Portillo Velez et al 2018a - Revision history

Rimni: /* 6.2 Results for the ten wells from ATG-zone Mexico */

2021-08-30T11:28:43Z

‎6.2 Results for the ten wells from ATG-zone Mexico

Rimni at 11:19, 30 August 2021

2021-08-30T11:19:46Z

Rimni: /* 6. Results */

2021-08-30T11:14:19Z

‎6. Results

Rimni at 11:12, 30 August 2021

2021-08-30T11:12:08Z

Rimni at 11:09, 30 August 2021

2021-08-30T11:09:51Z

Rimni at 11:08, 30 August 2021

2021-08-30T11:08:17Z

Rimni: /* 2. Introduction */

2021-08-30T11:07:06Z

‎2. Introduction

Rimni at 13:17, 8 May 2020

2020-05-08T13:17:50Z

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Rimni at 13:16, 8 May 2020

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Rimni at 13:13, 8 May 2020

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← Older revision		Revision as of 11:28, 30 August 2021
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	===6.2 Results for the ten wells from ATG-zone Mexico===		===6.2 Results for the ten wells from ATG-zone Mexico===

−	The rest of the wells were analyzed with the proposed DEA by considering <math display="inline">G_{max}=500</math> and <math display="inline">P=100</math>. Numerical results are depicted in [[#table-7\|Table 7]]. Note that power consumption is between 9 and 19 [HP], remarkably lower than the presented in ~~Table~~ [[#table-4\|4]]. Moreover, the efficiencies are incremented in all cases as shown in [[#img-5\|Figures 5]] and [[#img-6\|6]]. Worst DEA and Best DEA means the worst and best result using the Differential Evolution Algorithm, respectively; while real means the result for the implemented HJP. Note that in most cases <math display="inline">M=M_c</math>, thus putting in risk of cavitation in the HJP. Nonetheless this result can be improved by considering a safety factor <math display="inline">\beta < 1</math> such that <math display="inline">M < \beta M_c</math>.	+	The rest of the wells were analyzed with the proposed DEA by considering <math display="inline">G_{max}=500</math> and <math display="inline">P=100</math>. Numerical results are depicted in [[#table-7\|Table 7]]. Note that power consumption is between 9 and 19 [HP], remarkably lower than the presented in [[#table-4\|Table 4]]. Moreover, the efficiencies are incremented in all cases as shown in [[#img-5\|Figures 5]] and [[#img-6\|6]]. Worst DEA and Best DEA means the worst and best result using the Differential Evolution Algorithm, respectively; while real means the result for the implemented HJP. Note that in most cases <math display="inline">M=M_c</math>, thus putting in risk of cavitation in the HJP. Nonetheless this result can be improved by considering a safety factor <math display="inline">\beta < 1</math> such that <math display="inline">M < \beta M_c</math>.

@@ Line 864: / Line 864: @@
-In order to validate our design proposal, it has been evaluated a set of ten oil-wells from the asset ''Aceite Terciario del Golfo ''(ATG-Mexico), an important oil-well zone in Mexico. The values of the operating oil-well conditions that have been used to perform this analysis have been provided by the Mexican Company Geolis/Nuvoil (Table [[#table-4|4]]). In this Table, it can be observed low efficiencies and high power consumption for most oil-wells currently operating. It is important to mention that the efficiency and horsepower consumption, were actually computed with models considered in this paper, based in the operational parameters of the Geolis/Nuvoil Company.
+In order to validate our design proposal, it has been evaluated a set of ten oil-wells from the asset ''Aceite Terciario del Golfo ''(ATG-Mexico), an important oil-well zone in Mexico. The values of the operating oil-well conditions that have been used to perform this analysis have been provided by the Mexican Company Geolis/Nuvoil ([[#table-4|Table 4]]). In this Table, it can be observed low efficiencies and high power consumption for most oil-wells currently operating. It is important to mention that the efficiency and horsepower consumption, were actually computed with models considered in this paper, based in the operational parameters of the Geolis/Nuvoil Company.
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;font-size: 75%;">
 '''Table 4'''. Field data of ten wells form ATG-Mexico. (HP= <math>1.7 \cdot 10^{-5} q_1 \cdot P_s</math>)</div>
+<div id='tab-4'></div>
 {|  class="floating_tableSCP wikitable" style="text-align: left; margin: 1em auto;min-width:50%;font-size: 85%;"
 |- style="border-top: 2px solid;text-align: center;"
@@ Line 1,018: / Line 1,018: @@
 ===6.1 Benchmark oil-well===
-For the sake of clarity, the sixth oil-well in Table [[#table-4|4]] is selected as a benchmark to show our design proposal. Geolis/Nuvoil company disposed of a pressure-temperature sensor of the brand Pioneer Petrotech Services Inc., into the oil-well. The sensor was operating during one month getting the average value of <math display="inline">P_{wf}=1355 [PSI]</math>, while the predicted with equation ([[#eq-6|6]]) is <math display="inline">P_3=P_{wf}=1177 [Psi]</math> getting a error of 13.14 %
+For the sake of clarity, the sixth oil-well in [[#table-4|Table 4]] is selected as a benchmark to show our design proposal. Geolis/Nuvoil company disposed of a pressure-temperature sensor of the brand Pioneer Petrotech Services Inc., into the oil-well. The sensor was operating during one month getting the average value of <math display="inline">P_{wf}=1355 [PSI]</math>, while the predicted with equation ([[#eq-6|6]]) is <math display="inline">P_3=P_{wf}=1177 [Psi]</math> getting a error of 13.14 %
-After the application of our approach, the first set of results are depicted in Table [[#6.1 Benchmark oil-well|6.1]], considering the initial population of 20 individuals and varying the number of maximum generations from 50 to 500. As it can be observed with low generations, convergence is not achieved  and the optimal efficiency rounds 9% to 11% In these cases the cavitation indicator <math display="inline">M</math> is quite lower than <math display="inline">M_c</math> and power consumption rounds 40 [HP]. Then, with higher number of generations the efficiency is improved up to 16.88 %, with <math display="inline">M</math> closer to <math display="inline">M_c</math>. Note also that in this case the power consumption is close to 12 [HP] with a clear energy saving.
+After the application of our approach, the first set of results are depicted in [[#table-5|Table 5]], considering the initial population of 20 individuals and varying the number of maximum generations from 50 to 500. As it can be observed with low generations, convergence is not achieved  and the optimal efficiency rounds 9% to 11% In these cases the cavitation indicator <math display="inline">M</math> is quite lower than <math display="inline">M_c</math> and power consumption rounds 40 [HP]. Then, with higher number of generations the efficiency is improved up to 16.88 %, with <math display="inline">M</math> closer to <math display="inline">M_c</math>. Note also that in this case the power consumption is close to 12 [HP] with a clear energy saving.
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;font-size: 75%;">
 '''Table 5'''. Numerical results for <math>P=20</math> and different number of maximum generations</div>
+<div id='tab-5'></div>
 {|  class="floating_tableSCP wikitable" style="text-align: center; margin: 1em auto;min-width:50%;font-size: 85%;"
 |- style="border-top: 2px solid;"
@@ Line 1,184: / Line 1,184: @@
-Table [[#table-6|6]] presents numerical results by considering a fixed number of <math display="inline">G_{max}=250</math> generations and varying the number of initial population.
+[[#table-6|Table 6]] presents numerical results by considering a fixed number of <math display="inline">G_{max}=250</math> generations and varying the number of initial population.
 As it can be observed, with low initial population and <math display="inline">G_{max}</math> reasonably high, convergence is achieved and the optimal efficiency rounds 15.8% In this cases the cavitation indicator <math display="inline">M</math> is quite less than <math display="inline">M_c</math> and power consumption rounds 11 [HP], thus saving energy. Nevertheless, in this case with higher number of initial population the efficiency is improved up to 17.23 %, with <math display="inline">M</math> equal to <math display="inline">M_c</math> and more important, the power consumption is close to 19 [HP]. Here, the geometries selected for <math display="inline">A_n</math> and <math display="inline">A_{th}</math> are smaller than the selected for the case when the efficiency rounds 16.8 % Moreover, the input pressure must be increased twice in order to render higher efficiency, which explains the 19 [HP] of power consumption.
@@ Line 1,191: / Line 1,191: @@
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;font-size: 75%;">
 '''Table 6'''. Numerical results for <math>G_{max}=250</math> and different initial population</div>
+<div id='tab-6'></div>
 {|  class="floating_tableSCP wikitable" style="text-align: center; margin: 1em auto;min-width:50%;font-size: 85%;"
 |- style="border-top: 2px solid;"
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 ===6.2 Results for the ten wells from ATG-zone Mexico===
-The rest of the wells were analyzed with the proposed DEA by considering <math display="inline">G_{max}=500</math> and <math display="inline">P=100</math>. Numerical results are depicted in Table [[#table-7|7]]. Note that power consumption is between 9 and 19 [HP], remarkably lower than the presented in Table [[#table-4|4]]. Moreover, the efficiencies are incremented in all cases as shown in Figures [[#img-5|5]] and [[#img-6|6]]. Worst DEA and Best DEA means the worst and best result using the Differential Evolution Algorithm, respectively; while real means the result for the implemented HJP. Note that in most cases <math display="inline">M=M_c</math>, thus putting in risk of cavitation in the HJP. Nonetheless this result can be improved by considering a safety factor <math display="inline">\beta < 1</math> such that <math display="inline">M < \beta M_c</math>.
+The rest of the wells were analyzed with the proposed DEA by considering <math display="inline">G_{max}=500</math> and <math display="inline">P=100</math>. Numerical results are depicted in  [[#table-7|Table 7]]. Note that power consumption is between 9 and 19 [HP], remarkably lower than the presented in Table [[#table-4|4]]. Moreover, the efficiencies are incremented in all cases as shown in  [[#img-5|Figures 5]] and [[#img-6|6]]. Worst DEA and Best DEA means the worst and best result using the Differential Evolution Algorithm, respectively; while real means the result for the implemented HJP. Note that in most cases <math display="inline">M=M_c</math>, thus putting in risk of cavitation in the HJP. Nonetheless this result can be improved by considering a safety factor <math display="inline">\beta < 1</math> such that <math display="inline">M < \beta M_c</math>.
@@ Line 1,357: / Line 1,357: @@
 '''Table 7'''. Results obtained with the DEA algorithm for ten wells form ATG-zone Mexico
 </div>
+<div id='tab-7'></div>
 {|  class="floating_tableSCP wikitable" style="text-align: left; margin: 1em auto;min-width:50%;font-size: 85%;"
 |- style="border-top: 2px solid;text-align: center;"

← Older revision		Revision as of 11:14, 30 August 2021
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	In this work the vector design is set as <math display="inline">\mathbf{x}=[x_1,x_2,x_3,x_4]^T=[A_{th},A_n,P_s,q_1]^T</math> and the parameters of the DEA are set to <math display="inline">F=0.7</math> and <math display="inline">CR=0.8</math>. The algorithm was implemented in Matlab<math display="inline">^\mbox{©}</math>.		In this work the vector design is set as <math display="inline">\mathbf{x}=[x_1,x_2,x_3,x_4]^T=[A_{th},A_n,P_s,q_1]^T</math> and the parameters of the DEA are set to <math display="inline">F=0.7</math> and <math display="inline">CR=0.8</math>. The algorithm was implemented in Matlab<math display="inline">^\mbox{©}</math>.

−	It is important to remark that in order to implement the considerations presented in ~~Tables~~ [[#table-2\|2]] and [[#table-1\|1]], indexed lists are used in the DEA, i.e. any list item can be identified by a sequential integer number that identifies its position. In order to keep operational conditions feasible, as indicated by the technical data-sheet of the surface pumps, the range of values for the input flow and input pressure were set to minimum and maximum values as: <math display="inline">q_{1_{min}}=600 [BPD]</math>, <math display="inline">q_{1_{max}}=1500 [BPD]</math>, <math display="inline">P_{s_{min}}=900 [Psi]</math> and <math display="inline">P_{s_{max}}=2500 [Psi]</math>. ~~Table~~ [[#table-3\|3]] depicts testing parameters experimentally obtained, <span id='citeF-9'></span>[[#cite-9\|[9]]].	+	It is important to remark that in order to implement the considerations presented in [[#table-2\|Tables 2]] and [[#table-1\|1]], indexed lists are used in the DEA, i.e. any list item can be identified by a sequential integer number that identifies its position. In order to keep operational conditions feasible, as indicated by the technical data-sheet of the surface pumps, the range of values for the input flow and input pressure were set to minimum and maximum values as: <math display="inline">q_{1_{min}}=600 [BPD]</math>, <math display="inline">q_{1_{max}}=1500 [BPD]</math>, <math display="inline">P_{s_{min}}=900 [Psi]</math> and <math display="inline">P_{s_{max}}=2500 [Psi]</math>. [[#table-3\|Table 3]] depicts testing parameters experimentally obtained, <span id='citeF-9'></span>[[#cite-9\|[9]]].

@@ Line 339: / Line 339: @@
 ==5. Optimization design process using Differential Evolution==
-There exist several theoretical and numerical techniques, to solve non-linear constrained optimization problems. In this work, we consider a numerical approach by using a Differential Evolution Algorithm (DEA), <span id='citeF-13'></span>[[#cite-13|[13]]]. A DEA is a numerical method for the determination of the global minimum or maximum, for highly non-linear problems. It can handle an optimization problem with or without constraints, based on a process of natural selection that imitates biological evolution, <span id='citeF-14'></span>[[#cite-14|[14]]]. The DEA repeatedly updates a set of <math display="inline">P</math> initial vector designs <math display="inline">[\mathbf{x}_{1,0}, \mathbf{x}_{2,0},..., \mathbf{x}_{P,0}]</math> called ''population'', in order to reach a final set of vector designs <math display="inline">[\mathbf{x}_{1,f}, \mathbf{x}_{2,f},..., \mathbf{x}_{P,f}]</math>, for which an objective function <math display="inline">f(\mathbf{x}_{i,f})</math> is minimized or maximized for <math display="inline">i=1,2,..,P</math>, as shown in Figure [[#img-3|3]].
+There exist several theoretical and numerical techniques, to solve non-linear constrained optimization problems. In this work, we consider a numerical approach by using a Differential Evolution Algorithm (DEA), <span id='citeF-13'></span>[[#cite-13|[13]]]. A DEA is a numerical method for the determination of the global minimum or maximum, for highly non-linear problems. It can handle an optimization problem with or without constraints, based on a process of natural selection that imitates biological evolution, <span id='citeF-14'></span>[[#cite-14|[14]]]. The DEA repeatedly updates a set of <math display="inline">P</math> initial vector designs <math display="inline">[\mathbf{x}_{1,0}, \mathbf{x}_{2,0},..., \mathbf{x}_{P,0}]</math> called ''population'', in order to reach a final set of vector designs <math display="inline">[\mathbf{x}_{1,f}, \mathbf{x}_{2,f},..., \mathbf{x}_{P,f}]</math>, for which an objective function <math display="inline">f(\mathbf{x}_{i,f})</math> is minimized or maximized for <math display="inline">i=1,2,..,P</math>, as shown in  [[#img-3|Figure 3]].
 <div id='img-3'></div>
@@ Line 363: / Line 363: @@
 ===5.1 Remarks on the algorithm implementation===
-Continuing with the solution to the optimization problem, it is necessary to establish the dimensions that will have nozzle and throat according to standard sizes and relationships offered by manufacturers. Figure [[#img-4|4]] depicts in red squares commercial nozzle and throat.
+Continuing with the solution to the optimization problem, it is necessary to establish the dimensions that will have nozzle and throat according to standard sizes and relationships offered by manufacturers.  [[#img-4|Figure 4]] depicts in red squares commercial nozzle and throat.
 <div id='img-4'></div>
@@ Line 373: / Line 373: @@
 |}
-There are many manufacturers of HJPs in the world. In Table [[#table-1|1]], the nozzle and throat areas (in squared inches) are classified for three different manufacturers: Kobe, National and Guiberson. In this paper we select the last one, since Geolis/Nuvoil company uses Guiberson Jet pumps.
+There are many manufacturers of HJPs in the world. In [[#table-1|Table 1]], the nozzle and throat areas (in squared inches) are classified for three different manufacturers: Kobe, National and Guiberson. In this paper we select the last one, since Geolis/Nuvoil company uses Guiberson Jet pumps.
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;font-size: 75%;">
 '''Table 1'''. Designation of commercial nozzle and throat areas.</div>
+<div id='tab-1'></div>
 {|  class="floating_tableSCP wikitable" style="text-align: center; margin: 1em auto;min-width:50%;font-size:85%;"
 |- style="border-top: 2px solid;border-bottom: 2px solid;"
@@ Line 706: / Line 706: @@
-Eddie Smart <span id='citeF-16'></span>[[#cite-16|[16]]], proposed a throat and nozzle combinations in terms of the parameters <math display="inline">b</math> and <math display="inline">A_s</math>, that are implementable in practical applications. This represents a set of constraints as explained in Section [[#4 Problem Statement.|4]]. The feasible relationships between <math display="inline">b</math> and <math display="inline">A_s</math> are depicted in Table [[#table-2|2]].
+Eddie Smart <span id='citeF-16'></span>[[#cite-16|[16]]], proposed a throat and nozzle combinations in terms of the parameters <math display="inline">b</math> and <math display="inline">A_s</math>, that are implementable in practical applications. This represents a set of constraints as explained in Section [[#4 Problem Statement.|4]]. The feasible relationships between <math display="inline">b</math> and <math display="inline">A_s</math> are depicted in [[#table-2|Table 2]].
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;font-size: 75%;">
 '''Table 2'''. Search region considering practical implementations for Guiberson HJPs.</div>
+<div id='tab-2'></div>
 {|  class="floating_tableSCP wikitable" style="text-align: center; margin: 1em auto;min-width:50%;font-size:85%;"
 |- style="border-top: 2px solid;border-bottom: 1px solid;"

@@ Line 170: / Line 170: @@
 |}
-In equation ([[#eq-2|2]]), <math display="inline">q_3</math> represents the flow from the well in barrels per day (BPD) and <math display="inline">q_1</math> represents the flow injected from the surface in BPD. A third flow <math display="inline">q_2</math> is the sum of both flows, as shown in Figure [[#img-2|2]]. Note that the input flow <math display="inline">q_1</math> can be controlled via a hydraulic (piston or geared) pump on the surface.
+In equation ([[#eq-2|2]]), <math display="inline">q_3</math> represents the flow from the well in barrels per day (BPD) and <math display="inline">q_1</math> represents the flow injected from the surface in BPD. A third flow <math display="inline">q_2</math> is the sum of both flows, as shown in  [[#img-2|Figure 2]]. Note that the input flow <math display="inline">q_1</math> can be controlled via a hydraulic (piston or geared) pump on the surface.
 With respect to equation ([[#eq-3|3]]), it presents has a dual definition.  On the one hand, in this equation, <math display="inline">H</math> represents the dimensionless head recovery ratio for the pressures <math display="inline">P_1</math>, <math display="inline">P_2</math> and <math display="inline">P_3</math> of the HJP. On the other hand, the term <math display="inline">N</math> represents experimental information considering friction loss coefficients <math display="inline">K_j</math>, <math display="inline">K_s</math>, <math display="inline">K_t</math>, <math display="inline">K_d</math> and the geometry of the HJP, <span id='citeF-1'></span>[[#cite-1|[1]]]. Given the values of <math display="inline">M</math>, the adimensional coefficients, and once the nozzle area <math display="inline">A_n</math> and throat area <math display="inline">A_{th}</math> are selected to compute <math display="inline">b</math>, then <math display="inline">N</math> is obtained using equation ([[#eq-4|4]]), see <span id='citeF-1'></span>[[#cite-1|[1]]]

@@ Line 123: / Line 123: @@
 ==3. Mathematical models==
-The fundamental of operation of an HJP of an ALS is based on the Venturi principle <span id='citeF-8'></span>[[#cite-8|[8]]]. Basically, this principle consists of applying additional energy to the oil at the bottom of the oil-well, in order to force the fluid to flow to the surface. For this purpose, a driving or working fluid (typically water) is injected through the production pipe to the oil-well. At the return, the mixture between working fluid and oil, is forced to circulate through the annular space between the production and cladding pipes; this working principle is shown in Figure [[#img-2|2]].
+The fundamental of operation of an HJP of an ALS is based on the Venturi principle <span id='citeF-8'></span>[[#cite-8|[8]]]. Basically, this principle consists of applying additional energy to the oil at the bottom of the oil-well, in order to force the fluid to flow to the surface. For this purpose, a driving or working fluid (typically water) is injected through the production pipe to the oil-well. At the return, the mixture between working fluid and oil, is forced to circulate through the annular space between the production and cladding pipes; this working principle is shown in  [[#img-2|Figure 2]].
 <div id='img-2'></div>
@@ Line 172: / Line 172: @@
 In equation ([[#eq-2|2]]), <math display="inline">q_3</math> represents the flow from the well in barrels per day (BPD) and <math display="inline">q_1</math> represents the flow injected from the surface in BPD. A third flow <math display="inline">q_2</math> is the sum of both flows, as shown in Figure [[#img-2|2]]. Note that the input flow <math display="inline">q_1</math> can be controlled via a hydraulic (piston or geared) pump on the surface.
-With respect to Equation ([[#eq-3|3]]), it presents has a dual definition.  On the one hand, in this equation, <math display="inline">H</math> represents the dimensionless head recovery ratio for the pressures <math display="inline">P_1</math>, <math display="inline">P_2</math> and <math display="inline">P_3</math> of the HJP. On the other hand, the term <math display="inline">N</math> represents experimental information considering friction loss coefficients <math display="inline">K_j</math>, <math display="inline">K_s</math>, <math display="inline">K_t</math>, <math display="inline">K_d</math> and the geometry of the HJP, <span id='citeF-1'></span>[[#cite-1|[1]]]. Given the values of <math display="inline">M</math>, the adimensional coefficients, and once the nozzle area <math display="inline">A_n</math> and throat area <math display="inline">A_{th}</math> are selected to compute <math display="inline">b</math>, then <math display="inline">N</math> is obtained using equation ([[#eq-4|4]]), see <span id='citeF-1'></span>[[#cite-1|[1]]]
+With respect to equation ([[#eq-3|3]]), it presents has a dual definition.  On the one hand, in this equation, <math display="inline">H</math> represents the dimensionless head recovery ratio for the pressures <math display="inline">P_1</math>, <math display="inline">P_2</math> and <math display="inline">P_3</math> of the HJP. On the other hand, the term <math display="inline">N</math> represents experimental information considering friction loss coefficients <math display="inline">K_j</math>, <math display="inline">K_s</math>, <math display="inline">K_t</math>, <math display="inline">K_d</math> and the geometry of the HJP, <span id='citeF-1'></span>[[#cite-1|[1]]]. Given the values of <math display="inline">M</math>, the adimensional coefficients, and once the nozzle area <math display="inline">A_n</math> and throat area <math display="inline">A_{th}</math> are selected to compute <math display="inline">b</math>, then <math display="inline">N</math> is obtained using equation ([[#eq-4|4]]), see <span id='citeF-1'></span>[[#cite-1|[1]]]
 <span id="eq-4"></span>

@@ Line 105: / Line 105: @@
 In this work, we focus on the ALS of Hydraulic pumping with an HJP <span id='citeF-1'></span>[[#cite-1|[1]]]. Hence, HJPs are of vast interest in petroleum engineering because of their design characteristics, and volumetric oil production they can handle.  For the Hydraulic ALS, the HJP is introduced into the oil-well via the production pipe and it can be retrieved by simply reversing the working flow sense. In this application, the HJP has some disadvantages such as the cavitation phenomenon and typically low efficiency; nevertheless, both might be mitigated by an optimum design of the HJP and the selection of the best operating conditions for the ALS.
-In general, the fundamental parts of this ALS are: a combustion engine that drives a hydraulic piston (or geared) pump; an horizontal three-phase separator containing the mixture (oil, gas and sand) extracted from the oil-well; a control panel that controls the ALS and finally the HJP, installed at the bottom of the oil-well. Note that an HJP includes in a carrier that encloses the nozzle and throat (Figure [[#img-1|1]]).
+In general, the fundamental parts of this ALS are: a combustion engine that drives a hydraulic piston (or geared) pump; an horizontal three-phase separator containing the mixture (oil, gas and sand) extracted from the oil-well; a control panel that controls the ALS and finally the HJP, installed at the bottom of the oil-well. Note that an HJP includes in a carrier that encloses the nozzle and throat ([[#img-1|Figure 1]]).
 <div id='img-1'></div>