Patent Publication Number: US-10760387-B2

Title: Cooling systems and methods for downhole solid state pumps

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit and priority of U.S. Provisional Application Ser. No. 62/491,559 filed Apr. 28, 2017, the disclosure of which is incorporated herein by reference in its entirety. This application is also related to concurrently filed U.S. patent application Ser. No. 15/965,469, now U.S. Pat. No. 10,648,303, titled “Wireline-Deployed Solid State Pump for Removing Fluids from A Subterranean Well”, the disclosure of which is incorporated herein by reference in its entirety. 
    
    
     FIELD 
     The present disclosure is directed generally to systems and methods for artificial lift in a wellbore and more specifically to systems and methods that utilize a downhole solid state pump to remove a wellbore liquid from the wellbore. 
     BACKGROUND 
     A hydrocarbon well may be utilized to produce gaseous hydrocarbons from a subterranean formation. Often, a wellbore liquid may build up within one or more portions of the hydrocarbon well. This wellbore liquid, which may include water, condensate, and/or liquid hydrocarbons, may impede flow of the gaseous hydrocarbons from the subterranean formation to a surface region via the hydrocarbon well, thereby reducing and/or completely blocking gaseous hydrocarbon production from the hydrocarbon well. 
     Traditionally, plunger lift and/or rod pump systems have been utilized to provide artificial lift and to remove this wellbore liquid from the hydrocarbon well. While these systems may be effective under certain circumstances, they may not be capable of efficiently removing the wellbore liquid from long and/or deep hydrocarbon wells, from hydrocarbon wells that include one or more deviated (or nonlinear) portions (or regions), and/or from hydrocarbon wells in which the gaseous hydrocarbons do not generate at least a threshold pressure. 
     As an illustrative, non-exclusive example, plunger lift systems require that the gaseous hydrocarbons develop at least the threshold pressure to provide a motive force to convey a plunger between the subterranean formation and the surface region. As another illustrative, non-exclusive example, rod pump systems utilize a mechanical linkage (i.e., a rod) that extends between the surface region and the subterranean formation; and, as the depth of the well (or length of the mechanical linkage) is increased, the mechanical linkage becomes more prone to failure and/or more prone to damage the casing. As yet another illustrative, non-exclusive example, neither plunger lift systems nor rod pump systems may be utilized as effectively in wellbores that include deviated and/or nonlinear regions. 
     Improved hydrocarbon well drilling technologies permit an operator to drill a hydrocarbon well that extends for many thousands of meters within the subterranean formation, that has a vertical depth of hundreds, or even thousands, of meters, and/or that has a highly deviated wellbore. These improved drilling technologies are routinely utilized to drill long and/or deep hydrocarbon wells that permit production of gaseous hydrocarbons from previously inaccessible subterranean formations. 
     However, wellbore liquids cannot be removed efficiently from these hydrocarbon wells using traditional artificial lift systems. Thus, there exists a need for improved systems and methods for artificial lift to remove wellbore liquids from a hydrocarbon well. 
     SUMMARY 
     In one aspect, disclosed herein is a system for removing wellbore liquids from a wellbore, the wellbore traversing a subterranean formation and having a tubular that extends within at least a portion of the wellbore. The system includes a positive-displacement solid state pump comprising a fluid chamber, an inlet and an outlet port, each in fluid communication with the fluid chamber, at least one solid state actuator, a first one-way check valve positioned between the inlet port and the fluid chamber, and/or a second one-way check valve positioned between the outlet port and the fluid chamber, the solid state pump positioned within the wellbore; a heat sink for cooling the at least one solid state actuator, the heat sink comprising at least one of; (i) a dielectric oil bath, (ii) a thermoelectric cooling element, (iii) an aperture within the at least one solid state actuator for conveying a cooling fluid through the aperture, and (iv) combinations thereof; and an electrical source for powering the solid state pump. 
     In some embodiments, the at least one solid state actuator is selected from piezoelectric, electrostrictive and/or magnetorestrictive actuators. 
     In some embodiments, the at least one solid state actuator comprise a ceramic perovskite material. 
     In some embodiments, the ceramic perovskite material comprises lead zirconate titanate and/or lead magnesium niobate. 
     In some embodiments, the at least one solid state actuator comprise terbium dysprosium iron. 
     In some embodiments, the at least one solid state actuator includes one or more central throughbores, internal passageways, channels, or similar surface-area-enhancing features for enhanced cooling. 
     In some embodiments, the at least one solid state actuator is directly or indirectly cooled with thermoelectric cooling elements. 
     In some embodiments, the first one-way check valve and/or the second one-way check valve are passive one-way disk valves, active one-way disk valves, passive microvalve arrays, active microvalve arrays, passive MEMS valve arrays, active MEMS valve arrays or a combination thereof. 
     In some embodiments, the solid state pump further comprises a piston and a cylinder for housing the at least one solid state actuator and the first and/or second one-way check valves, so as to form a piston pump. 
     In some embodiments, the solid state pump further comprises a diaphragm operatively associated with the at least one solid state actuator and the first and/or second the one-way check valves, so as to form a diaphragm pump. 
     In some embodiments, the means for powering the solid state pump is a power cable, the power cable operable for deploying the solid state pump. 
     In some embodiments, the power cable comprises a synthetic conductor. 
     In some embodiments, the means for powering the solid state pump and/or cooling the pump, includes use of a rechargeable battery. 
     In some embodiments, the positive-displacement solid state pump is plugged into a downhole wet-mate connection and the means for powering the solid state pump is a power cable positioned on the outside of the tubular. 
     In some embodiments, the system further includes a fluid flowpath that conveys a produced wellbore fluid from the inlet port, along an exterior surface of a housing containing the at least one solid state actuator to cool the at least one solid state actuator. 
     In some embodiments, the fluid flowpath conveys a produced wellbore fluid from the inlet port, through the aperture within the at least one solid state actuator. 
     In some embodiments, the at least one solid state actuator is at least partially immersed within the dielectric oil bath. 
     In some embodiments, the system further includes an electrical power source for powering the thermoelectric cooling element. 
     In some embodiments, the electrical power source for powering the solid state pump also powers the thermoelectric cooling element. 
     In some embodiments, the system further includes a thermoelectric power interrupt for turning the pump off in event that an operating temperature limit for the pump is exceeded. 
     In some embodiments, the solid state pump further comprises a diaphragm operatively associated with the at least one solid state actuator and the first and/or second the one-way check valves, so as to form a diaphragm pump; and the diaphragm conveys heat from at least one of the at least one of the oil bath and the thermoelectric cooling element to a wellbore fluid pumped by the diaphragm pump. 
     In some embodiments, the electrical power source the solid state pump and the thermoelectric cooling element is a power cable, the power cable operable for deploying the solid state pump. 
     In some embodiments, the power cable comprises a synthetic conductor. 
     In some embodiments, the electrical power source for at least one of the solid state pump and the thermoelectric cooling element includes a rechargeable battery. 
     In some embodiments, the positive-displacement solid state pump is plugged into a downhole wet-mate connection and the electrical power source the solid state pump is a power cable positioned on the outside of the tubular. 
     Methods are disclosed for removing produced wellbore liquid from a wellbore using the solid state, electrically actuated pumps as disclosed herein, the wellbore traversing a subterranean formation producing a wellbore fluid and having a tubular that extends within at least a portion of the wellbore, the method comprising: providing an electrically powered downhole positive-displacement solid state pump including pump housing containing at least a fluid chamber, an inlet and an outlet port each in fluid communication with the fluid chamber, at least one solid state actuator, a first one-way check valve positioned between the inlet port and the fluid chamber, and a second one-way check valve positioned between the outlet port and the fluid chamber, an electrical power supply for powering the at least one solid state actuator, a heat sink for cooling the at least one solid state actuator, the heat sink comprising at least one of; (i) a dielectric oil bath, (ii) a thermoelectric cooling element, (iii) an aperture within the at least one solid state actuator for conveying a cooling fluid through the aperture, and (iv) combinations thereof; positioning the electrically powered downhole solid state pump within a portion of the wellbore; electrically powering the downhole solid state pump; pumping the produced wellbore liquid from the wellbore with the downhole positive-displacement solid state pump, the pumping generating heat; and cooling the at least one solid state actuator by removing at least a portion of the generated heat with the heat sink. 
     In some embodiments, wherein the step of pumping includes; (i) pressurizing the wellbore liquid with the downhole positive-displacement solid state pump to generate a pressurized wellbore liquid at a discharge pressure within the fluid chamber; and (ii) opening the second one-way discharge valve with the pressurized wellbore liquid to flowing the pressurized wellbore liquid into the tubular and at least a threshold vertical distance toward a surface region. 
     In some embodiments, the step of cooling includes immersing at least a portion of the at least one solid state actuator in a static cooling fluid bath. 
     In some embodiments, the methods further include providing a coolant housing for containing the static cooling fluid bath and the at least partially immersed at least one solid state actuator. 
     In some embodiments, the methods further include providing a dielectric oil as the cooling fluid bath. 
     In some embodiments, the methods further comprise flowing at least a portion of the produced wellbore within an interior portion of the pump housing. 
     In some embodiments, the methods further include flowing at least a portion of the produced wellbore fluid in thermal contact with an exterior surface of the coolant housing. 
     In some embodiments, the methods further include providing an aperture within the at least one solid state actuator, and conveying a cooling fluid through the aperture. 
     In some embodiments, the cooling fluid may be conveyed through the aperture comprises at least a portion of the produced wellbore fluid. 
     In some embodiments, the methods further include providing a thermoelectric cooling element within the pump housing as the heat sink for cooling the at least one solid state actuator and electrically powering the thermoelectric cooling element with a portion of electrical power provided to the downhole solid state pump. 
     In some embodiments, the methods further include providing a fluid flowpath within the pump housing that conveys a produced wellbore fluid from the inlet port, along an exterior surface of a housing containing the at least one solid state actuator to cool the at least one solid state actuator. 
     In some embodiments, the methods further include providing the downhole positive displacement pump with a thermoelectric power interrupt for turning the pump off to prevent overheating of the pump if an operating temperature limit for the pump is exceeded. 
     In some embodiments, cooling the at least one solid state actuator with a heat sink further comprises: providing the downhole positive displacement pump with a thermally conductive diaphragm operatively associated with the at least one solid state actuator and the first and/or the second one-way check valves, and fluid chamber so as to form a diaphragm pump; and conveying heat produced from the at least one solid state actuator through the thermally conductive diaphragm and to the produced wellbore fluid within the fluid chamber. 
     In some embodiments, the methods further comprise electrically powering at least one of the solid state pump and the thermoelectric cooling element using a rechargeable battery. 
     In some embodiments, the methods further include positioning the battery at a downhole location within the wellbore and charging the battery with an electrical cable running within the wellbore between the downhole battery and a surface location. 
     In some embodiments, the methods further include positioning the battery at a surface location, charging the battery with at least one of a generated electrical source and a solar-powered battery charging system. 
     In some embodiments, the methods further include pumping the produced wellbore liquid from the wellbore with the downhole solid state pump when the battery contains sufficient charge to operate the pump for a determined minimum duty cycle. 
     In some embodiments, the methods further include controlling the downhole solid state pump using an operating control system. 
     In some embodiments, the methods further include controlling the downhole solid state pump using a pump-off control system. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present disclosure is susceptible to various modifications and alternative forms, specific exemplary implementations thereof have been shown in the drawings and are herein described in detail. It should be understood, however, that the description herein of specific exemplary implementations is not intended to limit the disclosure to the particular forms disclosed herein. This disclosure is to cover all modifications and equivalents as defined by the appended claims. It should also be understood that the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating principles of exemplary embodiments of the present invention. Moreover, certain dimensions may be exaggerated to help visually convey such principles. Further where considered appropriate, reference numerals may be repeated among the drawings to indicate corresponding or analogous elements. Moreover, two or more blocks or elements depicted as distinct or separate in the drawings may be combined into a single functional block or element. Similarly, a single block or element illustrated in the drawings may be implemented as multiple steps or by multiple elements in cooperation. The forms disclosed herein are illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings and in which like reference numerals refer to similar elements and in which: 
         FIG. 1  is a schematic representation of illustrative, non-exclusive examples of a hydrocarbon well that may be utilized with and/or may include the systems and methods, according to the present disclosure. 
         FIG. 2  is a schematic block diagram of illustrative, non-exclusive examples of a positive-displacement solid state pump, according to the present disclosure. 
         FIG. 3  is a fragmentary partial cross-sectional view of illustrative, non-exclusive examples of a hydrocarbon well that includes a positive-displacement solid state pump, according to the present disclosure. 
         FIG. 4  is a fragmentary partial cross-sectional view of illustrative, non-exclusive examples of a positive-displacement solid state pump, according to the present disclosure. 
         FIG. 5  is a fragmentary partial cross-sectional view of additional illustrative, non-exclusive examples of a positive-displacement solid state pump, according to the present disclosure. 
         FIG. 6  is a fragmentary partial cross-sectional view of additional illustrative, non-exclusive examples of a positive-displacement solid state pump, according to the present disclosure. 
         FIG. 7  is a schematic representation of illustrative, non-exclusive examples of a hydrocarbon well that may be utilized with and/or may include the systems and methods, according to the present disclosure. 
         FIGS. 8-10  present schematic representations of illustrative, non-exclusive examples of a positive-displacement solid state pump, according to the present disclosure. 
         FIG. 11  presents a schematic representation of an illustrative, non-exclusive examples of a positive-displacement solid state pump, according to the present disclosure. 
         FIG. 11A  shows a preferred active disc. 
         FIGS. 12-13  illustrate the operation of the positive-displacement solid state pump of  FIG. 11 . 
         FIGS. 14-15  shows further schematic representations of illustrative, non-exclusive examples of a positive-displacement solid state pump, according to the present disclosure. 
         FIGS. 16-18  shows another set of schematic representations of illustrative, non-exclusive examples of a positive-displacement solid state pump, according to the present disclosure. 
         FIG. 19  presents a cross-sectional view of an illustrative, nonexclusive example of a velocity fuse having utility in the flushable well screen or filter assemblies of the present disclosure. 
         FIG. 20  presents a schematic view of an illustrative, nonexclusive example of a system for removing fluids from a well, according to the present disclosure. 
         FIG. 21  presents a schematic view of an illustrative, nonexclusive example of a system for removing fluids from a subterranean well, depicted in a pumping mode, according to the present disclosure. 
         FIG. 22  presents a schematic view of an illustrative, nonexclusive example of the system for removing fluids from a subterranean well of  FIG. 21 , wherein the system is placed in the charging mode, according to the present disclosure. 
         FIG. 23  is a flowchart depicting methods according to the present disclosure of removing a wellbore liquid from a wellbore. 
         FIGS. 24-25  illustrates an exemplary embodiment for cooling the pumping system using both a cooling fluid bath and a method of circulating produced wellbore fluid within the pumping system and through an internal aperture in an actuator stack. 
         FIGS. 26-27  illustrates an exemplary embodiment for cooling the pumping system using both a cooling fluid bath and a method of circulating produced wellbore fluid within the pumping system but not including an internal aperture through the actuator stack. 
         FIGS. 28-29  illustrate the operation of the positive-displacement solid state pump using thermoelectric cooling elements for cooling the actuator stack. 
     
    
    
     DETAILED DESCRIPTION 
     Terminology 
     The words and phrases used herein should be understood and interpreted to have a meaning consistent with the understanding of those words and phrases by those skilled in the relevant art. No special definition of a term or phrase, i.e., a definition that is different from the ordinary and customary meaning as understood by those skilled in the art, is intended to be implied by consistent usage of the term or phrase herein. To the extent that a term or phrase is intended to have a special meaning, i.e., a meaning other than the broadest meaning understood by skilled artisans, such a special or clarifying definition will be expressly set forth in the specification in a definitional manner that provides the special or clarifying definition for the term or phrase. 
     For example, the following discussion contains a non-exhaustive list of definitions of several specific terms used in this disclosure (other terms may be defined or clarified in a definitional manner elsewhere herein). These definitions are intended to clarify the meanings of the terms used herein. It is believed that the terms are used in a manner consistent with their ordinary meaning, but the definitions are nonetheless specified here for clarity. 
     A/an: The articles “a” and “an” as used herein mean one or more when applied to any feature in embodiments and implementations of the present invention described in the specification and claims. The use of “a” and “an” does not limit the meaning to a single feature unless such a limit is specifically stated. The term “a” or “an” entity refers to one or more of that entity. As such, the terms “a” (or “an”), “one or more” and “at least one” can be used interchangeably herein. 
     About: As used herein, “about” refers to a degree of deviation based on experimental error typical for the particular property identified. The latitude provided the term “about” will depend on the specific context and particular property and can be readily discerned by those skilled in the art. The term “about” is not intended to either expand or limit the degree of equivalents which may otherwise be afforded a particular value. Further, unless otherwise stated, the term “about” shall expressly include “exactly,” consistent with the discussion below regarding ranges and numerical data. 
     Above/below: In the following description of the representative embodiments of the invention, directional terms, such as “above”, “below”, “upper”, “lower”, etc., are used for convenience in referring to the accompanying drawings. In general, “above”, “upper”, “upward” and similar terms refer to a direction toward the earth&#39;s surface along a wellbore, and “below”, “lower”, “downward” and similar terms refer to a direction away from the earth&#39;s surface along the wellbore. Continuing with the example of relative directions in a wellbore, “upper” and “lower” may also refer to relative positions along the longitudinal dimension of a wellbore rather than relative to the surface, such as in describing both vertical and horizontal wells. 
     And/or: The term “and/or” placed between a first entity and a second entity means one of (1) the first entity, (2) the second entity, and (3) the first entity and the second entity. Multiple elements listed with “and/or” should be construed in the same fashion, i.e., “one or more” of the elements so conjoined. Other elements may optionally be present other than the elements specifically identified by the “and/or” clause, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, a reference to “A and/or B”, when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements). As used herein in the specification and in the claims, “or” should be understood to have the same meaning as “and/or” as defined above. For example, when separating items in a list, “or” or “and/or” shall be interpreted as being inclusive, i.e., the inclusion of at least one, but also including more than one, of a number or list of elements, and, optionally, additional unlisted items. Only terms clearly indicated to the contrary, such as “only one of” or “exactly one of,” or, when used in the claims, “consisting of,” will refer to the inclusion of exactly one element of a number or list of elements. In general, the term “or” as used herein shall only be interpreted as indicating exclusive alternatives (i.e. “one or the other but not both”) when preceded by terms of exclusivity, such as “either,” “one of,” “only one of,” or “exactly one of”. 
     Any: The adjective “any” means one, some, or all indiscriminately of whatever quantity. 
     At least: As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and/or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements). The phrases “at least one”, “one or more”, and “and/or” are open-ended expressions that are both conjunctive and disjunctive in operation. For example, each of the expressions “at least one of A, B and C”, “at least one of A, B, or C”, “one or more of A, B, and C”, “one or more of A, B, or C” and “A, B, and/or C” means A alone, B alone, C alone, A and B together, A and C together, B and C together, or A, B and C together. 
     Based on: “Based on” does not mean “based only on”, unless expressly specified otherwise. In other words, the phrase “based on” describes both “based only on,” “based at least on,” and “based at least in part on.” 
     Comprising: In the claims, as well as in the specification, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” “composed of,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of” and “consisting essentially of” shall be closed or semi-closed transitional phrases, respectively, as set forth in the United States Patent Office Manual of Patent Examining Procedures, Section 2111.03. 
     Couple: Any use of any form of the terms “connect”, “engage”, “couple”, “attach”, or any other term describing an interaction between elements is not meant to limit the interaction to direct interaction between the elements and may also include indirect interaction between the elements described. 
     Determining: “Determining” encompasses a wide variety of actions and therefore “determining” can include calculating, computing, processing, deriving, investigating, looking up (e.g., looking up in a table, a database or another data structure), ascertaining and the like. Also, “determining” can include receiving (e.g., receiving information), accessing (e.g., accessing data in a memory) and the like. Also, “determining” can include resolving, selecting, choosing, establishing and the like. 
     Embodiments: Reference throughout the specification to “one embodiment,” “an embodiment,” “some embodiments,” “one aspect,” “an aspect,” “some aspects,” “some implementations,” “one implementation,” “an implementation,” or similar construction means that a particular component, feature, structure, method, or characteristic described in connection with the embodiment, aspect, or implementation is included in at least one embodiment and/or implementation of the claimed subject matter. Thus, the appearance of the phrases “in one embodiment” or “in an embodiment” or “in some embodiments” (or “aspects” or “implementations”) in various places throughout the specification are not necessarily all referring to the same embodiment and/or implementation. Furthermore, the particular features, structures, methods, or characteristics may be combined in any suitable manner in one or more embodiments or implementations. 
     Exemplary: “Exemplary” is used exclusively herein to mean “serving as an example, instance, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments. 
     Flow diagram: Exemplary methods may be better appreciated with reference to flow diagrams or flow charts. While for purposes of simplicity of explanation, the illustrated methods are shown and described as a series of blocks, it is to be appreciated that the methods are not limited by the order of the blocks, as in different embodiments some blocks may occur in different orders and/or concurrently with other blocks from that shown and described. Moreover, less than all the illustrated blocks may be required to implement an exemplary method. In some examples, blocks may be combined, may be separated into multiple components, may employ additional blocks, and so on. In some examples, blocks may be implemented in logic. In other examples, processing blocks may represent functions and/or actions performed by functionally equivalent circuits (e.g., an analog circuit, a digital signal processor circuit, an application specific integrated circuit (ASIC)), or other logic device. Blocks may represent executable instructions that cause a computer, processor, and/or logic device to respond, to perform an action(s), to change states, and/or to make decisions. While the figures illustrate various actions occurring in serial, it is to be appreciated that in some examples various actions could occur concurrently, substantially in series, and/or at substantially different points in time. In some examples, methods may be implemented as processor executable instructions. Thus, a machine-readable medium may store processor executable instructions that if executed by a machine (e.g., processor) cause the machine to perform a method. 
     Full-physics: As used herein, the term “full-physics,” “full physics computational simulation,” or “full physics simulation” refers to a mathematical algorithm based on first principles that impact the pertinent response of the simulated system. 
     May: Note that the word “may” is used throughout this application in a permissive sense (i.e., having the potential to, being able to), not a mandatory sense (i.e., must). 
     Operatively connected and/or coupled: Operatively connected and/or coupled means directly or indirectly connected for transmitting or conducting information, force, energy, or matter. 
     Optimizing: The terms “optimal,” “optimizing,” “optimize,” “optimality,” “optimization” (as well as derivatives and other forms of those terms and linguistically related words and phrases), as used herein, are not intended to be limiting in the sense of requiring the present invention to find the best solution or to make the best decision. Although a mathematically optimal solution may in fact arrive at the best of all mathematically available possibilities, real-world embodiments of optimization routines, methods, models, and processes may work towards such a goal without ever actually achieving perfection. Accordingly, one of ordinary skill in the art having benefit of the present disclosure will appreciate that these terms, in the context of the scope of the present invention, are more general. The terms may describe one or more of: 1) working towards a solution which may be the best available solution, a preferred solution, or a solution that offers a specific benefit within a range of constraints; 2) continually improving; 3) refining; 4) searching for a high point or a maximum for an objective; 5) processing to reduce a penalty function; 6) seeking to maximize one or more factors in light of competing and/or cooperative interests in maximizing, minimizing, or otherwise controlling one or more other factors, etc. 
     Order of steps: It should also be understood that, unless clearly indicated to the contrary, in any methods claimed herein that include more than one step or act, the order of the steps or acts of the method is not necessarily limited to the order in which the steps or acts of the method are recited. 
     Ranges: Concentrations, dimensions, amounts, and other numerical data may be presented herein in a range format. It is to be understood that such range format is used merely for convenience and brevity and should be interpreted flexibly to include not only the numerical values explicitly recited as the limits of the range, but also to include all the individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly recited. For example, a range of about 1 to about 200 should be interpreted to include not only the explicitly recited limits of 1 and about 200, but also to include individual sizes such as 2, 3, 4, etc. and sub-ranges such as 10 to 50, 20 to 100, etc. Similarly, it should be understood that when numerical ranges are provided, such ranges are to be construed as providing literal support for claim limitations that only recite the lower value of the range as well as claims limitation that only recite the upper value of the range. For example, a disclosed numerical range of 10 to 100 provides literal support for a claim reciting “greater than 10” (with no upper bounds) and a claim reciting “less than 100” (with no lower bounds). 
     As used herein, the term “formation” refers to any definable subsurface region. The formation may contain one or more hydrocarbon-containing layers, one or more non-hydrocarbon containing layers, an overburden, and/or an underburden of any geologic formation. 
     As used herein, the term “hydrocarbon” refers to an organic compound that includes primarily, if not exclusively, the elements hydrogen and carbon. Examples of hydrocarbons include any form of natural gas, oil, coal, and bitumen that can be used as a fuel or upgraded into a fuel. 
     As used herein, the term “hydrocarbon fluids” refers to a hydrocarbon or mixtures of hydrocarbons that are gases or liquids. For example, hydrocarbon fluids may include a hydrocarbon or mixtures of hydrocarbons that are gases or liquids at formation conditions, at processing conditions, or at ambient conditions (20° C. and 1 atm pressure). Hydrocarbon fluids may include, for example, oil, natural gas, gas condensates, coal bed methane, shale oil, shale gas, and other hydrocarbons that are in a gaseous or liquid state. 
     As used herein, the term “potting” refers to the encapsulation of electrical components with epoxy, elastomeric, silicone, or asphaltic or similar compounds for the purpose of excluding moisture or vapors. Potted components may or may not be hermetically sealed. 
     As used herein, the term “sensor” includes any electrical sensing device or gauge. The sensor may be capable of monitoring or detecting pressure, temperature, fluid flow, vibration, resistivity, or other formation data. Alternatively, the sensor may be a position sensor. 
     As used herein, the term “subsurface” refers to geologic strata occurring below the earth&#39;s surface. 
     The terms “tubular member” or “tubular body” refer to any pipe, such as a joint of casing, a portion of a liner, a drill string, a production tubing, an injection tubing, a pup joint, a buried pipeline, underwater piping, or above-ground piping. solid lines therein, and any suitable number of such structures and/or features may be omitted from a given embodiment without departing from the scope of the present disclosure. 
     As used herein, the term “wellbore” refers to a hole in the subsurface made by drilling or insertion of a conduit into the subsurface. A wellbore may have a substantially circular cross section, or other cross-sectional shape. As used herein, the term “well,” when referring to an opening in the formation, may be used interchangeably with the term “wellbore.” 
     The terms “zone” or “zone of interest” refer to a portion of a subsurface formation containing hydrocarbons. The term “hydrocarbon-bearing formation” may alternatively be used. 
     Description 
     Specific forms will now be described further by way of example. While the following examples demonstrate certain forms of the subject matter disclosed herein, they are not to be interpreted as limiting the scope thereof, but rather as contributing to a complete description. 
       FIGS. 1-23  provide illustrative, non-exclusive examples of a system and method for removing fluids from a subterranean well, according to the present disclosure, together with elements that may include, be associated with, be operatively attached to, and/or utilize such a method or system. 
     In  FIGS. 1-23 , like numerals denote like, or similar, structures and/or features; and each of the illustrated structures and/or features may not be discussed in detail herein with reference to the figures. Similarly, each structure and/or feature may not be explicitly labeled in the figures; and any structure and/or feature that is discussed herein with reference to the figures may be utilized with any other structure and/or feature without departing from the scope of the present disclosure. 
     In general, structures and/or features that are, or are likely to be, included in a given embodiment are indicated in solid lines in the figures, while optional structures and/or features are indicated in broken lines. However, a given embodiment is not required to include all structures and/or features that are illustrated in solid lines therein, and any suitable number of such structures and/or features may be omitted from a given embodiment without departing from the scope of the present disclosure. 
     Although the approach disclosed herein can be applied to a variety of subterranean well designs and operations, the present description will primarily be directed to systems for removing fluids from a subterranean well. 
       FIG. 1  is a schematic representation of illustrative, non-exclusive examples of a hydrocarbon well  10  that may be utilized with and/or include the systems and methods according to the present disclosure, while  FIG. 2  is a schematic block diagram of illustrative, non-exclusive examples of a positive-displacement solid state pump  40  according to the present disclosure that may be utilized with hydrocarbon well  10 . Hydrocarbon well  10  includes a wellbore  20  that extends between a surface region  12  and a subterranean formation  16  that is present within a subsurface region  14 . The hydrocarbon well further includes a casing  30  that extends within the wellbore and defines a casing conduit  32 . 
     Positive-displacement solid state pump  40  is located within the casing conduit at least a threshold vertical distance  48  from surface region  12 . Threshold vertical distance  48  additionally or alternatively may be referred to herein as threshold vertical depth  48 . The positive-displacement solid state pump is configured to receive a wellbore liquid  22  and to pressurize the wellbore liquid to generate a pressurized wellbore liquid  24 . A tubing  78  defines a liquid discharge conduit  80  that may extend between positive-displacement solid state pump  40  and surface region  12 . The liquid discharge conduit is in fluid communication with casing conduit  32  via positive-displacement solid state pump  40  and is configured to convey pressurized wellbore liquid  24  from the casing conduit, such as to surface region  12 . 
     As illustrated in dashed lines in  FIG. 1 , hydrocarbon well  10  may include a lubricator  28  that may be utilized to locate (i.e., insert and/or position) positive-displacement solid state pump  40  within casing conduit  32  and/or to remove the positive-displacement solid state pump from the casing conduit. In addition, an injection conduit  38  may extend between surface region  12  and positive-displacement solid state pump  40  and may be configured to inject a corrosion inhibitor and/or a scale inhibitor into casing conduit  32  and/or into fluid contact with positive-displacement solid state pump  40 , such as to decrease a potential for corrosion of and/or scale build-up within the positive-displacement solid state pump. 
     As also illustrated in dashed lines, hydrocarbon well  10  and/or positive-displacement solid state pump  40  further may include a sand control structure  44 , which may be configured to limit flow of sand into an inlet  66  of positive-displacement solid state pump  40 , and/or a gas control structure  46 , which may limit flow of a wellbore gas  26  into inlet  66  of positive-displacement solid state pump  40 . As further illustrated in dashed lines in  FIG. 1 , tubing  78  may have a seat  34  attached thereto and/or included therein, with seat  34  being configured to receive positive-displacement solid state pump  40  and/or to retain positive-displacement solid state pump  40  at, or within, a desired region and/or location within tubing  78 . Additionally or alternatively, positive-displacement solid state pump  40  may include and/or be operatively attached to a packer  42 . Packer  42  may be configured to swell or otherwise be expanded within tubing conduit  80  and to thereby retain positive-displacement solid state pump  40  at, or within, the desired region and/or location within tubing  78 . 
     Still referring to  FIGS. 1-2 , hydrocarbon well  10  and/or positive-displacement solid state pump  40  thereof further may include a means for powering the solid state pump  54  that is configured to provide an electric current to positive-displacement solid state pump  40 . In addition, a sensor  92  may be configured to detect a downhole process parameter and may be located within wellbore  20 , may be operatively attached to positive-displacement solid state pump  40 , and/or may form a portion of the positive-displacement solid state pump. The sensor may be configured to convey a data signal that is indicative of the process parameter to surface region  12  and/or may be in communication with a controller  90  that is configured to control the operation of at least a portion of positive-displacement solid state pump  40 . 
     As also discussed, positive-displacement solid state pump  40  may be powered by (or receive an electric current  58  from) means for powering the solid state pump  54 , which may be operatively attached to the positive-displacement solid state pump, may form a portion of the positive-displacement solid state pump, and/or may be in electrical communication with the positive-displacement solid state pump via an electrical conduit  56 . Thus, positive-displacement solid state pump  40  according to the present disclosure may be configured to generate pressurized wellbore liquid  24  without utilizing a reciprocating mechanical linkage that extends between surface region  12  and the positive-displacement solid state pump (such as might be utilized with traditional rod pump systems) to provide a motive force for operation of the positive-displacement solid state pump. This may permit positive-displacement solid state pump  40  to be utilized in long, deep, and/or deviated wellbores where traditional rod pump systems may be ineffective, inefficient, and/or unable to generate the pressurized wellbore liquid  24 . 
     Similarly, and since positive-displacement solid state pump  40  is powered by means for powering the solid state pump  54 , the positive-displacement solid state pump may be configured to generate pressurized wellbore liquid  24  (and/or to remove the pressurized wellbore liquid from casing conduit  32  via liquid discharge conduit  80 ) without requiring a threshold minimum pressure of wellbore gas  26 . This may permit positive-displacement solid state pump  40  to be utilized in hydrocarbon wells  10  that do not develop sufficient gas pressure to permit utilization of traditional plunger lift systems and/or that define long and/or deviated casing conduits  32  that preclude the efficient operation of traditional plunger lift systems. 
     Furthermore, positive-displacement solid state pump  40  may operate as a positive displacement pump and thus may be sized, designed, and/or configured to generate pressurized wellbore liquid  24  at a pressure that is sufficient to permit the pressurized wellbore liquid to be conveyed via liquid discharge conduit  80  to surface region  12  without utilizing a large number of pumping stages. It follows that reducing the number of pumping stages may decrease a length  41  of the positive-displacement solid state pump (as illustrated in  FIG. 1 ). As illustrative, non-exclusive examples, positive-displacement solid state pump  40  may include fewer than five stages, fewer than four stages, fewer than three stages, or a single stage. 
     As additional illustrative, non-exclusive examples, the length of the positive-displacement solid state pump may be less than 30 meters (m), less than 28 m, less than 26 m, less than 24 m, less than 22 m, less than 20 m, less than 18 m, less than 16 m, less than 14 m, less than 12 m, less than 10 m, less than 8 m, less than 6 m, or less than 4 m. Additionally or alternatively, an outer diameter of the positive-displacement solid state pump may be less than 20 centimeters (cm), less than 18 cm, less than 16 cm, less than 14 cm, less than 12 cm, less than 10 cm, less than 9 cm, less than 8 cm, less than 7 cm, less than 6 cm, or less than 5 cm. 
     This small length and/or small diameter of positive-displacement solid state pumps  40 , according to the present disclosure, may permit the positive-displacement solid state pumps  40  to be located within and/or to flow through and/or past deviated regions  33  within wellbore  20  and/or casing conduit  32 . These deviated regions might obstruct and/or retain longer and/or larger-diameter traditional pumping systems that do not include positive-displacement solid state pump  40  and/or that utilize a larger number (such as more than 5, more than 6, more than 8, more than 10, more than 15, or more than 20) of stages to generate pressurized wellbore liquid  24 . Thus, positive-displacement solid state pumps  40  according to the present disclosure may be operable in hydrocarbon wells  10  that are otherwise inaccessible to more traditional artificial lift systems. This may include locating positive-displacement solid state pump  40  uphole from deviated regions  33 , as schematically illustrated in dashed lines in  FIG. 1 , and/or locating positive-displacement solid state pump  40  downhole from deviated regions  33 , such as in a horizontal portion of wellbore  20  and/or near a toe end  21  of wellbore  20  (as schematically illustrated in dash-dot lines in  FIG. 1 ). 
     Additionally or alternatively, the (relatively) small length and/or the (relatively) small diameter of positive-displacement solid state pumps  40  according to the present disclosure may permit the positive-displacement solid state pumps to be located within casing conduit  32  and/or removed from casing conduit  32  via lubricator  28 . This may permit the positive-displacement solid state pumps to be located within the casing conduit without depressurizing hydrocarbon well  10 , without killing well  10 , without first supplying a kill weight fluid to wellbore  20 , and/or while containing wellbore fluids within the wellbore. This may increase an overall efficiency of operations that insert positive-displacement solid state pumps into and/or remove positive-displacement solid state pumps from wellbore  20 , may decrease a time required to permit positive-displacement solid state pumps  40  to be inserted into and/or removed from wellbore  20 , and/or may decrease a potential for damage to hydrocarbon well  10  when positive-displacement solid state pumps  40  are inserted into and/or removed from wellbore  20 . 
     Furthermore, and as discussed in more detail herein, positive-displacement solid state pumps  40 , according to the present disclosure, may be configured to generate pressurized wellbore liquid  24  at relatively low discharge flow rates and/or at selectively variable discharge flow rates. This may permit positive-displacement solid state pumps  40  to efficiently operate in low production rate hydrocarbon wells and/or in hydrocarbon wells that generate low volumes of wellbore liquid  22 , in contrast to more traditional artificial lift systems. 
     Positive-displacement solid state pump  40  includes a solid state element  60  and a fluid chamber  64 . Solid state element  60  may be configured to selectively and/or repeatedly transition from an extended state to a contracted state during an intake stroke of the positive-displacement solid state pump and to subsequently transition from the contracted state to the expanded state during an exhaust stroke of the positive-displacement solid state pump. This may include transitioning between the extended state and the contracted state responsive to receipt of electric current  58 , which may be an AC electric current. 
     Fluid chamber  64  may be configured to receive wellbore liquid  22  from wellbore  20 , such as via inlet  66 , during the intake stroke of the positive-displacement solid state pump and to emit, or discharge, pressurized wellbore liquid  24 , such as through an outlet  67 , during the exhaust stroke of the positive-displacement solid state pump. As illustrated schematically in  FIG. 2  and discussed in more detail hereinbelow, positive-displacement solid state pump  40  further may include a housing  50 , a first one-way check valve positioned between the inlet port and the fluid chamber  69 , a second one-way check valve positioned between the outlet port and the fluid chamber  68 , a sealing structure  72 , and/or an isolation structure  74 . Positive-displacement solid state pump  40  also may include a liquid inlet valve  62 . Liquid inlet valve  62  may be configured to selectively introduce wellbore liquid  22  into fluid chamber  64  of positive-displacement solid state pump  40 , as discussed in more detail herein. 
     As discussed, wellbore  20  may define deviated region  33 , which also may be referred to herein as a nonlinear region  33 , that may have a deviated (i.e., nonvertical) and/or nonlinear trajectory within subsurface region  14  and/or subterranean formation  16  thereof (as schematically illustrated in  FIG. 1 ). In addition and as also discussed, positive-displacement solid state pump  40  may be located downhole from deviated region  33 . As illustrative, non-exclusive examples, nonlinear region  33  may include and/or be a tortuous region, a curvilinear region, an L-shaped region, an S-shaped region, and/or a transition region between a (substantially) horizontal region and a (substantially) vertical region that may define a tortuous trajectory, a curvilinear trajectory, a deviated trajectory, an L-shaped trajectory, an S-shaped trajectory, and/or a transitional, or changing, trajectory. 
     Means for powering the solid state pump  54  may include any suitable structure that may be configured to provide the electric current to positive-displacement solid state pump  40 , and/or to solid state element  60  thereof, and may be present in any suitable location. As an illustrative, non-exclusive example, means for powering the solid state pump  54  may be located in surface region  12 , and electrical conduit  56  may extend between the means for powering the solid state pump and the positive-displacement solid state pump. Illustrative, non-exclusive examples of electrical conduit  56  include any suitable wire, cable, wireline, and/or working line and electrical conduit  56  may connect to positive-displacement solid state pump  40  via any suitable electrical connection and/or wet-mate connection. 
     As another illustrative, non-exclusive example, means for powering the solid state pump  54  may include and/or be a battery pack. The battery pack may be located within surface region  12 , may be located within wellbore  20 , and/or may be operatively and/or directly attached to positive-displacement solid state pump  40 . 
     As additional illustrative, non-exclusive examples, means for powering the solid state pump  54  may include and/or be a generator, an AC generator, a DC generator, a turbine, a solar-powered means for powering the solid state pump, a wind-powered means for powering the solid state pump, and/or a hydrocarbon-powered means for powering the solid state pump that may be located within surface region  12  and/or within wellbore  20 . When means for powering the solid state pump  54  is located within wellbore  20 , the means for powering the solid state pump also may be referred to herein as a downhole power generation assembly  54 . 
     As discussed in more detail herein, a discharge flow rate of pressurized wellbore liquid  24  that is generated by positive-displacement solid state pump  40  may be controlled, regulated, and/or varied by controlling, regulating, and/or varying a frequency of an AC electric current that is provided to positive-displacement solid state pump  40  and/or to solid state element  60  thereof. This may include increasing the frequency of the AC electric current to increase the discharge flow rate (by decreasing a time that it takes for the positive-displacement solid state pump to transition between the extended state and the contracted state) and/or decreasing the frequency of the AC electric current to decrease the discharge flow rate (by increasing the time that it takes for the positive-displacement solid state pump to transition between the extended state and the contracted state). 
     Illustrative, non-exclusive examples of the frequency of the AC electric current include frequencies of at least 0.01 Hertz (Hz), at least 0.05 Hz, at least 0.1 Hz, at least 0.5 Hz, at least 1 Hz, at least 5 Hz, at least 10 Hz, at least 20 Hz, at least 30 Hz, at least 40 Hz, at least 60 Hz, at least 80 Hz, and/or at least 100 Hz. Additional illustrative, non-exclusive examples of the frequency of the AC electric current include frequencies of less than 4000 Hz, less than 3500 Hz, less than 3000 Hz, less than 2500 Hz, less than 2000 Hz, less than 1500 Hz, less than 1000 Hz, less than 750 Hz, less than 500 Hz, less than 250 Hz, less than 200 Hz, less than 150 Hz, and/or less than 100 Hz. Further illustrative, non-exclusive examples of the frequency of the AC electric current include frequencies in any range of the preceding minimum and maximum frequencies. 
     Sensor  92  may include any suitable structure that is configured to detect the downhole process parameter. Illustrative, non-exclusive examples of the downhole process parameter include a downhole temperature, a downhole pressure, a discharge pressure from the positive-displacement solid state pump, system vibration, a downhole flow rate, and/or a discharge flow rate from the positive-displacement solid state pump. 
     It is within the scope of the present disclosure that sensor  92  may be configured to detect the downhole process parameter at any suitable location within wellbore  20 . As an illustrative, non-exclusive example, the sensor may be located such that the downhole process parameter is indicative of a condition at an inlet to positive-displacement solid state pump  40 . As another illustrative, non-exclusive example, the sensor may be located such that the downhole process parameter is indicative of a condition at an outlet from positive-displacement solid state pump  40 . 
     When hydrocarbon well  10  includes sensor  92 , the hydrocarbon well also may include a data communication conduit  94  (as illustrated in  FIG. 1 ) that may be configured to convey a signal that is indicative of the downhole process parameter between sensor  92  and surface region  12 . As an illustrative, non-exclusive example, controller  90  may be located within surface region  12 , and data communication conduit  94  may convey the signal to the controller. As another illustrative, non-exclusive example, the data communication conduit may convey the signal to a display and/or to a terminal that is located within surface region  12 . 
     Controller  90  may include any suitable structure that may be configured to control the operation of any suitable portion of hydrocarbon well  10 , such as positive-displacement solid state pump  40 . This may include controlling using methods  300 , which are discussed in more detail herein. 
     As illustrated in  FIG. 1 , controller  90  may be located in any suitable portion of hydrocarbon well  10 . As an illustrative, non-exclusive example, the controller may include and/or be an autonomous and/or automatic controller that is located within wellbore  20  and/or that is directly and/or operatively attached to positive-displacement solid state pump  40 . Thus, controller  90  may be configured to control the operation of positive-displacement solid state pump  40  without requiring that a data signal be conveyed to surface region  12  via data communication conduit  94 . Additionally or alternatively, controller  90  may be located within surface region  12  and may communicate with positive-displacement solid state pump  40  via data communication conduit  94 . 
     As an illustrative, non-exclusive example, controller  90  may be programmed to maintain a target wellbore liquid level within wellbore  20  above positive-displacement solid state pump  40 . This may include increasing a discharge flow rate of pressurized wellbore liquid  24  that is generated by the positive-displacement solid state pump to decrease the wellbore liquid level and/or decreasing the discharge flow rate to increase the wellbore liquid level. 
     As another illustrative, non-exclusive example, controller  90  may be programmed to regulate the discharge flow rate to control the discharge pressure from the positive-displacement solid state pump. This may include increasing the discharge flow rate to increase the discharge pressure and/or decreasing the discharge flow rate to decrease the discharge pressure. 
     As a more specific but still illustrative, non-exclusive example, and when hydrocarbon well  10  includes sensor  92 , controller  90  may be programmed to control a frequency of the AC electric current that is provided to positive-displacement solid state pump  40 , thus controlling the discharge flow rate, based, at least in part, on the downhole process parameter. This may include increasing the frequency of the AC electric current to increase the discharge flow rate and/or decreasing the frequency of the AC electric current to decrease the discharge flow rate. 
     As another more specific but still illustrative, non-exclusive example, and when positive-displacement solid state pump  40  includes liquid inlet valve  62 , controller  90  may be programmed to control the operation of the liquid inlet valve. This may include opening the liquid inlet valve to permit wellbore fluid to enter fluid chamber  64  of the positive-displacement solid state pump responsive to the downhole process parameter indicating a gas lock condition of the positive-displacement solid state pump. 
     As discussed, positive-displacement solid state pump  40 , according to the present disclosure, may be utilized to provide artificial lift in wellbores that define a large vertical distance, or depth,  48 , in wellbores that define a large overall length, and/or in wellbores in which positive-displacement solid state pump  40  is located at least a threshold vertical distance from surface region  12 . 
     As illustrative, non-exclusive examples, the vertical depth of wellbore  20 , the overall length of wellbore  20 , and/or the threshold vertical distance of positive-displacement solid state pump  40  from surface region  12  may be at least 250 meters (m), at least 500 m, at least 750 m, at least 1000 m, at least 1250 m, at least 1500 m, at least 1750 m, at least 2000 m, at least 2250 m, at least 2500 m, at least 2750 m, at least 3000 m, at least 3250 m, and/or at least 3500 m. Additionally or alternatively, the vertical depth of wellbore  20 , the overall length of wellbore  20 , and/or the threshold vertical distance of positive-displacement solid state pump  40  from surface region  12  may be less than 8000 m, less than 7750 m, less than 7500 m, less than 7250 m, less than 7000 m, less than 6750 m, less than 6500 m, less than 6250 m, less than 6000 m, less than 5750 m, less than 5500 m, less than 5250 m, less than 5000 m, less than 4750 m, less than 4500 m, less than 4250 m, and/or less than 4000 m. Further additionally or alternatively, the vertical depth of wellbore  20 , the overall length of wellbore  20 , and/or the threshold vertical distance of positive-displacement solid state pump  40  from surface region  12  may be in a range defined, or bounded, by any combination of the preceding maximum and minimum depths. 
       FIG. 3  provides a further illustrative, non-exclusive example of a hydrocarbon well  10  that includes a positive-displacement solid state pump  40  according to the present disclosure. In  FIG. 3 , positive-displacement solid state pump  40  is located within a casing conduit  32  that is defined by a casing  30  that extends within a wellbore  20 . Casing  30  includes a plurality of perforations  36  that provide fluid communication between casing conduit  32  and a subterranean formation  16  that is present within a subsurface region  14 . Positive-displacement solid state pump  40  is retained within a liquid discharge conduit  80  by a seat  34  and/or by a packer  42  and is configured to receive wellbore liquid  22  from casing conduit  32  and to generate pressurized wellbore liquid  24  therefrom. 
     As illustrated in  FIG. 3 , a wellbore gas  26  may flow within an annular space  79  within casing conduit  32 . As illustrated, annular space  79  is defined between casing  30  and a tubing  78  that defines liquid discharge conduit  80 . Annular space  79  also may be referred to herein as and/or may be a gas discharge conduit  79 . As also illustrated in  FIG. 3 , a plurality of sensors  92  may detect a plurality of downhole process parameters at, or near, an inlet  66  to positive-displacement solid state pump  40  and/or at, or near, an outlet  67  from the positive-displacement solid state pump. A sand control structure  44  may restrict flow of sand from subterranean formation  16 , into the positive-displacement solid state pump  40 . In addition, a gas control structure  46  may restrict flow of wellbore gas  26  into the positive-displacement solid state pump. 
       FIG. 3  further illustrates that positive-displacement solid state pump  40  may include one or more first one-way check valves  69 . First one-way check valves  69 , positioned between the inlet port and the fluid chamber  64 , may be configured to permit wellbore liquid  22  to enter a fluid chamber  64  of the positive-displacement solid state pump from wellbore  32 . However, the one or more first one-way check valves  69 , positioned between the inlet port and the fluid chamber  64 , may resist, restrict, and/or block flow of pressurized wellbore liquid  24  therethrough and/or back into wellbore  32 . This may permit creation of pressurized wellbore liquid  24  and/or pumping of pressurized wellbore liquid  24  from wellbore  32  via liquid discharge conduit  80 . 
     As also illustrated in  FIG. 3 , positive-displacement solid state pump  40  further may include one or more second one-way check valves  68 . Second one-way check valves  68 , positioned between the outlet port and the fluid chamber  64 , may be configured to permit pressurized wellbore liquid  24  to enter liquid discharge conduit  80  from fluid chamber  64  of positive-displacement solid state pump  40 . However, the one or more second one-way check valves  68 , which are positioned between the outlet port and the fluid chamber  64  may resist, restrict, and/or block flow of pressurized wellbore liquid  24  from liquid discharge conduit  80  into fluid chamber  64 . This further may permit creation of pressurized wellbore liquid  24  and/or pumping of the pressurized wellbore liquid from wellbore  32  via liquid discharge conduit  80 . 
     The one or more first one-way check valves  69 , positioned between the inlet port and the fluid chamber  64 , and/or the one or more second one-way check valves  68 , positioned between the outlet port and the fluid chamber  64 , may include any suitable structure. As illustrative, non-exclusive examples, first one-way check valve  69  and/or second one-way check valve  68  may include and/or be a mechanically actuated check valve and/or a check valve that is not electrically actuated. As a further illustrative, non-exclusive example, first one-way check valve  69  and/or second one-way check valve  68  may be an electrically actuated and/or electrically controlled check valve. 
     Fluid chamber  64  may define a volume that varies with a state of a solid state element  60  of positive-displacement solid state pump  40 . Thus, fluid chamber  64  may define an expanded volume when the solid state element is in a contracted state, as schematically illustrated in solid lines in  FIG. 3 . Conversely, fluid chamber  64  may define a contracted volume when solid state element  60  is in an extended state, as schematically illustrated in dash-dot lines in  FIG. 3 . In addition, and as illustrated, the expanded volume may be greater than the contracted volume. 
     As illustrative, non-exclusive examples, the expanded volume may be at least 0.01 cubic centimeters, at least 0.1 cubic centimeters, at least 1 cubic centimeter, at least 5 cubic centimeters, at least 10 cubic centimeters, at least 20 cubic centimeters, at least 30 cubic centimeters, at least 40 cubic centimeters, at least 50 cubic centimeters, at least 60 cubic centimeters, at least 70 cubic centimeters, at least 80 cubic centimeters, at least 90 cubic centimeters, and/or at least 100 cubic centimeters greater than the contracted volume. Additionally or alternatively, the expanded volume also may be less than 400 cubic centimeters, less than 350 cubic centimeters, less than 300 cubic centimeters, less than 250 cubic centimeters, less than 200 cubic centimeters, less than 180 cubic centimeters, less than 160 cubic centimeters, less than 140 cubic centimeters, less than 120 cubic centimeters, and/or less than 100 cubic centimeters greater than the contracted volume. As further illustrative, non-exclusive examples, the expanded volume may be in a range defined by any combination of the preceding minimum and maximum values. 
     As illustrated in  FIG. 3 , positive-displacement solid state pump  40  further may include a housing  50 . Housing  50  may at least partially define fluid chamber  64 . Additionally or alternatively, solid state element  60  may be located at least partially within housing  50 . In addition, and as discussed in more detail herein with reference to  FIGS. 4-5 , positive-displacement solid state pump  40  further may include a sealing structure  72  and/or an isolation structure  74 . 
       FIG. 4  provides a further illustrative, non-exclusive example of a portion of a downhole piezoelectric pump  40 , according to the present disclosure, that includes an isolation structure  74 . Isolation structure  74  may be configured to fluidly isolate piezoelectric element  60  from compression chamber  64 . This may include fluidly isolating the piezoelectric element from the compression chamber when the piezoelectric element is in the contracted state, as illustrated in solid lines in  FIG. 4 , as well as fluidly isolating the piezoelectric element from the compression chamber when the piezoelectric element is in the extended state, as illustrated in dash-dot lines in  FIG. 4 . 
     Isolation structure  74  may include any suitable structure. As illustrative, non-exclusive examples, isolation structure  74  may include and/or be a flexible isolation structure  75 , a diaphragm  76 , and/or an isolation coating  77 . 
       FIG. 5  provides a further illustrative, non-exclusive example of a downhole piezoelectric pump  40  according to the present disclosure that includes a sealing structure  72 . Sealing structure  72  may be configured to create a fluid seal between piezoelectric element  60  and housing  50  during (or despite) motion of piezoelectric element  60  and/or transitioning of the piezoelectric element between the contracted state, as illustrated in solid lines in  FIG. 5 , and the extended state (as illustrated in dash-dot lines in  FIG. 5 . Thus, sealing structure  72  may permit piezoelectric element  60  to transition between the extended state and the contracted state while restricting fluid flow from compression chamber  64  past the sealing structure. 
     Sealing structure  72  may include any suitable structure. As an illustrative, non-exclusive example, sealing structure  72  may include and/or be at least one O-ring. 
     Referring now to  FIG. 6 , a schematic representation of illustrative, non-exclusive examples of a system  110  for removing wellbore liquids from a wellbore  120 , the wellbore  120  traversing a subterranean formation  116  and having a tubular  178  that extends within at least a portion of the wellbore  120 , according the present disclosure is presented. The system  110  includes a positive-displacement solid state pump  140  comprising a fluid chamber  164 , an inlet port  163  and an outlet port  165 , each in fluid communication with the fluid chamber  164 . At least one solid state element or actuator  160  is provided, together with a first one-way check valve  169  positioned between the inlet port  163  and the fluid chamber  164 , and a second one-way check valve  168  positioned between the outlet port  165  and the fluid chamber  164 . In some embodiments, the at least one solid state actuator  160  may be configured to operate at or near its resonance frequency. As shown, the solid state pump  140  is positioned within the wellbore  120 . 
     A means for powering the solid state pump  154  is provided and may include any suitable structure that may be configured to provide the electric current to positive-displacement solid state pump  140 , and/or to solid state element or actuator  160  thereof, and may be present in any suitable location. As an illustrative, non-exclusive example, means for powering the solid state pump  154  may be located in surface region, and electrical conduit  156  may extend between the means for powering the solid state pump and the positive-displacement solid state pump  140 . Illustrative, non-exclusive examples of electrical conduit  156  include any suitable wire, power cable, wireline, and/or working line and electrical conduit  156  may connect to positive-displacement solid state pump  140  via any suitable electrical connection and/or wet-mate connection. 
     As another illustrative, non-exclusive example, means for powering the solid state pump  154  may include and/or be a rechargeable battery pack. The battery pack may be located within surface region, may be located within wellbore  120 , and/or may be operatively and/or directly attached to positive-displacement solid state pump  140 . 
     As indicated above, means for powering the solid state pump  154  may include and/or be a generator, an AC generator, a DC generator, a turbine, a solar-powered means for powering the solid state pump, a wind-powered means for powering the solid state pump, and/or a hydrocarbon-powered means for powering the solid state pump that may be located within surface region and/or within wellbore  120 . When means for powering the solid state pump  154  is located within wellbore  120 , the means for powering the solid state pump also may be referred to herein as a downhole power generation assembly. In some embodiments, the means for powering the solid state pump  154  is a power cable, the power cable operable for deploying the solid state pump  140 . In some embodiments, the power cable comprises a synthetic conductor. 
     In some embodiments, the positive-displacement solid state pump may be plugged into a downhole wet-mate connection (not shown) and the means for powering the solid state pump  154 , is a power cable positioned on the outside of the tubular  120 . 
     As indicated, at least one solid state element or actuator  160  is provided. The at least one solid state actuator  160  may be selected from piezoelectric, electrostrictive and/or magnetorestrictive actuators. In some embodiments, the at least one solid state actuator  160  comprises a ceramic perovskite material. The ceramic perovskite material may comprise lead zirconate titanate and/or lead magnesium niobate. In some embodiments, the at least one solid state actuator  160  may comprise terbium dysprosium iron. 
     In some embodiments, the at least one solid state actuator  160  may be configured to accommodate heat exchange with the pumped fluid to cool the actuator  160 . For example, a concentric aperture may be provided to enable through-flow of pumped fluids to improve cooling. In some embodiments, the at least one solid state actuator  160  is directly or indirectly cooled with thermoelectric cooling elements. In some embodiments, the at least one solid state actuator includes one or more central throughbores, internal passageways, channels, or similar surface-area-enhancing features for enhanced cooling. These features enable wellbore fluids to circulate through, around, or otherwise in contact with the increased surface area of the at least one solid state actuator to facilitate enhanced cooling for the at least one solid state actuator. In some embodiments, the wellbore fluid is pumped or flows through the at least one solid state actuator circulation of wellbore fluids in response to pumping action by the at least one solid state actuator, while in other embodiments, the wellbore fluid may be pumped or flowed through the at least one solid state actuator. 
     As shown in  FIG. 6  and described above, a first one-way check valve  169  may be positioned between the inlet port  163  and the fluid chamber  164 . Likewise, a second one-way e check valve  168  may be positioned between the outlet port  165  and the fluid chamber  164 . In some embodiments, the first one-way check valve  169  and the second one-way check valve  168  are active microvalve arrays. In some embodiments, the first one-way check valve  169  and the second one-way check valve  168  are active MEMS valve arrays. In some embodiments, the first one-way check valve  169  and/or the second one-way check valve  168  are either passive one-way disc valves, active microvalve arrays, or active MEMS valve arrays, or a combination thereof. 
     In some embodiments, the solid state pump  140  includes a piston  130  and a cylinder  132  for housing the at least one solid state actuator  160  and the first and second one-way check valves,  169  and  168 , respectively, so as to form a piston pump. 
     In some embodiments, the solid state pump  140  includes a diaphragm, described in more detail below, that is operatively associated with the at least one solid state actuator  160  and the first and second the one-way check valves,  169  and  168 , respectively, so as to form a diaphragm pump. 
     In some embodiments, the system  110  may include a profile seating nipple  134  positioned within the tubular  178  for receiving the solid state pump  140 . In some embodiments, the profile seating nipple  134  comprises a locking groove  136  structured and arranged to matingly engage the solid state pump  140 . 
     As shown in  FIG. 7 , the system  110  of  FIG. 6  may include a well screen or filter  270  in fluid communication with the inlet end  163  of the solid state pump  140 , the well screen or filter  270  having an inlet end  272  and an outlet end  274 . As shown in  FIG. 7 , a velocity fuse  276  may be positioned after the outlet end  274  of the well screen or filter  270 . In some embodiments, the velocity fuse or standing valve  276  may be structured and arranged to back-flush the well screen or filter  270  and maintain a column of fluid within the tubular  178  in response to an increase in pressure drop across the velocity fuse  276 . 
     Referring now to  FIG. 7 , another schematic representation of an illustrative, non-exclusive example of a system  210  for removing wellbore liquids from a wellbore  220 , the wellbore  220  traversing a subterranean formation  216  and having a tubular  278  that extends within at least a portion of the wellbore  220 , according the present disclosure is presented. The system  210  includes a positive-displacement solid state pump  240  comprising a fluid chamber  264 , an inlet port  263  and an outlet port  265 , each in fluid communication with the fluid chamber  264 . At least one solid state element or actuator  260  is provided, together with a first one-way check valve  269  positioned between the inlet port  263  and the fluid chamber  264 , and a second one-way check valve  268  positioned between the outlet port  265  and the fluid chamber  264 . In some embodiments, the at least one solid state actuator  260  may be configured to operate at or near its resonance frequency. As shown, the solid state pump  240  positioned within the wellbore  220 . 
     A means for powering the solid state pump  254  is provided and may include any suitable structure that may be configured to provide the electric current to positive-displacement solid state pump  240 , and/or to solid state element or actuator  260  thereof, and may be present in any suitable location. 
     The system  210  further includes at least one secondary pump  280  for transferring the wellbore liquids from the wellbore  220 . In the configuration of  FIG. 7 , the inlet port  263  and the outlet port  265  of the positive-displacement solid state pump  240  are operatively connected to a hydraulic system  282  to drive the at least one secondary pump  284  and form a pump assembly  284 . 
     In some embodiments, the at least one secondary pump  280  may comprise a bladder pump. In some embodiments, the at least one secondary pump  280  may comprise a centrifugal pump. In some embodiments, the at least one secondary pump  280  may comprise a rotary screw pump and/or a rotary lobe pump. In some embodiments, the at least one secondary pump  280  may comprise a gerotor pump and/or a progressive cavity pump. In some embodiments, the bladder pump is a metal bellows pump or an elastomer pump. 
     As an illustrative, non-exclusive example, means for powering the solid state pump  254  may be located in surface region S, and electrical conduit  256  may extend between the means for powering the solid state pump  254  and the positive-displacement solid state pump  240 . Illustrative, non-exclusive examples of electrical conduit  256  include any suitable wire, power cable, wireline, and/or working line, and electrical conduit  256  may connect to positive-displacement solid state pump  240  via any suitable electrical connection and/or wet-mate connection. 
     As another illustrative, non-exclusive example, means for powering the solid state pump  254  may include and/or be a rechargeable battery pack. The battery pack may be located within surface region, may be located within wellbore  220 , and/or may be operatively and/or directly attached to positive-displacement solid state pump  240 . 
     As indicated above, means for powering the solid state pump  254  may include and/or be a generator, an AC generator, a DC generator, a turbine, a solar-powered means for powering the solid state pump, a wind-powered means for powering the solid state pump, and/or a hydrocarbon-powered means for powering the solid state pump that may be located within surface region S and/or within wellbore  220 . When means for powering the solid state pump  254  is located within wellbore  220 , the means for powering the solid state pump also may be referred to herein as a downhole power generation assembly. In some embodiments, the means for powering the solid state pump  254  is a power cable  256 , the power cable operable for deploying the solid state pump  240 . In some embodiments, the power cable  256  comprises a synthetic conductor. 
     In some embodiments, the positive-displacement solid state pump  240  may be plugged into a downhole wet-mate connection (not shown) and the means for powering the solid state pump  254 , is a power cable positioned on the outside of the tubular  220 . 
     As indicated above, at least one solid state element or actuator  260  is provided. The at least one solid state actuator  260  may be selected from piezoelectric, electrostrictive and/or magnetorestrictive actuators. In some embodiments, the at least one solid state actuator  260  comprises a ceramic perovskite material. The ceramic perovskite material may comprise lead zirconate titanate and/or lead magnesium niobate. In some embodiments, the at least one solid state actuator  260  may comprise terbium dysprosium iron. In some embodiments, the at least one solid state actuator  260  contains functional shapes or configurations to enhance actuator cooling, such as providing apertures for through-flow of pumped fluids. In some embodiments, the at least one solid state actuator  260  is directly or indirectly cooled with thermoelectric cooling elements. 
     A first one-way check valve  269  may be positioned between the inlet port  263  and the fluid chamber  264 . Likewise, a second one-way check valve  268  may be positioned between the outlet port  265  and the fluid chamber  264 . In some embodiments, the first one-way check valve  269  and the second one-way check valve  268  are active microvalve arrays. In some embodiments, the first one-way check valve  269  and the second one-way check valve  268  are active MEMS valve arrays. In some embodiments, the first one-way check valve  269  and/or the second one-way check valve  268  are either passive one-way disc valves, active microvalve arrays, or active MEMS valve array, or a combination thereof. 
     In some embodiments, the solid state pump  240  includes a diaphragm  230 , described in more detail below, that is operatively associated with the at least one solid state actuator  260  and the first and second the one-way check valves,  269  and  268 , respectively, so as to form a diaphragm pump. 
     As shown in the example of  FIG. 6 , in some embodiments, the solid state pump  240  may include a piston and a cylinder for housing the at least one solid state actuator and the first and second one-way check valves, so as to form a piston pump. 
     In some embodiments, the system  210  may include a profile seating nipple  234  positioned within the tubular  220  for receiving the solid state pump  240 . In some embodiments, the profile seating nipple  234  comprises a locking groove  236  structured and arranged to matingly engage the pump assembly  284 . 
     The system  210  may include a well screen or filter  270  in fluid communication with the inlet end  290  of the pump assembly  284 , the well screen or filter  270  having an inlet end  272  and an outlet end  274 . As shown, a velocity fuse or standing valve  276  may be positioned after the outlet end  274  of the well screen or filter  270 . In some embodiments, the velocity fuse  276  may be structured and arranged to back-flush the well screen or filter  270  and maintain a column of fluid within the tubular  278  in response to an increase in pressure drop across the velocity fuse  276 . 
     Suitable velocity fuses are commercially available from a variety of sources, including the Hydraulic Valve Division of Parker Hannifin Corporation, Elyria, Ohio, USA, and Vonberg Valve, Inc., Rolling Meadows, Ill., USA. In particular, two sizes of commercially available velocity fuses are expected to have utility in the practice of the present disclosure. These are: a velocity fuse having a 1″ OD, with a flow range of 11 liters/minute (3 GPM) to 102 liters/minute (27 GPM), and a velocity of having a 1.5″ OD, with a flow range of: 23 liters/minute (6 GPM) to 227 liters/minute (60 GPM). Each of these commercially available velocity sleeves have a maximum working pressure of 5,000 psi and a temperature ratings of −20 F to +350 F (−27C to +177C). The body and sleeve are made of brass, and the poppet, roll pin, and spring are made of stainless steel. O-rings are both nitrile and PTFE. Custom-built velocity fuses are envisioned and may provide a higher pressure rated device, if needed, which may be incorporated into a housing for seating in the no-go profile nipple. 
     Referring now to  FIGS. 8-10 , one embodiment of a positive-displacement solid state pump  305 , in accordance herewith, is presented. As shown in  FIG. 8 , a power source  301 , which may be an AC power source, provides power to at least one solid state actuator,  304  of positive-displacement solid state pump  305 . A frequency modulator  302  and an amplitude modulator  303  may be connected in series, as shown, and can be adjusted to vary the frequency and amplitude of the signal reaching at least one solid state actuator  304 . In some embodiments, the at least one solid state actuator  304  is selected from piezoelectric, electrostrictive and/or magnetorestrictive actuators. In some embodiments, the at least one solid state actuator  304  is a piezoelectric actuator  320 . 
     In some embodiments, a diaphragm  306  is bonded to the top of piezoelectric actuator  320  and separates piezoelectric actuator  320  from fluid chamber  307 . A first one-way passive disc valve  310  controls the flow of fluid through inlet port  308  into fluid chamber  307 . Likewise, a second one-way passive disc valve  311  controls the flow of fluid leaving fluid chamber  307  through outlet port  309 . Suitable passive one-way disc valves are available from Kinetic Ceramics, Inc. of Hayward, Calif. Such passive one-way disc valves may fabricated from metal. 
     Referring to  FIGS. 8 and 9 , in operation, as voltage is applied to piezoelectric actuator  320  via power source  301 , piezoelectric actuator  320  will expand and contract in response to the signal, causing diaphragm  306  to bend up and down in a piston-like fashion. When diaphragm  306  bend downwards, fluid chamber  307  expands, as those skilled in the art would plainly understand. The expanding of the size of fluid chamber  307  causes a corresponding drop in pressure inside fluid chamber  307 . When the pressure inside fluid chamber  307  becomes less than the pressure inside fluid inlet port  308 , first one-way passive disc valve  310  will open permitting the flow of fluid into fluid chamber  307 . When the pressure inside fluid chamber  307  becomes less than the pressure inside fluid outlet port  309 , the second one-way passive disc valve  311  will close preventing a back flow of fluid from outlet port  309  into fluid chamber  307 . 
     Referring to  FIGS. 8 and 10 , when diaphragm  306  bends upwards, the size of fluid chamber  307  decreases. The decreasing of the size of fluid chamber  307  causes a corresponding increase in pressure inside fluid chamber  307 . When the pressure inside fluid chamber  307  becomes greater than the pressure inside fluid outlet port  309 , second one-way passive disc valve  311  will open permitting the flow of fluid out of fluid chamber  307 . When the pressure inside fluid chamber  307  becomes greater than the pressure inside fluid inlet port  308 , first one-way passive disc valve  310  will close preventing a back flow of fluid from fluid chamber  307  into inlet port  308 . In this fashion, positive-displacement solid state pump  305  will continue to pump fluid from inlet port  308  to outlet port  309  until power source  301  is removed. 
     Referring now to  FIGS. 11-13 , another embodiment of a positive-displacement solid state pump  405 , in accordance herewith, is presented. As shown in  FIG. 11 , first one-way active disc valve  415  and second one-way active disc valve  416  have replaced first one-way passive disc valve  310  and second one-way active disc valve  311  of the  FIG. 8  embodiment. First one-way active disc valve  415  and second one-way active disc valve  416  are electrically connected to power sources  412  and  413  as to open and close based on electrical signals. 
     As shown in  FIG. 11 , a power source  401 , which may be an AC power source, provides power to at least one solid state actuator,  404  of positive-displacement solid state pump  405 . A frequency modulator  402  and an amplitude modulator  403  may be connected in series, as shown, and can be adjusted to vary the frequency and amplitude of the signal reaching at least one solid state actuator  404 . In some embodiments, the at least one solid state actuator  404  is selected from piezoelectric, electrostrictive and/or magnetorestrictive actuators. In some embodiments, the at least one solid state actuator  404  is a piezoelectric actuator  420 . A stack of the at least one solid state actuators  404  may be referred to herein collectively as an actuator  420 . Although the actuators  404  may be selected from piezoelectric, electrostrictive, and/or magnetostrictive, because many embodiments will actually utilize piezoelectric type solid state actuators  404 , a stack of the actuators  404  may also be referred to herein for convenience purposes as a piezoelectric actuator  420 , with intention that piezoelectric actuators may actually be the electrostrictive type and/or the magnetostrictive type of actuators  404 . In some embodiments, a diaphragm  406  is bonded to or engaged with the top of piezoelectric actuator  420  to move or flex in response to actuator flexing action. In some embodiments diaphragm  406  separates piezoelectric actuator  420  from wellbore fluid chamber  407 . 
       FIG. 11A  shows a top view of first active disc valve  415 . Piezoelectric actuator  415   a  is bonded to the top of a metal disc valve  415   b . Piezoelectric actuator  415   a  utilizes the d 31  piezoelectric mode of operation (d 31  describes the strain perpendicular to the polarization vector of the ceramics). In operation, when no electricity has been applied to the piezoelectric actuator  415   a , metal disc valve  415   b  will seal flow inlet port  408 . When electricity has been applied to piezoelectric actuator  415   a , it contracts, causing metal disc valve  415   b  to bend, thereby breaking the seal over inlet port  408 . Fluid can now flow through the first active disc valve  415 . 
     Referring again to  FIG. 11 , the voltage output of power source  401  is at a maximum. Second one-way active disc valve  416  is closing in response to power source  412  and first one-way active disc valve  415  is opening in response to power source  413 . 
     Referring to  FIG. 12 , the voltage output of power source  401  may be a negative sine function. Voltage from power source  401  has caused piezoelectric actuator  420  to contract bending diaphragm  406  downward resulting in a pressure drop in fluid chamber  407 . Pressure sensor  419  has sensed a decrease in pressure inside fluid chamber  407  and has sent a signal to microprocessor  418 . Microprocessor  418  has sent a control signal to power sources  412  and  413  directing them to transmit control voltages to first one-way active disc valve  415  and second one-way active disc valve  416 , respectively. The positive voltage from power source  413  has caused first one-way active disc valve  415  to open and the negative voltage from power source  412  has caused second one-way active disc valve  416  to remain closed. Fluid from inlet port  408  enters pumping chamber  407 . 
     In  FIG. 13 , the voltage output of power source  401  is a positive going sine function, causing piezoelectric actuator  420  to expand bending diaphragm  406  upward and resulting in a pressure increase in fluid chamber  407 . Pressure sensor  419  has sensed an increase in pressure inside pumping chamber  407  and has sent a signal to microprocessor  418 . Microprocessor  418  has sent control signals to power sources  412  and  413  causing them to transmit control voltages to second one-way active disc valve  416 , and first one-way active disc valve  415 , respectively. The negative voltage from power source  413  has caused first one-way active disc valve  415  to close and the positive voltage from power source  412  has caused second one-way active disc valve  416  to open. Fluid from pumping chamber  407  has entered outlet port  409 . 
     When the voltage output of power source  401  is again at a maximum and piezoelectric actuator  420  is at a fully expanded condition, as shown in  FIG. 11 , first one-way active disc valve  415  is opening in response to power source  413  and second one-way active disc valve  416  is closing in response to power source  412  preventing fluid from flowing back to fluid chamber  407  through second one-way active disc valve  416 . In this fashion, positive-displacement solid state pump  405  will continue to pump fluid from inlet port  408  to outlet port  409  until power sources  401 ,  412 , and  413  are removed. 
     Due to the fast response of the active disc valves, the piezoelectric actuator  420  can be cycled faster than it could with the passive disc valve. This will allow for more pump strokes per second and an increase in pump output. 
     Work performed by the pumping systems disclosed herein will generate heat and in some instances, substantial quantity of heat such that heat dissipation and removal is likely a key consideration in efficient pump operation. The amount of heat generated by the pump depends upon a number of factors, such as the amount of work performed, wellbore environment and temperature conditions, electrical resistance and impedance, operating depth, volume pumped, duty cycle, heat capacity of fluid being pumped, and similar variables. In some embodiments, such as illustrated in  FIGS. 12 and 13 , diaphragm  406  isolates piezoelectric actuator  420  and dielectric fluid  442  from wellbore fluid chamber  407 . Adequate cooling for the actuator  420  may be provided by positioning the actuator assembly  420  within an actuator housing filled with a static bath of a thermally stable, compatible fluid  442 , such as a dielectric oil. Fluid entering the wellbore fluid inlet  408  and moving through fluid chamber  407  in contact with the diaphragm  406  may transfer the electrically generated heat from the static fluid bath  442  to the relatively cooler wellbore fluid in the fluid chamber  407 . 
     For example, an actuator  420  according to this disclosure may consume more than 2 kW to lift wellbore liquids from 10,000 ft (+3000 m) TVD (true vertical distance) to surface. Each actuator stack  420  may be less than one foot tall (0.33 m) and less than an inch (&lt;2.54 cm) in diameter. The assembly may include a plurality of actuator stacks positioned adjacent one another, and positioned within a wellbore that has an internal diameter of about 4.5″ (11.4 cm). The heat generated by operation of the stacks  420  within the wellbore may be further confined to a small internal diameter area inside the stack housing. It is generally well known and that electronic components are more reliable when operated at lower relative temperatures. Increased temperature can produce increased impedance, which in turn may produce still additional heat. The cycle duty or run time of the stack and the pumping system in general should be considered and operated to ensure that generated heat is adequately transferred away from the stack and into the wellbore. 
     Continuing with the example, a typical, conventional electric submersible pumping system (ESP) (not the piezoelectric actuator pumps as disclosed herein) using an AC electric motor is cooled by wellbore fluid flow past the motor housing. The motor internals are bathed in a static dielectric oil which helps to conduct heat away from the rotor/stator to the housing and wellbore. A rule-of-thumb for the flow velocity past an ESP motor to promote acceptable cooling is 1 ft/second. Flow rates in ESP wells are typically in the several hundred to over 1000 bfpd (e.g., &gt;500+bfpd), so it is not difficult to achieve sufficient cooling velocity with flowing the wellbore fluid through the annular gap between the motor housing and the production casing ID. Commonly, these ESP systems pump sufficient fluid volumes such that they can run continuously (e.g., ˜100% duty cycle) duty to their ability to adequately cool the motors with fluid merely flowing externally past the motor housing. 
     In contrast to cooling an ESP however, the presently described and claimed piezoelectric pump and actuator systems are designed to lift far lower volumes of fluid as compared to an ESP installation. A typical installation for a piezoelectric pump and actuator system as described herein may only pump, for example, ˜30 bfpd or less. Thereby, a much lower volume of wellbore fluid is even available in the wellbore for cooling, so in many installations adequate actuator cooling that is solely dependent on annular fluid flow external to the housing may be much more difficult to achieve than is possible with an ESP (while maintaining adequate equipment clearance). Although the piezoelectric stack could be bathed in a static dielectric oil and cooled merely by moving wellbore fluid through the fluid changer  407  and across diaphragm  406 , the static fluid-bath embodiments may not be adequate in all applications to provide sufficient cooling, especially considering the lower fluid movement velocity within the wellbore generated by these typically lower relative output volumes of pumps as disclosed herein. The lower fluid movement rate on the outside of the pump housing will mean greater heating of that fluid as compared to an ESP in similar circumstances. The presently described pumps will typically experience relatively low fluid movement rates in the annulus outside of the pump housing, as well as lower circulation rates within the housing. Utilizing the diaphragm for removing heat from the solid state actuator stack may be inadequate. 
     In applications generating relatively substantial heat, the actuators and pumping system may be configured to facilitate enhanced surface area exposure for cooling and to maximize the heat transfer capacity for the available (typically limited) wellbore fluid production volumes and flow rates moving externally past or through the pump. The previously discussed dielectric oil bath  442  may be included or eliminated in certain configurations, as needed. Produced wellbore fluid entering pump inlet port  408  may be directed or routed to flow around and/or through the actuator stack  420  and housing prior to entering the fluid chamber  407  to provide an internal wellbore-fluid type of cooling configuration for the actuators  420 . In still other configurations, the wellbore fluid may be externally and/or internally circulated about the actuators  420  for cooling in lieu of or in combination with the static oil bath  442 . Exemplary enhanced cooling embodiments are illustrated in  FIGS. 24-29 . 
     In some embodiments, such as illustrated in  FIGS. 24-27 , the actuators  420  may include heat sink features to enhance cooling, such as one or more central throughbores, internal passageways, channels, or similar surface-area-enhancing features for enhanced cooling. These heat sink features enable wellbore fluids to circulate through, around, or otherwise in contact with the increased surface area of the at least one solid state actuator to facilitate enhanced cooling for the at least one solid state actuator. In some embodiments, the wellbore fluid is pumped or flows through the at least one solid state actuator circulation of wellbore fluids in response to pumping action by the at least one solid state actuator, while in other embodiments, the wellbore fluid may be separately pumped or flowed through the at least one solid state actuator, such as via a closed loop system or a circulation system that merely circulates wellbore fluid about the actuators for cooling, prior to the wellbore fluid being lifted from the wellbore by the primary pumping actuators  420 . 
     Piezoelectric actuator stacks  420  are typically cylinders composed of stacked piezoelectric discs, each disc being an individual actuator  404 . However, the piezoelectric discs  404  can still function if they are configured to include a non-cylindrical feature, such as including one or more central apertures for cooling fluid passage.  FIG. 24  illustrates inflow  430  of wellbore fluid into a pump through inlet  408 , into the pump assembly following flow line arrows  430 , external to actuator housing  411 , and through a central through bore, on the inflow stroke of the diaphragm  406 .  FIG. 25  illustrates an exhaust or pumping stroke of diaphragm  406 , with exhaust arrow  440  through outlet port  409 .  FIG. 26  illustrates another embodiment circulating wellbore fluid externally around the actuator diaphragm  406 , while  FIG. 27  illustrates fluid flow  440  during the exhaust or pumping stroke. 
     An additional cooling option may include providing a thermoelectric cooler  438 , as illustrated in  FIGS. 28-29 . Search thermoelectric coolers  438  are solid-state devices that use electricity and a thermoelectric effect (i.e., Peltier effect) to pull heat away from a surface. Thermoelectric coolers have no moving parts and are known to have a long operational life. The piezoelectric stack could be surrounded with thermoelectric coolers that are in contact with the stack housing. The coolers could be powered with the same electrical source used by the pumping system and would move heat away from the stack to the housing and wellbore. Each of the illustrated, exemplary cooling solutions of  FIGS. 24-29  may take advantage of the various pumping embodiment&#39;s operational characteristics to create a benign (e.g., no extra moving parts) cooling environment for improved pumping system reliability and performance. 
     As illustrated in exemplary embodiments of  FIGS. 24-29 , improved methods are provided for removing produced wellbore liquid from a wellbore using the solid state, electrically actuated pumps as disclosed herein. The methods may include providing an electrically powered downhole positive-displacement solid state pump including pump housing  401  containing at least a fluid chamber  407 , an inlet  408  and an outlet  409  port each in fluid communication with the fluid chamber  407 , at least one solid state actuator  404 , a first one-way check valve positioned between the inlet port and the fluid chamber, and a second one-way check valve positioned between the outlet port and the fluid chamber, an electrical power supply for powering the at least one solid state actuator  404 , a heat sink for cooling the at least one solid state actuator, the heat sink comprising at least one of; (i) a dielectric oil bath*( FIGS. 24-27 ), (ii) a thermoelectric cooling element ( FIGS. 28-29 ), (iii) an aperture within the at least one solid state actuator for conveying a cooling fluid through the aperture ( FIGS. 24-25 ), and (iv) combinations thereof. At least a portion of the generated heat is removed or remotely dissipated away from the actuators at least in part by the heat sink or combinations of the heat sinks. Further heat load handling may be managed by operating the pumps on an intermittent cycle. A controller is used to control pump operational functions, such as but not limited to pump operating frequency, voltage, current, start-stop functions, etc. A pump-off controller may also be provided to coordinate pump operating duty with corresponding fluid availability or buildup within the wellbore. Thereby, operation in the absence of sufficient cooling fluid volumes may be avoided. The operating controller and pump-off control features may be controlled by the same control system or separate systems. The control system and/or pump-off controller may also work in conjunction with the power control systems, such as the battery charge and/or power availability control systems. 
     In some embodiments, wherein the step of pumping includes; (i) pressurizing the wellbore liquid with the downhole positive-displacement solid state pump to generate a pressurized wellbore liquid at a discharge pressure within the fluid chamber; and (ii) opening the second one-way discharge valve with the pressurized wellbore liquid to flowing the pressurized wellbore liquid into the tubular and at least a threshold vertical distance toward a surface region. 
     Referring now back to  FIGS. 14 and 15 , another embodiment of a positive-displacement solid state pump  505 , in accordance herewith, is presented. This embodiment utilizes two passive micro-electromechanical system (MEMS) valve arrays. Positive-displacement solid state pump  505  is similar to pump  305  shown in  FIG. 8 , with the exception that first one-way passive disc valve  310  and second one-way passive disc valve  311  of pump  305  have been replaced with a first one-way passive microvalve array  531  and a second one-way passive microvalve array  532 , as shown in  FIG. 14 . Preferably, microvalve arrays  531  and  532  are two micro machined MEMS valves. 
     Referring now to  FIG. 15 , microvalve array  531  is fabricated from silicon, silicone nitride or nickel and includes an array of fluid flow ports  531   a  approximately 200 microns in diameter. The array of fluid flow ports  531   a  is covered by diaphragm layer  531   b .  FIG. 15  shows an enlarged top view of a cutout portion of microvalve array  531 . Microvalve array  531  has a plurality of diaphragms  531   c  covering each fluid flow port  531   a.    
     In operation, first one-way passive microvalve array  531  and second one-way passive microvalve array  532  function in a fashion similar to passive disc valves  310  and  311  of  FIG. 8 . In  FIG. 15 , the pressure pressing downward on diaphragm  531   c  is greater than the pressure of fluid inside fluid flow port  531   a . Therefore, diaphragm  531   c  seals fluid flow port  531   a . Conversely, the pressure pressing downward on diaphragm  531   c  is less than the pressure of fluid inside fluid flow port  531   a . Therefore, diaphragm  531   c  is forced open and fluid flows through fluid flow port  531   a.    
     Referring again to  FIG. 14 , when the pressure inside fluid chamber  507  becomes less than the pressure inside fluid inlet port  508 , individual valves within the multitude of microvalves in microvalve array  531  will open permitting the flow of fluid into fluid chamber  507 . When the pressure inside fluid chamber  507  becomes less than the pressure inside fluid outlet port  509 , the individual valves within the multitude of micro valves in the microvalve array  532  will close preventing a back flow of fluid from outlet port  509  into fluid chamber  507 . 
     Likewise, when the pressure inside fluid chamber  507  becomes greater than the pressure inside fluid outlet port  509 , the individual valves within the multitude of micro valves in microvalve array  532  will open permitting the flow of fluid into outlet port  509 . When the pressure inside fluid chamber  507  becomes greater than the pressure inside fluid inlet port  508 , the individual valves within the multitude of micro valves in microvalve array  531  will close preventing a back flow of fluid from fluid chamber  507  into inlet port  508 . 
     Due to its small size and low inertia, the microvalve array can respond quickly to pressure changes. Therefore, the pump output may be increased because it can cycle faster than it could with a more massive valve. 
     Referring now to  FIGS. 16-18 , another embodiment of a positive-displacement solid state pump  605 , in accordance herewith, is presented. This embodiment is similar to the embodiment described above in reference to  FIGS. 11 and 11A , with the exception that first one-way active disc valve  415  and second one-way active disc valve  416  of  FIG. 11  are replaced with first one-way active microvalve array  641  and second one-way active microvalve array  642 . 
       FIG. 17  shows an enlarged side view of first one-way active microvalve array  641 . First one-way active microvalve array  641  is fabricated from silicon and includes an array of “Y” shaped fluid flow ports  641   a , approximately 200 microns in diameter. In some embodiments, second one-way active microvalve array  642  may be identical to first one-way active microvalve array  641 . Below the junction of each “Y” are heaters  641   b . Heaters  641   b  for first one-way active microvalve array  641  are electrically connected to power source  651  and heaters  641   b  for second one-way active microvalve array  642  are electrically connected to power source  652 . Pressure sensor  619  senses the pressure inside fluid chamber  607  and sends a corresponding signal to microprocessor  618 . Microprocessor  618  is configured to send control signals to power sources  651  and  652 . 
     In operation, first one-way active microvalve array  641  and second one-way active microvalve array  642  function in a fashion similar to first one-way active disc valve  415  and second one-way active disc valve  416  of  FIG. 11 . For example, in  FIG. 17 , first one-way active microvalve array  641  is open. Fluid is able to flow freely through fluid flow ports  641   a . In  FIG. 18 , first one-way active microvalve array  641  is closed. Power source  651  has sent voltage to heaters  641   b  of first one-way active microvalve array  641 . Heaters  641   b  have heated the adjacent fluid causing a phase change to a vapor phase and the formation of high pressure bubbles  641   c . High pressure bubbles  41   c  block fluid flow ports  641   a  for a short time closing first one-way active microvalve array  641 . The lack of mass or inertia due to there being no valve diaphragm permits very fast response which enables the valves to open and close at high a frequency beyond 100 kHz. 
     When piezoelectric actuator  620  contracts and the pressure inside fluid chamber  607  becomes less than the pressure inside fluid inlet port  608 , pressure sensor  619  will send a corresponding signal to microprocessor  618 . Microprocessor  618  will then send a control signal to power sources  651  and  652 . Consequently, individual valves within the multitude of microvalves in first one-way active microvalve array  641  will open permitting the flow of fluid into fluid chamber  607  ( FIG. 17 ). Also, individual valves within the multitude of micro valves in the second one-way active microvalve array  642  will close ( FIG. 18 ) preventing a back flow of fluid from outlet port  609  into fluid chamber  607 . 
     Likewise, when piezoelectric actuator  620  expands and the pressure inside fluid chamber  607  becomes greater than the pressure inside fluid outlet port  609 , pressure sensor  619  will send a corresponding signal to microprocessor  618 . Microprocessor  618  will then send control signals to power sources  651  and  652 . Consequently, the individual valves within the multitude of micro valves in second one-way active microvalve array  642  will open permitting the flow of fluid into outlet port  609 . Also, the individual valves within the multitude of micro valves in first one-way active microvalve array  641  will close preventing a back flow of fluid from fluid chamber  607  into inlet port  608 . Due to its ability to anticipate the need to open and close, the active microvalve array can respond very quickly. Hence, the pump can cycle faster and pump output is increased. 
     In some embodiments, at certain frequencies generated by the power source, piezoelectric actuator  320 ,  420 ,  520 ,  620  will resonate. As piezoelectric actuator  320 ,  420 ,  520 ,  620  resonates, the amount of electrical energy required to piezoelectric actuator  320 ,  420 ,  520 ,  620  by a given amount will decrease. Therefore, the efficiency of the piezoelectric pump will be increased. 
     Any electromechanical spring/mass system (including piezoelectric actuator  320 ,  420 ,  520 ,  620 ) will resonate at certain frequencies. The “primary” or “first harmonic” frequency is the preferred frequency. In some embodiments, the power source sends an electrical drive signal to the piezoelectric actuator  320 ,  420 ,  520 ,  620  at or near the primary resonant frequency. That frequency is calculated by using the mass and modulus of elasticity for the piezoelectric actuator  320 ,  420 ,  520 ,  620 : f=(k/m) 1/2  where m is the mass of the resonant system and k is the spring rate (derived from the modulus of elasticity). When in resonance, the amplitude of the motion will increase by a factor of 4 or 5. Thus for a given pump stoke, the drive voltage and electrical input power can be reduced by a similar factor. 
     Referring now to  FIG. 19 , a schematic view of an illustrative, nonexclusive example of a system for  700  removing fluids from a well, according to the present disclosure is presented. As shown, the system  700  may include an apparatus  710  for reducing the force required to pull a positive-displacement solid state pump  702  from a tubular  712 . The system  700  includes the positive-displacement solid state pump  702  having an inlet end  704  and a discharge end  706 . A telemetry section  708  is operatively connected to the positive-displacement solid state pump  702 . 
     As shown, the apparatus  710  may be positioned upstream of the pump  702 . Apparatus  710  includes a tubular sealing device  714  for mating with a downhole tubular component  716 , the tubular sealing device  714  having an axial length L′ and a longitudinal bore  718  therethrough. 
     Apparatus  710  also includes an elongated rod  720 , slidably positionable within the longitudinal bore  718  of the tubular sealing device  714 . The elongated rod  720  includes a first end  722 , a second end  724 , and an outer surface  726 . As shown in  FIG. 19 , the outer surface  726  is structured and arranged to provide a hydraulic seal when the elongated rod is in a first position (when position A′ is aligned with point P′) within the longitudinal bore  718  of the tubular sealing device  714 . Also, as shown in  FIG. 19 , the outer surface  726  of elongated rod  720  is structured and arranged to provide at least one external flow port  728  for pressure equalization upstream and downstream of the tubular sealing device  714  when the elongated rod  720  is placed in a second position (when position B′ is aligned with point P′) within the longitudinal bore  718  of the tubular sealing device  714 . 
     In some embodiments, the elongated rod  720  includes an axial flow passage  730  extending therethrough, the axial flow passage in fluid communication with the positive-displacement solid state pump  702 . 
     In some embodiments, the tubular sealing device  714  is structured and arranged for landing within a nipple profile (not shown) or for attaching to a collar stop  732  for landing directly within the tubular  712 . 
     In some embodiments, a well screen or filter  734  is provided, the well screen or filter  734  in fluid communication with the inlet end  704  of the positive-displacement solid state pump  702 , the well screen or filter  734  having an inlet end  736  and an outlet end  738 . 
     In some embodiments, a velocity fuse or standing valve  740  is positioned between the outlet end  738  of the well screen or filter  134  and the first end  122  of the elongated rod  720 . As shown, the velocity fuse or standing valve  740  is in fluid communication with the well screen or filter  734 . 
     In some embodiments, the velocity fuse  740  is structured and arranged to back-flush the well screen or filter  734  and maintain a column of fluid within the tubular  712  in response to an increase in pressure drop across the velocity fuse  740 . In some embodiments, the velocity fuse  740  is normally open and comprises a spring-loaded piston responsive to changes in pressure drop across the velocity fuse  740 . 
     In some embodiments, the apparatus  710  is structured and arranged to be installed and retrieved from the tubular  712  by a wireline or a coiled tubing  742 . In some embodiments, the apparatus  710  is integral to the tubing string. 
     In some embodiments, the first end  722  of the elongated rod  720  includes an extension  744  for applying a jarring force to the tubular sealing device  714  to assist in the removal thereof. 
     In some embodiments, the velocity fuse or standing valve  740  may be installed within a housing  146 . In some embodiments, the housing  746  is structured and arranged for sealingly engaging the tubular  712 . In some embodiments, the housing  746  comprises at least one seal  748 . In some embodiments, the housing  746  may be configured to seat within a tubular  712 , as shown. 
     Referring now to  FIG. 20 , a schematic view of an illustrative, nonexclusive example of a system for  800  removing fluids from a well, according to the present disclosure is presented. The system  800  includes a positive-displacement solid state pump  802  having an inlet end  804  and a discharge end  806 . A telemetry section  808  is operatively connected to the positive-displacement solid state pump  802 . 
     The system  800  also includes an apparatus  810  for reducing the force required to pull the pump  802  from a tubular  812 . As shown, the apparatus  810  may be positioned downstream of the pump  802 . Apparatus  810  includes a tubular sealing device  814  for mating with a downhole tubular component  816 , the tubular sealing device  814  having an axial length L″ and an longitudinal bore  818  therethrough. 
     Apparatus  810  also includes an elongated rod  820 , slidably positionable within the longitudinal bore  818  of the tubular sealing device  814 . The elongated rod  820  includes a first end  822 , a second end  824 , and an outer surface  826 . As shown in  FIG. 20 , the outer surface  826  is structured and arranged to provide a hydraulic seal when the elongated rod is in a first position (when position A″ is aligned with point P″) within the longitudinal bore  818  of the tubular sealing device  814 . Also, as shown in  FIG. 20 , the outer surface  826  of elongated rod  820  is structured and arranged to provide at least one external flow port  828  for pressure equalization upstream and downstream of the tubular sealing device  814  when the elongated rod  820  is placed in a second position (when position B″ is aligned with point P″) within the longitudinal bore  818  of the tubular sealing device  814 . 
     In some embodiments, the elongated rod  820  includes an axial flow passage  830  extending therethrough, the axial flow passage in fluid communication with the positive-displacement solid state pump  802 . 
     In some embodiments, the tubular sealing device  814  is structured and arranged for landing within a nipple profile (not shown) or for attaching to a collar stop  832  for landing directly within the tubular  812 . 
     In some embodiments, a well screen or filter  834  is provided, the well screen or filter  834  in fluid communication with the inlet end  804  of the positive-displacement solid state pump  802 , the well screen or filter  834  having an inlet end  836  and an outlet end  838 . 
     In some embodiments, a velocity fuse or standing valve  840  is positioned between the outlet end  838  of the well screen or filter  834  and the first end  822  of the elongated rod  820 . As shown, the velocity fuse or standing valve  840  is in fluid communication with the well screen or filter  834 . 
     In some embodiments, the velocity fuse  840  is structured and arranged to back-flush the well screen or filter  832  and maintain a column of fluid within the tubular  812  in response to an increase in pressure drop across the velocity fuse  840 . In some embodiments, the velocity fuse  840  is normally open and comprises a spring-loaded piston responsive to changes in pressure drop across the velocity fuse  840 . 
     In some embodiments, the apparatus  810  is structured and arranged to be installed and retrieved from the tubular  812  by a wireline or a coiled tubing  842 . In some embodiments, the apparatus  810  is integral to the tubing string. 
     In some embodiments, the first end  822  of the elongated rod  820  includes an extension  844  for applying a jarring force to the tubular sealing device  814  to assist in the removal thereof. 
     In some embodiments, the velocity fuse or standing valve  840  may be installed within a housing  846 . In some embodiments, the housing  846  is structured and arranged for sealingly engaging the tubular  812 . In some embodiments, the housing  846  comprises at least one seal  848 . In some embodiments, the housing  846  may be configured to seat within a tubular  812 , as shown. 
     Referring now to  FIGS. 21-22 , illustrated is another embodiment of a system  910  for removing fluids L from a subterranean well  912 . The system  910  includes a housing  914 , the housing  914  including a hollow cylindrical body  916 , the hollow cylindrical body  916  having a first end  918  and a second end  920 . The system  910  includes a positive-displacement solid state pump  922  for removing fluids from the subterranean well  912 , the pump  922  positioned within the hollow cylindrical body  916 . Pump  922  includes an inlet end  924  and a discharge end  926 . 
     System  910  also includes a telemetry section  928 . As shown in  FIGS. 21-22 , the telemetry section  928  is positioned within the hollow cylindrical body  916 . To power positive-displacement solid state pump  922 , a rechargeable battery  930  may be provided. In some embodiments, the rechargeable battery  930  may be positioned within the hollow cylindrical body  916 . Rechargeable batteries having utility will be discussed in more detail below. 
     System  910  also includes an apparatus for releasably securing and sealing the housing  914 . As shown, in some embodiments, the apparatus  932  may be positioned within a tubular  972  of the subterranean well  912 . In some embodiments, the apparatus  932  may be a docking station  934 , as shown, which forms a mechanical connection with the first end  918  of the hollow cylindrical body  916 . In some embodiments, apparatus  932  may be in the form of a packer (not shown). In some embodiments, apparatus  932  may be a portion of the housing  914 , itself. Other forms of apparatus  932  may have utility herein, providing they meet the requirements of securing the housing  914  and sealing the first end  918  of the hollow cylindrical body  916 . In some embodiments, the apparatus  932  may include a latching bumper spring  956 . 
     In some embodiments, the system  910  may include a battery recharging station  938  In some embodiments, the battery recharging station  938  may be positioned above-ground G, as shown in  FIGS. 21-22 . In some embodiments, battery recharging station  938  includes a receiver  940 , which is structured and arranged to receive the housing  914  when the housing  914  is disengaged from the apparatus  932 . In some embodiments, receiver  940  of battery recharging station  938  has an opening  942  at one end thereof, the opening  942  in communication with the tubular  972 . As shown in  FIG. 22 , in some embodiments, the housing  914  is disengaged from the apparatus  932 , transferred through the tubular  972  to the receiver  940  of battery recharging station  938  for charging. When positioned within the receiver  940 , an electrical connection may be made with charger  944  and the rechargeable battery  930  is then charged. 
     In some embodiments, the system  910  may include a mobile charging unit  980  for charging the rechargeable battery  930  via cabling  984 . In some embodiments, the mobile charging unit  980  may be installed in a vehicle  982 , for convenience. 
     In some embodiments, the system  910  may include at least one sensor  946  for monitoring system conditions including the level of charge of the rechargeable battery  930 . In some embodiments, the system  910  may include a communications system  948  for transmitting data obtained from the at least one sensor  946 . In some embodiments, the communications system  948  transmits performance information to a supervisory control and data acquisition (SCADA) system (not shown). 
     Referring to  FIG. 21 , in some embodiments, the rechargeable battery  930  can be recharged via a downhole wet-mate connection  990  attached to wireline having multiple electrical conductors, or a slickline  992 , with a larger power-source battery (not shown), attached to the wet-mate. 
     As may be appreciated by those skilled in the art, a slickline is a single-strand wire used to run tools into a wellbore. Slicklines can come in varying lengths, according to the depth of the wells in the area. It may be connected to a wireline sheave, which is a round wheel grooved and sized to accept a specified line and positioned to redirect the line to another sheave that will allow it to enter the wellbore while keeping the pressure contained. 
     The slickline power-source battery may be transported to the subterranean well  912  on a temporary basis, or remain on or near location, and be passively charged via renewable sources such as solar or wind, or fuel cells, hydrocarbon-fueled generators, etc. 
     In some embodiments, the wireline or slickline  992 , or the power required for recharging, can be supplied by a mobile cable spooling and charging unit (not shown). This mobile spooling and charging unit can eliminate the requirement for permanent onsite power generation, as the unit could recharge rechargeable battery  930  of pump  922  while the pump  922  was in-place at its pumping position in the subterranean well  912 , eliminating the need to wait for the pump  922  to return. The charging unit could use many different methods to produce electricity including, but not limited to, natural gas diesel generators, renewable sources, or fuel cells. 
     Referring again to  FIGS. 21-22 , in some embodiments, the system  910  may include a surfacing system  950  for raising the housing  914  to a position within the battery recharging station  938  when the housing  914  is disengaged from the apparatus  936 . 
     In some embodiments, the housing  914  may be disengaged from the apparatus  932  in response to a signal received from the at least one sensor  946  that the rechargeable battery  930  has reached a predetermined level of discharge. 
     In some embodiments, the at least one sensor  946  for monitoring system conditions includes a sensor for monitoring downhole pressure  960 , and a sensor for monitoring downhole temperature  962 . In some embodiments, the downhole pressure sensor  960  provides a signal to a pump-off controller  64 . In some embodiments, the at least one sensor  946  provides a signal to the pump  922  to change its operating speed to maintain an optimal fluid level above the pump. 
     In some embodiments, the surfacing system  950  is structured and arranged to raise and lower the density of the housing  914 . In some embodiments, the surfacing system  950  comprises a buoyancy system. In some embodiments, the surfacing system  950  comprises a propeller system  966  or a jetting device (not shown). 
     In some embodiments, the subterranean well  912  further includes a casing  970 , the tubular  972  positioned within the casing  970  to form an annulus  952  for producing gas G therethrough, with liquids L removed by the pump  922  through the tubular  972 . In some embodiments, a standing valve  954  may be provided, the standing valve  954  positioned within the tubular  972  to retain liquids within the tubular  972 . 
     In some embodiments, the battery for powering the driver  928  may be a rechargeable battery  930 . 
     As is known by those skilled in the art, lithium-ion batteries belong to the family of rechargeable batteries in which lithium ions move from the negative electrode to the positive electrode during discharge and back when charging. Li-ion batteries use an intercalated lithium compound as one electrode material, compared to the metallic lithium used in a non-rechargeable lithium battery. The electrolyte, which allows for ionic movement, and the two electrodes are the consistent components of a lithium-ion cell. 
     Lithium-ion batteries are one of the most popular types of rechargeable batteries for portable electronics, having a high energy density, no memory effect, and only a slow loss of charge when not in use. Besides consumer electronics, lithium-ion batteries are used by the military, electric vehicle and aerospace industries. Chemistry, performance, cost and safety characteristics vary across lithium-ion battery types. Consumer electronics typically employ lithium cobalt oxide (LiCoO 2 ), which offers high energy density. Lithium iron phosphate (LFP), lithium manganese oxide (LMO) and lithium nickel manganese cobalt oxide (NMC) offer lower energy density, but longer lives and inherent safety. Such batteries are widely used for electric tools, medical equipment and other roles. NMC in particular is a leading contender for automotive applications. Lithium nickel cobalt aluminum oxide (NCA) and lithium titanate (LTO) are additional specialty designs. 
     Lithium-ion batteries typically have a specific energy density range of: 100 to 250 Wh/kg (360 to 900 kJ/kg); a volumetric energy density range of: 250 to 620 Wh/L (900 to 1900 J/cm 3 ); and a specific power density range of: 300 to 1500 W/kg at 20 seconds and 285 Wh/l). 
     With regard to lithium/air batteries, those skilled in the art recognize that the lithium/air couple has a theoretical energy density that is close to the limit of what is possible for a battery (10,000 Wh/kg). Recent advances directed to a protected lithium electrode (PLE) has moved the lithium/air battery closer to commercial reality. Primary Li/Air technology has achieved specific energies in excess of 700 Wh/kg. Rechargeable Li/Air technology is expected to achieve much higher energy densities than commercial Li-ion chemistry, since in a lithium/air battery, oxygen is utilized from the ambient atmosphere, as needed for the cell reaction, resulting in a safe, high specific energy means for powering the solid state pump. 
     The natural abundance, large gravimetric capacity (˜1600 mAh/g) and low cost of sulfur makes it an attractive positive electrode for advanced lithium batteries. With an average voltage of about 2 V, the theoretical energy density of the Li—S couple is about 2600 Wh/1 and 2500 Wh/kg. The electrochemistry of the Li—S battery is distinguished by the presence of soluble polysulfides species, allowing for high power density and a natural overcharge protection mechanism. The high specific energy of the Li—S battery is particularly attractive for applications where battery weight is a critical factor in system performance. 
     Lithium/seawater batteries have recently gained attention. While lithium metal is not directly compatible with water, the high gravimetric capacity of lithium metal, 3800 mA/g, and its highly negative standard electrode potential, Eo=−3.045 V, make it extremely attractive when combined as an electrochemical couple with oxygen or water. At a nominal potential of about 3 volts, the theoretical specific energy for a lithium/air battery is over 5000 Wh/kg for the reaction forming LiOH (Li+¼ O 2 +½ H 2 O=LiOH) and 11,000 Wh/kg for the reaction forming Li 2 O 2  (Li+O 2 =Li 2 O 2 ) or for the reaction of lithium with seawater, rivaling the energy density for hydrocarbon fuel cells and far exceeding Li-ion battery chemistry that has a theoretical specific energy of about 400 Wh/kg. The use of a protected lithium electrode (PLE) makes lithium metal electrodes compatible with aqueous and aggressive non-aqueous electrolytes. Aqueous lithium batteries may have cell voltages similar to those of conventional Li-ion or lithium primary batteries, but with much higher energy density (for H 2 O or O 2  cathodes). 
     The University of Tokyo experimental battery uses the oxidation-reduction reaction between oxide ions and peroxide ions at the positive electrode. Peroxides are generated and dispersed due to charge and discharge reactions by using a material made by adding cobalt (Co) to the crystal structure of lithium oxide (Li 2 O) for the positive electrode. The University of Tokyo experimental battery can realize an energy density seven times higher than that of existing lithium-ion rechargeable batteries. 
     The oxidation-reduction reaction between Li 2 O and Li 2 O 2  (lithium peroxide) and oxidation-reduction reaction of metal Li are used at the positive and negative electrodes, respectively. The battery has a theoretical capacity of 897 mAh per 1 g of the positive/negative electrode active material, a voltage of 2.87 V and a theoretical energy density of 2,570 Wh/kg. 
     The energy density is 370 Wh per 1 kg of the positive/negative electrode active material, which is about seven times higher than that of existing Li-ion rechargeable batteries using LiCoO 2  positive electrodes and graphite negative electrodes. The theoretical energy density of the University of Tokyo battery is lower than that of lithium-air batteries (3,460 Wh/kg). 
     In some embodiments, the rechargeable battery  930  is selected from lithium-ion, lithium-air, lithium-seawater, or an engineered combination of battery chemistries. In some embodiments, the rechargeable battery  930  comprises a plurality of individual batteries. 
     Referring now to  FIG. 23 , a method of removing wellbore liquid from a wellbore  1000 , the wellbore traversing a subterranean formation and having a tubular that extends within at least a portion of the wellbore is presented. The method  1000  includes the steps of  1002 , electrically powering a downhole positive-displacement solid state pump comprising a fluid chamber, an inlet and an outlet port, each in fluid communication with the fluid chamber, at least one solid state actuator, a first one-way check valve positioned between the inlet port and the fluid chamber, and a second one-way check valve positioned between the outlet port and the fluid chamber, the at least one solid state actuator configured to operate at or near its resonance frequency, the solid state pump positioned within the wellbore; and  1004  pumping the wellbore liquid from the wellbore with the downhole positive-displacement solid state pump, wherein the pumping includes: (i) pressurizing the wellbore liquid with the downhole positive-displacement solid state pump to generate a pressurized wellbore liquid at a discharge pressure; and (ii) flowing the pressurized wellbore liquid at least a threshold vertical distance to a surface region. 
     In some embodiments, the method  1000  includes the step of  1006 , positioning a profile seating nipple within the tubular for receiving the solid state pump, the profile seating nipple having a locking groove structured and arranged to matingly engage the solid state pump. 
     In some embodiments, the method  1000  includes the step of  1008 , positioning a well screen or filter in fluid communication with the inlet end of the solid state pump, the well screen or filter having an inlet end and an outlet end; and a velocity fuse or standing valve positioned between the outlet end of the well screen or filter and the inlet end of the solid state pump. 
     In some embodiments, the method  1000  includes the step of  1010 , reducing the force required to pull the positive-displacement solid state pump from the tubular by using an apparatus comprising a tubular sealing device for mating with the positive-displacement solid state pump, the tubular sealing device having an axial length and a longitudinal bore therethrough; and an elongated rod slidably positionable within the longitudinal bore of the tubular sealing device, the elongated rod having an axial flow passage extending therethrough, a first end, a second end, and an outer surface, the outer surface structured and arranged to provide a hydraulic seal when the elongated rod is in a first position within the longitudinal bore of the tubular sealing device, and at least one external flow port for pressure equalization upstream and downstream of the tubular sealing device when the elongated rod is placed in a second position within the longitudinal bore of the tubular sealing device, wherein the tubular sealing device is structured and arranged for landing within a nipple profile or for attaching to a collar stop for landing directly within the tubular. 
     In some embodiments, the method  1000  includes the step of  1012  forming a pump assembly by adding at least one secondary pump for transferring the wellbore liquids from the wellbore, wherein the inlet and outlet ports of the positive-displacement solid state pump are operatively connected to a hydraulic system to drive the at least one secondary pump. 
     In some embodiments, the method  1000  includes the step of  1014 , reducing the force required to pull the pump assembly from the tubular by using an apparatus comprising a tubular sealing device for mating with the pump assembly, the tubular sealing device having an axial length and a longitudinal bore therethrough; and an elongated rod slidably positionable within the longitudinal bore of the tubular sealing device, the elongated rod having an axial flow passage extending therethrough, a first end, a second end, and an outer surface, the outer surface structured and arranged to provide a hydraulic seal when the elongated rod is in a first position within the longitudinal bore of the tubular sealing device, and at least one external flow port for pressure equalization upstream and downstream of the tubular sealing device when the elongated rod is placed in a second position within the longitudinal bore of the tubular sealing device, wherein the tubular sealing device is structured and arranged for landing within a nipple profile or for attaching to a collar stop for landing directly within the tubular. 
     In some embodiments, the method  1000  includes the step of  1016 , a positioning a profile seating nipple within the tubular for receiving the pump assembly, the profile seating nipple having a locking groove structured and arranged to matingly engage the pump assembly. 
     In some embodiments, the method  1000  includes the step of  1018 , positioning a well screen or filter in fluid communication with the inlet end of the pump assembly, the well screen or filter having an inlet end and an outlet end; and a velocity fuse or standing valve positioned between the outlet end of the well screen or filter and the inlet end of the pump assembly. 
     In some embodiments, the first one-way check valve and/or the second one-way check valve are passive one-way disk valves, active one-way disk valves, passive microvalve arrays, active microvalve arrays, passive MEMS valve arrays, active MEMS valve arrays or a combination thereof. 
     In some embodiments, the at least one solid state actuator is selected from piezoelectric, electrostrictive and/or magnetorestrictive actuators. In some embodiments, the at least one solid state actuator comprise a ceramic perovskite material. In some embodiments, the ceramic perovskite material comprises lead zirconate titanate and/or lead magnesium niobate. In some embodiments, the at least one solid state actuator comprise terbium dysprosium iron. 
     In some embodiments, the solid state pump further comprises a piston and a cylinder for housing the at least one solid state actuator and the first and second one-way check valves, so as to form a piston pump. 
     In some embodiments, the solid state pump further comprises a diaphragm operatively associated with the at least one solid state actuator and the first and second one-way check valves, so as to form a diaphragm pump. 
     In some embodiments, the step of electrically powering the solid state pump comprises using a power cable, the power cable operable for deploying the solid state pump. In some embodiments, the power cable comprises a synthetic conductor. In some embodiments, the step of electrically powering the solid state pump comprises using a rechargeable battery. 
     In some embodiments, the positive-displacement solid state pump is plugged into a downhole wet-mate connection and the step of electrically powering the solid state pump comprises using a power cable positioned on the outside of the tubular. 
     In some embodiments, the velocity fuse is structured and arranged to back-flush the well screen or filter and maintain a column of fluid within the tubular in response to an increase in pressure drop across the velocity fuse. 
     In some embodiments, the at least one secondary pump is a bladder pump, a centrifugal pump, a rotary screw pump, a rotary lobe pump, a gerotor pump, and/or a progressive cavity pump. In some embodiments, the bladder pump is a metal bellows pump or an elastomer pump. 
     In some embodiments, the velocity fuse is structured and arranged to back-flush the well screen or filter and maintain a column of fluid within the tubular in response to an increase in pressure drop across the velocity fuse. 
     In some embodiments, the apparatus is structured and arranged to be installed and retrieved from the tubular by a wireline or a coiled tubing. 
     In some embodiments, the method further includes detecting a downhole process parameter. In some embodiments, the downhole process parameter includes at least one of a downhole temperature, a downhole pressure, the discharge pressure, system vibration, a downhole flow rate, and the discharge flow rate. 
     Illustrative, non-exclusive examples of assemblies, systems and methods according to the present disclosure have been provided. It is within the scope of the present disclosure that an individual step of a method recited herein, including in the following enumerated paragraphs, may additionally or alternatively be referred to as a “step for” performing the recited action. 
     INDUSTRIAL APPLICABILITY 
     The apparatus and methods disclosed herein are applicable to the oil and gas industry. 
     It is believed that the disclosure set forth above encompasses multiple distinct inventions with independent utility. While each of these inventions has been disclosed in its preferred form, the specific embodiments thereof as disclosed and illustrated herein are not to be considered in a limiting sense as numerous variations are possible. The subject matter of the inventions includes all novel and non-obvious combinations and subcombinations of the various elements, features, functions and/or properties disclosed herein. Similarly, where the claims recite “a” or “a first” element or the equivalent thereof, such claims should be understood to include incorporation of one or more such elements, neither requiring nor excluding two or more such elements. 
     It is believed that the following claims particularly point out certain combinations and subcombinations that are directed to one of the disclosed inventions and are novel and non-obvious. Inventions embodied in other combinations and subcombinations of features, functions, elements and/or properties may be claimed through amendment of the present claims or presentation of new claims in this or a related application. Such amended or new claims, whether they are directed to a different invention or directed to the same invention, whether different, broader, narrower, or equal in scope to the original claims, are also regarded as included within the subject matter of the inventions of the present disclosure. 
     While the present invention has been described and illustrated by reference to particular embodiments, those of ordinary skill in the art will appreciate that the invention lends itself to variations not necessarily illustrated herein. For this reason, then, reference should be made solely to the appended claims for purposes of determining the true scope of the present invention.