INLET RAMPS FOR PRESSURE EXCHANGE DEVICES

Abstract

A system includes a rotary isobaric pressure exchanger (IPX) having an oblique ramp disposed within a fluid inlet of an end cover at an oblique angle configured to direct a fluid toward an interior surface of a channel within a rotor to facilitate rotation of the rotor. In addition, the system may include one or vanes disposed within the fluid inlet to further direct the fluid toward the interior surface. Further, the system may include one or more passages extending from the fluid inlet toward a surface of the end cover that interfaces with the rotor, where the one or more passages utilize the fluid to apply additional force to the rotor to facilitate rotation.

Description

BACKGROUND

This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present invention, which are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present invention. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art.

Rotating equipment often utilizes the energy of fluids directed toward the rotating equipment to drive rotation. However, severe inlet configurations may lead to impingement, mixing of liquids, choked flow, cavitation, and/or reduced efficiencies and output of the rotating equipment.

BRIEF DESCRIPTION OF THE DRAWINGS

Various features, aspects, and advantages of the present invention will become better understood when the following detailed description is read with reference to the accompanying figures in which like characters represent like parts throughout the figures, wherein:

FIG. 1 is a schematic diagram of an embodiment of a frac system with a hydraulic energy transfer system;

FIG. 2 is a schematic cross-sectional view of an embodiment of an isobaric pressure exchanger (IPX);

FIG. 3 is an exploded perspective view of an embodiment of a rotary isobaric pressure exchanger (rotary IPX);

FIG. 4 is an exploded perspective view of an embodiment of a rotary IPX in a first operating position;

FIG. 5 is an exploded perspective view of an embodiment of a rotary IPX in a second operating position;

FIG. 6 is an exploded perspective view of an embodiment of a rotary IPX in a third operating position;

FIG. 7 is an exploded perspective view of an embodiment of a rotary IPX in a fourth operating position;

FIG. 8 is a graphical representation of an embodiment of operating conditions of the rotary IPX of FIG. 3;

FIG. 9 is a schematic cut-away view of a rotor of the rotary IPX of FIG. 3, having a sloped inlet ramp;

FIG. 10 is a graphical representation of an embodiment of an acceleration profile of a dynamic fluid interface of the rotary IPX of FIG. 3;

FIG. 11 is a graphical representation of an embodiment of a position profile and a velocity profile of a dynamic fluid interface of the rotary IPX of FIG. 3;

FIG. 12 is a flowchart of an embodiment of a process for determining an angle of a ramped inlet of the rotary IPX of FIG. 3;

FIG. 13 is a partial cross-sectional view of an embodiment of a ramped inlet and a rotor duct within line 13-13 of FIG. 2 (e.g., having vanes on the ramped inlet);

FIG. 14 is a partial cross-sectional view of an embodiment of a ramped inlet and a rotor duct within line 13-13 of FIG. 2 (e.g., having a vane within the rotor duct);

FIG. 15 is a partial cross-sectional view of an embodiment of a ramped inlet and a rotor duct within line 13-13 of FIG. 2; and

FIG. 16 is a cross-sectional view of an embodiment of an inlet of an end cover within line 16-16 of FIG. 15.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

One or more specific embodiments of the present invention will be described below. These described embodiments are only exemplary of the present invention. Additionally, in an effort to provide a concise description of these exemplary embodiments, all features of an actual implementation may not be described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure.

When introducing elements of various embodiments of the present invention, the articles “a,” “an,” “the,” and “said” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements.

As discussed in detail below, a hydraulic energy transfer system transfers work and/or pressure between a first fluid (e.g., a pressure exchange fluid) and a second fluid (e.g., frac fluid or a salinated fluid). In certain embodiments, the first fluid may be substantially “cleaner” than the second fluid. In other words, the second fluid may contain dissolved or suspended particles. Moreover, in certain embodiments, the second fluid may be more viscous than the first fluid. Additionally, the first fluid may be at a first pressure between approximately 5,000 kPa to 25,000 kPa, 20,000 kPa to 50,000 kPa, 40,000 kPa to 75,000 kPa, 75,000 kPa to 100,000 kPa or greater than a second pressure of the second fluid. In operation, the hydraulic energy transfer system may or may not completely equalize pressures between the first and second fluids. Accordingly, the hydraulic energy transfer system may operate isobarically, or substantially isobarically (e.g., wherein the pressures of the first and second fluids equalize within approximately +/−1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 percent of each other).

The hydraulic energy transfer system may also be described as a hydraulic protection system, hydraulic buffer system, or a hydraulic isolation system, because it blocks or limits contact between the second fluid and various pieces of hydraulic equipment (e.g., high-pressure pumps, heat exchangers), while still exchanging work and/or pressure between the first and second fluids. By blocking or limiting contact between various pieces of hydraulic equipment and the second fluid (e.g., more viscous fluid, fluid with suspended solids), the hydraulic energy transfer system reduces abrasion/wear, thus increasing the life/performance of this equipment (e.g., high-pressure pumps). Moreover, it may enable the hydraulic system to use less expensive equipment, for example high-pressure pumps that are not designed for abrasive fluids (e.g., fluids with suspended particles). In some embodiments, the hydraulic energy transfer system may be a hydraulic turbocharger, a rotating isobaric pressure exchanger (e.g., rotary IPX), or a non-rotating isobaric pressure exchanger (e.g., bladder, reciprocating isobaric pressure exchanger). Rotating and non-rotating isobaric pressure exchangers may be generally defined as devices that transfer fluid pressure between a high-pressure inlet stream and a low-pressure inlet stream at efficiencies in excess of approximately 50%, 60%, 70%, 80%, or 90% without utilizing centrifugal technology.

As explained above, the hydraulic energy transfer system transfers work and/or pressure between first and second fluids. These fluids may be multi-phase fluids such as gas/liquid flows, gas/solid particulate flows, liquid/solid particulate flows, gas/liquid/solid particulate flows, or any other multi-phase flow. Moreover, these fluids may be non-Newtonian fluids (e.g., shear thinning fluid), highly viscous fluids, non-Newtonian fluids containing proppant, or highly viscous fluids containing proppant. The proppant may include sand, solid particles, powders, debris, ceramics, or any combination therefore. For example, the disclosed embodiments may be used with oil and gas equipment, such as hydraulic fracturing equipment using a proppant (e.g., particle laden fluid) to frac rock formations in a well.

FIG. 1 is a schematic diagram of an embodiment of a frac system 10 (e.g., fluid handling system) with a hydraulic energy transfer system 12. In operation, the frac system 10 enables well completion operations to increase the release of oil and gas in rock formations. The frac system 10 may include one or more first fluid pumps 18 and one or more second fluid pumps 20 coupled to a hydraulic energy transfer system 12. For example, the hydraulic energy system 12 may include a hydraulic turbocharger, rotary IPX, reciprocating IPX, or any combination thereof. In addition, the hydraulic energy transfer system 12 may be disposed on a skid separate from the other components of a frac system 10, which may be desirable in situations in which the hydraulic energy transfer system 12 is added to an existing frac system 10. In operation, the hydraulic energy transfer system 12 transfers pressures without any substantial mixing between a first fluid (e.g., proppant free fluid) pumped by the first fluid pumps 18 and a second fluid (e.g., proppant containing fluid or frac fluid) pumped by the second fluid pumps 20. In this manner, the hydraulic energy transfer system 12 blocks or limits wear on the first fluid pumps 18 (e.g., high-pressure pumps), while enabling the frac system 10 to pump a high-pressure frac fluid into the well 14 to release oil and gas. In addition, because the hydraulic energy transfer system 12 is configured to be exposed to the first and second fluids, the hydraulic energy transfer system 12 may be made from materials resistant to corrosive and abrasive substances in either the first and second fluids. For example, the hydraulic energy transfer system 12 may be made out of ceramics (e.g., alumina, cermets, such as carbide, oxide, nitride, or boride hard phases) within a metal matrix (e.g., Co, Cr or Ni or any combination thereof) such as tungsten carbide in a matrix of CoCr, Ni, NiCr or Co.

In an embodiment using a hydraulic turbocharger, the first fluid (e.g., high-pressure proppant free fluid) enters a first side of the hydraulic turbocharger and the second fluid (e.g., low-pressure frac fluid) may enter the hydraulic turbocharger on a second side. In operation, the flow of the first fluid drives a first turbine coupled to a shaft. As the first turbine rotates, the shaft transfers power to a second turbine that increases the pressure of the second fluid, which drives the second fluid out of the hydraulic turbocharger and down a well during fracturing operations. In an embodiment using an isobaric pressure exchanger (IPX), the first fluid (e.g., high-pressure proppant free fluid) enters a first side of the hydraulic energy transfer system where the first fluid contacts the second fluid (e.g., low-pressure frac fluid) entering the IPX on a second side. The contact between the fluids enables the first fluid to increase the pressure of the second fluid, which drives the second fluid out of the IPX and down a well for fracturing operations. The first fluid similarly exits the IPX, but at a low-pressure after exchanging pressure with the second fluid.

As used herein, the isobaric pressure exchanger (IPX) may be generally defined as a device that transfers fluid pressure between a high-pressure inlet stream and a low-pressure inlet stream at efficiencies in excess of approximately 50%, 60%, 70%, or 80% without utilizing centrifugal technology. In this context, high pressure refers to pressures greater than the low pressure. The low-pressure inlet stream of the IPX may be pressurized and exit the IPX at high pressure (e.g., at a pressure greater than that of the low-pressure inlet stream), and the high-pressure inlet stream may be depressurized and exit the IPX at low pressure (e.g., at a pressure less than that of the high-pressure inlet stream). Additionally, the IPX may operate with the high-pressure fluid directly applying a force to pressurize the low-pressure fluid, with or without a fluid separator between the fluids. Examples of fluid separators that may be used with the IPX include, but are not limited to, pistons, bladders, diaphragms and the like. In certain embodiments, isobaric pressure exchangers may be rotary devices. Rotary isobaric pressure exchangers (IPXs) 20, such as those manufactured by Energy Recovery, Inc. of San Leandro, Calif., may include ramped inlets configured to induce rotation of a rotor of the IPX, as described in detail below with respect to FIGS. 2-12. Rotary IPXs may be designed to operate with internal pistons to isolate fluids and transfer pressure with relatively little mixing of the inlet fluid streams. However, in some embodiments, the rotary IPX may operate without internal pistons. Reciprocating IPXs may include a piston moving back and forth in a cylinder for transferring pressure between the fluid streams. Any IPX or plurality of IPXs may be used in the disclosed embodiments, such as, but not limited to, rotary IPXs, reciprocating IPXs, or any combination thereof. In addition, the IPX may be disposed on a skid separate from the other components of a fluid handling system, which may be desirable in situations in which the IPX is added to an existing fluid handling system.

FIG. 2 is a schematic cross-sectional view of an embodiment of an IPX 160. As shown in FIG. 2, the IPX 160 may have a variety of fluid connections, such as a first fluid inlet, a first fluid outlet, a second fluid inlet, and/or a second fluid outlet. In certain embodiments, the inlets and outlets (e.g., disposed within end covers 184, 186) may include ramped interfaces (e.g., tapered, curved, sloped, or angled interfaces) configured to direct the fluid at an angle (e.g., oblique angle) into the rotor 166. Additionally, in certain embodiments, the first and/or second fluids may include solids, such as particles, powders, debris, and so forth. Each of the fluid connections to the IPX may be made using flanged fittings, threaded fittings, bolted fittings, or other types of fittings. The IPX may include a rotating component, such as a rotor, which may rotate in the circumferential direction. As shown, the IPX 160 includes an axial axis 188, a radial axis 189, and a circumferential axis 191.

It will be appreciated that FIG. 2 is a simplified view of the rotatory IPX 160 and certain details have been omitted for clarity. In the illustrated embodiment, the rotary IPX 160 includes a housing 212 (e.g., annular housing) containing a sleeve 164 (e.g., annular sleeve), a rotor 166, and end covers 184, 186, among other components. For example, seals 214 (e.g., annular seals) may be disposed between the housing 212 and the end covers 184, 186 to substantially contain the first and second fluids 208, 206 within the housing 212. That is, the seals 214 may extend circumferentially about the end covers 184, 186. However, in other embodiments, the seals 214 may not be disposed about the end cover 184, thereby substantially enabling the first fluid 208 to flow between the housing 212 and the sleeve 164, as well as the sleeve 164 and the rotor 166. As will be described in detail below, a high pressure (HP) first fluid 208 may enter the rotary IPX 160 axially through an inlet 176 and an aperture 196 to drive a low pressure (LP) second fluid 206 out of a channel 190. The rotor 166 may have a plurality of channels 190 extending substantially longitudinally through the rotor 166 with openings at each end arranged symmetrically about the longitudinal axis 188.

In FIG. 2, a first interface 216 (e.g., axial interface along a radial plane) is positioned between the aperture 196 and the rotor 166. At the first interface 216, the first fluid 208 enters the channel 190, thereby driving the second fluid 206 from the channel 190 and axially out of the rotor 166 via an aperture 200. Additionally, a second interface 218 (e.g., axial interface along a radial plane) is positioned between an aperture 202 and the rotor 166. At the second interface 218, the second fluid 208 enters the channel 190, thereby driving the first fluid 208 from the channel 190 and axially out of the rotor 166 via an aperture 198.

FIG. 3 is an exploded perspective view of an embodiment of a rotary isobaric pressure exchanger 160 (rotary IPX) capable of transferring pressure and/or work between the first and second fluids with minimal mixing of the fluids. The rotary IPX 160 may include a generally cylindrical body portion 162 that includes a sleeve 164 and a rotor 166. The rotary IPX 160 may also include two end caps 168 and 170 that include manifolds 172 and 174, respectively. Manifold 172 includes respective inlet and outlet ports 176 and 178, while manifold 174 includes respective inlet and outlet ports 180 and 182. In operation, these inlet ports 176, 180 enabling the first fluid to enter the rotary IPX 160 to exchange pressure, while the outlet ports 180, 182 enable the first fluid to then exit the rotary IPX 160. In operation, the inlet port 176 may receive a high-pressure first fluid, and after exchanging pressure, the outlet port 178 may be used to route a low-pressure first fluid out of the rotary IPX 160. Similarly, inlet port 180 may receive a low-pressure second fluid and the outlet port 182 may be used to route a high-pressure second fluid out of the rotary IPX 160. The end caps 168 and 170 include respective end covers 184 and 186 disposed within respective manifolds 172 and 174 that enable fluid sealing contact with the rotor 166. The rotor 166 may be cylindrical and disposed in the sleeve 164, which enables the rotor 166 to rotate about the axis 188. The rotor 166 may have a plurality of channels 190 extending substantially longitudinally through the rotor 166 with openings 192 and 194 at each end arranged symmetrically about the longitudinal axis 188. The openings 192 and 194 of the rotor 166 are arranged for hydraulic communication with inlet and outlet apertures 196 and 198; and 200 and 202 in the end covers 184 and 186, in such a manner that during rotation the channels 190 are exposed to fluid at high-pressure and fluid at low-pressure. As illustrated, the inlet and outlet apertures 196 and 198, and 200 and 202 may be designed in the form of arcs or segments of a circle (e.g., C-shaped).

In some embodiments, a controller using sensor feedback may control the extent of mixing between the first and second fluids in the rotary IPX 160, which may be used to improve the operability of the fluid handling system. For example, varying the proportions of the first and second fluids entering the rotary IPX 160 allows the plant operator to control the amount of fluid mixing within the hydraulic energy transfer system. Three characteristics of the rotary IPX 160 that affect mixing are: (1) the aspect ratio of the rotor channels 190, (2) the short duration of exposure between the first and second fluids, and (3) the creation of a fluid barrier (e.g., an interface) between the first and second fluids within the rotor channels 190. First, the rotor channels 190 are generally long and narrow, which stabilizes the flow within the rotary IPX 160. In addition, the first and second fluids may move through the channels 190 in a plug flow regime with very little axial mixing. Second, in certain embodiments, the speed of the rotor 166 reduces contact between the first and second fluids. For example, the speed of the rotor 166 may reduce contact times between the first and second fluids to less than approximately 0.15 seconds, 0.10 seconds, or 0.05 seconds. Third, a small portion of the rotor channel 190 is used for the exchange of pressure between the first and second fluids. Therefore, a volume of fluid remains in the channel 190 as a barrier between the first and second fluids. All these mechanisms may limit mixing within the rotary IPX 160. Moreover, in some embodiments, the rotary IPX 160 may be designed to operate with internal pistons that isolate the first and second fluids while enabling pressure transfer.

FIGS. 4-7 are exploded views of an embodiment of the rotary IPX 160 illustrating the sequence of positions of a single channel 190 in the rotor 166 as the channel 190 rotates through a complete cycle. It is noted that FIGS. 2-5 are simplifications of the rotary IPX 160 showing one channel 190, and the channel 190 is shown as having a circular cross-sectional shape. In other embodiments, the rotary IPX 160 may include a plurality of channels 190 with the same or different cross-sectional shapes (e.g., circular, oval, square, rectangular, polygonal, etc.). Thus, FIGS. 4-7 are simplifications for purposes of illustration, and other embodiments of the rotary IPX 160 may have configurations different from that shown in FIGS. 4-7. As described in detail below, the rotary IPX 160 facilitates pressure exchange between the first and second fluids by enabling the first and second fluids to momentarily contact each other within the rotor 166. In certain embodiments, this exchange happens at speeds that result in limited mixing of the first and second fluids.

In FIG. 4, the channel opening 192 is in a first position. In the first position, the channel opening 192 is in fluid communication with the aperture 198 in endplate 184 and therefore with the manifold 172, while opposing channel opening 194 is in hydraulic communication with the aperture 202 in end cover 186 and by extension with the manifold 174. As will be discussed below, the rotor 166 may rotate in the clockwise direction indicated by arrow 204. In operation, the LP second fluid 206 passes through end cover 186 and enters the channel 190, where it contacts the LP first fluid 208 at a dynamic fluid interface 210. The second fluid 206 then drives the first fluid 208 out of the channel 190, through end cover 184, and out of the rotary IPX 160. However, because of the short duration of contact, there is minimal mixing between the second fluid 206 and the first fluid 208. As will be appreciated, a pressure of the second fluid 206 is greater than a pressure of the first fluid 208, thereby enabling the second fluid 206 to drive the first fluid 208 out of the channel 190.

In FIG. 5, the channel 190 has rotated clockwise through an arc of approximately 90 degrees. In this position, the outlet 194 is no longer in fluid communication with the apertures 200 and 202 of end cover 186, and the opening 192 is no longer in fluid communication with the apertures 196 and 198 of end cover 184. Accordingly, the LP second fluid 206 is temporarily contained within the channel 190.

In FIG. 6, the channel 190 has rotated through approximately 180 degrees of arc from the position shown in FIG. 2. The opening 194 is now in fluid communication with aperture 200 in end cover 186, and the opening 192 of the channel 190 is now in fluid communication with aperture 196 of the end cover 184. In this position, the HP first fluid 208 enters and pressurizes the LP second fluid 206 driving the second fluid 206 out of the fluid channel 190 and through the aperture 200 for use in the system or disposal.

In FIG. 7, the channel 190 has rotated through approximately 270 degrees of arc from the position shown in FIG. 6. In this position, the outlet 194 is no longer in fluid communication with the apertures 200 and 202 of end cover 186, and the opening 192 is no longer in fluid communication with the apertures 196 and 198 of end cover 184. Accordingly, the first fluid 208 is no longer pressurized and is temporarily contained within the channel 190 until the rotor 166 rotates another 90 degrees, starting the cycle over again.

As described above, the first fluid 208 enters the inlet 176 and is directed toward the rotor 166 via the aperture 196. In certain embodiments, the aperture 196 includes a sloped face configured to direct the first fluid 208 into the channel 90 at an angle (e.g., the aperture 196 directs the first fluid 208 against a wall of the channel 90). Accordingly, energy from the first fluid 208 may be transferred to the rotor 166, thereby facilitating rotation of the rotor 166 about the axis 188.

FIG. 8 is a graphical representation of an embodiment of operating conditions of the rotary IPX 160. For example, the graphical representation illustrates the torque utilized to maintain the rotor 166 spinning at a steady state speed (e.g., a desired rotational speed, an angular speed). In the illustrated embodiment, the vertical axis 212 represents a torque applied to the rotor 166. For example, the first fluid 208 entering the channels 190 may apply a force against the walls of the channels 190 to induce rotation of the rotor 166. As will be appreciated, a larger torque is indicated by a higher vertical position along the vertical axis 212. Additionally, a horizontal axis 214 represents the revolutions per minute (RPM) of the rotor 166. In other words, the horizontal axis 214 represents the rotational speed of the rotor 166. As will be appreciated, a higher RPM is indicated by a horizontal position farther to the right on the horizontal axis 214.

In the illustrated embodiment, the torque generated by a supply of fluid entering the rotor 166 is represented by a first line 216. The torque is a function of RPM as well as several characteristics of the system. For example, the flow rate of the first fluid 208 directed toward the rotary IPX 160 may affect the supply, and therefore the position of the first line 216. Accordingly, the flow rate of the first fluid 208 entering the rotor 166 may change the slope of the first line 216. Additionally, the geometry of the apertures 196, 198, 200, 202 may also impact the position of the first line 216. In certain embodiments, the flow rate may be substantially constant (e.g., constrained by associated equipment). Accordingly, to adjust the position of the first line 216, modifications to the inlet geometry of components of the rotary IPX 160 may be utilized.

A second line 218 represents a torque demand or load of the rotor 166. For example, the second line 218 may represent the torque associated with a given rotational speed. Like the supply, the demand is a function of several characteristics of the system. For example, the viscosity of the fluid utilized in the system may increase the load on the rotor 166, thereby shifting the position of the second line 218. Moreover, the inlet geometries, clearances between the rotor 166 and sleeve 164, clearance between the rotor 166 and the end covers 184, 186, operating conditions, and other equipment associated with the system may also affect the torque demand on the rotor 166. In the illustrated embodiment, the first and second lines 216, 218 intersect at a first steady state point 220. The first steady state point 220 represents the desired RPM (e.g., steady state RPM) of the rotor given a particular torque supplied and torque demand. As will be described below, changes and/or shifts in the torque supply or torque demand applied to the system may change the position of the steady state point.

Under certain operating conditions, the demand on the rotor 166 may change. For example, the viscosity of the first and/or second fluids 208, 206 may increase, thereby generating a greater demand on the rotor 166. As a result, the second line 218 shifts in the direction 222 to form a third line 224. In the illustrated embodiment, third line 224 intersects the first line 216 at a second steady state point 226. The second steady state point 226 is at a point representing a lower RPM, while also utilizing a higher torque than the first steady state point 220. As a result, the larger demand placed on the rotor 166 slows the rotor 166 down while simultaneously using a larger torque to induce rotation of the rotor 166.

As mentioned above, the supply, represented by the first line 216, is a function of the flow rate, geometry of the rotary IPX, and the like. In certain embodiments, it may be difficult or undesirable to raise the flow rate of the supply. For instance, increasing the flow rate may damage associated piping coupling the rotary IPX 160 to the system. Therefore, in certain embodiments, modifications to the inlet geometry of the rotary IPX 160 may increase the torque applied to the rotor 166 without modifying the flow rate. For instance, the geometry of the aperture 196 may direct the supply toward an interior surface of the channel 190, thereby transferring a larger amount of force to the rotor 166 to facilitate rotation. As shown, the first line 216 is shifted in a direction 228 to form a fourth line 230. The fourth line 230 represents a supply configured to apply a larger torque to the rotor 166 than the first line 216. The third line 224 and the fourth line 230 intersect at a third steady state point 232 to establish a desired speed of operation of the rotor 166. It should be noted that the RPM of the third steady state point 232 is substantially equal to the RPM at the first steady state point 220. Accordingly, modifications to the inlet geometry of the rotary IPX 160 may enable the rotor 166 to maintain a desired speed (e.g., steady state RPM) while a larger load is acting to the rotor 166.

FIG. 9 is a schematic cut-away view of the rotor 166 having the first fluid 208 entering the channel 190 via the aperture 196. In the illustrated embodiment, the first fluid 208 travels along a first flow path 234. As shown, the first flow path 234 enters the channel 190 at an angle 236 (e.g., oblique angle) relative to a channel axis 238. As a result, the energy (e.g., kinetic energy, force) in the first flow path 234 is split such that a portion of the force is applied to an interior surface 240 of the channel 190 and a portion travels down the channel 190 along the channel axis 238. The force applied to the interior surface 240 is configured to generate and/or maintain rotation of the rotor 166 about the axis 188. Additionally, the portion of the force that travels down the channel 190 is configured to drive the second fluid 206 out of the channel 190, as described in detail above.

The angle 236 of the first flow path 234 is configured to generate sufficient force to maintain rotation of the rotor 166 about the axis 188, while also decreasing the likelihood of mixing within the channel 190. For example, the first fluid 208 contacts the second fluid 206 in the channel (e.g., at the dynamic fluid interface 210) to drive the second fluid 206 from the channel 190. As a result, the portion of the flow directed along the channel axis 238 is configured to be sufficient to drive the second fluid 206 from the channel 190 while minimizing the contact time between the first and second fluids 208, 206. Minimizing the contact time between the first and second fluids 208, 206 reduces the likelihood of mixing.

In the illustrated embodiment, the angle 236 is approximately 30 degrees relative to the channel axis 238. However, in other embodiments, the angle 236 may be greater than, less than, or equal to approximately 10 degrees, approximately 20 degrees, approximately 40 degrees, approximately 50 degrees, approximately 60 degrees, approximately 70 degrees, approximately 80 degrees, or any suitable angle to facilitate rotation of the rotor 166. Moreover, the angle 236 may be between approximately 10 degrees and approximately 20 degrees, approximately 20 degrees and approximately 30 degrees, approximately 30 degrees and approximately 40 degrees, approximately 40 degrees and approximately 50 degrees, approximately 50 degrees and approximately 60 degrees, approximately 60 degrees and approximately 70 degrees, approximately 70 degrees and approximately 80 degrees, or any other suitable range. Additionally, the angle 236 may be less than approximately 20 degrees, less than approximately 30 degrees, less than approximately 40 degrees, less than approximately 50 degrees, less than approximately 60 degrees less than approximately 70 degrees, less than approximately 80 degrees, less than approximately 90 degrees, or any other angle configured to generate rotation of the rotor 166. Accordingly, the angle 236 is configured to direct the fluid into the channels 190 to facilitate rotation of the rotor 166 while also driving fluid from the channels 190.

In certain embodiments, the aperture 200 (e.g., the outlet) may also include a sloped interface to facilitate rotation of the rotor 166. For example, the geometry of the aperture 200 may mirror the geometry of the aperture 196. However, in other embodiments, the sloped interfaces of the apertures 196, 200 may be different. For example, the sloped interface of the aperture 196 may be more severe (e.g., a larger angle 236) than the sloped interface of the aperture 200.

To generate rotation of the rotor 166, the rotary IPX 160 may also include guide vanes positioned on the sloped interfaces of the apertures 196, 198, 200, 202 to direct the fluid. For example, the guide vanes may include raised protrusions on the sloped interface configured to direct the fluid toward the channels at the angle 236. In certain embodiments, the guide vanes may be distributed along the face of the apertures 196, 198, 200, 202. However, in other embodiments, the guide vanes may be positioned within the channels 190 to facilitate additional rotational force upon the rotor 166.

Furthermore, in certain embodiments, fluid jets may be positioned proximate to the rotor 166. For example, the fluid jets may include outlet nozzles positioned at an angle (e.g., the angle 236) relative to the channels 190. To this end, the fluid jets may direct the fluid toward the channels 190 at an angle sufficient to induce rotation of the rotor 166 while maintaining minimal mixing between the first fluid 208 and the second fluid 206. As will be appreciated, the outlet nozzles of the fluid jets may have smaller cross-sectional areas than the conduits directing the fluid toward the fluid jets, thereby increasing the velocity of the fluid as it exits the outlet nozzles. As a result, the supply (e.g., line 216) may shift in the direction 228 because of the configuration of the outlet nozzles of the fluid jets. Additionally, in other embodiments, apertures 196, 198, 200, 202 converge toward the channel, thereby increasing the velocity of the fluid as it enters the channels 190. Furthermore, in certain embodiments, the inlet angle may vary across the apertures (e.g., the aperture 196). For example, the inlet angle may be smaller at a first end of the aperture in which the dynamic fluid interface 210 is closer to the edge of the channel 190 and larger at a second end of the aperture in which the dynamic fluid interface 210 is farther from the edge of the channel 190. That is, as the dynamic fluid interface 210 is moved toward the second end of the channel 190 (e.g., toward the aperture 200), the inlet angle may increase to generate more torque.

FIG. 10 is a graphical representation of an embodiment of an acceleration profile of the dynamic fluid interface 210 over a full rotation of the channel 190. A vertical axis 242 represents acceleration and a horizontal axis 244 represents a rotor index angle over a full 360 degree rotation. Additionally, an acceleration line 246 represents the acceleration of the fluid. As shown, in a first section 248, the channel 190 is exposed to the aperture (e.g., the aperture 196) via rotation of the rotor 166. In the first section 248, the acceleration of the fluid has a positive slope as the fluid applies a force to the interior surface 240 of the channel 190 and facilitates rotation of rotor 166. In a second section 250, the channel 190 is fully exposed to the aperture. As a result, the slope of the acceleration line 246 is approximately zero. A third section 252 represents the acceleration 246 with a negative slope as the channel 190 is moved out of fluid contact with the aperture. As a result, the force applied by the fluid against the interior surface 240 of the channel 190 decreases because a smaller portion of the channel 190 is in fluid contact with the aperture.

A fourth section 254 represents a dead head in the channel 190 as the fluid drives the dynamic fluid interface 210 through the channel 190. In the illustrated embodiment, the channel 190 is not in fluid contact with the aperture (e.g., the aperture 200 at the outlet of the channel 190) through the fourth section 254. As a result, the outlet of the channel 190 is blocked, thereby blocking the first fluid 208 from driving the second fluid 206 from the channel 190. Accordingly, the acceleration line 246 has a negative value because of the decreased acceleration caused by the blockage of the outlet of the channel 190. A fifth section 256 illustrates the acceleration line 246 with a substantially zero slope. Additionally the magnitude of the acceleration line 246 is substantially zero because the channel 190 is not fluidly coupled to the apertures (e.g., the aperture 200). In other words, the fluid may be stationary in the channel 190 in the fifth section 256. However, once the outlet of the channel 190 aligns with the aperture (e.g., the aperture 200), the first fluid 208 may drive the second fluid 206 from the channel 190. Finally, a sixth section 258 represents a mirrored image of the first, second, third, fourth, and fifth sections 248, 250, 252, 254, 256 as the first fluid 208 (now having a low pressure as opposed to a high pressure) is driven from the channel 190 by the second fluid 206 (now having a higher pressure than the low pressure first fluid 208).

FIG. 11 is graphical representation of an embodiment of a position of the dynamic fluid interface 210 and a velocity of the dynamic fluid interface 210. In the illustrated embodiment, a left vertical axis 260 represents the displacement of the dynamic fluid interface 210. Additionally, a right vertical axis 262 represents the velocity of the dynamic fluid interface 210. A horizontal axis 264 represents a rotor index angle. That is, the horizontal axis 264 represents the rotor 166 through a full rotation from 0 to 360 degrees. A velocity line 266 represents the velocity of the dynamic fluid interface 210 as the dynamic fluid interface traverses through the channel 190. Furthermore, a position line 268 represents the position of the dynamic fluid interface 210 as the dynamic fluid interface 210 traverses through the channel 190. For example, as described above, the dynamic fluid interface 210 may laterally traverse a length of the rotor 166 as the first and second fluids 206, 208 enter and exit the channels 190.

The velocity line 266 is obtained by integrating the angular acceleration (e.g., the acceleration line 246) of the fluid (e.g., the first fluid 208) as the fluid moves through the channel 190. Additionally, the position line 268 is obtained by integrating the velocity line 266. As the fluid enters the channel 190, the fluid facilitates rotation of the rotor 166. In a first section 270, the velocity line 266 has a positive slope due to the force exerted on the dynamic fluid interface 210 by the fluid. Additionally, the position line 268 also has a positive slope, representing a change in the position of the dynamic fluid interface 210 facilitated by the driving force of fluid (e.g., the first fluid 208) entering the channel 190. A second section 272 represents a dead head scenario in which the dynamic fluid interface 210 substantially stops before the dynamic fluid interface 210 is driven toward a far end of the channel 190. For example, as described above, the channel 190 may not be in fluid contact with the apertures while the flow dead heads. As shown, the position line 268 is substantially unchanged in the second section 272. However, the velocity line 266 has a downward slope, indicating a slowing and/or stoppage of the dynamic fluid interface 210 (e.g., at approximately a center position of the channel 190).

Additionally, a third section 274 represents a substantial stoppage of the dynamic fluid interface 210. As shown, both the velocity line 266 and the position line 268 have substantially zero slope. In the illustrated embodiment, the third section 274 represents the dynamic fluid interface 210 before the entering fluid drives the fluid in the channel 190 out of the channel 190. A fourth section 276 substantially mirrors the first, second, and third sections 270, 272, 274 as the first fluid 208 is driven from the channel 190 by the second fluid 206 in an opposite direction.

FIG. 12 is a flowchart of an embodiment of a method 278 to determine the desired angle 236 of the inlet ramps. A desired acceleration profile of the fluid is determined, as represented by block 280. For example, acceleration may be modeled to correspond to the acceleration line 246 of FIG. 10. As used herein, models may refer to physics-based models, such as such as computational fluid dynamics (CFD) models, finite element analysis (FEA) models, solid models (e.g., parametric and non-parametric modeling), and/or 3-dimension to 2-dimension FEA mapping models that may be used to determine the fluid inlet angle. Models may also include artificial intelligence (AI) models, such as expert systems (e.g. forward chained expert systems, backward chained expert systems), neural networks, fuzzy logic systems, state vector machines (SVMs), inductive reasoning systems, Bayesian inference systems, or a combination thereof. That is, the acceleration may be modeled to increase (e.g., have a positive slope) as the channels 190 come into fluid contact with the apertures, to have substantially zero slope during full flow, and to have a negative slope as the channels 190 leave fluid contact with the apertures. Additionally, deceleration because of a blocked channel outlet may also be modeled.

The acceleration profile may be integrated to determine a velocity profile, as represented by block 282. For example, the acceleration profile may be integrated with respect to time. Accordingly, a representation of the velocity may be generated. In certain embodiments, the velocity profile may be compared to the acceleration profile. As will be appreciated, the velocity profile may substantially correspond to the acceleration profile (e.g., velocity increases as acceleration increases). Then, the velocity profile may be integrated to determine a position profile, as represented by block 284. For example, the velocity profile may be integrated with respect to time to determine the position of the dynamic fluid interface 210 in the channel 190. Thereafter, the velocity profile may be compared to the position profile, as represented by block 284. For example, the shape of the velocity profile may substantially correspond to the shape of the position profile, as represented by line 286. As will be appreciated, because the velocity of the dynamic fluid interface 210 is directly related to the position of the dynamic fluid interface 210, the profiles may substantially correspond to represent the dynamic fluid interface 210 moving through the channel 190. If the profiles correspond, as represented by line 288, the fluid inlet angle (e.g., plug flow angle) may be calculated, as represented by block 290. Upon determining the fluid inlet angle, end covers having the ramps at the calculated fluid inlet angle may be manufactured.

In certain embodiments, the fluid inlet angle may be determined as a function of the rotor index angle. For example, the axial component may be determined utilizing the velocity profile. Additionally, the circumferential velocity may be a product of the radius of the rotor 166 and the angular velocity of the rotor 166. Accordingly, the fluid inlet angle may be calculated to reduce mixing of the first and second fluids 208, 206 at the dynamic fluid interface 210 while generating sufficient torque on the rotor 166. In embodiments where the fluid inlet angle is greater (e.g., more severe) than the calculated inlet angle, a larger torque is applied to the rotor 166. Additionally, in embodiments where the fluid inlet angle is smaller (e.g., less severe) than the calculated angle, the rotor 166 may slow down.

However, in other embodiments, the position profile may not correspond to the velocity profile, as represented by the line 292. For example, the position profile may illustrate movement of the dynamic fluid interface 210 while the velocity profile has a negative slope, indicative of a blocked outlet of the channel 190. Accordingly, the acceleration profile may be adjusted by returning to block 280.

While the embodiments described above included modifications to the end covers 184, 186, in certain embodiments the channels 190 may include geometric modifications to facilitate rotation of the rotor 166. For example, the channels 190 may include sloped and/or chamfered inlets to direct the fluid toward the interior surface 240 of the channels 190 to induce rotation of the rotor 166. Moreover, as described above, guide vanes may be distributed along the interior surface 240 of the channels 190 to facilitate rotation of the rotor 166. Accordingly, geometric modifications may be made to the rotor 166 to direct the fluid toward the interior surface 240 at an angle to apply a force to the interior surface 240 sufficient to facilitate rotation of the rotor 166 about the axis 188.

FIG. 13 is a partial cross-sectional view of an embodiment of a ramped inlet within line 13-13 of FIG. 2. In the illustrated embodiment, a ramp 300 is positioned axially adjacent to an inlet of the channel 190. In certain embodiments, the ramp 300 may be integrated into the end cover (e.g., end covers 184, 186). Moreover, the ramp 300 may substantially correspond with the apertures (e.g., the apertures 196, 198, 200, 202) to direct the fluid into the channels 190. As shown, the ramp 300 is positioned at an angle 302 relative to the axis 188 to direct the fluid toward the channel 190 at the plug flow angle. In the illustrated embodiment, the ramp 300 has a curved shape (e.g., arcuate shape). In other embodiments, the ramp 300 is straight. Additionally, in the illustrated embodiment, one or more vanes 304 are positioned on the ramp 300 (e.g., surface of the ramp 300). As described above, the vanes 304 may be configured to direct the fluid toward the channel 190 at the plug flow angle. In particular, the vanes 304 may include an oblique angle relative to axis 188. In certain embodiments, one or more vanes 304 may be disposed in one or more of the apertures 196, 198, 200, 202. As depicted in FIG. 14, one or more vanes 304 may be disposed within one or more channels 190.

FIG. 15 is a partial cross-sectional view of an embodiment of a ramped inlet and a rotor duct (e.g., channel 190) within line 13-13 of FIG. 2. In the illustrated embodiment, jets or nozzles 306 (e.g., passages) are positioned axially adjacent to the channel 190 (e.g., within the apertures 196, 198, 200, 202, within the end covers 184, 186, within the end cap). As depicted, the jet 306 extends from upstream of a surface 307 of the end cover (e.g., end cover 184, 186) that interfaces with the end of the rotor 166 to the surface 307. As shown, one or more jets 306 may be positioned to enable adjustment of the plug flow angle during operation. For example, fluid may be routed through the jet 306 at an angle 308 (e.g., oblique angle), relative to the axis 188 and the aperture. In certain embodiments, angle 308 is different from angle 302. During operation, the fluid may be directed through the jet 306 at the angle 308 to adjust the rotational speed of the rotor 166. As depicted, the jet 306 includes a first cross-sectional area 310 and the aperture includes a second cross-sectional area 312. The second cross-sectional area 312 is greater than the first cross-sectional area 310, which enables a velocity of the fluid to increase as it flows through the jet. As depicted, the ramp 300 is straight or linear. In certain embodiments, the ramp 300 may curved.

FIG. 16 is a cross-sectional view of an embodiment of an inlet (e.g., aperture 196, 202) of an end cover (e.g., 184, 186) within line 16-16 of FIG. 15. The inlet typically includes a kidney-shaped cross-sectional shape (see FIGS. 3-7). As depicted in FIG. 16, the inlet includes an alternative dog bone shaped cross-sectional shape. In particular, the inlet includes a central shaft 314 coupled to a first lobe 316 at one end and a second lobe 318 at the other end. In other embodiments, the inlet may include a cross-sectional shape different form the both the kidney and dog bone shapes. The alternative shapes for the inlet may enable altering the flow and velocity of the fluid entering the channel 190. In certain embodiments, the outlet may also include different cross-sectional shapes such as the dog bone shape.

While the invention may be susceptible to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and have been described in detail herein. However, it should be understood that the invention is not intended to be limited to the particular forms disclosed. Rather, the invention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the following appended claims.

Claims

1. A rotary isobaric pressure exchanger (IPX) for transferring pressure energy from a high pressure first fluid to a low pressure second fluid, comprising: a cylindrical rotor configured to rotate circumferentially about a rotational axis and having a first end face and a second end face disposed opposite each other with a plurality of channels extending axially therethrough between respective apertures located in the first and second end faces;a first end cover having a first surface that interfaces with and slidingly and sealingly engages the first end face, wherein the first end cover has at least one first fluid inlet and at least one first fluid outlet that during rotation of the cylindrical rotor about the rotational axis alternately fluidly communicate with at least one channel of the plurality of channels, wherein the first end cover comprises a first oblique ramp disposed within the at least one first fluid inlet, and the first oblique ramp is configured to direct a first fluid at a first oblique angle relative to the rotational axis into one or more channels of the plurality of channels; anda second end cover having a second surface that interfaces with and slidingly and sealingly engages the second end face, wherein the second end cover has at least one second fluid inlet and at least one second fluid outlet that during rotation of the cylindrical rotor about the rotational axis alternately fluidly communicate with at least one channel of the plurality of channels, wherein the second end cover comprises a second oblique ramp disposed within the at least second fluid inlet, and the second oblique ramp is configured to direct a second fluid at a second oblique angle relative to the rotational axis into one or more channels of the plurality of channels;a first vane disposed within the first fluid inlet, the second fluid inlet, or at least one channel of the plurality of channels, wherein the first vane is disposed at a third oblique angle relative to the rotational axis; andwherein the first oblique ramp and the second oblique ramp are configured to direct the first fluid and the second fluid, respectively, at the first oblique angle and the second oblique angle to impart a force against an interior surface of a respective channel of the plurality of channels to further circumferential rotation of the cylindrical rotor, and the first vane is configured to direct the first fluid or the second fluid to impart an additional force against the interior surface of the respective channel of the plurality of channels to further circumferential rotation of the cylindrical rotor.

2. The rotary IPX of claim 1, wherein the first vane is disposed on a surface of the first oblique ramp.

3. The rotary IPX of claim 1, wherein first vane is disposed on a surface of the second oblique ramp.

4. The rotary IPX of claim 1, wherein the first vane is disposed on surface of the at least one channel.

5. The rotary IPX of claim 1, comprising a first vane disposed on a first surface of the first oblique ramp, a second vane disposed on a second surface of the second oblique ramp, and a third vane disposed on a third surface of the at least one channel.

6. The rotary IPX of claim 1, wherein at least one of the first fluid inlet, the first fluid outlet, the second fluid inlet, and the second fluid outlet comprises a cross-sectional shape along a plane orthogonal to the rotational axis, and the cross-sectional shape comprises a central shaft coupled to a first lobe at a first end and a second lobe at a second end.

7. The rotary IPX of claim 6, wherein each of the first fluid inlet, the first fluid outlet, the second fluid inlet and the second fluid outlet comprises the cross-sectional shape having the central shaft coupled to the first lobe and the second lobe.

8. The rotary IPX of claim 1, wherein the first end cover comprises a first passage extending from the first fluid inlet upstream of the first surface to the first surface, and the first passage is configured to inject the first fluid against a first respective interior surface of one the channels of the plurality of channels to impart a further additional force to further circumferential rotation of the cylindrical rotor.

9. The rotary IPX of claim 8, wherein the first passage comprises a first cross-sectional area and the first fluid inlet comprises a second cross-sectional area, and the second cross-sectional area is greater than the first cross-sectional area.

10. The rotary IPX of claim 8, wherein the first passage is disposed at a third oblique angle relative to the first fluid inlet.

11. The rotary IPX of claim 8, wherein the second end cover comprises a second passage extending from the second fluid inlet upstream of the second surface to the second surface, and the second passage is configured to inject the second fluid against a second respective interior surface of one the channels of the plurality of channels to impart a further additional force against the second respective interior surface to further circumferential rotation of the cylindrical rotor.

12. The rotary IPX of claim 1, wherein the rotary IPX is configured to be utilized with a frac system, and the first fluid comprises a proppant free fluid and the second fluid comprises a frac fluid having proppants.

13. A rotary isobaric pressure exchanger (IPX) for transferring pressure energy from a high pressure first fluid to a low pressure second fluid, comprising: a cylindrical rotor configured to rotate circumferentially about a rotational axis and having a first end face and a second end face disposed opposite each other with a plurality of channels extending axially therethrough between respective apertures located in the first and second end faces;a first end cover having a first surface that interfaces with and slidingly and sealingly engages the first end face, wherein the first end cover has at least one first fluid inlet and at least one first fluid outlet that during rotation of the cylindrical rotor about the rotational axis alternately fluidly communicate with at least one channel of the plurality of channels, wherein the first end cover comprises a first oblique ramp disposed within the at least one first fluid inlet, and the first oblique ramp is configured to direct a first fluid at a first oblique angle relative to the rotational axis to impart into one or more channels of the plurality of channels; anda second end cover having a second surface that interfaces with and slidingly and sealingly engages the second end face, wherein the second end cover has at least one second fluid inlet and at least one second fluid outlet that during rotation of the cylindrical rotor about the rotational axis alternately fluidly communicate with at least one channel of the plurality of channels, wherein the second end cover comprises a second oblique ramp disposed within the at least second fluid inlet, and the second oblique ramp is configured to direct a second fluid at a second oblique angle relative to the rotational axis into one or more channels of the plurality of channels;a first passage disposed within the first end cover extending from the first fluid inlet upstream of the first surface to the first surface; andwherein the first oblique ramp and the second oblique ramp are configured to direct the first fluid and the second fluid, respectively, at the first oblique angle and the second oblique angle to impart a force against an interior surface of a respective channel of the plurality of channels to further circumferential rotation of the cylindrical rotor, and the first passage is configured to inject the first fluid against a respective interior surface of one the channels of the plurality of channels to impart an additional force to further circumferential rotation of the cylindrical rotor.

14. The rotary IPX of claim 13, wherein the rotary IPX is configured to be utilized with a frac system, and the first fluid comprises a proppant free fluid and the second fluid comprises a frac fluid having proppants.

15. The rotary IPX of claim 13, wherein the first passage comprises a first cross-sectional area and the first fluid inlet comprises a second cross-sectional area, and the second cross-sectional area is greater than the first cross-sectional area.

16. The rotary IPX of claim 13, wherein the first passage is disposed at a third oblique angle relative to the first fluid inlet.

17. The rotary IPX of claim 13, wherein the second end cover comprises a second passage extending from the second fluid inlet upstream of the second surface to the second surface, and the second passage is configured to inject the second fluid against a second respective interior surface of one the channels of the plurality of channels to impart a further additional force to further circumferential rotation of the cylindrical rotor.

18. The rotary IPX of claim 13, wherein at least one of the first fluid inlet, the first fluid outlet, the second fluid inlet, and the second fluid outlet comprises a cross-sectional shape along a plane orthogonal to the rotational axis, and the cross-sectional shape comprises a central shaft coupled to a first lobe at a first end and a second lobe at a second end.

19. The rotary IPX of claim 18, wherein each of the first fluid inlet, the first fluid outlet, the second fluid inlet and the second fluid outlet comprises the cross-sectional shape having the central shaft coupled to the first lobe and the second lobe.

20. The rotary IPX of claim 13, comprising a first vane disposed within the first fluid inlet, the second fluid inlet, or at least one channel of the plurality of channels, wherein the first is disposed at a third oblique angle relative to the rotational axis, and the first vane is configured to direct the first fluid or the second fluid to impart a further additional force against the interior surface of the respective channel of the plurality of channels to further circumferential rotation of the cylindrical rotor.

21. The rotary IPX of claim 20, wherein the first vane is disposed on a surface of the first oblique ramp.

22. The rotary IPX of claim 20, wherein first vane is disposed on a surface of the second oblique ramp.

23. The rotary IPX of claim 20, wherein the first vane is disposed on surface of the at least one channel.

24. The rotary IPX of claim 20, comprising a first vane disposed on a first surface of the first oblique ramp, a second vane disposed on a second surface of the second oblique ramp, and a third vane disposed on a third surface of the at least one channel.

25. A method for determining an oblique angle of an oblique ramp disposed within a fluid inlet of an end cover of a rotary isobaric pressure exchanger (IPX) that transfers pressure energy from a high pressure first fluid to a low pressure second fluid, the end cover having a surface that interfaces with and slidingly and sealingly engages an end face of a cylindrical rotor of the rotary IPX, and the oblique ramp is configured to direct the first fluid or the second fluid at the oblique angle to impart a force against an interior surface of a respective channel of a plurality of channels disposed within the cylindrical rotor to further circumferential rotation of the cylindrical rotor, comprising: determining a desired axial acceleration profile of a dynamic fluid interface between the first fluid and the second fluid within the respective channel utilizing a model;integrating the desired axial acceleration profile with respect to time to determine an axial velocity profile for the dynamic fluid interface through the respective channel;comparing the desired axial acceleration profile to the axial velocity profile for correspondence;integrating the axial velocity profile with respect to time to determine a position profile of the dynamic fluid interface within the respective channel when the desired axial acceleration profile corresponds to the axial velocity profile;comparing the axial velocity profile to the position profile for correspondence; andcalculating the oblique angle of the oblique ramp when the axial velocity profile corresponds to the position profile so that the oblique angle reduces mixing of the first and second fluids at the dynamic fluid interface while generating sufficient torque on the cylindrical rotor to circumferentially rotate the cylindrical rotor.