Patent Publication Number: US-2021190053-A1

Title: Actuator for a reciprocating pump

Description:
CROSS-REFERNCE TO RELATED APPLICATION 
     This Application claims priority to and the benefit of U.S. Provisional Patent Application Ser. No. 62/719,478, filed on Aug. 17, 2018 and entitled ‘SYSTEMS AND METHODS FOR PROVIDING FLOW AND PRESSURE TO FRACTURE A WELL USING A LINEAR ACTUATOR_, and U.S. Provisional Patent Application Ser. No. 62/753,677, filed on Oct. 31, 2018 and entitled ‘SYSTEMS AND METHODS FOR PROVIDING FLOW AND PRESSURE TO FRACTURE A WELL USING A LINEAR ACTUATOR_, each of which is incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     This disclosure relates to reciprocating pumps, and, in particular, to actuators for reciprocating pumps. 
     BACKGROUND 
     In oilfield operations, reciprocating pumps are used for different applications such as fracturing subterranean formations to drill for oil or natural gas, cementing the wellbore, or treating the wellbore and/or formation. A reciprocating pump designed for fracturing operations is sometimes referred to as a ‘frac pump. _ A reciprocating pump typically includes a power end section and a fluid end section. The fluid end section can be formed of a one piece construction or a series of blocks secured together by rods. The fluid end section includes a fluid cylinder (sometimes referred to as a cylinder section or a fluid end block) having a plunger bore for receiving a plunger, an inlet fluid passage, and an outlet fluid passage (sometimes referred to as a discharge passage). The inlet and outlet passages each include a valve assembly to control the flow of fluid into and out of the fluid cylinder. For example, the valve assemblies can be differential pressure valves that are opened by differential pressure of fluid and allow the fluid to flow in only one direction through the corresponding inlet or outlet passage. 
     During operation of a reciprocating pump, rotation of a crankshaft of the power end section reciprocates the plunger within the plunger bore of the fluid end section to thereby pump fluid into the fluid cylinder through the inlet passage and out through the outlet passage. But, the crankshaft provides the plunger with a relatively short stroke length that increases the cyclical rate of the reciprocating pump. Accordingly, the valve assemblies experience a relatively large number of sealing events during operation of the reciprocating pump, which increases wear on the valve assemblies. Moreover, at least some known reciprocating pumps experience non-uniform flow rates. For example, at least some known reciprocating pumps experience flow rate surges, which for example may be undesirable during fracking operations. 
     SUMMARY 
     This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This summary is not intended to identify key features or essential features of the claimed subject matter. Nor is it intended to be used as an aid in determining the scope of the claimed subject matter. 
     In a first aspect, a reciprocating pump assembly includes a fluid end section having a pressure chamber and a plunger bore that fluidly communicates with the pressure chamber. The reciprocating pump assembly includes a plunger configured to be held within the plunger bore of the fluid end section, and a linear actuator operatively connected to the plunger such that the linear actuator is configured to reciprocate the plunger within the plunger bore during operation of the reciprocating pump to thereby pump fluid through the fluid end section. 
     In some embodiments, the linear actuator includes at least one of a mechanical linear actuator, an electrical linear actuator, an electro-mechanical linear actuator, a magnetic linear actuator, a hydraulic linear actuator, a pneumatic linear actuator, a screw-type actuator, a ball screw, a lead screw, a rotary screw, a screw jack, a roller screw, a hydraulic piston, a linear motor, a wheel and axle actuator, a telescoping linear actuator, a solenoid, or a servo. 
     In some embodiments, the reciprocating pump assembly includes a driver configured to drive operation of the linear actuator. The driver includes at least one of an engine, an electrical motor, a turbine, a hydraulic pump, a pneumatic pump, a mechanical pump, an electrical power source, an electrical circuit, a processor, a mechanical drive system, a pneumatic system, or a hydraulic system. 
     In some embodiments, the reciprocating pump assembly includes a power end section that includes the linear actuator. 
     In some embodiments, the reciprocating pump assembly includes a controller operatively connected to the linear actuator such that the controller is configured to electronically control a flow rate of fluid through the fluid end section. 
     In a second aspect, a reciprocating pump assembly includes a first fluid end section having a first pressure chamber and a first plunger bore that fluidly communicates with the first pressure chamber. The reciprocating pump assembly includes a first plunger rod assembly that includes a first plunger configured to be held within the first plunger bore of the first fluid end section. The reciprocating pump assembly includes a second fluid end section having a second pressure chamber and a second plunger bore that fluidly communicates with the second pressure chamber. The reciprocating pump assembly includes a second plunger rod assembly that includes a second plunger configured to be held within the second plunger bore of the second fluid end section. The reciprocating pump assembly includes at least one linear actuator operatively connected to the first and second plunger rod assemblies such that the at least one linear actuator is configured to reciprocate the first and second plungers within the first and second plunger bores, respectively, during operation of the reciprocating pump to thereby pump fluid through the first and second fluid end sections. 
     In some embodiments, the at least one linear actuator includes at least one of a mechanical linear actuator, an electrical linear actuator, an electro-mechanical linear actuator, a magnetic linear actuator, a hydraulic linear actuator, a pneumatic linear actuator, a screw-type actuator, a ball screw, a lead screw, a rotary screw, a screw jack, a roller screw, a hydraulic piston, a linear motor, a wheel and axle actuator, a telescoping linear actuator, a solenoid, or a servo. 
     In some embodiments, the reciprocating pump assembly includes at least one driver configured to drive operation of the at least one linear actuator. The driver includes at least one of an engine, an electrical motor, a turbine, a hydraulic pump, a pneumatic pump, a mechanical pump, an electrical power source, an electrical circuit, a processor, a mechanical drive system, a pneumatic system, or a hydraulic system. 
     In some embodiments, the reciprocating pump assembly includes a power end section that includes the at least one linear actuator. 
     In some embodiments, at least one of the first fluid end section includes only a single one of the first pressure chamber or the second fluid end section includes only a single one of the second pressure chamber. 
     In some embodiments, the first and second plunger rod assemblies are operatively connected to the at least one linear actuator such that the first and second plunger rod assemblies are coaxially aligned with each other. 
     In some embodiments, the at least one linear actuator is configured to simultaneously move the first and second plunger rod assemblies in the same direction. 
     In some embodiments, the at least one linear actuator is configured to simultaneously move the first and second plunger rod assemblies in opposite directions. 
     In some embodiments, the at least one linear actuator is at least one first linear actuator. The reciprocating pump assembly includes a third fluid end section having a third pressure chamber and a third plunger bore that fluidly communicates with the third pressure chamber. The reciprocating pump assembly includes a third plunger rod assembly that includes a third plunger configured to be held within the third plunger bore of the third fluid end section. The reciprocating pump assembly includes a fourth fluid end section having a fourth pressure chamber and a fourth plunger bore that fluidly communicates with the fourth pressure chamber. The reciprocating pump assembly includes a fourth plunger rod assembly that includes a fourth plunger configured to be held within the fourth plunger bore of the fourth fluid end section. The reciprocating pump assembly includes at least one second linear actuator operatively connected to the third and fourth plunger rod assemblies such that the at least one second linear actuator is configured to reciprocate the third and fourth plungers within the third and fourth plunger bores, respectively, during operation of the reciprocating pump to thereby pump fluid through the third and fourth fluid end sections. 
     In some embodiments, the reciprocating pump assembly includes a controller operatively connected to the at least one linear actuator such that the controller is configured to electronically control a flow rate of fluid through the first and second fluid end sections. 
     In some embodiments, the at least one linear actuator is at least one first linear actuator. The reciprocating pump assembly includes a third fluid end section having a third pressure chamber and a third plunger bore that fluidly communicates with the third pressure chamber. The reciprocating pump assembly includes a third plunger rod assembly that includes a third plunger configured to be held within the third plunger bore of the third fluid end section. The reciprocating pump assembly includes a fourth fluid end section having a fourth pressure chamber and a fourth plunger bore that fluidly communicates with the fourth pressure chamber. The reciprocating pump assembly includes a fourth plunger rod assembly that includes a fourth plunger configured to be held within the fourth plunger bore of the fourth fluid end section. The reciprocating pump assembly includes at least one second linear actuator operatively connected to the third and fourth plunger rod assemblies such that the at least one second linear actuator is configured to reciprocate the third and fourth plungers within the third and fourth plunger bores, respectively, during operation of the reciprocating pump to thereby pump fluid through the third and fourth fluid end sections. The reciprocating pump assembly includes a controller operatively connected to the at least one first linear actuator and the at least one second linear actuator such that the controller is configured to offset the duty cycle of the first and second fluid end sections from the duty cycle of the third and fourth fluid end sections. 
     In a third aspect, a method for operating a reciprocating pump assembly includes operatively connecting at least one linear actuator to a first plunger rod assembly of a first fluid end section having a first plunger bore; operatively connecting the at least one linear actuator to a second plunger rod assembly of a second fluid end section having a second plunger bore; and reciprocating respective first and second plungers of the first and second plunger rod assemblies within the first and second plunger bores, respectively, using the at least one linear actuator to pump fluid through the first and second fluid end sections. 
     In some embodiments, reciprocating the first and second plungers within the first and second plunger bores, respectively, using the at least one linear actuator includes simultaneously moving the first and second plunger rod assemblies in the same direction. 
     In some embodiments, reciprocating the first and second plungers within the first and second plunger bores, respectively, using the at least one linear actuator includes electronically controlling a flow rate of fluid through the first and second fluid end sections. 
     In some embodiments, the at least one linear actuator is at least one first linear actuator. The method further includes operatively connecting at least one second linear actuator to a third plunger rod assembly of a third fluid end section having a third plunger bore; operatively connecting the at least one second linear actuator to a fourth plunger rod assembly of a fourth fluid end section having a fourth plunger bore; reciprocating respective third and fourth plungers of the third and fourth plunger rod assemblies within the third and fourth plunger bores, respectively, using the at least one second linear actuator to pump fluid through the third and fourth fluid end sections; and offsetting the duty cycle of the first and second fluid end sections from the duty cycle of the third and fourth fluid end sections. 
     Other aspects, features, and advantages will become apparent from the following detailed description when taken in conjunction with the accompanying drawings, which are a part of this disclosure and which illustrate, by way of example, principles of the inventions disclosed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings facilitate an understanding of the various embodiments. 
         FIG. 1  is an elevational view of a reciprocating pump assembly according to an exemplary embodiment. 
         FIG. 2  is a cross-sectional view of a fluid end section of the reciprocating pump assembly shown in  FIG. 1  according an exemplary embodiment. 
         FIG. 3  is an elevational view illustrating a plurality of the reciprocating pump assemblies shown in  FIG. 1  combined together according to an exemplary embodiment. 
         FIG. 4  illustrates a chart showing the combined and individual flow rates of multiple reciprocating pump assemblies according to an exemplary embodiment. 
         FIG. 5  illustrates a chart showing the combined and individual flow rates of multiple reciprocating pump assemblies according to an exemplary embodiment. 
         FIG. 6  illustrates a chart showing the combined and individual flow rates of multiple reciprocating pump assemblies according to an exemplary embodiment. 
         FIG. 7  illustrates a chart showing the combined and individual flow rates of multiple reciprocating pump assemblies according to an exemplary embodiment. 
         FIG. 8  is a flowchart illustrating a method for operating a reciprocating pump assembly according to an exemplary embodiment. 
     
    
    
     Corresponding reference characters indicate corresponding parts throughout the drawings. 
     DETAILED DESCRIPTION 
     Certain embodiments of the disclosure provide a reciprocating pump assembly that includes a fluid end section having a pressure chamber and a plunger bore that fluidly communicates with the pressure chamber. The reciprocating pump assembly includes a plunger configured to be held within the plunger bore of the fluid end section, and a linear actuator operatively connected to the plunger such that the linear actuator is configured to reciprocate the plunger within the plunger bore during operation of the reciprocating pump to thereby pump fluid through the fluid end section. 
     Certain embodiments of the disclosure provide a reciprocating pump assembly includes a first fluid end section having a first pressure chamber and a first plunger bore that fluidly communicates with the first pressure chamber. The reciprocating pump assembly includes a first plunger rod assembly that includes a first plunger configured to be held within the first plunger bore of the first fluid end section. The reciprocating pump assembly includes a second fluid end section having a second pressure chamber and a second plunger bore that fluidly communicates with the second pressure chamber. The reciprocating pump assembly includes a second plunger rod assembly that includes a second plunger configured to be held within the second plunger bore of the second fluid end section. The reciprocating pump assembly includes at least one linear actuator operatively connected to the first and second plunger rod assemblies such that the at least one linear actuator is configured to reciprocate the first and second plungers within the first and second plunger bores, respectively, during operation of the reciprocating pump to thereby pump fluid through the first and second fluid end sections. 
     Certain embodiments of the disclosure provide a method for operating a reciprocating pump assembly includes operatively connecting at least one linear actuator to a first plunger rod assembly of a first fluid end section having a first plunger bore; operatively connecting the at least one linear actuator to a second plunger rod assembly of a second fluid end section having a second plunger bore; and reciprocating respective first and second plungers of the first and second plunger rod assemblies within the first and second plunger bores, respectively, using the at least one linear actuator to pump fluid through the first and second fluid end sections. 
     Certain embodiments of the disclosure increase the stroke length of the plunger of the fluid end section of a reciprocating pump assembly and thereby reduce the number of sealing events experienced by valve assemblies of the fluid end section during operation of the reciprocating pump assembly. Certain embodiments of the disclosure increase the longevity of the valve assemblies of a fluid end section of a reciprocating pump assembly and thereby reduce the operating costs of a reciprocating pump assembly. Certain embodiments of the disclosure provide a relatively steady flow of fluid (e.g., a relatively uniform flow rate, a relatively constant flow rate, a relatively consistent flow rate, etc.) through a fluid end section of a reciprocating pump assembly. Certain embodiments of the disclosure may reduce flow rate surges of a reciprocating pump assembly. 
     Referring to  FIG. 1 , an illustrative embodiment of a reciprocating pump assembly  100  is presented. The reciprocating pump assembly  100  includes a power end section  102  and a pair of fluid end sections  104  operably coupled thereto. Specifically, the reciprocating pump assembly  100  includes a fluid end section  104   a  operably coupled to the power end section  102  and a fluid end section  104   b  operably coupled to the power end section  102 . The power end section  102  includes a housing  106  in which a linear actuator  120  is disposed. Each of the fluid end sections  104   a  and  104   b  includes a fluid cylinder  108  (sometimes referred to as a ‘fluid end block_ or a ‘cylinder section_), which in the exemplary embodiments is connected to the housing  106  via a plurality of stay rods  110   a ,  110   b ,  110   c , and  110   d . Other structures may be used to connect the fluid end section  104  to the housing  106  in addition or alternatively to the stay rods  110   a ,  110   b ,  110   c , and/or  110   d.    
     The linear actuator  120  is operatively connected to plungers  114  of the plunger rod assemblies  112 . Specifically, the linear actuator  120  is operatively connected to a plunger  114   a  of a plunger rod assembly  112   a  via a plunger rod  113   a;  and the linear actuator  120  is operatively connected to a plunger  114   b  of a plunger rod assembly  112   b  via a plunger rod  113   b . In operation, the linear actuator  120  reciprocates plunger rod assemblies  112  between the power end section  102  and the fluid end sections  104   a  and  104   b  to thereby pump (i.e., move) fluid through the fluid cylinders  108  of the fluid end sections  104   a  and  104   b , as will be described in more detail below. 
     According to some embodiments, the reciprocating pump assembly  100  is freestanding on the ground, mounted to a trailer for towing between operational sites, mounted to a skid, loaded on a manifold, otherwise transported, and/or the like. The reciprocating pump assembly  100  is not limited to frac pumps. Rather, the embodiments disclosed herein may be used with any other type of pump that includes a plunger rod assembly. 
       FIG. 2  illustrates one of the fluid end sections  104  (e.g., the fluid end section  104   a , the fluid end section  104   b , etc.) of the reciprocating pump assembly  100  according to an exemplary embodiment. Referring now to  FIG. 2 , the fluid cylinder  108  of the fluid end section  104  includes a pressure chamber  118  and a plunger bore  116  that fluidly communicates with the pressure chamber  118 . The plunger  114  of the plunger rod assembly  112  is held within (e.g., extends through, etc.) the plunger bore  116  such that the plunger  114  extends into the pressure chamber  118 . At least the plunger bore  116 , the pressure chamber  118 , and the plunger  114  together may be characterized as a ‘plunger throw._ According to some embodiments, the reciprocating pump assembly  100  includes three plunger throws (i.e., a triplex pump assembly); however, in other embodiments, the reciprocating pump assembly  100  includes a greater or fewer number of plunger throws (e.g., only a single plunger throw, etc.). 
     As shown in  FIG. 2 , the fluid cylinder  108  includes inlet and outlet fluid passages  120  and  122 , respectively, formed therein. Optionally, the inlet and outlet fluid passages  120  and  122 , respectively, are coaxially disposed along a fluid passage axis  124 , for example as is shown in  FIG. 2 . Fluid is adapted to flow through the inlet and outlet fluid passages  120  and  122 , respectively, and along the fluid passage axis  124 . An inlet valve assembly  126  is disposed in the inlet fluid passage  120  and an outlet valve assembly  128  is disposed in the outlet fluid passage  122 . In the exemplary embodiments, the valve assemblies  126  and  128  are spring-loaded, which, as described in greater detail below, are actuated by at least a predetermined differential pressure across each of the valve assemblies  126  and  128 . 
     The inlet valve assembly  126  includes a valve seat  130  and a valve member  132  that is configured to be sealingly engaged therewith. The valve seat  130  includes an inlet valve bore  134  that extends along a valve seat axis  136  that is coaxial with the fluid passage axis  124  when the inlet valve assembly  126  is disposed in the inlet fluid passage  120 . The valve seat  130  further includes a shoulder  138 , which in the exemplary embodiment is tapered (i.e., extends at an oblique angle relative to the valve seat axis  136 ). In some other examples, the shoulder  138  of the valve seat  130  extends approximately perpendicular to the valve seat axis  136 . 
     The valve member  132  includes a valve head  142  and a tail segment  140  extending from the valve head  142 . As shown in  FIG. 2 , the tail segment  140  is received within the inlet valve bore  134  of the valve seat  130  when the inlet valve assembly  126  is assembled as shown. The valve head  142  includes a seal  144 . The valve head  142  of the valve member  132  is moveable relative to the valve seat  130  along the valve seat axis  136  between an open position and a closed position. In the closed position of the valve member  132 , the seal  144  of the valve head  142  sealingly engages the valve seat  130  to prevent fluid flow through the inlet valve assembly  126 . In the exemplary embodiments, the valve member  132  is engaged and otherwise biased by a spring  146 , which, as discussed in greater detail below, biases the valve member  132  to the closed position. 
     According to certain embodiments, at least a portion of the valve seat  130  and/or at least a portion of the valve head  142  is formed from stainless steel. But, the valve seat  130  and/or the valve head  142  may be formed from any other material in addition or alternative to stainless steel. Although shown herein as being a helical (i.e., coil) compression spring, additionally or alternatively the spring  146  can include any type of spring, such as, but not limited to, a flat spring, a machined spring, a serpentine spring, a torsion spring, a tension spring, a constant spring, a variable spring, a variable stiffness spring, a leaf spring, a cantilever spring, a volute spring, a v-spring, and/or the like. 
     In the embodiments illustrated herein, the outlet valve assembly  128  is substantially similar to the inlet valve assembly  126  and therefore will not be described in further detail herein. 
     In operation, the plunger  114  reciprocates within the plunger bore  116  for movement into and out of the pressure chamber  118 . That is, the plunger  114  moves back and forth horizontally, as viewed in  FIG. 2 , away from and towards the fluid passage axis  124 . As will be described below, the linear actuator  120  ( FIG. 1 ) moves the plunger  114  toward and away from the fluid passage axis  124 . Movement of the plunger  114  in the direction of arrow  148  away from the fluid passage axis  124  and out of the pressure chamber  118  will be referred to herein as the suction stroke of the plunger  114 . As the plunger  114  moves along the suction stroke, the inlet valve assembly  126  is opened to the open position of the valve member  132 . More particularly, as the plunger  114  moves away from the fluid passage axis  124  in the direction of arrow  148 , the pressure inside the pressure chamber  118  decreases, creating a differential pressure across the inlet valve assembly  126  and causing the valve head  142  of the valve member  132  to move (relative to the valve seat  130 ) upward, as viewed in  FIG. 2 , along the valve seat axis  136  in the direction of arrow  150 . As a result of the upward movement of the valve head  142  of the valve member  132  along the valve seat axis  136 , the spring  146  is compressed and the valve head  142  of the valve member  132  separates from the shoulder  138  of the valve seat  130  to move the valve member  132  to the open position. In the open position of the valve member  132 , fluid entering through an inlet  152  of the inlet fluid passage  120  flows along the fluid passage axis  124  and through the inlet valve assembly  126 , being drawn into the pressure chamber  118 . To flow through the inlet valve assembly  126 , the fluid flows through the inlet valve bore  134  and along the valve seat axis  136 . The inlet  152  defines a suction port of the fluid end section  104 . 
     During the fluid flow through the inlet valve assembly  126  and into the pressure chamber  118 , the outlet valve assembly  128  is in a closed position wherein a seal  154  of a valve member  156  of the outlet valve assembly  128  is sealingly engaged with a shoulder  158  of a valve seat  160  of the outlet valve assembly  128 . Fluid continues to be drawn into the pressure chamber  118  until the plunger  114  is at the end of the suction stroke of the plunger  114 , wherein the plunger  114  is at the farthest point from the fluid passage axis  124  of the range of motion of the plunger  114 . 
     At the end of the suction stroke of the plunger  114 , the differential pressure across the inlet valve assembly  126  is such that the spring  146  of the inlet valve assembly  126  begins to decompress and extend, forcing the valve head  142  of the valve member  132  of the inlet valve assembly  126  to move (relative to the valve seat  130 ) downward, as viewed in  FIG. 2 , along the valve seat axis  136  in the direction of arrow  162 . As a result, the inlet valve assembly  126  moves to the closed position of the valve member  132  wherein the valve head  142  of the valve member  132  is sealingly engaged with the valve seat  130 . 
     Movement of the plunger  114  in the direction of arrow  164  toward the fluid passage axis  124  and into the pressure chamber  118  will be referred to herein as the discharge stroke of the plunger  114 . As the plunger  114  moves along the discharge stroke into the pressure chamber  118 , the pressure within the pressure chamber  118  increases. The pressure within the pressure chamber  118  increases until the differential pressure across the outlet valve assembly  128  exceeds a predetermined set point, at which point the outlet valve assembly  128  opens and permits fluid to flow out of the pressure chamber  118  along the fluid passage axis  124 , being discharged through an outlet  165  of the fluid end section  104 . During the discharge stroke of the plunger  114 , the valve member  132  of the inlet valve assembly  126  is positioned in the closed position wherein the valve head  142  of the valve member  132  is sealingly engaged with the valve seat  130 . The outlet  165  of the fluid end section  104  defines a discharge port of the fluid end section  104 . 
     The fluid cylinder  108  of the fluid end section  104  of the reciprocating pump assembly  100  includes an access port  166 . The access port  166  is defined by an opening that extends through a body  168  of the fluid cylinder  108  to provide access to the pressure chamber  118  and thereby internal components of the fluid cylinder  108  (e.g., the inlet valve assembly  126 , the outlet valve assembly  128 , the plunger  114 , etc.) for service (e.g., maintenance, replacement, etc.) thereof. The access port  166  of the fluid cylinder  108  is closed using a suction cover assembly  170  to seal the pressure chamber  118  of the fluid cylinder  108  at the access port  166 . 
     The plunger bore  116  is defined by an inner wall  172  of the body  168  of the fluid cylinder  108 . In other words, the plunger bore  116  includes the inner wall  172 . As shown in  FIG. 2 , the plunger bore  116  includes a packing segment  174 . The plunger rod assembly  112  includes packing  176  that is received within the packing segment  174  of the plunger bore  116  such that the packing  176  extends radially between the plunger  114  and the inner wall  172  to facilitate sealing the plunger  114  within the plunger bore  116  of the fluid cylinder  108 . 
     The illustrated fluid end section  104  is but one example of a fluid end section that may be operably coupled to the power end section  102  ( FIG. 1 ) of the reciprocating pump assembly  100 . Other fluid end sections may additionally or alternatively be used. For example, the fluid end section  104  shown in  FIG. 2  includes only a single one of the pressure chamber  118 . In other embodiments, one or more of the fluid end sections disclosed herein includes two or more pressure chambers such that the fluid end section(s) provides a manifold having multiple suction and discharge ports. 
     Referring again to  FIG. 1 , and as briefly described above, the linear actuator  120  is operatively connected to the plunger  114   a  of the plunger rod assembly  112   a  via the plunger rod  113   a  such that the linear actuator  120  is configured to reciprocate the plunger  114   a  within the plunger bore  116  ( FIG. 2 ) of the fluid end section  104   a  during operation of the reciprocating pump assembly  100  to thereby pump fluid through the fluid end section  104   a . Specifically, the linear actuator  120  is configured to move the plunger rod  113   a  along an axis  178  in two opposite directions  180  and  182  toward and away, respectively, from the fluid end section  104   a , as is shown in  FIG. 1 . Accordingly, the linear actuator  120  is configured to move the plunger  114   a  along the axis  178  in the opposite directions  180  and  182  to thereby reciprocate the plunger  114   a  within the plunger bore  116  along the axis  178 . Movement of the plunger  114   a  along the axis  178  in the direction  182  draws fluid into a suction port  152   a  of the fluid end section  104   a , while movement of the plunger  114   a  along the axis  178  in the direction  180  discharges fluid through a discharge port  165   a  of the fluid end section  104   a . Accordingly, the linear actuator  120  is configured to pump fluid through the fluid end section  104   a  by reciprocating the plunger  114   a  within the plunger bore  116  of the fluid end section  104   a.    
     As is also briefly described above, the linear actuator  120  is operatively connected to the plunger  114   b  of the plunger rod assembly  112   b  via the plunger rod  113   b  such that the linear actuator  120  is configured to reciprocate the plunger  114   b  within the plunger bore  116  of the fluid end section  104   b  during operation of the reciprocating pump assembly  100  to thereby pump fluid through the fluid end section  104   b . Specifically, the linear actuator  120  is configured to move the plunger rod  113   b  along an axis  184  in two opposite directions  164  and  148  toward and away, respectively, from the fluid end section  104   b . The linear actuator  120  thus is configured to move the plunger  114   b  along the axis  184  in the opposite directions  148  and  164  to thereby reciprocate the plunger  114   b  within the plunger bore  116  along the axis  184 . Movement of the plunger  114   b  along the axis  184  in the direction  148  draws fluid into a suction port  152   b  of the fluid end section  104   a , while movement of the plunger  114   b  along the axis  184  in the direction  164  discharges fluid through a discharge port  165   b  of the fluid end section  104   b . Accordingly, the linear actuator  120  is configured to pump fluid through the fluid end section  104   b  by reciprocating the plunger  114   b  within the plunger bore  116  of the fluid end section  104   b.    
     In the exemplary embodiment, the axes  178  and  184  are aligned with each other such that the plunger rod assemblies  112   a  and  112   b  are coaxially aligned with each other. In other embodiments, the axes  178  are not aligned with each other such that the plunger rod assemblies  112   a  and  112   b  are not coaxially aligned. Moreover, the exemplary embodiment illustrates an embodiment wherein the linear actuator  120 : (1) moves the plunger rod assembly  112   a  in the direction  182  to draw fluid into the fluid end section  104   a  while simultaneously moving the plunger rod assembly  112   b  in the direction  164  to discharge fluid from the fluid end section  104   b ; and (2) moves the plunger rod assembly  112   a  in the direction  180  to discharge fluid from the fluid end section  104   a  while simultaneously moving the plunger rod assembly  112   b  in the direction  148  to draw fluid into the fluid end section  104   b . In other words, in the exemplary embodiment the linear actuator  120  simultaneously moves the plunger rod assemblies  112   a  and  112   b  in the same direction. In other embodiments, the linear actuator  120  simultaneously moves the plunger rod assemblies  112   a  and  112   b  in opposite directions (i.e., the plunger rod assemblies  112   a  and  112   b  are moved in reciprocal synchronization). Specifically, in some other embodiments, the linear actuator  120 : (1) moves the plunger rod assembly  112   a  in the direction  182  to draw fluid into the fluid end section  104   a  while simultaneously moving the plunger rod assembly  112   b  in the direction  148  to draw fluid into the fluid end section  104   b ; and (2) moves the plunger rod assembly  112   a  in the direction  180  to discharge fluid from the fluid end section  104   a  while simultaneously moving the plunger rod assembly  112   b  in the direction  164  to discharge fluid from the fluid end section  104   b.    
     Although the exemplary embodiment illustrates a single linear actuator  120  that moves both the plunger rod assembly  112   a  and the plunger rod assembly  112   b , other embodiments may include two or more linear actuators  120 . For example, the reciprocating pump assembly  100  may include a first linear actuator  120  that is operatively connected to the plunger rod assembly  112   a  for reciprocating the plunger  114   a  within the plunger bore  116  of the fluid end section  104   a  and a second linear actuator  120  that is operatively connected to the plunger rod assembly  112   b  for reciprocating the plunger  114   b  within the plunger bore  116  of the fluid end section  104   b.  In another example, the reciprocating pump assembly  100  includes a first linear actuator  120  that is operatively connected to the plunger rod assemblies  112   a  and  112   b  for moving the plungers  114   a  and  114   b  in the respective directions  182  and  164  and a second linear actuator  120  that is operatively connected to the plunger rod assemblies  112   a  and  112   b  for moving the plungers  114   a  and  114   b  in the respective directions  180  and  148 . 
     In the exemplary embodiment, the linear actuator  120  is housed within the housing  106  of the power end section  102  of the reciprocating pump assembly  100  such that the power end section  102  includes the linear actuator  120 . But, the linear actuator  120  additionally or alternatively may be: (1) housed within the fluid end section  104   a ; (2) housed within the fluid end section  104   b ; and/or (3) positioned external to the power end section  102 , the fluid end section  104   a , and/or the fluid end section  104   b.    
     Each linear actuator  120  may include any type of linear actuator, such as, but not limited to, a mechanical linear actuator, an electrical linear actuator, an electro-mechanical linear actuator, a magnetic linear actuator, a hydraulic linear actuator, a pneumatic linear actuator, a screw-type actuator, a ball screw, a lead screw, a rotary screw, a screw jack, a roller screw, a hydraulic piston, a linear motor, a wheel and axle actuator, a telescoping linear actuator, a solenoid, and/or a servo. 
     In some embodiments, an actuator driver  122  is operatively connected to the linear actuator  120  for controlling and/or driving (e.g., powering, etc.) operation of the linear actuator  120 . The actuator driver  122  may include any type of driver, such as, but not limited to, an engine, an electrical motor, a turbine, a hydraulic pump (e.g., hydrostatic, hydrodynamic, etc.), a pneumatic pump, a mechanical pump, an electrical power source, an electrical circuit, an electro-mechanical drive system, an electric pump, a magnetic drive system, a processor, a mechanical drive system, a pneumatic drive system, a hydraulic drive system, software (e.g., computer-executable instructions stored on a non-transitory computer-storage memory and executed by one or more processors, such as, but not limited to, a local processor, a remote processor, and/or the like, etc.), and/or the like. 
     The linear actuator  120  disclosed herein may enable the stroke length of the plungers  114   a  and  114   b  to be increased, for example as compared to at least some known reciprocating pump assemblies that utilize one or more crankshafts to reciprocate a plunger within a fluid end section. Moreover, the linear actuator  120  disclosed herein may enable the reciprocating pump assembly to provide a relatively steady flow of fluid (e.g., a relatively uniform flow rate, a relatively constant flow rate, a relatively consistent flow rate, etc.) through the fluid end sections  104   a  and  104   b . For example, the action of reciprocating the plungers  114  within the plunger bores  116  completes pumping cycles in which fluid is discharged from a first of the fluid end sections (e.g., the fluid end section  104   a  or 104b, etc.) while also drawn into a second of the fluid end sections (e.g., the fluid end section  104   a  or  104   b , etc.) and then discharged out of the second fluid end section while also drawn into the first fluid end section. Such pumping cycles can be continuously (or at least repeatedly) performed to create a relatively steady flow rate of fluid from the reciprocating pump assembly  100  (e.g., for fracking operations, etc.), which for example may reduce flow rate surges of the reciprocating pump assembly  100 . In some embodiments, a controller (not shown in  FIG. 1 ; e.g., the controller  200  shown in  FIG. 3 , etc.) is provided (e.g., as a component of the actuator driver  122 , etc.) that operatively connected to the linear actuator  120  such that the controller is configured to electronically control a flow rate of fluid through the fluid end sections  104   a  and  104   b.    
     In some embodiments, two or more of the reciprocating pump assemblies  100  can be combined, for example to facilitate providing a steady flow of fluid. For example, and referring now to  FIG. 3 , multiple reciprocating pump assemblies  100   a - n  are combined together such that linear actuators  120   a - n  thereof control fluid being pumped into and out of fluid end sections  104  thereof, for example in a manner that produces a relatively steady flow rate of fluid. In some embodiments, failure of a linear actuator  120  and/or another component of a reciprocating pump assembly  100  (e.g., the reciprocating pump assembly  100   a , the reciprocating pump assembly  100   n , etc.) may be compensated for by one or more of the other reciprocating pump assemblies  100  (e.g., the reciprocating pump assembly  100   a , the reciprocating pump assembly  100   n , etc.). While only two reciprocating pump assemblies  100   a  and  100   n  are shown, any number may be used, for example two, three, four, five, six, seven, eight, nine, or ten or more reciprocating pump assemblies  100 . 
     In some embodiments, a controller  200  is operatively connected to the linear actuators  120   a - n  such that the controller  200  is configured to synchronize the various reciprocating pump assemblies  100  to draw and discharge fluid, for example either synchronously and/or at different times that are offset from each other. For example, the controller  200  may be configured to offset the duty cycle of the fluid end sections  104   a  and  104   b  from the duty cycle of the fluid end sections  104   c  and  104   d  shown in  FIG. 3 . Specifically, and for example, combining multiple reciprocating pump assemblies  100  as is shown in  FIG. 3  may enable an operator to offset the linear actuation of plunger rod assemblies  112   a ,  112   b ,  112   c , and/or  112   d , and thus the plungers  114   a ,  114   b ,  114   c , and/or  114   d  in such a way that causes discharging of fluid from each reciprocating pump assembly  100   a  and  100   n  at optimal times, for example to produces a relatively steady flow of fluid (e.g., distributed to well operations, etc.). Examples of timing offsets for multiple reciprocating pump assemblies  100  include, but are not limited to, an offset by one-half of the duty cycle between two or more reciprocating pump assemblies  100 , an offset by one-third of the duty cycle between two or more reciprocating pump assemblies  100 , an offset by one-quarter of the duty cycle between two or more reciprocating pump assemblies  100 , and/or the like. 
     The controller  200  may be any type of controller, such as, but not limited to, a mechanical controller, an electrical controller, an electro-mechanical controller, a software controller, and/or the like. 
       FIG. 4  illustrates a chart  300  showing the combined and individual flow rates of multiple reciprocating pump assemblies  100  with two different banks of three cylinders, according to some embodiments. The following charts illustrate additional pumping details for such a configuration. The embodiment illustrated in  FIG. 4  depicts no delay (or offset) between the various reciprocating pump assemblies  100 . 
     
       
         
           
               
            
               
                   
               
               
                 Multi Cylinders with Trapezoidal flow rate curves, Haversine ramp 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Cycle 
                 Time 
                 Total 
                 Cyl 1 
                 Cyl 2 
                 Cyl 3 
                 Cyl 4 
                 Cyl 5 
                 Cyl 6 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 0.000 
                 0.000 
                 144.585 
                 0.000 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.021 
                 0.138 
                 144.585 
                 1.101 
                 27.816 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.042 
                 0.275 
                 144.585 
                 4.235 
                 24.682 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.063 
                 0.413 
                 144.585 
                 8.925 
                 19.991 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.083 
                 0.550 
                 144.585 
                 14.458 
                 14.458 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.104 
                 0.688 
                 144.585 
                 19.991 
                 8.925 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.125 
                 0.825 
                 144.585 
                 24.682 
                 4.235 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.146 
                 0.963 
                 144.585 
                 27.816 
                 1.101 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.167 
                 1.100 
                 144.585 
                 28.917 
                 0.000 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.188 
                 1.238 
                 144.585 
                 28.917 
                 1.101 
                 27.816 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.208 
                 1.375 
                 144.585 
                 28.917 
                 4.235 
                 24.682 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.229 
                 1.513 
                 144.585 
                 28.917 
                 8.925 
                 19.991 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.250 
                 1.650 
                 144.585 
                 28.917 
                 14.458 
                 14.458 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.271 
                 1.788 
                 144.585 
                 28.917 
                 19.991 
                 8.925 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.292 
                 1.925 
                 144.585 
                 28.917 
                 24.682 
                 4.235 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.313 
                 2.063 
                 144.585 
                 28.917 
                 27.816 
                 1.101 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.333 
                 2.200 
                 144.585 
                 28.917 
                 28.917 
                 0.000 
                 28.917 
                 28.917 
                 28.917 
               
               
                 0.354 
                 2.338 
                 144.585 
                 28.917 
                 28.917 
                 1.101 
                 27.816 
                 28.917 
                 28.917 
               
               
                 0.375 
                 2.475 
                 144.585 
                 28.917 
                 28.917 
                 4.235 
                 24.682 
                 28.917 
                 28.917 
               
               
                 0.396 
                 2.613 
                 144.585 
                 28.917 
                 28.917 
                 8.925 
                 19.991 
                 28.917 
                 28.917 
               
               
                 0.417 
                 2.750 
                 144.585 
                 28.917 
                 28.917 
                 14.458 
                 14.458 
                 28.917 
                 28.917 
               
               
                 0.438 
                 2.888 
                 144.585 
                 28.917 
                 28.917 
                 19.991 
                 8.925 
                 28.917 
                 28.917 
               
               
                 0.458 
                 3.025 
                 144.585 
                 28.917 
                 28.917 
                 24.682 
                 4.235 
                 28.917 
                 28.917 
               
               
                 0.479 
                 3.163 
                 144.585 
                 28.917 
                 28.917 
                 27.816 
                 1.101 
                 28.917 
                 28.917 
               
               
                 0.500 
                 3.300 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 0.000 
                 28.917 
                 28.917 
               
               
                 0.521 
                 3.438 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 1.101 
                 27.816 
                 28.917 
               
               
                 0.542 
                 3.575 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 4.235 
                 24.682 
                 28.917 
               
               
                 0.563 
                 3.713 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 8.925 
                 19.991 
                 28.917 
               
               
                 0.583 
                 3.850 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 14.458 
                 14.458 
                 28.917 
               
               
                 0.604 
                 3.988 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 19.991 
                 8.925 
                 28.917 
               
               
                 0.625 
                 4.125 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 24.682 
                 4.235 
                 28.917 
               
               
                 0.646 
                 4.263 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 27.816 
                 1.101 
                 28.917 
               
               
                 0.667 
                 4.400 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 0.000 
                 28.917 
               
               
                 0.688 
                 4.538 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 1.101 
                 27.816 
               
               
                 0.708 
                 4.675 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 4.235 
                 24.682 
               
               
                 0.729 
                 4.813 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 8.925 
                 19.991 
               
               
                 0.750 
                 4.950 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 14.458 
                 14.458 
               
               
                 0.771 
                 5.088 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 19.991 
                 8.925 
               
               
                 0.792 
                 5.225 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 24.682 
                 4.235 
               
               
                 0.813 
                 5.363 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 27.816 
                 1.101 
               
               
                 0.833 
                 5.500 
                 144.585 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 0.000 
               
               
                 0.854 
                 5.638 
                 144.585 
                 27.816 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 1.101 
               
               
                 0.875 
                 5.775 
                 144.585 
                 24.682 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 4.235 
               
               
                 0.896 
                 5.913 
                 144.585 
                 19.991 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 8.925 
               
               
                 0.917 
                 6.050 
                 144.585 
                 14.458 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 14.458 
               
               
                 0.938 
                 6.188 
                 144.585 
                 8.925 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 19.991 
               
               
                 0.958 
                 6.325 
                 144.585 
                 4.235 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 24.682 
               
               
                 0.979 
                 6.463 
                 144.585 
                 1.101 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 27.816 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
                 28.917 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
            
               
                   
               
               
                 Hydraulic Horsepower Table 10 in stroke 
               
               
                 4.5 in plunger 12 kpsi pressure 
               
            
           
           
               
               
            
               
                   
                 Cylinders that determine Profile 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                   
                 263 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
                 8 
                 9 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 
                   
                 
                 1 
                 263 
                 263 
                 263 
                 263 
                 263 
                 263 
                 263 
                 263 
               
               
                   
                 2 
                 526 
                 526 
                 526 
                 526 
                 526 
                 526 
                 526 
                 526 
               
               
                   
                 3 
                 789 
                 789 
                 789 
                 789 
                 789 
                 789 
                 789 
                 789 
               
               
                   
                 4 
                 1052 
                 1052 
                 1052 
                 1052 
                 1052 
                 1052 
                 1052 
                 1052 
               
               
                   
                 5 
                 1314 
                 1314 
                 1314 
                 1314 
                 1314 
                 1314 
                 1314 
                 1314 
               
               
                   
                 6 
                 1577 
                 1577 
                 1577 
                 1577 
                 1577 
                 1577 
                 1577 
                 1577 
               
               
                   
                 7 
                 1840 
                 1840 
                 1840 
                 1840 
                 1840 
                 1840 
                 1840 
                 1840 
               
               
                   
                 8 
                 2103 
                 2103 
                 2103 
                 2103 
                 2103 
                 2103 
                 2103 
                 2103 
               
               
                   
                 9 
                 2366 
                 2366 
                 2366 
                 2366 
                 2366 
                 2366 
                 2366 
                 2366 
               
               
                   
               
               
                     indicates data missing or illegible when filed 
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Number of Cylinders C 
                 6 
                 0.833333 
               
               
                   
                 Multiple of synched Cylinders 
                 1 
               
               
                   
                 Stroke 
                 10 
                 in 
               
               
                   
                 Ramp Time t r   
                 1.1 
                 sec 
               
               
                   
                 Plunger Diameter 
                 4.5 
                 in 
               
               
                   
                 Intensifier Ratio 
                 3 
                 :1 
               
               
                   
                 Job Pressure 
                 12000 
                 psi 
               
               
                   
                 Dwell Time t d   
                 4.4 
               
               
                   
                 Maximum Pressure 
                 15000 
                 psi 
               
               
                   
                 T 
                 6.6 
                 sec 
               
               
                   
                 Cylinder Rod Length 
                 42 
                 in 
               
               
                   
                 Cylinder Rod Modulus 
                 2.90E+07 
                 psi 
               
               
                   
                 Min Cylinder Rod diameter 
                 4.00 
                 in 
               
               
                   
                 Actual Cylinder Rod diameter 
                 4.50 
                 in 
               
               
                   
                 Cylinder Piston Diameter 
                 9.00 
                 in 
               
               
                   
                 Job Cylinder Pressure 
                 4000 
                 psi 
               
               
                   
                 Stroke Volume per stroke per 
                 159 
                 in 3   
               
               
                   
                 cylinder 
               
               
                   
                 Volume rate per cylinder 
                 28.91693 
                 in 3 /sec 
               
               
                   
                 Volume rate all cylinders 
                 144.5847 
                 in 3 /sec 
               
               
                   
                 A for Plunger 
                 28.91693 
                 in 3 /sec 
               
               
                   
                 A for Hydraulic Piston 
                 86.7508 
                 in 3 /sec 
               
               
                   
                 Rod Load 
                 190851.8 
                 lbf 
               
               
                   
                 Max Rod Load 
                 238564.7 
                 lbf 
               
               
                   
                   
               
            
           
         
       
     
       FIG. 5  illustrates a chart  400  showing the combined and individual flow rates of multiple reciprocating pump assemblies  100  with two different banks of three cylinders, according to some embodiments. The following charts illustrate additional pumping details for such a configuration. The embodiment of  FIG. 5  depicts a ramp-up delay (or offset) between the various reciprocating pump assemblies  100 . 
     
       
         
           
               
            
               
                   
               
               
                 Multi Cylinders with Trapezoidal flow rate curves, Haversine ramp 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Cycle 
                 Time 
                 Total 
                 Cyl 1 
                 Cyl 2 
                 Cyl 3 
                 Cyl 4 
                 Cyl 5 
                 Cyl 6 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 0.000 
                 0.000 
                 144.585 
                 0.000 
                 0.000 
                 36.146 
                 36.146 
                 36.146 
                 36.146 
               
               
                 0.021 
                 0.138 
                 144.585 
                 1.376 
                 0.000 
                 34.770 
                 36.146 
                 36.146 
                 36.146 
               
               
                 0.042 
                 0.275 
                 144.585 
                 5.293 
                 0.000 
                 30.853 
                 36.146 
                 36.146 
                 36.146 
               
               
                 0.063 
                 0.413 
                 144.585 
                 11.157 
                 0.000 
                 24.989 
                 36.146 
                 36.146 
                 36.146 
               
               
                 0.083 
                 0.550 
                 144.585 
                 18.073 
                 0.000 
                 18.073 
                 36.146 
                 36.146 
                 36.146 
               
               
                 0.104 
                 0.688 
                 144.585 
                 24.989 
                 0.000 
                 11.157 
                 36.146 
                 36.146 
                 36.146 
               
               
                 0.125 
                 0.825 
                 144.585 
                 30.853 
                 0.000 
                 5.293 
                 36.146 
                 36.146 
                 36.146 
               
               
                 0.146 
                 0.963 
                 144.585 
                 34.770 
                 0.000 
                 1.376 
                 36.146 
                 36.146 
                 36.146 
               
               
                 0.167 
                 1.100 
                 144.585 
                 36.146 
                 0.000 
                 0.000 
                 36.146 
                 36.146 
                 36.146 
               
               
                 0.188 
                 1.238 
                 144.585 
                 36.146 
                 1.376 
                 0.000 
                 34.770 
                 36.146 
                 36.146 
               
               
                 0.208 
                 1.375 
                 144.585 
                 36.146 
                 5.293 
                 0.000 
                 30.853 
                 36.146 
                 36.146 
               
               
                 0.229 
                 1.513 
                 144.585 
                 36.146 
                 11.157 
                 0.000 
                 24.989 
                 36.146 
                 36.146 
               
               
                 0.250 
                 1.650 
                 144.585 
                 36.146 
                 18.073 
                 0.000 
                 18.073 
                 36.146 
                 36.146 
               
               
                 0.271 
                 1.788 
                 144.585 
                 36.146 
                 24.989 
                 0.000 
                 11.157 
                 36.146 
                 36.146 
               
               
                 0.292 
                 1.925 
                 144.585 
                 36.146 
                 30.853 
                 0.000 
                 5.293 
                 36.146 
                 36.146 
               
               
                 0.313 
                 2.063 
                 144.585 
                 36.146 
                 34.770 
                 0.000 
                 1.376 
                 36.146 
                 36.146 
               
               
                 0.333 
                 2.200 
                 144.585 
                 36.146 
                 36.146 
                 0.000 
                 0.000 
                 36.146 
                 36.146 
               
               
                 0.354 
                 2.338 
                 144.585 
                 36.146 
                 36.146 
                 1.376 
                 0.000 
                 34.770 
                 36.146 
               
               
                 0.375 
                 2.475 
                 144.585 
                 36.146 
                 36.146 
                 5.293 
                 0.000 
                 30.853 
                 36.146 
               
               
                 0.396 
                 2.613 
                 144.585 
                 36.146 
                 36.146 
                 11.157 
                 0.000 
                 24.989 
                 36.146 
               
               
                 0.417 
                 2.750 
                 144.585 
                 36.146 
                 36.146 
                 18.073 
                 0.000 
                 18.073 
                 36.146 
               
               
                 0.438 
                 2.888 
                 144.585 
                 36.146 
                 36.146 
                 24.989 
                 0.000 
                 11.157 
                 36.146 
               
               
                 0.458 
                 3.025 
                 144.585 
                 36.146 
                 36.146 
                 30.853 
                 0.000 
                 5.293 
                 36.146 
               
               
                 0.479 
                 3.163 
                 144.585 
                 36.146 
                 36.146 
                 34.770 
                 0.000 
                 1.376 
                 36.146 
               
               
                 0.500 
                 3.300 
                 144.585 
                 36.146 
                 36.146 
                 36.146 
                 0.000 
                 0.000 
                 36.146 
               
               
                 0.521 
                 3.438 
                 144.585 
                 36.146 
                 36.146 
                 36.146 
                 1.376 
                 0.000 
                 34.770 
               
               
                 0.542 
                 3.575 
                 144.585 
                 36.146 
                 36.146 
                 36.146 
                 5.293 
                 0.000 
                 30.853 
               
               
                 0.563 
                 3.713 
                 144.585 
                 36.146 
                 36.146 
                 36.146 
                 11.157 
                 0.000 
                 24.989 
               
               
                 0.583 
                 3.850 
                 144.585 
                 36.146 
                 36.146 
                 36.146 
                 18.073 
                 0.000 
                 18.073 
               
               
                 0.604 
                 3.988 
                 144.585 
                 36.146 
                 36.146 
                 36.146 
                 24.989 
                 0.000 
                 11.157 
               
               
                 0.625 
                 4.125 
                 144.585 
                 36.146 
                 36.146 
                 36.146 
                 30.853 
                 0.000 
                 5.293 
               
               
                 0.646 
                 4.263 
                 144.585 
                 36.146 
                 36.146 
                 36.146 
                 34.770 
                 0.000 
                 1.376 
               
               
                 0.667 
                 4.400 
                 144.585 
                 36.146 
                 36.146 
                 36.146 
                 36.146 
                 0.000 
                 0.000 
               
               
                 0.688 
                 4.538 
                 144.585 
                 34.770 
                 36.146 
                 36.146 
                 36.146 
                 1.376 
                 0.000 
               
               
                 0.708 
                 4.675 
                 144.585 
                 30.853 
                 36.146 
                 36.146 
                 36.146 
                 5.293 
                 0.000 
               
               
                 0.729 
                 4.813 
                 144.585 
                 24.989 
                 36.146 
                 36.146 
                 36.146 
                 11.157 
                 0.000 
               
               
                 0.750 
                 4.950 
                 144.585 
                 18.073 
                 36.146 
                 36.146 
                 36.146 
                 18.073 
                 0.000 
               
               
                 0.771 
                 5.088 
                 144.585 
                 11.157 
                 36.146 
                 36.146 
                 36.146 
                 24.989 
                 0.000 
               
               
                 0.792 
                 5.225 
                 144.585 
                 5.293 
                 36.146 
                 36.146 
                 36.146 
                 30.853 
                 0.000 
               
               
                 0.813 
                 5.363 
                 144.585 
                 1.376 
                 36.146 
                 36.146 
                 36.146 
                 34.770 
                 0.000 
               
               
                 0.833 
                 5.500 
                 144.585 
                 0.000 
                 36.146 
                 36.146 
                 36.146 
                 36.146 
                 0.000 
               
               
                 0.854 
                 5.638 
                 144.585 
                 0.000 
                 34.770 
                 36.146 
                 36.146 
                 36.146 
                 1.376 
               
               
                 0.875 
                 5.775 
                 144.585 
                 0.000 
                 30.853 
                 36.146 
                 36.146 
                 36.146 
                 5.293 
               
               
                 0.896 
                 5.913 
                 144.585 
                 0.000 
                 24.989 
                 36.146 
                 36.146 
                 36.146 
                 11.157 
               
               
                 0.917 
                 6.050 
                 144.585 
                 0.000 
                 18.073 
                 36.146 
                 36.146 
                 36.146 
                 18.073 
               
               
                 0.938 
                 6.188 
                 144.585 
                 0.000 
                 11.157 
                 36.146 
                 36.146 
                 36.146 
                 24.989 
               
               
                 0.958 
                 6.325 
                 144.585 
                 0.000 
                 5.293 
                 36.146 
                 36.146 
                 36.146 
                 30.853 
               
               
                 0.979 
                 6.463 
                 144.585 
                 0.000 
                 1.376 
                 36.146 
                 36.146 
                 36.146 
                 34.770 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 0.000 
                 36.146 
                 36.146 
                 36.146 
                 36.146 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 0.000 
                 36.146 
                 36.146 
                 36.146 
                 36.146 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 0.000 
                 36.146 
                 36.146 
                 36.146 
                 36.146 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 0.000 
                 36.146 
                 36.146 
                 36.146 
                 36.146 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 0.000 
                 36.146 
                 36.146 
                 36.146 
                 36.146 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 0.000 
                 36.146 
                 36.146 
                 36.146 
                 36.146 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 0.000 
                 36.146 
                 36.146 
                 36.146 
                 36.146 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 0.000 
                 36.146 
                 36.146 
                 36.146 
                 36.146 
               
               
                 1.000 
                 6.600 
                 144.585 
                 0.000 
                 0.000 
                 36.146 
                 36.146 
                 36.146 
                 36.146 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                   
               
             
            
               
                 Number of Cylinders C 
                 6 
                 0.833333 
                   
               
               
                 Multiple of synched Cylinders 
                 1 
               
               
                 Stroke 
                 10 
                 in 
                 2.272727 
               
               
                 Ramp Time t r   
                 1.1 
                 sec 
                 Matzner 
               
               
                 Plunger Diameter 
                 4.5 
                 in 
               
               
                 Intensifier Ratio 
                 3 
                 :1 
               
               
                 Job Pressure 
                 12000 
                 psi 
               
               
                 Dwell Time t d   
                 3.3 
               
               
                 Maximum Pressure 
                 15000 
                 psi 
               
               
                 T 
                 6.6 
                 sec 
               
               
                 Cylinder Rod Length 
                 42 
                 in 
               
               
                 Cylinder Rod Modulus 
                 2.90E+07 
                 psi 
                 Alternate 
               
               
                 Min Cylinder Rod diameter 
                 4.00 
                 in 
               
               
                 Actual Cylinder Rod diameter 
                 4.50 
                 in 
               
               
                 Cylinder Piston Diameter 
                 9.00 
                 in 
               
               
                 Job Cylinder Pressure 
                 4000 
                 psi 
               
               
                 Stroke Volume per stroke per 
                 159 
                 in 3   
                 0.69 
               
               
                 cylinder 
               
               
                 Volume rate per cylinder 
                 36.14617 
                 in 3 /sec 
                 9.388614 
               
               
                 Volume rate all cylinders 
                 144.5847 
                 in 3 /sec 
                 37.55446 
               
               
                 A for Plunger 
                 36.14617 
                 in 3 /sec 
                 1.818182 
               
               
                 A for Hydraulic Piston 
                 108.4385 
                 in 3 /sec 
                 2.272727 
               
               
                 Rod Load 
                 190851.8 
                 lbf 
               
               
                 Max Rod Load 
                 238564.7 
                 lbf 
               
               
                   
               
            
           
         
       
     
       FIG. 6  illustrates a chart  500  showing the combined and individual flow rates of multiple reciprocating pump assemblies  100  with two different banks of three cylinders, according to some embodiments. The following charts illustrate additional pumping details for such a configuration. The embodiment of  FIG. 6  depicts a half overlap between different sets of the reciprocating pump assemblies  100 . 
     
       
         
           
               
            
               
                   
               
               
                 Multi Cylinders with Trapezoidal flow rate curves, Haversine ramp 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Cycle 
                 Time 
                 Total 
                 Cyl 1 
                 Cyl 2 
                 Cyl 3 
                 Cyl 4 
                 Cyl 5 
                 Cyl 6 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 0.000 
                 0.000 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 0.042 
                 0.138 
                 289.169 
                 5.503 
                 0.000 
                 0.000 
                 44.627 
                 139.082 
                 99.957 
               
               
                 0.083 
                 0.275 
                 289.169 
                 21.174 
                 0.000 
                 0.000 
                 21.174 
                 123.411 
                 123.411 
               
               
                 0.125 
                 0.413 
                 289.169 
                 44.627 
                 0.000 
                 0.000 
                 5.503 
                 99.957 
                 139.082 
               
               
                 0.167 
                 0.550 
                 289.169 
                 72.292 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
               
               
                 0.208 
                 0.688 
                 289.169 
                 99.957 
                 5.503 
                 0.000 
                 0.000 
                 44.627 
                 139.082 
               
               
                 0.250 
                 0.825 
                 289.169 
                 123.411 
                 21.174 
                 0.000 
                 0.000 
                 21.174 
                 123.411 
               
               
                 0.292 
                 0.963 
                 289.169 
                 139.082 
                 44.627 
                 0.000 
                 0.000 
                 5.503 
                 99.957 
               
               
                 0.333 
                 1.100 
                 289.169 
                 144.585 
                 72.292 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
               
               
                 0.375 
                 1.238 
                 289.169 
                 139.082 
                 99.957 
                 5.503 
                 0.000 
                 0.000 
                 44.627 
               
               
                 0.417 
                 1.375 
                 289.169 
                 123.411 
                 123.411 
                 21.174 
                 0.000 
                 0.000 
                 21.174 
               
               
                 0.458 
                 1.513 
                 289.169 
                 99.957 
                 139.082 
                 44.627 
                 0.000 
                 0.000 
                 5.503 
               
               
                 0.500 
                 1.650 
                 289.169 
                 72.292 
                 144.585 
                 72.292 
                 0.000 
                 0.000 
                 0.000 
               
               
                 0.542 
                 1.788 
                 289.169 
                 44.627 
                 139.082 
                 99.957 
                 5.503 
                 0.000 
                 0.000 
               
               
                 0.583 
                 1.925 
                 289.169 
                 21.174 
                 123.411 
                 123.411 
                 21.174 
                 0.000 
                 0.000 
               
               
                 0.625 
                 2.063 
                 289.169 
                 5.503 
                 99.957 
                 139.082 
                 44.627 
                 0.000 
                 0.000 
               
               
                 0.667 
                 2.200 
                 289.169 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
                 0.000 
                 0.000 
               
               
                 0.708 
                 2.338 
                 289.169 
                 0.000 
                 44.627 
                 139.082 
                 99.957 
                 5.503 
                 0.000 
               
               
                 0.750 
                 2.475 
                 289.169 
                 0.000 
                 21.174 
                 123.411 
                 123.411 
                 21.174 
                 0.000 
               
               
                 0.792 
                 2.613 
                 289.169 
                 0.000 
                 5.503 
                 99.957 
                 139.082 
                 44.627 
                 0.000 
               
               
                 0.833 
                 2.750 
                 289.169 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
                 0.000 
               
               
                 0.875 
                 2.888 
                 289.169 
                 0.000 
                 0.000 
                 44.627 
                 139.082 
                 99.957 
                 5.503 
               
               
                 0.917 
                 3.025 
                 289.169 
                 0.000 
                 0.000 
                 21.174 
                 123.411 
                 123.411 
                 21.174 
               
               
                 0.958 
                 3.163 
                 289.169 
                 0.000 
                 0.000 
                 5.503 
                 99.957 
                 139.082 
                 44.627 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                 1.000 
                 3.300 
                 289.169 
                 0.000 
                 0.000 
                 0.000 
                 72.292 
                 144.585 
                 72.292 
               
               
                   
               
            
           
         
       
     
       FIG. 7  illustrates a chart  600  showing the combined and individual flow rates of multiple reciprocating pump assemblies  100  with two different banks of three cylinders, according to some embodiments. The following chart illustrates additional pumping details for such a configuration. The embodiment of  FIG. 7  depicts a quarter overlap between different sets of the reciprocating pump assemblies  100 . 
     
       
         
           
               
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 Number of Cylinders C 
                 3 
                 0.666667 
               
               
                   
                 Multiple of synched Cylinders 
                 1 
               
               
                   
                 Stroke 
                 10 
                 in 
               
               
                   
                 Ramp Time t r   
                 1.1 
                 sec 
               
               
                   
                 Plunger Diameter 
                 4.5 
                 in 
               
               
                   
                 Intensifier Ratio 
                 3 
                 :1 
               
               
                   
                 Job Pressure 
                 12000 
                 psi 
               
               
                   
                 Dwell Time t d   
                 0 
               
               
                   
                 Maximum Pressure 
                 15000 
                 psi 
               
               
                   
                 T 
                 3.3 
                 sec 
               
               
                   
                 Cylinder Rod Length 
                 42 
                 in 
               
               
                   
                 Cylinder Rod Modulus 
                 2.90E+07 
                 psi 
               
               
                   
                 Min Cylinder Rod diameter 
                 4.00 
                 in 
               
               
                   
                 Actual Cylinder Rod diameter 
                 4.50 
                 in 
               
               
                   
                 Cylinder Piston Diameter 
                 9.00 
                 in 
               
               
                   
                 Job Cylinder Pressure 
                 4000 
                 psi 
               
               
                   
                 Stroke Volume per stroke per 
                 159 
                 in 3   
               
               
                   
                 cylinder 
               
               
                   
                 Volume rate per cylinder 
                 144.5847 
                 in 3 /sec 
               
               
                   
                 Volume rate all cylinders 
                 144.5847 
                 in 3 /sec 
               
               
                   
                 A for Plunger 
                 144.5847 
                 in 3 /sec 
               
               
                   
                 A for Hydraulic Piston 
                 433.754 
                 in 3 /sec 
               
               
                   
                 Rod Load 
                 190851.8 
                 lbf 
               
               
                   
                 Max Rod Load 
                 238564.7 
                 lbf 
               
               
                   
                   
               
            
           
         
       
     
       FIG. 8  is a flowchart illustrating a method  700  for operating a reciprocating pump assembly according to an exemplary embodiment. The method  700  includes operatively connecting, at  702 , at least one linear actuator to a first plunger rod assembly of a first fluid end section having a first plunger bore. At  704 , the method  700  includes operatively connecting the at least one linear actuator to a second plunger rod assembly of a second fluid end section having a second plunger bore. At  706 , the method  700  includes reciprocating respective first and second plungers of the first and second plunger rod assemblies within the first and second plunger bores, respectively, using the at least one linear actuator to pump fluid through the first and second fluid end sections. 
     In some embodiments, reciprocating at  706  the first and second plungers within the first and second plunger bores, respectively, using the at least one linear actuator includes simultaneously moving, at  706   a , the first and second plunger rod assemblies in the same direction. Reciprocating at  706  the first and second plungers within the first and second plunger bores, respectively, using the at least one linear actuator includes electronically controlling, at  706   b,  a flow rate of fluid through the first and second fluid end sections in some embodiments. 
     Optionally, the at least one linear actuator is at least one first linear actuator and the method  700  further includes: operatively connecting, at  708 , at least one second linear actuator to a third plunger rod assembly of a third fluid end section having a third plunger bore; operatively connecting, at  710 , the at least one second linear actuator to a fourth plunger rod assembly of a fourth fluid end section having a fourth plunger bore; reciprocating, at  712 , respective third and fourth plungers of the third and fourth plunger rod assemblies within the third and fourth plunger bores, respectively, using the at least one second linear actuator to pump fluid through the third and fourth fluid end sections; and offsetting, at  714 , the duty cycle of the first and second fluid end sections from the duty cycle of the third and fourth fluid end sections. 
     Various embodiments disclosed herein increase the stroke length of the plunger of the fluid end section of a reciprocating pump assembly and thereby reduce the number of sealing events experienced by valve assemblies of the fluid end section during operation of the reciprocating pump assembly. Various embodiments disclosed herein increase the longevity of the valve assemblies of a fluid end section of a reciprocating pump assembly and thereby reduce the operating costs of a reciprocating pump assembly. Various embodiments disclosed herein provide a relatively steady flow of fluid (e.g., a relatively uniform flow rate, a relatively constant flow rate, a relatively consistent flow rate, etc.) through a fluid end section of a reciprocating pump assembly. Various embodiments disclosed herein may reduce flow rate surges of a reciprocating pump assembly. 
     The following clauses describe further aspects of the disclosure: 
     Clause Set A: 
     A1. A reciprocating pump assembly comprising: 
     a fluid end section having a pressure chamber and a plunger bore that fluidly communicates with the pressure chamber; 
     a plunger configured to be held within the plunger bore of the fluid end section; and 
     a linear actuator operatively connected to the plunger such that the linear actuator is configured to reciprocate the plunger within the plunger bore during operation of the reciprocating pump to thereby pump fluid through the fluid end section. 
     A2. The reciprocating pump assembly of clause Al, wherein the linear actuator comprises at least one of a mechanical linear actuator, an electrical linear actuator, an electro-mechanical linear actuator, a magnetic linear actuator, a hydraulic linear actuator, a pneumatic linear actuator, a screw-type actuator, a ball screw, a lead screw, a rotary screw, a screw jack, a roller screw, a hydraulic piston, a linear motor, a wheel and axle actuator, a telescoping linear actuator, a solenoid, or a servo. 
     A3. The reciprocating pump assembly of clause Al, further comprising a driver configured to drive operation of the linear actuator, the driver comprising at least one of an engine, an electrical motor, a turbine, a hydraulic pump, a pneumatic pump, a mechanical pump, an electrical power source, an electrical circuit, a processor, a mechanical drive system, a pneumatic system, or a hydraulic system. 
     A4. The reciprocating pump assembly of clause Al, further comprising a power end section that comprises the linear actuator. 
     A5. The reciprocating pump assembly of clause Al, further comprising a controller operatively connected to the linear actuator such that the controller is configured to electronically control a flow rate of fluid through the fluid end section. Clause Set B: 
     B1. A reciprocating pump assembly comprising: 
     a first fluid end section having a first pressure chamber and a first plunger bore that fluidly communicates with the first pressure chamber; 
     a first plunger rod assembly comprising a first plunger configured to be held within the first plunger bore of the first fluid end section; 
     a second fluid end section having a second pressure chamber and a second plunger bore that fluidly communicates with the second pressure chamber; 
     a second plunger rod assembly comprising a second plunger configured to be held within the second plunger bore of the second fluid end section; and 
     at least one linear actuator operatively connected to the first and second plunger rod assemblies such that the at least one linear actuator is configured to reciprocate the first and second plungers within the first and second plunger bores, respectively, during operation of the reciprocating pump to thereby pump fluid through the first and second fluid end sections. 
     B2. The reciprocating pump assembly of clause B1, wherein the at least one linear actuator comprises at least one of a mechanical linear actuator, an electrical linear actuator, an electro-mechanical linear actuator, a magnetic linear actuator, a hydraulic linear actuator, a pneumatic linear actuator, a screw-type actuator, a ball screw, a lead screw, a rotary screw, a screw jack, a roller screw, a hydraulic piston, a linear motor, a wheel and axle actuator, a telescoping linear actuator, a solenoid, or a servo. 
     B3. The reciprocating pump assembly of clause B1, further comprising at least one driver configured to drive operation of the at least one linear actuator, the driver comprising at least one of an engine, an electrical motor, a turbine, a hydraulic pump, a pneumatic pump, a mechanical pump, an electrical power source, an electrical circuit, a processor, a mechanical drive system, a pneumatic system, or a hydraulic system. 
     B4. The reciprocating pump assembly of clause B1, further comprising a power end section that comprises the at least one linear actuator. B5. The reciprocating pump assembly of clause B1, wherein at least one of the first fluid end section includes only a single one of the first pressure chamber or the second fluid end section includes only a single one of the second pressure chamber. 
     B6. The reciprocating pump assembly of clause B1, wherein the first and second plunger rod assemblies are operatively connected to the at least one linear actuator such that the first and second plunger rod assemblies are coaxially aligned with each other. 
     B7. The reciprocating pump assembly of clause B1, wherein the at least one linear actuator is configured to simultaneously move the first and second plunger rod assemblies in the same direction. 
     B8. The reciprocating pump assembly of clause B1, wherein the at least one linear actuator is configured to simultaneously move the first and second plunger rod assemblies in opposite directions. 
     B9. The reciprocating pump assembly of clause B1, wherein the at least one linear actuator is at least one first linear actuator, the reciprocating pump assembly further comprising: 
     a third fluid end section having a third pressure chamber and a third plunger bore that fluidly communicates with the third pressure chamber; 
     a third plunger rod assembly comprising a third plunger configured to be held within the third plunger bore of the third fluid end section; 
     a fourth fluid end section having a fourth pressure chamber and a fourth plunger bore that fluidly communicates with the fourth pressure chamber; 
     a fourth plunger rod assembly comprising a fourth plunger configured to be held within the fourth plunger bore of the fourth fluid end section; and 
     at least one second linear actuator operatively connected to the third and fourth plunger rod assemblies such that the at least one second linear actuator is configured to reciprocate the third and fourth plungers within the third and fourth plunger bores, respectively, during operation of the reciprocating pump to thereby pump fluid through the third and fourth fluid end sections. 
     B10. The reciprocating pump assembly of clause B1, further comprising a controller operatively connected to the at least one linear actuator such that the controller is configured to electronically control a flow rate of fluid through the first and second fluid end sections. 
     B11. The reciprocating pump assembly of clause B1, wherein the at least one linear actuator is at least one first linear actuator, the reciprocating pump assembly further comprising: 
     a third fluid end section having a third pressure chamber and a third plunger bore that fluidly communicates with the third pressure chamber; 
     a third plunger rod assembly comprising a third plunger configured to be held within the third plunger bore of the third fluid end section; 
     a fourth fluid end section having a fourth pressure chamber and a fourth plunger bore that fluidly communicates with the fourth pressure chamber; 
     a fourth plunger rod assembly comprising a fourth plunger configured to be held within the fourth plunger bore of the fourth fluid end section; 
     at least one second linear actuator operatively connected to the third and fourth plunger rod assemblies such that the at least one second linear actuator is configured to reciprocate the third and fourth plungers within the third and fourth plunger bores, respectively, during operation of the reciprocating pump to thereby pump fluid through the third and fourth fluid end sections; and 
     a controller operatively connected to the at least one first linear actuator and the at least one second linear actuator such that the controller is configured to offset the duty cycle of the first and second fluid end sections from the duty cycle of the third and fourth fluid end sections. 
     Clause Set C: 
     C1. A method for operating a reciprocating pump assembly comprising: 
     operatively connecting at least one linear actuator to a first plunger rod assembly of a first fluid end section having a first plunger bore; 
     operatively connecting the at least one linear actuator to a second plunger rod assembly of a second fluid end section having a second plunger bore; and 
     reciprocating respective first and second plungers of the first and second plunger rod assemblies within the first and second plunger bores, respectively, using the at least one linear actuator to pump fluid through the first and second fluid end sections. 
     C2. The method of clause C1, wherein reciprocating the first and second plungers within the first and second plunger bores, respectively, using the at least one linear actuator comprises simultaneously moving the first and second plunger rod assemblies in the same direction. 
     C3. The method of clause C1, wherein reciprocating the first and second plungers within the first and second plunger bores, respectively, using the at least one linear actuator comprises electronically controlling a flow rate of fluid through the first and second fluid end sections. 
     C4. The method of clause C1, wherein the at least one linear actuator is at least one first linear actuator, the method further comprising: 
     operatively connecting at least one second linear actuator to a third plunger rod assembly of a third fluid end section having a third plunger bore; 
     operatively connecting the at least one second linear actuator to a fourth plunger rod assembly of a fourth fluid end section having a fourth plunger bore; 
     reciprocating respective third and fourth plungers of the third and fourth plunger rod assemblies within the third and fourth plunger bores, respectively, using the at least one second linear actuator to pump fluid through the third and fourth fluid end sections; and 
     offsetting the duty cycle of the first and second fluid end sections from the duty cycle of the third and fourth fluid end sections. 
     It is to be understood that the above description is intended to be illustrative, and not restrictive. For example, the above-described embodiments (and/or aspects thereof) may be used in combination with each other. Furthermore, invention(s) have been described in connection with what are presently considered to be the most practical and preferred embodiments, it is to be understood that the invention is not to be limited to the disclosed embodiments, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the invention(s). Further, each independent feature or component of any given assembly may constitute an additional embodiment. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the disclosure without departing from its scope. Dimensions, types of materials, orientations of the various components, and the number and positions of the various components described herein are intended to define parameters of certain embodiments, and are by no means limiting and are merely exemplary embodiments. Many other embodiments and modifications within the spirit and scope of the claims will be apparent to those of skill in the art upon reviewing the above description. The scope of the disclosure should, therefore, be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled. 
     In the foregoing description of certain embodiments, specific terminology has been resorted to for the sake of clarity. However, the disclosure is not intended to be limited to the specific terms so selected, and it is to be understood that each specific term includes other technical equivalents which operate in a similar manner to accomplish a similar technical purpose. Terms such as ‘clockwise_ and ‘counterclockwise_, ‘left_ and right_, ‘front_ and rear_, ‘above_ and ‘below_ and the like are used as words of convenience to provide reference points and are not to be construed as limiting terms. 
     When introducing elements of aspects of the disclosure or the examples thereof, 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. For example, in this specification, the word ‘comprising_ is to be understood in its ‘open_ sense, that is, in the sense of ‘including_, and thus not limited to its ‘closed_ sense, that is the sense of consisting only of_. A corresponding meaning is to be attributed to the corresponding words ‘comprise_, ‘comprised_, ‘comprises_, ‘having_, ‘has_, includes_, and ‘including_ where they appear. Further, references to “one embodiment” are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. Moreover, unless explicitly stated to the contrary, embodiments “comprising” or “having” an element or a plurality of elements having a particular property can include additional elements not having that property. The term ‘exemplary_ is intended to mean ‘an example of._ The phrase ‘one or more of the following: A, B, and C_ means ‘at least one of A and/or at least one of B and/or at least one of C.” Moreover, in the following claims, the terms “first,” “second,” and “third,” etc. are used merely as labels, and are not intended to impose numerical requirements on their objects. Further, the limitations of the following claims are not written in means-plus-function format and are not intended to be interpreted based on 35 U.S.C. § 112(f), unless and until such claim limitations expressly use the phrase ‘means for_ followed by a statement of function void of further structure. 
     Although the terms ‘step_ and/or ‘block_ may be used herein to connote different elements of methods employed, the terms should not be interpreted as implying any particular order among or between various steps herein disclosed unless and except when the order of individual steps is explicitly described. The order of execution or performance of the operations in examples of the disclosure illustrated and described herein is not essential, unless otherwise specified. The operations may be performed in any order, unless otherwise specified, and examples of the disclosure may include additional or fewer operations than those disclosed herein. It is therefore contemplated that executing or performing a particular operation before, contemporaneously with, or after another operation is within the scope of aspects of the disclosure. 
     Having described aspects of the disclosure in detail, it will be apparent that modifications and variations are possible without departing from the scope of aspects of the disclosure as defined in the appended claims. As various changes could be made in the above constructions, products, and methods without departing from the scope of aspects of the disclosure, it is intended that all matter contained in the above description and shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.