Horizontal wells have been applied in bottom-water reservoir since their advantages were found on distribution of linear dropdown near wellbore, higher critical production, and more OOIP (original oil in place) controlled. In the paper, one 3D visible physical model of horizontal physical model is designed and built to simulate the water cresting process during the horizontal well producing and find water breakthrough point in homogenous and heterogeneous reservoir with bottom water. Water cresting shape and water cut of horizontal well in between homogenous and heterogeneous reservoir are compared on the base of experiment’s result. The water cresting pattern of horizontal well in homogeneous reservoir can be summarized as “central breakthrough, lateral expansion, thorough flooding, and then flank uplifting.” Furthermore, a simple analysis model of horizontal well in bottom water reservoir is established and water breakthrough point is analyzed. It can be drawn from the analysis result that whether or not to consider the top and bottom border, breakthrough would be located in the middle of horizontal segment with equal flow velocity distribution.
In the 1990s, with wide application of Hele-Shaw model, 2-D (two-dimensional) physical experiment had been gradually used to investigate performance of horizontal wells in reservoirs with bottom water. Permadi’s research showed that water cresting will first present at heel of horizontal segment; then it would gradually move toward to toe [
Logarithmic pressure distribution of vertical well would result in higher pressure loss near wellbore than that of horizontal well [
At present, investigation on horizontal wells developing bottom water reservoir is not yet systematical due to complex wellbore structure. First, there are few literatures particularly describing water cresting process and detecting breakthrough location, which led to unreasonable completion design and undirected measures of water shutoff and water control; finally it is unfavorable for development of bottom water reservoir [
In this paper, combined with numerical simulation and 3-D physical simulation, fluid mechanics in porous medium was used to investigate water cresting and breakthrough location, providing consistent theory for reasonable measures of water shutoff and water control.
After heel-toe pressure difference of horizontal wells was calculated with coupling model [
With extremely simplified formula; most scholars believe that water cresting would rise asymmetrically, and breakthrough would present at the heel [
Firstly, 2-D model can only simulate piston-displacement in heterogeneous reservoir while ellipsoid pressure field cannot be simulated due to walls of device; therefore the water cresting simulated would have a large difference with the one in reservoir.
Secondly, the experiment devices without sand keep distance of two parallel glasses only 0.00625 m in order to increase flow resistance, and the obtained permeability about 32000
If the flow velocity gets to a certain value, both viscous resistance and inertial resistance are generated; meanwhile nonlinear relationship would present between flow velocity and pressure difference, and the flow velocity was defined as critical velocity for Darcy’s law. Reynolds criterion was used by Katja Hof to calculate the critical flow velocity [
As mentioned in literature the lowest average velocity of experiments is 7.04 × 10−3 m/s, which is much higher than critical velocity of 1.66 × 10−3 m/s from a certain reservoir and is not coordinate with flow velocity in porous media. Without sand, Hele-Shaw mode has extremely high permeability and nearly no flow resistant for bottom water. As a result, generation as well as development of water cresting has no practical significance in that model.
Rather than 2-D model, 3-D physical model had been carried out successively to accurately simulated reservoir parameters, to reflect inflow performance of horizontal wells with different completions, and to better analyze influence factors of well productivity; therefore, a new device was designed to investigate water cresting shape and to detect breakthrough location in Figure
3-D physical model of horizontal wells in bottom water reservoir.
As shown in Figure
The formation and development of water cresting with different horizontal segment length.
Throughout the whole process, flat OWC will rise steady firstly; then it was gradually deformed into water cresting and breakthrough at the middle of horizontal well; finally the length of water cresting would extended along the horizontal segment from the middle to the toe and the heel until the whole segment was flooded.
Two physical models with different horizontal segment length were designed (Figure
Physical models with different horizontal segment length.
In the first model (Figure
The formation and development of water cresting with low and high permeability section.
In the second model (Figure
Permeability heterogeneity had distinguished impact on watercut, rising step by step, and the number of steps was coordinate with number of nonconsecutive high permeability areas covered by horizontal segment.
To better investigate coupling effect between flow in reservoir and variable mass flow in wellbore, a new model was established to analyze the water cresting with different parameters.
As shown in Figure
Crest schematic chart of horizontal wells with
The longitudinal velocity of middle perforation is always the highest, and the water cresting shape was shown in Figure
When
Physical model shown in Figure
Physical model of horizontal wells in bottom water reservoir (with upper and lower boundaries).
With Behçet formula, (
Therefore, longitudinal velocity would be
According to superposition principle, the longitudinal velocity of point
It could be proved that
While
Due to influence of supply area, permeability, reservoir damage, perforation density, flow velocity at any point of horizontal segment is usually unequal. Meanwhile the water cresting shape was carried out with different flow velocity at different nodes.
For different flow velocity at different perforation, (
In this model, inputting node number and flow velocity of each node, longitudinal velocity of any point below perforations could be calculated with equal (
As a result, the water cresting can be calculated with variable nodes and arbitrary flow velocity distribution considering the top and bottom boundaries.
Supposed that, reservoir thickness—30 m, height of water avoidance—25 m, horizontal segment length—300 m with 61 nodes evenly. In
Crest rising shapes with different flow velocity distributions.
Crest rising shapes with equal inflow velocity.
Calculated results (Figure
In order to investigate water cresting shape with different velocity distribution, the whole wellbore was simplified as five perforations supposing breakthrough time as
When
When
Crest rising shapes with declining inflow velocity from heel to toe.
The water cresting (Figure
When
Crest rising shapes with inflow velocity of
When
Crest rising shapes with inflow velocity of
When
Crest rising shapes with inflow velocity of
With comparison of flow velocity distribution above, conclusions were obtained. For horizontal wells in bottom water reservoir, breakthrough would be usually located in the middle of horizontal segment rather than the point with high flow velocity. If its middle part was located in high permeability area and was perforated, horizontal well would have shorter water free production period and smaller water free production. Therefore we should pay much more attention to completion and water shutoff. Permeability distribution pattern of “central high-flank low” would result in longer water free period and more production without water.
With 3-D visible physical experiments, water cresting in homogeneous reservoir was “central breakthrough → lateral expansion→ thorough flooding → flank uplifting.” All water cresting shapes are almost similar at the same watercut for horizontal wells with different length. In preceding development, higher drawdown would result in steeper water cresting and much more severe fingering. While watercut > 90%, the whole OWC would arrive at horizontal well. Whether or not to consider the top and bottom border, breakthrough would be located in the middle of horizontal segment with equal flow velocity distribution. To some extent, velocity distribution will have some influence on watercut trend, even though the velocity at heel or at toe is 4 times that of other points; breakthrough point would be still located in the middle of horizontal segment with rich remaining oil in flanks of water cresting. Therefore, for horizontal wells in the bottom water reservoir, bottom water will breakthrough not at the point with higher flow velocity but at the middle of horizontal segment for superposed pressure field.
The authors declare that there is no conflict of interests regarding the publication of this paper.