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   Lithology from Matrix Slowness    Lithology Codes from Matrix Slowness     Slowness Parameters

Lithology from Matrix TRAVEL TIME
"Slowness" is the new word for sonic or acoustic travel time. The inverse of slowness is speediness or velocity. We continue to use travel time in this Handbook - it's hard to teach old dogs new tricks.

The apparent matrix travel time can be calculated in a similar fashion to the matrix density, again by rearrangement of the response equation.

DELTma - Apparent Matrix Travel Time
Calculate Matrix
      1: IF Vsh + PHIe < 0.95
      2: THEN DTCms = (DTC - PHIe * DTCW - Vsh * DTCSH) / (1 - PHIe - Vsh)
      3: OTHERWISE DTCma = DTC

Calculate mineral volumes (relative to each other)
      4: Min1 = (DTCma - DTC2) / (DTC1 - DTC2)
      5: Min2 = 1.00 - Min1

Calculate mineral volumes (relative to total rock volume)
      6: Vrock = (1.0 - Vsh - PHIe)
      7: Vmin1 = Min1 * Vrock
      8: Vmin2 = Min2 * Vrock

WHERE:
  DTC = sonic log reading (usec/ft or usec/m)
  DTCma = computed matrix travel time (usec/ft or usec/m)
  DTC1 = matrix travel time for first mineral (usec/ft or usec/m)
  DTC2 = matrix travel time for second mineral (usec/ft or usec/m)
  DTCSH = sonic log reading in shale (usec/ft or usec/m)
  DTCW = sonic log reading in water (usec/ft or usec/m)
  PHIe = effective porosity from any method (fractional)
  Vsh = volume of shale (fractional)
  Vrock = rock volume (fractional)
  Vmin1 = true volume of first mineral (fractional)
  Vmin2 =  true volume of second mineral (fractional)
  Min1 = relative volume of first mineral (fractional)
  Min2 = relative volume of second mineral (fractional)

COMMENTS:
This equation breaks down with high values of PHIe + Vsh, so we set DELTma = DELT when PHIe + Vsh > 0.95.

This model is not very sensitive in carbonates - the matrix density model is better, if data is available.

The matrix travel time can be obtained graphically from the chart below.

Sonic neutron crossplot to find DELTma

NUMERICAL EXAMPLE:
1. Assume Sand D in Example 1.
DTC = 300 usec/m
DTCSH = 328 usec/m
Vsh = 0.33
DTCW = 616 usec/m
PHIe = 0.11
DCTma = (300 - 0.11 * 616 - 0.33 * 328) / (1 - 0.11 - 0.33) = 229 usec/m

This value falls in the impossible area and is too high because the sonic log reads high compared to effective porosity found from the density neutron crossplot. If porosity was 0.16, the matrix travel time would be 183 usec/ft (close to the sandstone value).

This is another quality control indicator, and in this example demonstrates a lack of coherence between the sonic and density neutron data, when the matrix, shale and fluid assumption are as given above. Either these parameters, or the log data, or the whole rock model are in error.

Sonic Lithology Codes
Lithology codes are more difficult to generate with sonic data then with density data.

SlithCode - Sonic Lithology Codes

COMMENTS:
The bad hole code does not intervene in sonic calculations.

Should not be used in shallow unconsolidated sandstones.

SONIC PARAMETERS:

	PHIN	DENS	DTC	DTC	PE	Uma	Mlith	Nlith	Alith	Klith	Plith   
		g/cc	usec/m	usec/ft						  	          
Salt Wtr	1.050	1.10	616	188							
Fresh Wtr	1.000	1.00	656	200							
Quartz    	-0.028	2.65	182	55.5	1.82	4.82	0.876	0.623	1.605	1.406	1.103
Calcite	0.000	2.71	155	47.2	5.09	13.79	0.893	0.585	1.710	1.528	2.977
Dolomite	0.005	2.87	144	43.9	3.13	8.98	0.835	0.532	1.879	1.569	1.674
Anhydrite	0.002	2.95	164	50.0	5.08	14.99	0.769	0.512	1.954	1.503	2.605
Gypsum	0.051	2.35	172	52.4	4.04	9.49	1.093	0.703	1.422	1.555	2.993
Muscovite	0.165	2.83	155	47.2	2.40	6.79	0.835	0.456	2.192	1.829	1.311
Biotite	0.225	3.20	182	55.5	8.59	27.49	0.657	0.352	2.839	1.865	3.905
Kaolinite	0.491	2.64	211	64.3	1.47	3.88	0.827	0.310	3.222	2.666	0.896
Glauconit	0.175	2.83	182	55.5	4.77	13.50	0.790	0.451	2.218	1.752	2.607
Illite	0.158	2.77	211	64.3	3.03	8.39	0.767	0.476	2.102	1.612	1.712
Chlorite	0.428	2.87	182	55.5	4.77	13.69	0.773	0.306	3.269	2.527	2.551
Montmori	0.115	2.62	212	64.6	1.64	4.30	0.836	0.546	1.831	1.530	1.012
Barite      	0.002	4.08	229	69.8	 261	1065	0.423	0.324	3.086	1.305	84.74
Albite	0.013	2.58	155	47.2	1.70	4.39	0.967	0.625	1.601	1.548	1.076
Anorthite	-0.018	2.74	148	45.1	3.14	8.60	0.890	0.585	1.709	1.522	1.805
Orthoclas	-0.011	2.54	226	68.9	2.87	7.29	0.851	0.656	1.523	1.297	1.864
Siderite	0.129	3.91	144	43.9	14.30	55.91	0.536	0.299	3.341	1.792	4.914
Ankerite	0.057	3.08	150	45.7	8.37	25.78	0.742	0.453	2.206	1.636	4.024
Pyrite	-0.019	5.00	130	39.6	16.40	82.00	0.401	0.255	3.925	1.574	4.100
Fluorite	-0.006	3.12	150	45.7	6.66	20.78	0.728	0.475	2.107	1.534	3.142
Halite	-0.010	2.03	219	66.7	4.72	9.58	1.877	0.981	1.020	1.914	4.583
Sylvite     	-0.041	1.86	242	73.8	8.76	16.29	1.468	1.210	0.826	1.213	10.18
Carnalite	0.584	1.56	256	78.0	4.29	6.69	2.178	0.743	1.346	2.932	7.661
Anthracit  0.414	1.47	345	105.2	0.20	0.29	2.018	1.247	0.802	1.619	0.426
Lignite	0.542	1.19	525	160.0	0.25	0.30	2.105	2.411	0.415	0.873	1.316

* Multiply DENS (g/cc) by 1000 to get Kg/m3 where needed

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