A Study to Determine Reservoir Parameters and Remaining Oil Saturation by using Inter-well Tracer Test

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1 A Study t Determine Reservir Parameters and Remaining Oil Saturatin by using Inter-ell Tracer Test Erlng YANG, Tingting GU * Key Labratry n Enhanced Oil and Gas Recvery f the Ministry f Educatin, Nrtheast Petrleum University, Daqing, Heilngjiang , hina Abstract -- Fr the mathematical mdel f cnventinal 3-D t-phase nn-distributive and distributive tracer prblems, there are unknn parameters (the cncentratin f ater cmpnent in ater phase) and (the cncentratin f il cmpnent in il phase) in the ater and il cmpnent functins, hich uld increase the cmputatinal lad in the basic mdel t slve differences. Taking int accunt 1 and 1, the ater and the il cmpnent functins can be simplified thrugh substituting =1 and =1. The implicit difference schemes f this simplified mdel are presented and slved by Gauss-Seidel iteratin methd. By means f ratinal design f the differential lattice, the btained cefficient matrix f linear equatins is strictly diagnally dminant, hich can make the result uncnditinally stable. mpared ith the results f the nn simplified mdel, the frmatin permeability errr is less than %, and the layer thickness errr is less than 5%, hich indicates the peratin accuracy f this simplified mdel can meet the requirements, and greatly reduce the calculated amunt at the same time. The mdel has been put int practical use fr the ell grup N--P38 in suthern district Ⅱin Daqing Oilfield. The amunt f 10 tns ammnium thicyanate as injected int the test area, and the amunt f 14 tns nrmal butyl alchl as used. The prductin cncentratin curves have been measured in three nearby prductin ells, and ne f them is nt perfratin and the tracer is nt detected. The time that ammnium thicyanate cncentratin ccur peak value is 15, 5and 4 days. The fling velcity f injected ater beteen the injectin and the prductin ells is 1.65, 1.11 and 5.95 m/d. Then the average ater-phase permeability f the reservir is 0.090, and 0.477μm, hich are calculated and determined fr prductin ells N-D3-P38, N-D-P38 and N--P138 respectively. Based n the dynamic parameters f ater, prductin fluid, pressure and curve fitting f tracer cncentratin, the reservir parameters and remaining il saturatin distributin f the 4 sediments, namely, PI1, PI, PI3 and PI4 are btained. Keyrds - tracers; reservir parameters; residual il saturatin; ammnium thicyanate; nrmal butyl alchl; Daqing il fields I. INTRODUTION Since 1980s, tracer technique has been idely used in many ilfields in ur cuntry [1], and it has been develped rapidly. The qualitative reservir descriptin develped frm the single ell chemical tracer methd t using the methd f inter-ell tracer t btain the frmatin parameters and the remaining il saturatin distributin []. The methd f determining the residual il saturatin by using the tracer utput cncentratin curve is mainly analytical methd and numerical simulatin methd. The analytical methd is simple, but the average residual il saturatin is btained, and it can't be used t determine the remaining il saturatin distributin. Als, the analytical methd is nly suitable fr the ell pattern f regular gemetry. Therefre, the numerical simulatin methd is used t determine the residual il saturatin in rder t vercme the shrtcmings f the analytical methd in this paper. On the basis f the reservir numerical simulatin, the numerical simulatin sftare fr the interpretatin f the inter-ell tracer data is develped and perfected by Li Shuxia et al in the mdeling sectin since 1990s [3-5]. The principle f numerical simulatin methds t determine residual il saturatin is t use multi phase and multi cmpnent mdel t deal ith the prcess f injectin, migratin and prductin. By repeatedly adjusting the frmatin parameters, the tracer utput curve that the prductin ells calculated shuld be cnsistent ith the actual curve. Finally, the frmatin parameters and the remaining il saturatin are btained. Under the precnditin f rbust results, the numerical simulatin mdel f il-ater t phase and fur cmpnents f il, ater, distributin f tracer and nn distributive tracer are simplified in this paper, hich greatly reduce the amunt f cmputatin. II. THE PRINIPLE INTER-WELL TRAER TEHNOLOGY The remaining il saturatin f il reservir is determined by using the principle f chrmatgraphy [6-8]. One is lipphilic distributin tracer, hich is disslve in il and ater. The ther is a hydrphilic nn-distributin tracer, hich is mainly disslved in ater. In the fl prcess, the t kinds f tracers are separated, and the cncentratin peak ill create a time difference hen it reach the grund, hich has quantitative relatin ith the remaining il saturatin. III. ADVANTAGES OF NUMERIAL SIMULATION METHODS The analytical methd and numerical simulatin methd are mainly used t determine the residual il saturatin by using the tracer prductin cncentratin curve. Althugh the analytical methd is simple, the average residual il DOI /IJSSST.a ISSN: x nline, print

2 saturatin can be determined, and the residual il saturatin distributin can nt be determined. And analytic methd is nly applicable t the regular gemetry f the ell pattern. In this paper, the numerical simulatin methd is used t determine the residual il saturatin in rder t vercme the shrtcmings f the analytical methd. The principle f determining the residual il saturatin by the numerical simulatin methd is that the multi phase and multi cmpnent mdel is used t deal ith the injectin, migratin and prductin prcess f tracer. By repeatedly adjusting the frmatin parameters, the tracer prductin curves f the prductin ell is cnsistent ith the actual curves, and the frmatin parameters and inter ell residual il saturatin are btained. S P c S 1 P P K Where: H --- reservir thickness, m; ---prsity, decimal; (5) (6) (7) IV. THE THREE-DIMENSIONAL TWO-PHASE FOUR-OMPONENT MATHEMATIAL MODEL Nte: cmpnents 1: nn-distributin tracer, nly disslve in ater phase; cmpnents : distributin tracer, disslve in bth il and ater; cmpnents 3: ater cmpnent, nly exist in the ater phase; cmpnents 4: il cmpnent, nly exist in the il phase. The three-dimensinal t-phase fur-cmpnent mathematical mdel is the: mpnents 1: H kk ( P gd) Hq t H S K ( H S ) mpnents: r H kk H kk r HS K H S K r ) 1 1 ( P gd) Hq ( P gd) 1 ( H S t mpnents 3: H kk 1 1 H S ( P H S K ( H S ) mpnents 4: H kk r 1 ( P gd) Hq t gd) Hq t H S K ( H S ) r Auxiliary equatin: 1 (1) () (3) (4),, ---the viscsity f the il and ater, Pa s; ---the density f il and ater, k ---the abslute permeability, m; 3 kg/m ; K r, K r ---the relative permeability f il and ater, dimensinless; D ---gravity gradient, Pa/m; P, S, Pc P ---the pressure f il and ater, Pa; S ---the saturatin f il and ater, decimal; ---the capillary pressure beteen il and ater, Pa; 1,, ---the mass cncentratin f the nn-distributin tracer, distributin tracer and the ater cmpnent in the ater phase, %;, ---the mass cncentratin f distributin tracer and the il cmpnent in the il phase, %; K ---the distributin cefficient f distributin tracer. A. Simplificatin f the Mdel The and are unknn in the ater and the il cmpnent functins, hich uld cause massive calculatins t slve difference equatins in the basic mdel. Given 1 and 1,the ater and the il cmpnent functins can be simplified thrugh substituting =1 and =1. The ater cmpnent: DOI /IJSSST.a ISSN: x nline, print

3 H kk r The il cmpnent: H kk B. Slving Mdel r ( P gd) Hq ( H S ) t ( P gd) Hq ( HS ) t The equatins (1) and () carry n difference, hich using implicit expressin t slve the pressure and shing the slved ater saturatin. And then by establishing an implicit difference scheme fr the nn-distributin tracer cmpnent and the distributin tracer, thereby the tracer cncentratin is calculated. And it as slved by Gauss Seidel iteratin methd. Thrugh the reasnable design f the differential case, the linear equatin set is strictly diagnally dminant, hich can be used t slve the nn cnditinal stability. The pressure equatin and the saturatin equatin f the il phase can be btained by the simplified mathematical mdel. The pressure and saturatin are slved by using the implicit pressure explicit saturatin methd in the black il mdel. The pressure equatin is slved by the implicit slutin ith precnditining cnjugate gradient methd, and pressure distributin can be btained. Then the pressure value is substituted int the saturatin equatin, and explicit saturatin distributin can be btained. Finally, the value f pressure and saturatin is int the frmula (1)-(4), and the cncentratin distributin f each cmpnent can be btained. S repeatedly slved, the cncentratin f each cmpnent f the curve changing ith time can be btained, (8) (9) fr the tracer cmpnent, that is, the tracer prductin curve. The calculated tracer prductin curve is cmpared ith the measured tracer prductin curve, and if it is nt cnsistent, the frmatin parameters can be mdified, and the calculated results are in agreement ith the t. The cnventinal numerical simulatin is a step by step t seek ut reservir pressure, saturatin and related develpment dynamic index, and then cmparing the dynamic develpment data ith practical develpment t carry ut the fitting calculatin and dynamic predictin. Numerical simulatin f tracer in inter ell is nt nly the calculatin f il pressure, saturatin and dynamic prductin, but als the calculatin f tracer utput curve. Finally, the calculated dynamic prductin and tracer prductin curves ill be fitted t the measured results. Because the measured tracer utput curve is mre accurate and reliable than the histry f ilfield develpment. S the fitting f tracer prductin curves can reflect the actual cnditin, and the calculatin results mre reliable. Fr the il field ith lnger prductin time, the time f tracer test is very shrt cmpared ith the develpment histry f the hle il field. S it des nt fit the prductin histry f the il field, and the main curve f the tracer prductin is fitted. The same as the cnventinal numerical simulatin, the input parameters are adjusted t fit the calculatin until the calculated tracer prductin curve cincides ith the measured prductin curve. After the t matching, the il saturatin distributin at the end f the fitting calculatin is the remaining il saturatin distributin at the end f the tracer test. This is the basic principle f determining the residual il saturatin by the ell tracing methd.. Reliability Test In rder t test the reliability f the methd, the results f this methd are cmpared ith dcument [3]. Table 1 shs that the errr f the frmatin permeability is ithin %, and the errr f the thickness is ithin 5%, hich indicates that the methd is reliable. TABLEⅠ RESULT OMPARISON TABLE BETWEEN DOUMENT [3] AND THE METHOD OF THIS PAPER Well number E F G Frmatin parameter k / μm H / m k / μm H / m k / μm H / m k / μm H / m Dcument [3] Methd f this paper Errr/% V. THE ONDITON OF TRAER TEST A. General Situatin f Test Area The ell grup f N--P38 injectin ells in the suth f Daqing il field is selected as the test area f tracer injectin, hich including N--P138, N--P139, N-D-P38, N-D3-P38 4 prductin ells, t cmpse the regular five pint area f ell pattern, and the average ell spacing is 50m. The ammnium thicyanate as chsen as a nn - distributin tracer and nrmal butyl alchl as chsen as a distributin tracer. The mining layer f the ell grup is PuⅠ1-4 reservir, the middle depth f il layer is m, the temperature f il layer is 45, the viscsity f crude il is 8.1mPa s, the experimental zne cntrl area is 0.1km, the average sandstne thickness f single ell is 0.1m, the effective thickness is 15.m, the pre vlume is m 3, the riginal gelgical reserves is t. DOI /IJSSST.a ISSN: x nline, print

4 B. The Design f Tracer Dsage alculatin f tracer dsage by Brigham-Smith frmula: G HS p L (10) Where: G is the tracer dsage, t; H is reservir thickness, m; is reservir prsity, decimal number; S is ater saturatin, decimal number; P is the peak value f design mining cncentratin, mg/l ; is dispersin cnstant, fr the ammnium thicyanate as and the nrmal butyl alchl as 0.05, m; L is ell spacing, 100m. The dsage f ammnium thicyanate and nrmal butyl alchl determine respectively as 9.77t and 13.44t.. The Test Situatin In rder t reduce the adsrptin, the ater slutin f sdium hydrxide ith the mass cncentratin f.1% as injected 4m 3 in advance; then the frmaldehyde slutin ith the mass cncentratin f 0.417% as injected 14m 3 t reduce the influence f bacteria. The injectin pressure is abut 7MPa, the mixed slutin as injected 36m 3, hich ere cmpsed f ammnium thicyanate ith the mass Figure 3. The recvery cncentratin curves f Suth -P138. cncentratin f 5% and the nrmal butyl alchl ith the mass cncentratin f 7%. The actual injectin amunt f ammnium thicyanate and nrmal butyl alchl ere respectively 10t and 14t. After the ater injectin as nrmal, the utput cnditin f tracer as sampled and analyzed frm the surrunding ells. At present, the recvery cncentratin curves f the three ells, hich already have been tracer, are shn in Figure 1, and 3. In additin t the Suth -P138 ells, there are nly ammnium thicyanate in the ther t ells and n nrmal butyl alchl. There is n tracer in the Suth -P139 ell ith the main reasn f the majr reservir ithut perfratin. VI. THE ANALYSIS OF TEST RESULT Figure 1. Figure. The recvery cncentratin curves f Suth -J3P38. The recvery cncentratin curves f Suth -JP38. The simplified numerical simulatin methd as used t make the histry matching fr the cncentratin curve f the distributin tracer and nn-distributin tracer and have higher fitting precisin, hich tke N--P138 as example and ere shn in Figure 4 and Figure 5. On this basis, the frmatin parameters and residual il distributin ere btained. A. The Evaluatin f Frmatin Parameter The time that the peak value f ammnium thicyanate slutin appeared f N-D3-P38, N-D-P38 and N--P138 as 15 days, 5 days and 4 days, the fl velcity f the injected ater alng the directin f the three ells as 5.95m/d, 1.11m/d and 1.65m/d respectively. The average permeability f the three il ells is 0.090μm, μm and 0.477μm. It can be seen that in the main il layer, the difference f permeability in the different il ell directin is als relatively large. The permeability that is calculated here is the ater phase, nt the abslute permeability f the reservir. Based n the dynamic parameters f ater cut, prductin fluid, pressure and the curve fitting f tracer cncentratin, the distributin f permeability is btained. The permeability distributin f Pu I unit is shn in Figure 6. B. The Analysis f Remaining Oil Saturatin Accrding t the cncentratin curve peak value f ammnium thicyanate and nrmal butyl alchl, the DOI /IJSSST.a ISSN: x nline, print

5 calculatin f the average remaining il saturatin is 0.46 by using a landmark cmparative la frmula f dcument [5]. Because the peak value f the cncentratin curve represents the cnditin f main il layer, therefre the calculated remaining il saturatin is the value f Pu I layer, and the remaining il saturatin f ther small layer is higher than this value. Accrding t the curve fitting f tracer cncentratin, the distributin f permeability is btained and using the tracer numerical simulatin mdel, and the remaining il saturatin distributin f the 4 units in the ell grup is btained, the remaining il saturatin distributin f Pu I unit is shn in Figure 7. The unit is the main reservir and permeability is relatively high, the average residual il saturatin is abut 0.43 hich agrees ith the calculatin results f landmark cmparisn methd, hich explains that the unit has been in a state f ater flding after years f ater flding. In the plane, the il saturatin f N--P138 ell is l, the ater ashing intensity is large, and the tracer time is early, and the remaining il saturatin f ther directin f ell is relatively high. This la is cnsistent ith the cnclusin that the dynamic respnse characteristics f the il field. N-S-P37 N-D-P138 N-1-P Figure 4. The curve fitting f nn-distributin tracer cncentratin. N--P138 N-D-P N-D3-P138 N--P38 N-D-P N-D3-P38 N--P N-D3-P139 N--P Figure 7. The remaining il saturatin distributin f Pu I unit. Figure 5. The curve fitting f distributin tracer cncentratin. VII. ONLUSIONS N-S-P37 N-D-P138 N-1-P N--P138 N-D-P N-D3-P138 N--P38 N-D-P N-D3-P38 N--P The three-dimensinal t-phase fur-cmpnent mathematical mdel has been given, hich cmpared ith the nn simplified case, the results are reliable and the calculatin amunt is greatly reduced. The distributin la f remaining il saturatin in reservir befre tracer injectin shuld be cnsidered hen using the cncentratin curve t explain the remaining il saturatin f reservir. The fitting f the cncentratin curve and the fitting f ater cut can be cmbined t calculate the mre bjective and accurate remaining il distributin la. 3 The prductin cncentratin curve fitting and landmark cmparisn calculatin are used t calculate the remaining il saturatin f reservir. The results sh that Pu I reservir is already in strng ater cnditin in the cnditin f N--P138 ells hich takes the N--P38 ell as the centre..00 N-D3-P139 N--P Figure 6. The permeability distributin f Pu I unit. AKNOWLEDGEMENTS This rk as financially supprted by the Heilngjiang Natural Science Fundatin (F01500). DOI /IJSSST.a ISSN: x nline, print

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