SUPERCAPACITORS HAVE ATTRACTED A GREAT DEAL OF ATTENTION AS AN ELECTRICAL STORAGE DEVICE. THE MAIN MATERIALS THAT USED IN SUPERCAPACITOR ELECTRODES ARE CARBONS, METAL OXIDES, AND CONDUCTING POLYMERS. GRAPHENEBASED MATERIAL PLAYS AN IMPORTANT ROLE IN SUPERCAPACITOR ELECTRODE MATERIALS THANKS TO THEIR LOW PRODUCTION COST, HIGH SURFACE AREA AND EXCELLENT CONDUCTIVITY. HOWEVER, THERE IS A MAJOR LIMITATION OF LOW ENERGY DENSITY IN GRAPHENE-BASED ELECTRODE COMPARED TO OTHER MATERIAL SUCH AS METAL OXIDES. RECENTLY, SCIENTISTS HAVE FOUND THAT THIS LIMITATION IS DUE TO THE Quantum Capacitance. IN FACT, THE TOTAL CAPACITY OF SUPERCAPACITORS CONSIDERED AS THE SUM OF TWO SERIES Capacitance OF DOUBLE-LAYER Capacitance AND ELECTRODE Capacitance (Quantum Capacitance). THUS, DEFICIENCIES IN EACH OF THEM WILL MAKE A REDUCTION IN TOTAL DEVICE Capacitance. IN THIS PAPER, WE EXPLORED THE EFFECT OF NITROGEN DOPING AND STRUCTURAL DEFECT AS SIMULTANEOUSLY ON Quantum Capacitance. THE MIXED SYSTEMS THAT WE USED ARE N-DOPED GRAPHENE WITH SOME STRUCTURAL DEFECTS SUCH AS DIVACANCY (5-8-5), MONOVACANCY (5-9) AND STONE-WALES DEFECT. DENSITY FUNCTIONAL THEORY (DFT) CALCULATIONS WERE PERFORMED WITHIN THE PLANE-WAVE PSEUDOPOTENTIAL FORMALISM, AS IMPLEMENTED IN THE Quantum-ESPRESSO CODE. INTEGRATED Quantum Capacitance IS GIVEN WITH EQUATION 1.CINTQ (V)=1/VE ÒV0 CQ (V’) DV’ (1)WHERE, CQ IS THE DIFFERENTIAL Quantum Capacitance AND V IS THE VOLTAGE THAT REFERENCED TO THE ZERO-BIAS FERMI LEVEL. OUR RESULTS SHOW THAT GOOD ENHANCEMENT HAS BEEN REACHED WITH DOPING AND MAKING STRUCTURAL DEFECT IN GRAPHENE SHEET AS AN INDIVIDUALLY OR SIMULTANEOUSLY. THIS SIGNIFICANT ENHANCEMENT IS MAINLY DUE TO THE ADDITIONAL IMPURITY STATES NEAR THE FERMI LEVEL. IN SUCH A MIXED SYSTEM, EACH TYPE OF MIXED SYSTEMS ALTER THE ELECTRONIC STRUCTURE AND CREATE UNIQUE DOS AND SUBSEQUENTLY Quantum Capacitance. EXPLORING OF PROJECTED DOS SUGGEST THAT PZ STATES NEAR THE DEFECT AND P ORBITALS OF HETEROATOM (N) CONTRIBUTE TO THE INDUCED IMPURITY STATES. IN PRACTICE, A FABRICATED N-DOPED GRAPHENE ELECTRODE MAY HAVE MANY TYPES OF THIS MIXED SYSTEM, WHICH IS OUTSIDE THE RANGE OF THIS WORK. OUR FINDINGS SUGGEST THAT, UNDER CHARGING CONDITIONS, THESE MIXED SYSTEMS WILL BE MORE EFFECTIVE AT POSITIVE BIAS. THESE RESULTS REPRESENT DESIGN STRATEGIES FOR IMPROVING THE PERFORMANCE OF SUPERCAPACITORS.

SUPERCAPACITORS IS ONE OF THE MOST PROMISING ENERGY STORAGE DEVICES IN THE FIELD OF ELECTRICAL ENERGY. GRAPHENE AND ITS DERIVATIVES ARE THE MOST COMMONLY USED MATERIALS IN SUPERCAPACITORS ELECTRODE. HOWEVER, THE MAJOR LIMITATION OF THIS TYPE OF ELECTRODES IS THEIR LOW ENERGY DENSITY. RECENTLY, IT HAS BEEN FOUND THAT LIMITATION FACTOR IN TOTAL Capacitance OF GRAPHENE-BASED SUPERCAPACITORS IS THEIR FINITE Quantum Capacitance AT CONVENTIONAL ELECTROLYTE STABILITY VOLTAGE RANGE. THE TOTAL Capacitance (CT) AT THE ELECTRODE/IONIC-LIQUID INTERFACE IS GIVEN BY 1/CT=1/CQ+1/CD(1)WHERE IS THE ELECTRIC DOUBLE LAYER CapacitanceAND IS THE Quantum Capacitance, WHICH GIVEN BY CQ(V)=E2 Ò+¥-¥ D(E) FT (E-M) DE (2)WHERE D(E) IS THE ELECTRON DENSITY OF STATE (DOS),FT(E) IS THE THERMAL BROADENING FUNCTION, E IS THE RELATIVE ENERGY WITH RESPECT TO THE FERMI LEVEL EF, AND E IS THE ELEMENTARY CHARGE. IN THIS WORK, WE USED OF DENSITY FUNCTIONAL THEORY CALCULATIONS TO EXPLORE THE EFFECT OF THE FUNCTIONALIZATION OF GRAPHENE WITH SOME SUBSTITUTED GROUPS ON THE ELECTRONIC STRUCTURE AND CONSEQUENTLY ON THE Quantum Capacitance OF GRAPHENE. SUBSTITUTED GROUPS THAT WERE USED CONTAIN -CH3, -H, -OH, -NH2, AND -COOH. THE FULL GEOMETRY OPTIMIZATIONS AND DENSITY OF STATE CALCULATIONS WERE CARRIED OUT BY THE ESPRESSO CODE. WE CONSIDER THE HEXAGONAL 3´3 SUPERCELL WITH ONE FUNCTIONAL GROUP AND 25 Å A VACUUM GAP IN THE VERTICAL (Z) DIRECTION TO SEPARATE THE GRAPHENE SYSTEM FROM ITS PERIODIC IMAGES. OBTAINED RESULTS SHOW THAT THIS TYPE OF FUNCTIONALIZATION SHOWS ONE PEAK NEAR THE FERMI LEVEL AT THE PLOT OF DOS. THE IMPURITY DOS THAT ARISES AROUND THE FERMI LEVEL IS A DIRECT RESULT OF PRODUCED LOCAL SP3 HYBRIDIZATION. INSPECTION OF PROJECTED DOSS SUGGESTS THAT PZ ORBITAL OF CARBON ATOM THAT SUBSTITUTED GROUP CONNECTED TO IT, CONTRIBUTES TO THE IMPURITY STATES NEAR THE FERMI LEVEL. OUR RESULTS DEMONSTRATE THAT THE Quantum Capacitance AND CONSEQUENTLY STORED CHARGE IN FUNCTIONALIZED GRAPHENE WITH EACH SUBSTITUTED GROUPSHAS INCREASED COMPARED TO THE PRISTINE GRAPHENE. THIS ENHANCEMENT IN Quantum Capacitance IS DIRECTLY RELATED TO ADDITIONAL AVAILABILITY OF STATES NEAR THE FERMI LEVEL. IN THIS TYPE OF FUNCTIONALIZATION OF GRAPHENE, THE Capacitance IS SYMMETRICAL AROUND ZERO VOLTAGE. IN OTHER WORD, THE USE OF THESE MATERIALS IN BOTH POSITIVE AND NEGATIVE ELECTRODES IS SUGGESTED.

SUPER CAPACITORS DUE TO HIGH POWER DENSITY, ENABLING FAST CHARGING AND DISCHARGING, ARE USED TO STORE ELECTRICAL ENERGY. HOWEVER, THEIR LOWER ENERGY DENSITY IN COMPARISON WITH CONVENTIONAL BATTERIES, LIMITS THE USE OF THIS ENERGY STORAGE DEVICE. IN THIS REGARD, EXTENSIVE RESEARCHES IN THE FIELD OF SUPERCAPACITORS ARE PERFORMED TO INCREASE THE CAPACITY OF SUPER CAPACITORS [1]. CARBON NANOTUBE (CNTS) -BASED MATERIAL ARE PROMISING MATERIALS FOR USE IN SUPER CAPACITOR ELECTRODES [2].DESPITE OF ADVANTAGE OF CNTS-BASED ELECTRODE, MAJOR LIMITATION OF LOW QUANTITY OF SPECIFIC CAPACITY DUE TO THEIR LOW Quantum Capacitance REMAIN [3]. ALL DENSITY FUNCTIONAL THEORY (DFT) CALCULATIONS WERE COMPLETED USING Quantum ESPRESSO CODE AND PREDEW-WANG91 (GGAPW91) EXCHANGE-CORRELATION FUNCTIONAL. OUR RESULTS INDICATE THAT Quantum Capacitance SIGNIFICANTLY IS IMPROVED BY CHANGING IN THE ELECTRONIC STRUCTURE THROUGH DOPANTS AND DEFECTS. THE OBTAINED RESULTS FROM DENSITY OF STATE (DOS) OF P-DOPED (6, 6) CNTS INDICATES THAT IMPURITY STATES ARE CREATED AROUND THE FERMI LEVEL (SEE FIGURE 1A). Quantum Capacitance OF P-DOPED (6, 6) CNTS IN THE WATER STABILITY RANGE (FOR V=-0.4-0.83) ARE INCREASED COMPARED WITH Quantum Capacitance OF PURE (6, 6) CNTS. IN THESE CASES THE Quantum Capacitance IS ALMOST SYMMETRIC AROUND ZERO VOLTAGE AND INCREASED BOTH THE NEGATIVE AND THE POSITIVE BIAS (SEE FIGURE 1B).

DIFFERENT SCIENTISTS HAVE TRIED TO COMBINE PETROPHYSICS, GEOPHYSICS, AND THERMODYNAMICS WITH ECONOMIC FACTORS IN ORDER TO FIND OUT THE BEST RECOVERY SCENARIO. HAVING A GOOD PRODUCTION SCENARIO AND A PROPER FIELD DEVELOPMENT STRATEGY REQUIRE TEDIOUS CALCULATIONS AND SIMULATIONS. PRESENT COMMERCIAL SIMULATORS ARE COMPLEX TO WORK WITH AND TIME-CONSUMING;  THEREFORE, HAVING AN OVERVIEW BY LESS PRIMARY DATA IS NECESSARY TO MANAGE THE FIELD AND TO OPTIMIZE THE RECOVERY. IT WAS A TRIGGER FOR RESERVOIR ENGINEERS TO DEVELOP A FAST AND RELIABLE SIMULATOR. SIMPLE PREDICTIVE MODELS, WHICH USUALLY USE MATERIAL OR ENERGY BALANCE ON A RESERVOIR TO FIND OUT ITS PERFORMANCE, ARE VERY FAST AND LOW-COST.Capacitance-RESISTANCE MODEL (CRM) SHOWED EFFICIENT AS A FAST RESERVOIR SIMULATION TOOL USING FIELD-AVAILABLE DATA OF PRODUCTION AND INJECTIONS RATES. THIS APPROACH SETS A WEIGHTING FACTOR OR WELL-CONNECTIVITY PARAMETER AND A TIME-CONSTANT BETWEEN EACH PAIR OF INJECTION AND PRODUCTION WELLS ACCORDING TO THEIR HISTORY. IN THIS STUDY, A REAL CASE HAS BEEN MODELED USING CRM AND AN EFFICIENT AND OPTIMUM FIELD TIME-CONSTANT, WHICH COULD BE USED FOR ENTIRE FIELD, HAS BEEN DETERMINED USING CRM SIMULATION RESULTS. ITS ACCURACY IS VERIFIED BY COMPARING THE TOTAL OIL PRODUCTION RATE ERROR AND WELL-PAIR CONNECTIVITIES BETWEEN ORIGINAL AND OPTIMUM CASES.