A New Intermittent Pumping Design for Fluid Shortage Wells

Low oil price requires oil companies to reduce costs and increase benefits. The wells with deficient fluid supplies approximately account for 20–30% of all producing wells, and this situation is even worse in the old oilfields. Intermittent production is an effective way to reduce the cost and increase the system efficiency to overcome the shortage of oil supply from the reservoir. The key is to optimize the intermittent pumping scheme, i.e., to design reasonable shut-in and operating periods. In this study, this is achieved using the dynamic change of the fluid level in the wellbore. From the electrical power curve to the dynamometer card, the dynamic drop of the fluid level can be obtained, and thus the optimal operation time of the well; at last, from the inflow performance of the well, the optimal shut-in period can be obtained. This method shows a good application in the field through a case study.


Method: Optimization of Intermittent Pumping Scheme
Using electrical power curve to get the surface dynamometer card. A working pumping unit (PU) can show different kinds of working patterns. Powered by electricity, the motor of the PU drives the horsehead up and down. Since the electrical energy is converted into mechanical energy, any change of stress at suspension point can be detected from the consumption of electrical energy. For example, if PU gets stuck in vertical motion or the viscosity of oil becomes more viscous, the stress at suspension point would increase, increasing of the input power. On the contrary, if PU has leakage or experiences a blowout, energy consumption would decrease. Therefore, the working conditions can be interpreted from the energy consumption curve.
By studying the relationship of power, torque, and loading, a mathematical model between loading and electrical power can be established.
The relationship between electrical power and loading is then calculated from the above two formulas.
The displacement curve and surface dynamometer card are interpreted from the crank angle and the electrical power curve, respectively.
Getting dynamic fluid level from surface dynamometer card. Using the Gibbs equation can interpret the pump dynamometer card from the surface dynamometer card 12 . The dynamic fluid level is defined as the height of fluid in the annulus (as shown in Fig. 1).
When the horsehead is at the bottom dead center, the stress at the suspension point (F d ) can be expressed as the Eq. (4). When the horsehead is at the top dead center, the stress at the suspension point (F u ) can be expressed as the Eq. (5).
The dynamic depth can be calculated as Eq. (6).
The resistance of travel (ΔP t ) and affix valve (ΔP s ) can be calculated as the Eq. (7).  Variation law of the submergence. Declining law of the submergence. The submergence depth of a pump in the wellbore fluid equals the depth of the pump subtracting the dynamic fluid depth. The submergence is high when PU starts working. The submergence decreases fast at the beginning of the pumping suction. When the submergence falls to a certain low level, the fluid in the pump would also be at a low degree. The typical decreasing curve of submergence is shown in Fig. 2.
Increasing law of the submergence. During the shut-in period when PU stops working, the increasing law of submergence can be studied through the inflow performance of the well 2 . The pressure difference between surface and bottom-hole forces fluid flowing into the bottom of the well. And raising fluid in the annulus leads to an increase of submergence. The increase of dynamic fluid level further enhances the bottom-hole pressure, which reduces the pressure difference and the fluid flowing into the well. At the end of the shut-in period, the submergence approaches a plateau. It turns out that a longer shut-in period reduces the cumulative production. The submergence of fluid shortage wells firstly increases fast then tends to a stable position in the end. The typical increasing curve during the shut-in period is shown in Fig. 3. www.nature.com/scientificreports www.nature.com/scientificreports/ Determination of well-operation period. Once the decreasing curve of submergence is obtained from the monitored electrical curve, the slope of the decreasing region is calculated for determining the optimal period of good operation. The absolute value of the slope within a chosen time interval is calculated since the beginning of the well-operation. This is repeated until the absolute value of the slope is smaller than a pre-determined value (ε, as described later), and the period till this moment is recorded as the working time T 1 for operating the well. The details are shown as follows.
After the obtained submergence decreasing curve is evenly divided into N intervals, the slope of each interval can be determined from coordinates of two adjacent points are recorded ((t 1 , h 1 ) and (t 2 , h 2 ) in Fig. 4). PU stops working when the absolute value of the slope is small than a certain value (ε 1 ), i.e.; ; and this moment is recorded as T 1 as shown in Fig. 4. For the first time, the ε 1 can be obtained by the former experience, then the ε 1 would be corrected by the method in this paper. Thus, the former ε 1 would be used to help determine the next new ε 1 in the end.
Determination of well-shut-in period. The buildup law of fluid depth can be interpreted from the bottom hole inflow performance. Because of three-phase (oil, gas, and water) in the late production period, here the Petrobras way is introduced to calculate the production 13 .
w oil w water The total oil output is calculated as Eq. (14).
The total water output is calculated as Eqs. (15) and (16).
Finally, Eq. (17) can be obtained from the Eqs. (12) to (16). Gas-Oil Ratio(dimensionless) 30 Bubble Pressure (MPa) 6.5 Depth of Layer (m) 3000 The Temperature in the Bottom of Well (K) 353  Table 2. Parameters of suction rod and motor.