Microtrabeculae type focused logging device impedance scale network design method
Technical field
The present invention relates to a kind of microtrabeculae type focused logging device impedance scale network design method。
Background technology
Along with new technique, new technology, the appearance of new material and development, the reliability of downhole instrument string and integrated level improve constantly, and the volume and weight of instrument string develops to small and light direction。Develop high reliability, high efficiency integrated downhole logging instruments has become the important directions that domestic and international logger develops。Microtrabeculae type focused logging device (MCFL) is a kind of shallow investigation resistivity logger, measure invaded zone resistivity, there is the experiment curv of three kinds of investigation depths, it is used for replacing microspheric focused logging device, better estimation mud cake parameter, thus contributing to detection permeable formation, provide two synthesis HMNO, HMIN (Micro-electrode Log Curves) simultaneously。May be provided for cake thickness and mud cake resistivity parameter, meeting once goes into the well obtains the ability of 4 curves。Microtrabeculae type focused logging device, in development process and use, in the certainty of measurement of Factory Building domestic demand detecting instrument, makes instrument measurements corresponding with the resistivity relation on stratum, supports instrument development and work on the spot。The design of current other kinds of logger scale network is all be designed according to the circuit after simplifying, simple as far as possible resistor network so can be utilized to carry out simulated formation information, but, this design can only simulate the simple stratum such as uniform stratum, is difficult to Simulation of Complex formation information。
Summary of the invention
In order to solve above-mentioned technical problem, the present invention provides a kind of microtrabeculae type focused logging device impedance scale network design method, suitable in the situation of bad ground, it utilizes impedance network that stratum is carried out equivalence when not simplifying formation information, can effective testing circuit certainty of measurement。
For this, technical scheme is as follows:
A kind of microtrabeculae type focused logging device impedance scale network design method, comprises the steps:
1) drawing an equilateral polygon, this equilateral polygonal vertex number is equal with the electrode number that microtrabeculae type focused logging device comprises, and is designated as k;Being electrode by polygonal vertex, each electrode is connected between two with other electrode respectively, the straight line that electrode is connected between two marks admittance successively, constitutes the impedance scale network of microtrabeculae type focused logging device, and admittance number isIt is designated as h;
2) add current source between electrode between two, be designated as ins, with formula Ynφn=insThe point calculating electrode node ranks vector φn, wherein n refers to any one natural number in 1~k, and s represents current source;YnFor the admittance matrix of resistor network, φnFor the column vector that each electrode potential forms;The admittance matrix Y of correspondence is calculated again according to circuit equivalent principlen, by Ynφn=insDerive into formula AnG=ins;Wherein, G is a column vector of the admittance composition of h resistance, i.e. G=[G1G2…Gh]T, T represents transposition, AnFor coefficient matrix, obtain An;
3) step 2 is repeated) calculate h current source, obtain all An, form matrix A G=is, s represents current source;In formula, A=[A1A2…Ah]T, is=[i1si2s…ihs]T, T represents transposition;Wherein A1, A2... AhIt is the matrix of (k-1) × h;Solve, obtain the resistance of h resistance。
Microtrabeculae type focused logging device impedance scale network design method described above:
Step 1) in the electrode number k=9 that comprises of microtrabeculae type focused logging device, draw equilateral 9 deformation, corresponding resistance number, namely admittance numberEquilateral 9 deformation will mark admittance;
Step 2) in add current source between electrode between two, be designated as ins, with formula Ynφn=insThe point calculating electrode node ranks vector φn, wherein n refers to any one natural number in 1~9, and s represents current source;YnFor the admittance matrix of resistor network, φnFor the column vector that each electrode potential forms;The admittance matrix Y of correspondence is calculated again according to circuit equivalent principlen, by Ynφn=insDerive into formula AnG=ins;Wherein, G is a column vector of the admittance composition of 36 resistance, i.e. G=[G1G2…G36]T, T represents transposition, AnFor coefficient matrix, obtain An;
3) step 2 is repeated) calculate 36 current sources, obtain all An, form matrix A G=is, s represents current source;In formula, A=[A1A2…A36]T, is=[i1si2s…i36s]T, T represents transposition;Wherein A1, A2... A36It is the matrix of 8 × 36;Solve, obtain the resistance of 36 resistance。
A kind of microtrabeculae type focused logging device impedance scale network design method, comprises the steps:
1) drawing an equilateral polygon, this equilateral polygonal vertex number is equal with the electrode number that microtrabeculae type focused logging device comprises, and is designated as k;Being electrode by polygonal vertex, each electrode is connected between two with other electrode respectively, the straight line that electrode is connected between two marks admittance successively, constitutes the impedance scale network of microtrabeculae type focused logging device, and admittance number isIt is designated as h;
2) list extension admittance matrix Y ([1:k], [1:k]), wherein each point be with it in step 1) between electrode corresponding in polygon the marked admittance of line and;
3) add current source between electrode between two, be designated as ins, with formula Ynφn=insThe point calculating electrode node ranks vector φn, wherein n refers to any one natural number in 1~k, and s represents current source;YnFor the admittance matrix of resistor network, φnFor the column vector that each electrode potential forms;Corresponding extraction from described extension admittance matrix adds the admittance matrix Y that two electrodes of current source producen, extracting method is: removes the row and column that ground electrode is corresponding in extension admittance matrix, namely obtains the admittance matrix Y of correspondencen;By Ynφn=insDerive into formula AnG=ins;Wherein, G is a column vector of the admittance composition of h resistance, i.e. G=[G1G2…Gh]T, T represents transposition, AnFor coefficient matrix, obtain An;
4) step 3 is repeated) calculate h current source, obtain all An, form matrix A G=is, s represents current source;In formula, A=[A1A2…Ah]T, is=[i1si2s…ihs]T, T represents transposition;Wherein A1, A2... AhIt is the matrix of (k-1) × h;Solve, obtain the resistance of h resistance。
Microtrabeculae type focused logging device impedance scale network design method described above:
Step 1) in the electrode number k=9 that comprises of microtrabeculae type focused logging device, draw equilateral 9 deformation, corresponding resistance number, namely admittance numberEquilateral 9 deformation will mark admittance;
2) list extension admittance matrix Y ([1:9], [1:9]), wherein each point be with it in step 1) between electrode corresponding in polygon the marked admittance of line and, it may be assumed that
3) add current source between electrode between two, be designated as ins, with formula Ynφn=insCalculate the some position row vector φ of electrode noden, wherein n refers to any one natural number in 1~9, and s represents current source;YnFor the admittance matrix of resistor network, φnFor the column vector that each electrode potential forms;Corresponding extraction from described extension admittance matrix adds the admittance matrix Y that two electrodes of current source producen, extracting method is: removes the row and column that ground electrode is corresponding in extension admittance matrix, namely obtains the admittance matrix Y of correspondencen;By Ynφn=insDerive into formula AnG=ins;Wherein, G is a column vector of the admittance composition of 36 resistance, i.e. G=[G1G2…G36]T, T represents transposition, AnFor coefficient matrix, obtain An;
4) step 3 is repeated) calculate 36 current sources, obtain all An, form matrix A G=is, s represents current source;In formula, A=[A1A2…A36]T, is=[i1si2s…i36s]T, T represents transposition;Wherein A1, A2... A36It is the matrix of 8 × 36;, solve, obtain the resistance of h resistance。
The present invention proposes the computational methods of the equivalent resistance of a kind of microtrabeculae type focused logging device impedance network, and establish impedance rate resistor network according to the method, compensate for simplify scale network cannot the shortcoming of complete reaction formation characteristics under bad ground, can effectively be used for side circuit is tested, can carry out testing to microtrabeculae type focused logging device in Factory Building and analyze, save scheduling and planning cost, considerably improve development and production and the application efficiency of instrument。Current the method is successfully used for the equipment such as microtrabeculae logging instrument, achieves good effect。
Accompanying drawing explanation
Fig. 1 is microtrabeculae type focused logging device schematic diagram;
Fig. 2 is the impedance scale network of microtrabeculae type focused logging device;
Fig. 3 is the resistor network of microtrabeculae type focused logging device。
Detailed description of the invention
Below in conjunction with the drawings and specific embodiments, technical scheme is described。
Fig. 1 is microtrabeculae type focused logging device schematic diagram;In figure, A0, A1, A1', B0, B1, B2 are emission electrode, and M and M' is monitor electrode, and N is potential reference electrode, and B is loop electrode;Microtrabeculae is utilized respectively between A1 and A1', M and M' electrode wire connect, scale network is considered as an electrode, also have not shown earth point D in Fig. 1;The material that each electrode all uses electric conductivity good is made, it is seen then that this microtrabeculae type focused logging device has 9 electrodes, and it is numbered 1~9 respectively。
Microtrabeculae type focused logging device impedance scale network design method provided by the invention is that the microtrabeculae type focused log instrument shown in Fig. 1 is calibrated, quantify the impact of the circuit gain of instrument own and circuit design is verified, between measured value and stratigraphic model resistivity, setting up quantitative relationship。It is to say, its design key is to calculate each resistance value in scale network, in accordance with Ohm's law, it may be assumed that
Rij=Uij/Iij(1)
In formula, subscript i, j all refer to any one natural number in 1~9。
Be connected between two according to configuration of electrodes the electric network that constitutes by the calculated resistance of the method, it is simply that it is considered that standard stratum scale network impedance scale network。Being apparent from, when the number of poles of instrument is N, for given stratum, resistance number contained by this scale network is
Be computed obtaining between two between electrode the equivalent resistance under Different Strata set up equation group according to Kirchoff s voltage current law, thus obtaining the resistance of each resistance, the method is suitable for when resistance number is few。
As N=9, resistance number M=36 contained by scale network。Resistance quantity is more, is not suitable for the resistance utilizing Kirchhoff's theorem to determine each resistance, is all carry out simulated formation information with the resistor network simplified at present, but it cannot Simulation of Complex stratum。The present invention lists a nonagon, utilizing each summit to represent 9 electrodes of microtrabeculae type focused logging device, each electrode and all the other 8 electrodes are respectively connected with, and mark admittance therebetween between two on the line between electrode, the i.e. inverse of resistance, it is followed successively by G1, G2, G3, ..., G36, as in figure 2 it is shown, here it is the impedance scale network of microtrabeculae type focused logging device。
Utilize balanced bridge method and Network topology method can set up the relation between admittance matrix and each electrode potential, current source
Ynφn=ins(3)
Wherein, n, s all refers to any one natural number in 1~9;InsIt is be added in certain two interelectrode current source vector, YnFor the admittance matrix of resistor network, after current source position is determined, this matrix can be derived by by circuit equation, φnFor the column vector that each electrode potential forms。
Work as φnAnd insTime known, formula (3) can be organized into following matrix form
AnG=ins(4)
In formula, G is a column vector of the admittance composition of 36 resistance, i.e. G=[G1G2…G36]T, T represents transposition, AnFor coefficient matrix, 36 current sources of calculating, eventually form following matrix successively
AG=is(5)
In formula, A=[A1A2…A36]T, is=[i1si2s…i36s]T, T represents transposition。Wherein A1, A2... A36It is the matrix of 8 × 36。
In formula (4), (5), n all refers to any one natural number in 1~9, and s represents current source。
Its specific algorithm is as follows:
A () adds current source i between two electrodes1s, it is thus achieved that the current potential row vector φ of all electrode nodes1;
B () utilizes circuit equivalent principle to calculate admittance matrix Y1;
C (), by formula (3), is converted to formula (4), namely obtains A1;
D () change current source position, adds current source i between two electrodes2s, repeat above-mentioned three steps, until calculating 35 current sources of complete residue;
E () solving equations (5), obtains each resistance, the resistor network designed, as it is shown on figure 3, the subscript of resistance R represents two electrodes adding current source in figure。
From above-mentioned algorithm it can be seen that the most loaded down with trivial details step seeks to the corresponding admittance matrix Y that repeatedly derives1,Y2,…Y36。
A kind of simple algorithm given below, the matrix shown in matrix given below (6) because all admittance matrixs of impedance network can directly from this matrix extracting directly out, therefore be referred to as to extend admittance matrix, and it is symmetrical matrix。
In formula: GT1=G1+G9+G16+G22+G27+G31+G34+G36;
GT2=G1+G2+G3+G4+G5+G6+G7+G8;
GT3=G8+G9+G10+G11+G12+G13+G14+G15;
GT4=G7+G15+G16+G17+G18+G19+G20+G21;
GT5=G6+G14+G21+G22+G23+G24+G25+G26;
GT6=G5+G13+G20+G26+G27+G28+G29+G30;
GT7=G4+G12+G19+G25+G30+G31+G32+G33;
GT8=G3+G11+G18+G24+G29+G33+G34+G35;
GT9=G2+G10+G17+G23+G28+G32+G35+G36。
The derivation method of formula (6) is: admittance matrix Y is formed according to node given in Fig. 2, such as Y (1,1)=GT1 determines according to the related limit of node 1, when namely electrode 1 is connected between two with other electrode, admittance therebetween, i.e. G1, G9, G16, G22, G27, G31, G34, G36;Y (1,2)=-G1, and (namely electrode 1 and electrode 2 two ends add current source) related only G1 between node 1 and 2, the like, form general admittance matrix Y。
The method that admittance matrix in impedance network extracts from this formula (6) matrix is:
When current source is added between electrode (1) and (9) time, (9) are loop, due to (9) ground connection, remove the 9th row in Y and the 9th row, and Y ([1:8], [1:8]) is designated as admittance matrix Y1;When current source is added between electrode (1) and (2) time, (2) are loop, remove the 2nd row in Y and the 2nd row, and Y ([13:9], [13:9]) is designated as admittance matrix Y2;When current source is added between electrode (1) and (5), (5) are loop, remove the 5th row in Y and the 5th row, then Y ([1:46:9], [1:46:9]) is designated as admittance matrix Y5。
The admittance matrix that through type (6) provides determines Y1, through type (4) obtains A1;Same procedure is utilized to obtain Y2... Y36, by equation AG=is(5) obtain A, finally ask for the resistance of scale network。
The program calculation of impedance network is provided huge facility by the concept of extension admittance matrix, the admittance matrix that each electrode is corresponding need not be listed respectively, dramatically reducing workload, after extension admittance matrix writes out, the admittance matrix that each electrode is corresponding can be obtained easily very much。
The present invention proposes the computational methods of the equivalent resistance of a kind of microtrabeculae type focused logging device impedance network, and establish impedance rate resistor network according to the method, compensate for simplify scale network cannot the shortcoming of complete reaction formation characteristics under bad ground, can effectively be used for side circuit is tested, can carry out testing to microtrabeculae type focused logging device in Factory Building and analyze, save scheduling and planning cost, considerably improve development and production and the application efficiency of instrument。Current the method is successfully used for the equipment such as microtrabeculae logging instrument, achieves good effect。