facts of salt deposition provide evidence that the presence of dissolved salts in associated water and their condition are just a prerequisite. The sufficient condition for the formation of salt deposits in centrifugal-pump stages is high temperature, namely the boiling of associated water in the pump [8, 9, 10, 11].

Salt Deposition Dynamics

The process of salt deposition in a centrifugal pump may be represented in temperature and pressure coordinates at the pump suction (Figure 1). Water thermal behavior vs. pressure has been studied rather extensively [1]. Depending on the salts dissolved in the water, curve К has a certain “width” in the form of deviation (in either direction) from the pure water parameter. According to the research, this deviation of the water boiling point from the chemically-pure water boiling point amounts to a maximum of 3–60С.

When the pump’s suction pressure decreases from point A to point Б, no salt deposition is observed. Point Б – the water boiling point–represents the start of salt deposition. During operation of the pump, its suction pressure will stay within the range of Б-С and will be accompanied by salt deposition. Curve К represents the “water boiling point Т – pressure Р” function.

If, during operation, the pump’s suction pressure moves from А to Б, the temperature ramp-up of both the pump and the pumped liquid-gas takes place. When the pump’s temperature reaches point Б, the gas-liquid mixture’s temperature becomes equal to the water boiling point. Reverse movement from point Б towards point А can be achieved by changing the centrifugal pump’s capacity, e.g. by reducing the pump’s shaft rotation speed with a frequency converter. Return from point Б towards point А is possible by means of shutting-down the ESP unit for a certain period of time (autoreclosing mode) [15, 16, 17].

Concerning the Possibility of Changing Operating Parameters

From the above theoretical speculations it becomes clear that by changing the centrifugal pump’s operating parameters one way or the other, the pump’s temperature can be suppressed below the associated water boiling point. However, theoretical (and practical for that matter) studies show that there is an operating mode in which the pump’s temperature rises uncontrolled and the ESP immediately breaks down. Let’s call this mode “heat shock.” This mode arises during pump heatup, when two concurrent and mutually-competing processes take place: on the one hand, the gas-liquid mixture’s pressure boost causes dilution of the liberated gas. On the other, along with the pump’s temperature rise, oil saturation pressure goes up, promoting a reversal process – gas escape from oil. Under certain operating conditions, the pump’s temperature rise may lead to increasing gas escape. Meanwhile, the pump’s condition surpasses its critical behavior. Heat shock behavior can be predicted if the saturation pressure change as a function of the pump’s temperature is taken into account. Depending

on the temperature at a constant volume of associated gas, saturation pressure can be calculated according to the formula [18], provided the proportional content of methane and nitrogen is known:

(2) where Ps,v – saturation pressure value (MPa) at the temperature T; Trt–reservoir temperature value, °K; Psp – saturation pressure at reservoir temperature; Гgs – gas saturation (gas factor) in m3/t of the reservoir oil, characterized by the ratio of the volume (normalized to standard conditions) of dissolved gas to the mass of degassed oil; yм, yа – respective content of methane and nitrogen in the gas (in unit fractions) of reservoir oil-flash liberation under standard conditions. Combining (1) and (2), we get:

(3) where θ – temperature gradient in the well, [°K/м], ∆x = Lvd – LvdESP, Lvd– vertical depth of the formation top, LvdESP – vertical depth of the ESP unit’s installation.

Thus, for pump temperature regulation according to (1), the critical parameters must be calculated by the formula (3).

Oil Production Economics

The exploitation of oil fields is performed using electric submersible centrifugal pumps.

The ESP unit capacity affecting specific energy consumption depends on the pump’s operating mode. This significantly determines oil production profitability. It has been shown that by analyzing the centrifugal pump’s operating mode according to (1), it is possible to achieve the highest pump efficiency and the lowest specific energy consumption in all operating modes. That’s why the ESP control process demands automation.

The economic benefit of ESP control automation is shown in Table 1.

Oil Production Ecology

Today, the environmental impact is huge, causing global environmental changes. Therefore, all countries are now obliged – to one degree or another – to tackle the issues associated with reducing damaging environmental impacts. A similar problem arises during the exploitation of oil fields using centrifugal pumps. Chemical compounds – acids destroying oil wells with the further ingress of well products into the aqueous layers – are widely used in current oil production. Modern methods of oil recovery risk causing drinking water shortages for all of mankind. As was shown above, all of these environmental threats associated with oil production can be minimized by transitioning to ESP control automation [6, 12].